the ontological argument thesis statement

A Level Philosophy & Religious Studies

The Ontological Argument

Introduction.

In 1077 AD, St Anselm created an argument for God’s existence which came to be known (thanks to Kant) as the Ontological argument. Ontology refers to ‘being’ or ‘existing’ or the nature of being / what exists.

The argument has proven controversial, with many of its critics actually being religious themselves but doubtful about it’s validity.

Nonetheless, something about the argument has proven attractive for many great philosophers who have been motivated to pay it attention, whether to support or undermine it.

“it is easier to feel convinced that [the Ontological Argument] must be fallacious than it is to find out precisely where the fallacy lies.” – Bertrand Russell

Ontological arguments are a priori because they are based solely on an analysis of the concept of God. They essentially argue that if you think carefully about what God is, you’ll understand that God must exist. A strength of a priori arguments for God is that they can’t be undermined by new scientific evidence, unlike some a posteriori arguments.

Ontological arguments are deductive. The truth of their premises logically entails the truth of their conclusion. The strength of deductive arguments is that the only ways to attack them is to either deny that the conclusion really follows from the premises (deny validity) or attack the truth of the premises (deny soundness).

St Anselm’s Ontological argument

P1. God is the greatest conceivable being (by definition) P2. It is greater to exist in reality than the mind alone P3. God exists in the mind C1. Therefore, God exists in reality

Anselm uses the illustration of a painter who has an idea of what they will paint in their mind before painting it in reality. This illustrates the distinction between our idea of something existing in the mind alone, verses existing both in the mind and in reality.

Anselm points to Psalm 14:1 “the fool says in his heart, ‘there is no God’.”

An atheist says they do not believe in God. That implies they at least have an idea of God in their mind.

The force of Anselm’s argument is that God cannot be an idea that exists in the mind alone. That would be incoherent, since then we could conceive of something greater, i.e., God also existing in reality. Yet, God is the greatest being, so conceiving of anything greater is incoherent. So, our idea of God must therefore be of a being that exists in reality. To say that God does not exist in reality is to say that the greatest being is not the greatest being. It is self-contradictory.

“that, than which nothing greater can be conceived, cannot exist in the understanding alone: then it can be conceived to exist in reality; which is greater. Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and reality.” – Anselm.

Proslogion chapter 3 & necessary existence.

Anselm’s ontological argument underwent a revival of interest in the 20 th century thanks to N. Malcolm and C. Hartshorne. They argued that the strongest form of the argument was in chapter 3 of the Proslogion. There, Anselm concludes not merely that God exists, but that God is a necessary being (one which contains its own reason for existence; whose existence doesn’t depend on anything else).

A necessary being whose nonexistence is impossible is greater than a contingent being whose non-existence is possible.

This is because, on Malcolm’s interpretation, Anselm links the concepts ‘greatness’, ‘dependence’ and ‘limitation’. God’s necessity implies being unlimited, positioning God as the ‘greatest’ conceivable being.

A being greater than which none may be conceived is one whose nonexistence is impossible.

Hartshorne calls this insight “Anselm’s discovery”. Later, in his response to critics, Anselm writes:

“If it [a being greater than which cannot be conceived] can be conceived at all it must exist.” – Anselm.

God is a being whose non-existence is impossible. So, if such a being is logically possible, then it must exist.

Whether God is within our understanding

A strength of the ontological argument its definition of God

Anselm uses a theologically and philosophically convincing definition of God, carefully designed to avoid the problem of defining something that is beyond our understanding. Anselm presents an analogy. We can’t fully look at the sun but can still see daylight. Similarly, we can’t fully know God, but can at least understand that he is the greatest conceivable being.

“If you say that what is not entirely understood is not understood and is not in the understanding: say, then, that since someone is not able to gaze upon the purest light of the sun does not see light that is nothing but sunlight.”  – Anselm

Weakness: God is not ‘in’ the mind/understanding

Gaunilo raises an objection to P3; the premise that the greatest conceivable being exists in the mind/understanding. Gaunilo draws on the traditional Christian premise that God is beyond our understanding to argue that God therefore cannot be in the understanding.

Anselm cannot then proceed to reason about whether it would be greater also in reality. The ontological argument seems to fail because it relies on our ability to understand and reason about things that are beyond our ability to understand or reason about.

Aquinas also made this argument against Anselm – that God’s nature, such as the ‘eternal law’ is beyond our understanding and that people have different understandings of God.

“Perhaps not everyone who hears this word “God” understands it to signify something than which nothing greater can be thought” – Aquinas.

Gaunilo even doubts that we can understand this idea of the greatest conceivable being:  

“of God, or a being greater than all others, I could not conceive at all” – Gaunilo.

“So much for the assertion that this supreme nature already is in my understanding.” – Gaunilo.

Evaluation defending the ontological argument

However, Gaunilo’s argument is unsuccessful because a full understanding of the greatest conceivable being or of God’s nature is not required for the ontological argument to work.

Peter van Inwagen explains that Anselm would not accept that we either understand God fully or not at all. Our limited understanding of God is enough to justify attributing the name “that than which nothing greater can be conceived” to God.

God has traits but infinitely, i.e., omnipotence, omniscience etc. It is impossible to conceive of anything greater. So, we can understand enough of that idea. We may not be able to conceive of the ‘being’ itself, as Gaunilo says, but that seems to commit a straw man fallacy. Anselm doesn’t rely on conceiving the being itself. We can grasp the concept of a being greater than which none may be conceived. We can then follow Anselm’s reasoning that since it is greater to exist, that being must exist.

Evaluation criticizing the ontological argument

Gaunilo has a point. When we think about the concept of a being greater than anything we could possibly imagine, the idea of that actual being is not in our understanding.

Furthermore, the insights of Apophatic theology show that reasoning about God is impossible. Pseudo-Dionysius argues that if we are true to God’s transcendent unknowability, we would recognize that God is simply beyond any human concepts that we can understand. God therefore cannot be grasped by the understanding and so cannot be ‘in’ the understanding.

Pseudo-Dionysius explicitly says that God is ‘beyond assertion and denial’. So although the atheist is indeed wrong to deny God, proponents of the ontological argument are also wrong to assert God. God is beyond all these philosophical terms, even beyond truth and falsity itself.

Gaunilo’s ‘lost island’ response to Anselm

Gaunilo denies that the ontological argument is actually a valid deductive argument, attacking the inference from the premises to the conclusion of God existing in reality

“I have in my understanding all manner of unreal objects” – Gaunilo.

“I should not admit that this being is in my understanding and concept even in the way in which many objects whose real existence is uncertain and doubtful, are in my understanding and concept. For it should be proved first that this being itself really exists somewhere; and then, from the fact that it is greater than all, we shall not hesitate to infer that it also subsists in itself.” – Gaunilo.

Anselm’s argument could succeed in showing that if God exists, then God is the greatest being and even that it subsists in itself, i.e., has necessary existence. However, this is not enough to show that God does exist necessarily.

“he who says that this being exists, because otherwise the being which is greater than all will not be greater than all, does not attend strictly enough to what he is saying. – Gaunilo.

Gaunilo illustrates this with the case of a perfect lost island, an illustration of a thing whose real existence is ‘uncertain and doubtful’ yet exists in his understanding as a concept.

Applying the logic of Anselm’s argument to this island has an absurd result (reductio ad absurdum). It is greater for this island to exist in reality, so it must exist. This would work not just for an island. The greatest or supremely perfect member of every category must exist. This is sometimes called the ‘overload’ objection because it suggests that reality would be overloaded with greatest/perfect things.

Firstly, Gaunilo’s critique is unsatisfying as far as it goes. Gaunilo asserts, but does not demonstrate, the absurdity of Anselm’s logic proving the existence of a perfect island. He merely asserts that such reasoning must either be a joke or a symptom of foolishness.

To demonstrate absurdity requires showing a contradiction, which Gaunilo has not shown. Proving existence a priori might seem counter-intuitive. Gaunilo remarks that the logic seems like joke or sign of foolishness when applied to the island. Nonetheless, Gaunilo has not demonstrated it actually absurd. Perhaps a perfect island does indeed exist.

Anselm himself made a different response to Gaunilo. He insisted that a proper understanding of his argument showed that it can only prove the existence of God. Testing the logic through applying it to a different case like an island is not valid.

Something is greater if it doesn’t depend on anything for its existence. By definition an island is land enclosed by water. Definitionally then, no matter how great or perfect an island is, in order to be an island it will be dependent on something else to exist, such as an ocean, planet, sun, etc. So, the greatest possible Island will be contingent, which means by definition it could either exist or not.

This is why a priori analysis of its definition cannot prove its existence. The existence of contingent beings cannot be proven a priori because their existence is not a matter of definition. Their existence is a matter of whether what they depend on exists.

There is nothing in the concept of the greatest being that involves dependence, making it a necessary being. So, the reason for the logic not working in the case of the island (or any contingent being) does not apply for God.

Anselm’s defense is successful and highlights the main issue with responses to the ontological argument even to this day. There is something unique about God’s existence. Our ordinary way of understanding existence does not apply.

Anselm successfully refutes the relevance of the perfect island.

However, Anselm arguably failed to respond to Gaunilo’s central contention.

Even if Anselm is right that we cannot conceive of God without existence, that only proves that God is a necessary being, such that if God existed it would be in a special way where God could not cease to exist. This is not the same as proving that this necessary being actually does exist. Anselm doesn’t deal with this point.

Descartes’ Ontological argument

Descartes aimed to strengthen the ontological argument through founding it on his rationalist epistemology. Rationalism claims that we can gain absolutely certain knowledge of some truths a priori.

Anselm is often called the father of Scholasticism, a theological movement influenced by Aristotle’s approach to argumentation. At its core is subject-predicate analysis. Propositions are combinations of subjects and predicates which assert something as true or false.

Descartes rejected scholasticism. He instead argued that the foundation of knowledge was intuition. Intuition operates through direct intellectual awareness, not the indirect analysis of linguistic representation employed by logical terms.

Intuition provides absolute certainty. We can bring ideas before our mind and apprehend truths about them due to the psychological character in which they strike us.

E.g., we intuitively know that it is impossible to bring a triangle before our mind without it having three sides. Similarly, we intuitively know it impossible to think of a supremely perfect being separated from existence. We thus rationally appreciate that God contains the perfection of existence.

“t he idea of God, or a supremely perfect being, is one that I find within me just as surely as the idea of any shape or number. And my understanding that it belongs to his nature that he always exists is no less clear and distinct than is the case when I prove of any shape or number that some property belongs to its nature” – Descartes

Descartes did put it into the form of a deductive argument:

P1 – I have an idea of a supremely perfect being which contains all perfections P2 – Existence is a perfection C3 – God exists

The argument is deliberately short, suggestive of Descartes’ view that God’s existence can be known intuitively.

Hume’s empiricist response to the ontological argument

Hume is an empiricist who rejects a priori demonstrations of existence and the concept of a ‘necessary being’.

Truths of logic/definition are true or false no matter the factual state of the universe. There is no logically possible factual state of affairs that is incompatible with ‘1+1=2’, for example. Hume thinks this shows that logical truth and factual truth are distinct, including our means of knowing them. This is called ‘Hume’s fork’.

Analytic: true by definition. Cannot be denied without contradiction. E.g. “a bachelor is an unmarried man”. A priori reasoning involves the analysis of the relation between ideas. So, only analytic truths can be known a priori.

Synthetic: true because of the way the world is. Can be denied without contradiction.  “E.g. “The sun will rise tomorrow”. A posteriori reasoning involves experience of the factual state of the world. So, only synthetic truths can be known a posteriori.

Applying this to the ontological argument:

“there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori” – Hume.

“It will always be possible for us at any time to conceive the non-existence of something we formerly conceived to exist; the mind can never have to suppose some object to remain always in existence, in the way in which we always have to conceive twice two to be four” – Hume

A necessary being must exist. So, we shouldn’t even be able to conceive of it not existing. However, Hume claims that whatever we conceive of as existing, we can conceive of as not existing. It follows that there is no being that we cannot conceive to not exist. So, our mind is incapable of giving meaning to the idea of a being existing necessarily. Hume concludes:

“The words, therefore, necessary existence, have no meaning.” – Hume.

Any belief we have about what exists could be imagined as either true or false. Therefore, we cannot coherently understand any being to be logically necessary.

Whether something exists is a contingent matter of fact. It cannot be logically necessary. The term “necessary existence” seems to ignore the disconnect between logical and factual truth established by Hume’s fork.

The consequence is that any claim about what exists (existential propositions, like ‘God exists’) can be denied without contradiction.

Existential propositions are therefore always synthetic. So, they can only be known a posteriori. The premises of ontological arguments are claimed to be known priori. In that case, they cannot allow us to know the conclusion that God exists.

Kant’s objection that existence is not a predicate

Kant develops Hume’s criticism, arguing that the reason any being is conceivably non-existent is that existence is not a property a thing possesses. Existence thus cannot be an essential property of a thing, inconceivably separate from it.

Descartes implies that perfection is a defining attribute of God. Anselm argues God must exist in order to be God. They both try to show that denying God’s existence denies what God is. This seems to treat ‘existence’ as if it described a defining property a thing possesses. That would make the word ‘exists’ a predicate.

Kant objects. If existence were a predicate, it would be added to our concept of a thing that exists. A thing that exists would be conceptually different to that same thing when not existing.

If I say my cat exists, I do not describe a feature of the cat. I may be describing reality in a general sense, so Kant allows that existence can be a ‘logical predicate’. However, existence is not a ‘real predicate’, meaning it does not describe an attribute of a thing itself.

To use Kant’s example, if existence were a predicate, then 100 thalers (coins) in reality would be conceptually different to 100 thalers in the mind.

However, the concept ‘100 thalers’ is the same whether a mere concept in your mind or instantiated in reality. A thing is what it is, regardless of whether it exists or not. 100 thalers is just 100 thalers. It has the predicates of shininess, roundness, 100, etc. Being only in the mind doesn’t make the concept somehow less of a complete description of what 100 thalers is. So, existence is not a description of a thing. It is not a predicate.

We cannot determine whether a thing exists merely through understanding what it is. So, Anselm and Descartes are incorrect when they claim it’s incoherent to think of God not existing. This then blocks the ontological argument’s inference from the incoherence of God’s non-existence to the conclusion that God exists.

Counter: Kant’s criticism faces two counters.

Firstly, Kant’s objection fails to target Descartes’ version of the argument. Anselm understands ‘God exists’ as a subject-predicate relationship.

Descartes’ rejection of Aristotelian subject-predicate analysis means he can’t be accused of inferring God’s existence by assuming that existence is a predicate of God.

Descartes’ argument doesn’t operate by assigning predicates to subjects, but by determining whether the idea of a supremely perfect being can be clearly and distinctly perceived while excluding necessary existence from it through a purely intellectual operation.

Furthermore, Malcolm defended Anselm’s approach, arguing that Kant only shows that contingent existence is not a predicate.

Something is contingent if it is dependent on something else for its existence. The reason for the existence of a contingent thing is external to it and so does not describe or define it. However, a necessary being doesn’t depend on anything else for its existence. It contains the reason for its existence within itself. ‘necessary existence’ therefore does describe something about a being. It is a defining part of a thing in a way that contingent existence is not. So, necessary existence is a predicate.

So, Kant made the same mistake that Gaunilo did. We cannot test the logic of the ontological argument through its application to contingent things, such as islands or thalers. Like Gaunilo, Kant did not fully appreciate the significance of God’s necessity and the consequently truly unique nature of God’s relationship with existence.

Malcolm’s ontological argument

Norman Malcolm created his own version of the ontological argument, referring to God as an unlimited being.

Malcolm uses modal logic, which involves analysis of the logical consequences of necessity and possibility.

P1. God either exists or does not exist. P2. If God exists, God cannot go out of existence as that would require dependence on something else. So, if God exists, God’s existence is necessarily P3. If God does not exist, God cannot come into existence as that would make God dependent on whatever brought God into existence. So, if God does not exist, God’s existence is impossible. C1. So, God’s existence is either necessary or impossible P4. The concept of God is not self-contradictory (like a four-sided triangle), therefore God’s existence is not impossible. C2. Therefore, God exists necessarily.

Malcolm points to this quote from Anselm’s reply to Gaunilo:

“If it [the thing a greater than which cannot be conceived] can be conceived at all it must exist. For no one who denies or doubts the existence of a being a greater than which is inconceivable, denies or doubts that if it did exist its non-existence, either in reality or in the understanding, would be impossible. For otherwise it would not be a being a greater than which cannot be conceived. But as to whatever can be conceived but does not exist: if it were to exist its non-existence either in reality or in the understanding would be possible. Therefore, if a being a greater than which cannot be conceived, can even be conceived, it must exist.” – Anselm

Malcolm remarks:

“What Anselm has proved is that the notion of contingent existence or of contingent nonexistence cannot have any application to God. His existence must either be logically necessary or logically impossible. The only intelligible way of rejecting Anselm’s claim that God’s existence is necessary is to maintain that the concept of God, as a being a greater than which cannot be conceived, is self-contradictory or nonsensical” – Malcolm.

Malcolm’s interpretation of Anselm is that neither contingent existence nor contingent non-existence can apply to God. The only way to deny God’s existence is for God to be necessarily non-existent, i.e., incoherent.

Kant’s objection that the argument cannot prove actual existence

Gaunilo’s underlying point was to show the difference between existing in the mind and existing in reality. His lost island was an illustration of that. Anselm defeated the relevance of the lost island, but arguably not Gaunilo’s underlying point. Kant developed this type of objection.

Kant takes Descartes example of a triangle. It is necessary that ‘having three sides’ is part of the concept of a triangle. This doesn’t mean ‘three sides’ are necessary. It means that if a triangle exists, then it necessarily has three sides. We could not accept a triangle, but deny three sides, without contradiction. Yet we could deny the triangle exists, and then also its three sides.

Similarly, the ontological argument shows that ‘necessary existence’ is part of the concept of God. Kant’s objection is that this only shows that if God exists, then God exists necessarily. It doesn’t show that God-the-necessary-being does exist. If God does not exist, then neither does God’s necessity.

It would be contradictory to say that God exists, but not necessarily. Yet we can still deny that God exists, and with that, deny that God’s necessity exists. God may be necessary, but if God does not exist then God’s necessity does not exist.

Like Gaunilo, Kant is drawing a distinction between judgement and reality. A priori reasoning showing that existence is necessary to the definition of God in our minds is not the same as showing that God necessarily exists in reality.

“The unconditioned necessity of judgements is not the same as an absolute necessity of things” – Kant.

“the illusion of this logical necessity has proved so powerful that when one has made a concept a priori of a thing that was set up so that its existence was comprehended within the range of its meaning, one believed one could infer with certainty that because existence necessarily pertains to the object of this concept, i.e., under the condition that I posit this thing as given (existing), its existence can also be posited necessarily” – Kant.

Counter : Malcolm argued this critique from Kant is incoherent.

“ I think that Caterus, Kant, and numerous other philosophers have been mistaken in supposing that the proposition ‘God is a necessary being’ (or “God necessarily exists”) is equivalent to the conditional proposition ‘If God exists then He necessarily exists’ … Can anything be clearer than that the conjunction ‘God necessarily exists but it is possible that He does not exist’ is self-contradictory?” – Malcolm

Kant seems to accept that the ontological argument shows that God is a necessary being. Malcolm argues this means God is a being which is characterised by the impossibility of non-existence. In that case, it can’t be possible for God to not exist.

Malcolm concludes It is incoherent of Kant to grant necessity to God while maintaining the possibility of God’s non-existence. So, the Ontological argument does show that God-the-necessary-being actually exists.

Hartshorne agrees with Malcolm, adding that the only valid way to suppose that God does not exist is to suppose that God’s existence is self-contradictory (logically impossible).

If one accepts the logical coherence of a being which contains the impossibility of non-existence, one must accept that it necessarily exists.

This is the insight behind Malcolm’s premise that God is either necessary or impossible.

Kant seems to want to propose a third option, that God is necessary and yet could not exist. Yet Malcolm argues that is a contradiction in terms.

Malcolm’s point is successful because it blocks what Hartshorne called ‘empirical’ attacks on the ontological argument. These attempt to accept the logical possibility of God yet deny the logical necessity of god’s existence.

If God’s existence is not necessary, it must be contingent.

However, it is very difficult it is to understand contingency when applied to God. God is an eternal being and thus causeless. Contingency is understood as some sort of causal dependency on something else.

“Such a causeless yet contingent existence is without connection with our ordinary ways of understanding contingency … They [Hume, Kant & Hick] accuse Anselm of violating rules; but they violate the elementary rule that logically contingent matters are intelligible in genetic and causal terms, or not at all.” – Hartshorne

Supposing that God’s non-existence could be logically contingent is absurd given what God is.

So, we are left with Malcolm and Hartshorne’s position, that God is either logically impossible or logically necessary.

Hick successfully defends Kant’s style of objection from Malcolm’s counter.

Hick argues the ontological argument fails to distinguish between two types of necessity.

Logical necessity refers to propositions that cannot be false.

Ontological necessity refers to beings that contain their own reason for existence and are not dependent on anything else (aseity).

God’s ‘impossibility of non-existence’ can be understood as ontological necessity, allowing us to accept the definition of God, yet deny God’s logical necessity.

Malcolm argues it is incoherent to think a necessary being could not exist. However, when we add Hick’s distinction, we get a less conspicuously incoherent claim:

It is logically possible for an ontologically necessary being to not exist.

This shows that Malcolm commits the fallacy of equivocation.

P2 & P3, Malcolm uses ‘necessary’ and ‘impossible’ in the ontological sense, of nothing being able to cause God to go out of or come into existence, respectively.

Malcolm’s inference to C1 is therefore not justified, since it uses ‘necessary’ and ‘impossible’ in the logical sense (as seen by P4 (God’s non-impossibility involves being logically coherent).

Similarly, when Anselm and Descartes define God as the greatest conceivable or supremely perfect being, that only justifies ascribing ontological necessity to God. Their inference to the conclusion that God’s existence being logical necessity is not justified.

So, the ontological argument at most proves that if God exists, then God exists in a special way, such as with ontological necessity.

The question of God’s logical impossibility

Hartshorne claims there are two ways one could attack the ontological argument. One is the ‘empirical’ method of Hume, Kant & Hick. They argued that existence can never be logically necessary, even for a being which contains the impossibility of non-existence. Kant says that impossibility is just in our mental judgement, Hick says it only establishes ‘ontological necessity’.

Since Leibniz, proponents of the ontological argument have accepted that it depends on God being logically possible. If empiricist approaches fail, Hartshorne argues this is the only remaining other way to attack the ontological argument. To argue that the God of classical theism, or the idea of a being that contains the impossibility of non-existence, is actually incoherent and thus impossible.

There are numerous philosophical debates about the coherence of God, including:

• The paradox of the stone
• The Euthyphro dilemma
• The incompatibility of free will and omniscience
• The logical problem of evil

These debates over the logical coherence of God are ongoing and have a long history. Neither side seems to have a knock-down criticism of the other.

Modern defenders of the Ontological argument, Malcolm, Hartshorne and Plantinga, agree that our inability to know for certain that God is coherent does limit what it can achieve by itself.

The ontological argument at most shows that if God is logically possible, then God necessarily exists.

Malcolm’s version incorporates this dependence, making God’s logical possibility a premise of the argument.

Plantinga accepts that the ontological argument can at most make religious belief rational, but cannot prove that God actually does exist.

“reformulated versions of St. Anselm’s argument … cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion” – Plantinga.

Plantinga admits it is rational to believe that God’s existence is logically impossible. However, he maintains that it is also rational for a theist to believe that God’s existence is logically possible, from which the ontological argument then shows that it is rational to believe that God exists. If a being whose non-existence is impossible could exist, then it must exist. It must exist, because its non-existence is impossible. So it could only not exist if such a being is somehow logically absurd.

This was Anselm’s initial insight, that if God is even conceivable, then God must exist.

“if a being a greater than which cannot be conceived, can even be conceived, it must exist.” – Anselm

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Kant on the Ontological Argument

Related Papers

J. Colin McQuillan

Throughout his career, Immanuel Kant objects that Leibniz and Wolff make the distinction between sensible and intellectual cognition into a “merely logical” distinction. Although it is not clear that anyone in the Leibnizian-Wolffian tradition actually holds this view, Kant’s objection helps to define the “real” distinction between sensible and intellectual cognition that he defends in his inaugural dissertation in 1770. Kant raises the same objection against Leibniz and Wolff in the Critique of Pure Reason, but replaces the “real” distinction he defends in his inaugural dissertation with a new “transcendental” distinction between intuitions and concepts. This paper examines Kant’s objection to Leibniz and Wolff and the different alternatives he proposes, in order to highlight an important element in the development of his critical philosophy.

Kant-Studien

Nicholas Everitt

Andree Hahmann

Kant famously criticizes Leibniz for his apparent neglect to observe the difference between two sources of cognition: understanding and intuition. This is the reason that Leibniz supposedly intellectualized the phenomena by identifying them with things in themselves. In Kantian terms, Leibniz fell prey to an amphiboly of concepts which, in the case of his understanding of substance, has led him to assume monads—that is to say, ideal unities which exist in a state of pre-established harmony; for this is the only possible form of community between ideal substances. Distinct versions of this argument can be found in Kant’s Critique of Pure Reason, notably in the notoriously difficult passage entitled “On the amphiboly of concepts of reflections”, and in some later writings, such as the Kantian reply to the self-declared Leibnizian Johann August Eberhard or the late fragment What Real Progress has Metaphysics made in Germany since the Time of Leibniz and Wolff? As is well known, Leibniz’ conception of monad lies at the heart of his metaphysics. Hence, it is hardly surprising that Kant’s understanding and critique of this conception attracted vast scholarly attention. The question has been asked, for instance, whether his critique is justified and what his own positive account is. Further, it is questionable how far Kant’s critical philosophy—and in particular his conception of substance—relates to Leibniz. The last two questions especially have given rise to some original contributions to Kant scholarship in the last years. To name but two, Rae Langton put forward a novel understanding of the relationship between things in themselves and appearances against the backdrop of the Kantian critique of Leibniz, and Eric Watkins addressed Kant’s concept of causality in light of the debate surrounding Leibniz’ theory of pre-established harmony. Common to both, however, is not only the emphasis they put on Kant’s early so-called pre-critical works, in which he engaged mainly with problems created by Leibnizian metaphysics, but their tendency to minimize the differences between this pre-critical work and the later mature writings. In this paper, I want to reassess Kant’s understanding of Leibniz in light of these two interpretations. I will argue that even though both Langton and Watkins correctly emphasize the importance of Leibnizian metaphysics for a proper understanding of Kant’s own critical project, they nevertheless fail to take seriously enough the crucial differences between Kant’s pre-critical and critical philosophy, and especially the new and extraordinary role attributed to transcendental aesthetics for cognition in general but in particular with respect to the rejection of Leibnizian metaphysics. Thus, only against this background can Kant’s critical reading of Leibniz become clear to the fullest extent.

Philosophia

Stefan Storrie

Daniel Garber has put forward an argument that aims to show that Kant’s understanding of Leibniz’ metaphysics should be discounted because he could only have had access to a small and narrow sample of Leibniz’ works from around 1710–1714. In particular, Garber argues that as Kant could not have read Leibniz’ correspondence with Arnauld or his correspondence with Des Bosses he could not have had an adequate conception of Leibniz’ understanding of the relation between substance and body. I will show that Kant could have read some of the Arnauld correspondence and practically all of the Des Bosses correspondence, as well as a number of other related texts that are important for understanding Leibniz’ metaphysics, over a decade before writing the Critique of Pure Reason. Garber’s historical-textual argument for dismissing Kant’s account of Leibniz’ metaphysics is therefore seriously misleading.

Kant-studien

luigi caranti

ESSERE E PERSONA (Milan1989 ch 15) Theologia (Athens 1985), 3-30. Thémata 2 (Universidades de Malaga y Sevilla, 1985): 129-147. Further developed in GOTT ALS GOTTESBEWEIS

Josef M SEIFERT

Revista de Filosofia Aurora

Daniel Omar Perez

The aim of this paper is to present the core of Kant´s critique of traditional metaphysics and ontology as a transcendental semantics that allows reformulating the problem about the objects and their reality. In order to achieve this purpose, we propound a paper divided in two parts: 1. A brief justification of Kant’s semantics interpretation; 2. A work program based on a semantics comprehended as a fundamental part of a method of resolution of philosophical problems. Basically, we can state that the critical position against traditional metaphysics and ontology leads to the question upon: how are a priori synthetic judgments possible? This question leads to its conditions of possibility, that is: sensible representations; intellectual representations; syntactic rules; semantic rules (or referential rules, on the relation between intellectual representations and some sort of sensibility or affection); the operator of the syntactic and semantic rules (subject, man, human nature, gend...

The Palgrave Kant Handbook

Manuel Sánchez Rodríguez

This chapter explores how Kant’s philosophy connects with the spirit and the systematic interest of the Leibniz-Wolffian philosophy. Sánchez-Rodríguez then shows how this tradition undergoes a critical transformation at the same time, mainly due to Kant’s rejection of its metaphysical foundations. Specifically, the chapter explains how Leibniz’s system of pre-established harmony theory is adopted and transformed in Kant’s critical theory of reflective judgment and teleology. This chapter has been translated into English by David Nesbitt.

Kenneth R Westphal

Justin Shaddock

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

RELATED TOPICS

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

University of Notre Dame

Notre Dame Philosophical Reviews

• Home ›
• Reviews ›

The Ontological Argument from Descartes to Hegel

Kevin J. Harrelson, The Ontological Argument from Descartes to Hegel , Humanity Books, 2009, $39.98 (hbk), ISBN 9781591026396.

Reviewed by Charles Taliaferro, St. Olaf College

In 1945, Bertrand Russell announced in his famous The History of Western Philosophy (a brilliant but sometimes eccentric and flawed book) that the ontological argument has been proved to be invalid, despite the fact that the soundness of the argument would be very good news indeed for philosophy:

The real question is: Is there anything we can think of which, by the mere fact that we can think of it, is shown to exist outside our thoughts. Every philosopher would like to say yes, because a philosopher’s job is to find out things about the world by thinking rather than observing. 1

While Russell pronounced the argument dead (albeit with regret), perhaps Anthony Kenny was wiser in his four volume New History of Western Philosophy when he ended the fourth volume with a warning to those who think the argument has been refuted:

Plantinga’s reinstatement of the [ontological] argument, using logical techniques more modern than any available to Russell, serves as a salutary warning of the danger that awaits any historian of logic who declares a philosophical issue definitively closed. 2

Kevin J. Harrelson has written a welcome historical and critical analysis of the ontological argument in early modern European philosophy. In the Introduction, he writes:

In the following chapters I argue that the strategy for proving a priori the existence of God that remains in place during this period, from Descartes’ initial argument in the Discourse on the Method (1637) to Hegel’s final lectures in Berlin (1831), is both internally consistent and free of any easily identifiable error. More importantly, I try to show that the most common objections to the modern ontological proof, raised by the likes of Gassendi, Hobbes, Hume, and Kant, fail to identify any conclusive and universal fallacy. (p. 18)

His book is not, however, “an outright defense of the ontological argument”, for Harrelson is convinced most versions of the ontological argument face serious obstacles and are not persuasive to those not already committed to what he finds philosophically problematic. The book is rich with historical references and nuanced readings of canonical texts, and is packed with arguments and counter-arguments.

The book opens with a compact overview of the ontological arguments found in Anselm, the scholastics, Descartes, and Leibniz. Some of the arguments’ exposition is a bit hard to follow. In discussing the relationship between perfection and necessary existence (which Anselmians usually seek to secure on the grounds that existing necessarily is a perfection or great-making attribute), Harrelson writes: “If God is indeed identical to his own existence, then it could only represent a shortcoming of human reason to distinguish the notion of a ‘perfect being’ from that of ‘necessary existence’” (p. 25). Why is this a problem? Can’t a case for the ontological argument begin with a consideration of great-making properties and an inquirer come to reason that necessary existence plus theistic attributes would be (or is) more excellent than theistic attributes and contingent existence? If one does not realize this prior to entertaining the argument, perhaps that is a “shortcoming”, but no worse than if someone did not realize 6 is the smallest perfect number before she reasoned that 6 is equivalent to 3 + 2+ 1.

In the same chapter, and on the same page as the claim just considered, Harrelson writes, “the peculiar identification of ‘God’ and ‘necessary existence’ renders misleading all theological statements about the existence of the deity” (p. 25). It is not clear, however, which philosopher (if any) claims that what we mean by “perfection” is “necessary existence” (as in “grandmother” is “a female whose child has a child”). Harrelson writes:

In early modern philosophy we find rather that theological propositions are understood to be akin to identical statements, and the philosophers in question fall just short of claiming that “perfect being” and “necessary existence” have the same meaning. “Necessary existence,” like God’s other predicates, is identical with God’s whole nature. This identity of subject and predicate would seem to exempt theological statements from the rules governing normal attributive statements. (p. 25)

Why, however, would a defender of the ontological argument claim that “necessary existence” means the same as “perfect being”, or claim that necessary existence “is identical with God’s whole nature”, rather than claim that necessary existence (or existing necessarily) is a mode of being distinct from being contingent (or having the property being contingent) ? Presumably, for an Anselmian theist, claiming that God exists necessarily involves claiming that there necessarily exists a being of unsurpassable excellence or perfection. I do not yet see how linking necessity and perfection is a theological disaster. At the least, some clarification of how the thesis of divine simplicity comes into play on this issue would have been desirable.

In the same chapter, Harrelson has an interesting treatment of Descartes’ analogy about the idea of a triangle in discussing the idea of God. The format Harrelson employs in clarifying the points at issue is complex.

The following is a short list of those objections, other than the possibility and Thomistic, that are prevalent in the modern period. After each objection I give a caricature of the kind of reply that is frequently found among proponents of the modern argument. I also give a brief explanation of the debate, in which I try to indicate, very roughly, the historical contexts in which the respective objections and replies appear and reappear. (p. 29)

The deliberate use of caricature made the reasoning less easy to follow (for me, anyway).

Thus, the problem with the argument is that it involves the existence of God (!), experience and/or intuition (perhaps especially theological intuition), and insight. One difficulty readers will have so far is that it is not easy to see “the downfall” of the argument without seeing more of “the rise”.

First, from the fact that our perception is incorporated in the premise of the argument it follows that the conclusion is not true for everyone. In other words, whoever does not actually perceive the connection between “a supremely perfect being” and “necessary existence” cannot assent to the claim in the minor premise, in which case the conclusion remains undemonstrated. It is not the case that these individuals fail to grasp a premise that is objectively true; rather, their perceiving a certain “truth” is itself part of the premise. The premise is in fact false in any instance in which the perception is lacking. The ontological argument is thus unsound in those cases. Regardless of whether the ontological argument is ever sound, then, it will sometimes be unsound. The objections will always be, in some sense, in the right, despite their inability to discover an internal flaw in the argument. (p. 67)

This strikes me as odd. Any argument in philosophy might well be considered unsound if not everyone grasps its entailment relations. Even a simple entailment like “if all humans are mortal, no immortal being is a human” might sometimes be unsound because someone, somewhere does not accept the entailment.

In “Refutation of Atheism”, there is a welcome discussion of Cambridge Platonist treatments of the ontological argument. Harrelson has some sympathy with Henry More and Ralph Cudworth, even if he thinks both present arguments with fatal flaws or fail to persuade. As before, I find Harrelson’s autopsy of the argument neither obvious or clear. Here is an analysis of More:

Like Descartes, [More] assents to the following maxim: "we are first to have a settled notion of what God is , before we go about to demonstrate that he is." The various subsidiary arguments to the minor premise (the proof of innateness, the deduction of necessary existence from the idea of God, etc.) serve this end, comprising a preliminary examination of the essence or notion of God. The inference to God’s actual existence appears only at the end of this discussion. This last fact, however, represents the fatal consequence of the systematic presentation of the ontological argument: in order to clarify the various steps in the argument, it was necessary to distinguish the essence of God (i.e., “what God is”) from his existence (“that he is”). The systematic presentation of the ontological argument thereby contradicts the basic presupposition of that same argument, viz., that the essence and existence of God are inseparable. (pp. 87-88)

I do not quite see the problem. More does not think God’s essence and existence can be metaphysically separated, but he thinks one can epistemically consider God’s essence and then come to see that it (together with the thesis that God exists either necessarily or God’s existence is impossible , plus the premise that God’s existence is possible ) entails that God exists.

Harrelson offers a helpful exposition of the work of Ralph Cudworth and Samuel Clark. He is probably correct that Locke’s attack on innate ideas undermined the popularity of the ontological argument, though there are many versions of the argument that do not require or presuppose the existence of innate ideas.

In the chapter “Being and Intuition”, Harrelson takes up the work of Malebranche. There is a useful examination of how Malebranche advances the ontological argument beyond Descartes. At least one of Harrelson’s objections to Malebranche seems strained: “the revised form of the argument is indefensible against the nominalist’s objection that ‘being’ is a mere concept” (p. 115). It is indefensible, unless of course nominalism turns out to be deeply problematic and then the objection carries no weight.

Chapter four contains a helpful analysis of Spinoza’s work, showing how his version of the ontological argument is closely tied in with the whole of Spinoza’s philosophy: "No one can accept [Spinoza’s] argument without accepting his other doctrines in toto , or at least without offering alternative versions of them." (p. 135)

Chapter five offers a detailed exploration of the ontological argument in pre-Kantian German philosophy. Arguments by Leibniz, Wolff, Baumgarten, and Crusius are addressed.

Chapter six on Kant is excellent. Harrelson places Kant’s famous criticism of the ontological argument in perspective and shows why it is not decisive. Harrelson thinks Kant was effective in challenging the authority of the ontological argument largely because of Kant’s general case about the limits of human thought:

The ontological argument, in 1785, is still not the object of any directly successful critique. Its temporary disappearance is a product only of the belief that humans are incapable of obtaining any genuine cognition beyond the field of “experience,” as this term is defined in the opening chapters of the Critique of Pure Reason . (p. 191)

The final chapter on Hegel provides a good context for Harrelson’s thesis that the ontological argument might work for some people. If one can (in Hegel’s terms) “elevate” one’s mind to God, the argument succeeds:

Whoever “grasps” or comprehends that “being is the concept,” i.e., whoever gazes from the summit of absolute knowledge and thereby understands the inferences of Hegelian logic, also perceives the existence of God via participation in God’s self-knowledge. (p. 220)

In Harrelson’s view, while (to echo Russell) every philosopher would like to have such elevation, few of us succeed and so Hegel’s ontological argument (like Descartes’) fails in its ambition as a demonstration or proof.

• Search Menu

Sign in through your institution

• Browse content in Arts and Humanities
• Browse content in Archaeology
• Anglo-Saxon and Medieval Archaeology
• Archaeological Methodology and Techniques
• Archaeology by Region
• Archaeology of Religion
• Archaeology of Trade and Exchange
• Biblical Archaeology
• Contemporary and Public Archaeology
• Environmental Archaeology
• Historical Archaeology
• History and Theory of Archaeology
• Industrial Archaeology
• Landscape Archaeology
• Mortuary Archaeology
• Prehistoric Archaeology
• Underwater Archaeology
• Zooarchaeology
• Browse content in Architecture
• Architectural Structure and Design
• History of Architecture
• Residential and Domestic Buildings
• Theory of Architecture
• Browse content in Art
• Art Subjects and Themes
• History of Art
• Industrial and Commercial Art
• Theory of Art
• Biographical Studies
• Byzantine Studies
• Browse content in Classical Studies
• Classical History
• Classical Philosophy
• Classical Mythology
• Classical Numismatics
• Classical Literature
• Classical Reception
• Classical Art and Architecture
• Classical Oratory and Rhetoric
• Greek and Roman Epigraphy
• Greek and Roman Law
• Greek and Roman Papyrology
• Greek and Roman Archaeology
• Late Antiquity
• Religion in the Ancient World
• Social History
• Digital Humanities
• Browse content in History
• Colonialism and Imperialism
• Diplomatic History
• Environmental History
• Genealogy, Heraldry, Names, and Honours
• Genocide and Ethnic Cleansing
• Historical Geography
• History by Period
• History of Emotions
• History of Agriculture
• History of Education
• History of Gender and Sexuality
• Industrial History
• Intellectual History
• International History
• Labour History
• Legal and Constitutional History
• Local and Family History
• Maritime History
• Military History
• National Liberation and Post-Colonialism
• Oral History
• Political History
• Public History
• Regional and National History
• Revolutions and Rebellions
• Slavery and Abolition of Slavery
• Social and Cultural History
• Theory, Methods, and Historiography
• Urban History
• World History
• Browse content in Language Teaching and Learning
• Language Learning (Specific Skills)
• Language Teaching Theory and Methods
• Browse content in Linguistics
• Applied Linguistics
• Cognitive Linguistics
• Computational Linguistics
• Forensic Linguistics
• Grammar, Syntax and Morphology
• Historical and Diachronic Linguistics
• History of English
• Language Acquisition
• Language Evolution
• Language Reference
• Language Variation
• Language Families
• Lexicography
• Linguistic Anthropology
• Linguistic Theories
• Linguistic Typology
• Phonetics and Phonology
• Psycholinguistics
• Sociolinguistics
• Translation and Interpretation
• Writing Systems
• Browse content in Literature
• Bibliography
• Children's Literature Studies
• Literary Studies (Asian)
• Literary Studies (European)
• Literary Studies (Eco-criticism)
• Literary Studies (Romanticism)
• Literary Studies (American)
• Literary Studies (Modernism)
• Literary Studies - World
• Literary Studies (1500 to 1800)
• Literary Studies (19th Century)
• Literary Studies (20th Century onwards)
• Literary Studies (African American Literature)
• Literary Studies (British and Irish)
• Literary Studies (Early and Medieval)
• Literary Studies (Fiction, Novelists, and Prose Writers)
• Literary Studies (Gender Studies)
• Literary Studies (Graphic Novels)
• Literary Studies (History of the Book)
• Literary Studies (Plays and Playwrights)
• Literary Studies (Poetry and Poets)
• Literary Studies (Postcolonial Literature)
• Literary Studies (Queer Studies)
• Literary Studies (Science Fiction)
• Literary Studies (Travel Literature)
• Literary Studies (War Literature)
• Literary Studies (Women's Writing)
• Literary Theory and Cultural Studies
• Mythology and Folklore
• Shakespeare Studies and Criticism
• Browse content in Media Studies
• Browse content in Music
• Applied Music
• Dance and Music
• Ethics in Music
• Ethnomusicology
• Gender and Sexuality in Music
• Medicine and Music
• Music Cultures
• Music and Religion
• Music and Media
• Music and Culture
• Music Education and Pedagogy
• Music Theory and Analysis
• Musical Scores, Lyrics, and Libretti
• Musical Structures, Styles, and Techniques
• Musicology and Music History
• Performance Practice and Studies
• Race and Ethnicity in Music
• Sound Studies
• Browse content in Performing Arts
• Browse content in Philosophy
• Aesthetics and Philosophy of Art
• Epistemology
• Feminist Philosophy
• History of Western Philosophy
• Metaphysics
• Moral Philosophy
• Non-Western Philosophy
• Philosophy of Science
• Philosophy of Language
• Philosophy of Mind
• Philosophy of Perception
• Philosophy of Action
• Philosophy of Law
• Philosophy of Religion
• Philosophy of Mathematics and Logic
• Practical Ethics
• Social and Political Philosophy
• Browse content in Religion
• Biblical Studies
• Christianity
• East Asian Religions
• History of Religion
• Judaism and Jewish Studies
• Qumran Studies
• Religion and Education
• Religion and Health
• Religion and Politics
• Religion and Science
• Religion and Law
• Religion and Art, Literature, and Music
• Religious Studies
• Browse content in Society and Culture
• Cookery, Food, and Drink
• Cultural Studies
• Customs and Traditions
• Ethical Issues and Debates
• Hobbies, Games, Arts and Crafts
• Natural world, Country Life, and Pets
• Popular Beliefs and Controversial Knowledge
• Sports and Outdoor Recreation
• Technology and Society
• Travel and Holiday
• Visual Culture
• Browse content in Law
• Arbitration
• Browse content in Company and Commercial Law
• Commercial Law
• Company Law
• Browse content in Comparative Law
• Systems of Law
• Competition Law
• Browse content in Constitutional and Administrative Law
• Government Powers
• Judicial Review
• Local Government Law
• Military and Defence Law
• Parliamentary and Legislative Practice
• Construction Law
• Contract Law
• Browse content in Criminal Law
• Criminal Procedure
• Criminal Evidence Law
• Sentencing and Punishment
• Employment and Labour Law
• Environment and Energy Law
• Browse content in Financial Law
• Banking Law
• Insolvency Law
• History of Law
• Human Rights and Immigration
• Intellectual Property Law
• Browse content in International Law
• Private International Law and Conflict of Laws
• Public International Law
• IT and Communications Law
• Jurisprudence and Philosophy of Law
• Law and Politics
• Law and Society
• Browse content in Legal System and Practice
• Courts and Procedure
• Legal Skills and Practice
• Legal System - Costs and Funding
• Primary Sources of Law
• Regulation of Legal Profession
• Medical and Healthcare Law
• Browse content in Policing
• Criminal Investigation and Detection
• Police and Security Services
• Police Procedure and Law
• Police Regional Planning
• Browse content in Property Law
• Personal Property Law
• Restitution
• Study and Revision
• Terrorism and National Security Law
• Browse content in Trusts Law
• Wills and Probate or Succession
• Browse content in Medicine and Health
• Browse content in Allied Health Professions
• Arts Therapies
• Clinical Science
• Dietetics and Nutrition
• Occupational Therapy
• Operating Department Practice
• Physiotherapy
• Radiography
• Speech and Language Therapy
• Browse content in Anaesthetics
• General Anaesthesia
• Browse content in Clinical Medicine
• Acute Medicine
• Cardiovascular Medicine
• Clinical Genetics
• Clinical Pharmacology and Therapeutics
• Dermatology
• Endocrinology and Diabetes
• Gastroenterology
• Genito-urinary Medicine
• Geriatric Medicine
• Infectious Diseases
• Medical Toxicology
• Medical Oncology
• Pain Medicine
• Palliative Medicine
• Rehabilitation Medicine
• Respiratory Medicine and Pulmonology
• Rheumatology
• Sleep Medicine
• Sports and Exercise Medicine
• Clinical Neuroscience
• Community Medical Services
• Critical Care
• Emergency Medicine
• Forensic Medicine
• Haematology
• History of Medicine
• Browse content in Medical Dentistry
• Oral and Maxillofacial Surgery
• Paediatric Dentistry
• Restorative Dentistry and Orthodontics
• Surgical Dentistry
• Browse content in Medical Skills
• Clinical Skills
• Communication Skills
• Nursing Skills
• Surgical Skills
• Medical Ethics
• Medical Statistics and Methodology
• Browse content in Neurology
• Clinical Neurophysiology
• Neuropathology
• Nursing Studies
• Browse content in Obstetrics and Gynaecology
• Gynaecology
• Occupational Medicine
• Ophthalmology
• Otolaryngology (ENT)
• Browse content in Paediatrics
• Neonatology
• Browse content in Pathology
• Chemical Pathology
• Clinical Cytogenetics and Molecular Genetics
• Histopathology
• Medical Microbiology and Virology
• Patient Education and Information
• Browse content in Pharmacology
• Psychopharmacology
• Browse content in Popular Health
• Caring for Others
• Complementary and Alternative Medicine
• Self-help and Personal Development
• Browse content in Preclinical Medicine
• Cell Biology
• Molecular Biology and Genetics
• Reproduction, Growth and Development
• Primary Care
• Professional Development in Medicine
• Browse content in Psychiatry
• Addiction Medicine
• Child and Adolescent Psychiatry
• Forensic Psychiatry
• Learning Disabilities
• Old Age Psychiatry
• Psychotherapy
• Browse content in Public Health and Epidemiology
• Epidemiology
• Public Health
• Browse content in Radiology
• Clinical Radiology
• Interventional Radiology
• Nuclear Medicine
• Radiation Oncology
• Reproductive Medicine
• Browse content in Surgery
• Cardiothoracic Surgery
• Gastro-intestinal and Colorectal Surgery
• General Surgery
• Neurosurgery
• Paediatric Surgery
• Peri-operative Care
• Plastic and Reconstructive Surgery
• Surgical Oncology
• Transplant Surgery
• Trauma and Orthopaedic Surgery
• Vascular Surgery
• Browse content in Science and Mathematics
• Browse content in Biological Sciences
• Aquatic Biology
• Biochemistry
• Bioinformatics and Computational Biology
• Developmental Biology
• Ecology and Conservation
• Evolutionary Biology
• Genetics and Genomics
• Microbiology
• Molecular and Cell Biology
• Natural History
• Plant Sciences and Forestry
• Research Methods in Life Sciences
• Structural Biology
• Systems Biology
• Zoology and Animal Sciences
• Browse content in Chemistry
• Analytical Chemistry
• Computational Chemistry
• Crystallography
• Environmental Chemistry
• Industrial Chemistry
• Inorganic Chemistry
• Materials Chemistry
• Medicinal Chemistry
• Mineralogy and Gems
• Organic Chemistry
• Physical Chemistry
• Polymer Chemistry
• Study and Communication Skills in Chemistry
• Theoretical Chemistry
• Browse content in Computer Science
• Artificial Intelligence
• Computer Architecture and Logic Design
• Game Studies
• Human-Computer Interaction
• Mathematical Theory of Computation
• Programming Languages
• Software Engineering
• Systems Analysis and Design
• Virtual Reality
• Browse content in Computing
• Business Applications
• Computer Security
• Computer Games
• Computer Networking and Communications
• Digital Lifestyle
• Graphical and Digital Media Applications
• Operating Systems
• Browse content in Earth Sciences and Geography
• Atmospheric Sciences
• Environmental Geography
• Geology and the Lithosphere
• Maps and Map-making
• Meteorology and Climatology
• Oceanography and Hydrology
• Palaeontology
• Physical Geography and Topography
• Regional Geography
• Soil Science
• Urban Geography
• Browse content in Engineering and Technology
• Agriculture and Farming
• Biological Engineering
• Civil Engineering, Surveying, and Building
• Electronics and Communications Engineering
• Energy Technology
• Engineering (General)
• Environmental Science, Engineering, and Technology
• History of Engineering and Technology
• Mechanical Engineering and Materials
• Technology of Industrial Chemistry
• Transport Technology and Trades
• Browse content in Environmental Science
• Applied Ecology (Environmental Science)
• Conservation of the Environment (Environmental Science)
• Environmental Sustainability
• Environmentalist Thought and Ideology (Environmental Science)
• Management of Land and Natural Resources (Environmental Science)
• Natural Disasters (Environmental Science)
• Nuclear Issues (Environmental Science)
• Pollution and Threats to the Environment (Environmental Science)
• Social Impact of Environmental Issues (Environmental Science)
• History of Science and Technology
• Browse content in Materials Science
• Ceramics and Glasses
• Composite Materials
• Metals, Alloying, and Corrosion
• Nanotechnology
• Browse content in Mathematics
• Applied Mathematics
• Biomathematics and Statistics
• History of Mathematics
• Mathematical Education
• Mathematical Finance
• Mathematical Analysis
• Numerical and Computational Mathematics
• Probability and Statistics
• Pure Mathematics
• Browse content in Neuroscience
• Cognition and Behavioural Neuroscience
• Development of the Nervous System
• Disorders of the Nervous System
• History of Neuroscience
• Invertebrate Neurobiology
• Molecular and Cellular Systems
• Neuroendocrinology and Autonomic Nervous System
• Neuroscientific Techniques
• Sensory and Motor Systems
• Browse content in Physics
• Astronomy and Astrophysics
• Atomic, Molecular, and Optical Physics
• Biological and Medical Physics
• Classical Mechanics
• Computational Physics
• Condensed Matter Physics
• Electromagnetism, Optics, and Acoustics
• History of Physics
• Mathematical and Statistical Physics
• Measurement Science
• Nuclear Physics
• Particles and Fields
• Plasma Physics
• Quantum Physics
• Relativity and Gravitation
• Semiconductor and Mesoscopic Physics
• Browse content in Psychology
• Affective Sciences
• Clinical Psychology
• Cognitive Psychology
• Cognitive Neuroscience
• Criminal and Forensic Psychology
• Developmental Psychology
• Educational Psychology
• Evolutionary Psychology
• Health Psychology
• History and Systems in Psychology
• Music Psychology
• Neuropsychology
• Organizational Psychology
• Psychological Assessment and Testing
• Psychology of Human-Technology Interaction
• Psychology Professional Development and Training
• Research Methods in Psychology
• Social Psychology
• Browse content in Social Sciences
• Browse content in Anthropology
• Anthropology of Religion
• Human Evolution
• Medical Anthropology
• Physical Anthropology
• Regional Anthropology
• Social and Cultural Anthropology
• Theory and Practice of Anthropology
• Browse content in Business and Management
• Business Strategy
• Business Ethics
• Business History
• Business and Government
• Business and Technology
• Business and the Environment
• Comparative Management
• Corporate Governance
• Corporate Social Responsibility
• Entrepreneurship
• Health Management
• Human Resource Management
• Industrial and Employment Relations
• Industry Studies
• Information and Communication Technologies
• International Business
• Knowledge Management
• Management and Management Techniques
• Operations Management
• Organizational Theory and Behaviour
• Pensions and Pension Management
• Public and Nonprofit Management
• Social Issues in Business and Management
• Strategic Management
• Supply Chain Management
• Browse content in Criminology and Criminal Justice
• Criminal Justice
• Criminology
• Forms of Crime
• International and Comparative Criminology
• Youth Violence and Juvenile Justice
• Development Studies
• Browse content in Economics
• Agricultural, Environmental, and Natural Resource Economics
• Asian Economics
• Behavioural Finance
• Behavioural Economics and Neuroeconomics
• Econometrics and Mathematical Economics
• Economic Systems
• Economic History
• Economic Methodology
• Economic Development and Growth
• Financial Markets
• Financial Institutions and Services
• General Economics and Teaching
• Health, Education, and Welfare
• History of Economic Thought
• International Economics
• Labour and Demographic Economics
• Law and Economics
• Macroeconomics and Monetary Economics
• Microeconomics
• Public Economics
• Urban, Rural, and Regional Economics
• Welfare Economics
• Browse content in Education
• Adult Education and Continuous Learning
• Care and Counselling of Students
• Early Childhood and Elementary Education
• Educational Equipment and Technology
• Educational Strategies and Policy
• Higher and Further Education
• Organization and Management of Education
• Philosophy and Theory of Education
• Schools Studies
• Secondary Education
• Teaching of a Specific Subject
• Teaching of Specific Groups and Special Educational Needs
• Teaching Skills and Techniques
• Browse content in Environment
• Applied Ecology (Social Science)
• Climate Change
• Conservation of the Environment (Social Science)
• Environmentalist Thought and Ideology (Social Science)
• Management of Land and Natural Resources (Social Science)
• Natural Disasters (Environment)
• Pollution and Threats to the Environment (Social Science)
• Social Impact of Environmental Issues (Social Science)
• Sustainability
• Browse content in Human Geography
• Cultural Geography
• Economic Geography
• Political Geography
• Browse content in Interdisciplinary Studies
• Communication Studies
• Museums, Libraries, and Information Sciences
• Browse content in Politics
• African Politics
• Asian Politics
• Chinese Politics
• Comparative Politics
• Conflict Politics
• Elections and Electoral Studies
• Environmental Politics
• Ethnic Politics
• European Union
• Foreign Policy
• Gender and Politics
• Human Rights and Politics
• Indian Politics
• International Relations
• International Organization (Politics)
• Irish Politics
• Latin American Politics
• Middle Eastern Politics
• Political Methodology
• Political Communication
• Political Philosophy
• Political Sociology
• Political Behaviour
• Political Economy
• Political Institutions
• Political Theory
• Politics and Law
• Politics of Development
• Public Administration
• Public Policy
• Qualitative Political Methodology
• Quantitative Political Methodology
• Regional Political Studies
• Russian Politics
• Security Studies
• State and Local Government
• UK Politics
• US Politics
• Browse content in Regional and Area Studies
• African Studies
• Asian Studies
• East Asian Studies
• Japanese Studies
• Latin American Studies
• Middle Eastern Studies
• Native American Studies
• Scottish Studies
• Browse content in Research and Information
• Research Methods
• Browse content in Social Work
• Addictions and Substance Misuse
• Adoption and Fostering
• Care of the Elderly
• Child and Adolescent Social Work
• Couple and Family Social Work
• Direct Practice and Clinical Social Work
• Emergency Services
• Human Behaviour and the Social Environment
• International and Global Issues in Social Work
• Mental and Behavioural Health
• Social Justice and Human Rights
• Social Policy and Advocacy
• Social Work and Crime and Justice
• Social Work Macro Practice
• Social Work Practice Settings
• Social Work Research and Evidence-based Practice
• Welfare and Benefit Systems
• Browse content in Sociology
• Childhood Studies
• Community Development
• Comparative and Historical Sociology
• Disability Studies
• Economic Sociology
• Gender and Sexuality
• Gerontology and Ageing
• Health, Illness, and Medicine
• Marriage and the Family
• Migration Studies
• Occupations, Professions, and Work
• Organizations
• Population and Demography
• Race and Ethnicity
• Social Theory
• Social Movements and Social Change
• Social Research and Statistics
• Social Stratification, Inequality, and Mobility
• Sociology of Religion
• Sociology of Education
• Sport and Leisure
• Urban and Rural Studies
• Browse content in Warfare and Defence
• Defence Strategy, Planning, and Research
• Land Forces and Warfare
• Military Administration
• Military Life and Institutions
• Naval Forces and Warfare
• Other Warfare and Defence Issues
• Peace Studies and Conflict Resolution
• Weapons and Equipment

• < Previous chapter
• Next chapter >

14 The Ontological Argument

• Published: April 2021
• Cite Icon Cite
• Permissions Icon Permissions

This chapter argues that Kant’s criticism of the ontological argument is targeted, in the first instance, at Leibniz’s sympathetic revamping of the Cartesian argument. But Kant’s discussion actually contains a suite of objections to the ontological argument, some of them effective against Descartes, others (less successfully) directed against Wolff and Baumgarten, and one—the famous objection that being is not a real predicate—directed exclusively against Leibniz. It argues that this last objection, which appeals to the example of a hundred thalers, succeeds against Leibniz because he is prevented by his stance on the Euthyphro contrast from offering the obvious reply. Kant’s most famous objection is thus an ‘ad hominem’ argument in the original (and now largely forgotten) sense of that term: a perfectly rational argument that does not attack an opponent’s character, but rather uses one of their own commitments against them.

Personal account

• Sign in with email/username & password
• Get email alerts
• Save searches
• Purchase content
• Activate your purchase/trial code
• Add your ORCID iD

Institutional access

Sign in with a library card.

• Sign in with username/password
• Recommend to your librarian
• Institutional account management
• Get help with access

Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:

IP based access

Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.

Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.

• Click Sign in through your institution.
• Select your institution from the list provided, which will take you to your institution's website to sign in.
• When on the institution site, please use the credentials provided by your institution. Do not use an Oxford Academic personal account.
• Following successful sign in, you will be returned to Oxford Academic.

If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.

Enter your library card number to sign in. If you cannot sign in, please contact your librarian.

Society Members

Society member access to a journal is achieved in one of the following ways:

Sign in through society site

Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:

• Click Sign in through society site.
• When on the society site, please use the credentials provided by that society. Do not use an Oxford Academic personal account.

If you do not have a society account or have forgotten your username or password, please contact your society.

Sign in using a personal account

Some societies use Oxford Academic personal accounts to provide access to their members. See below.

A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.

Some societies use Oxford Academic personal accounts to provide access to their members.

Viewing your signed in accounts

Click the account icon in the top right to:

• View your signed in personal account and access account management features.
• View the institutional accounts that are providing access.

Signed in but can't access content

Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.

For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.

Our books are available by subscription or purchase to libraries and institutions.

• About Oxford Academic
• Publish journals with us
• University press partners
• What we publish
• New features  
• Open access
• Rights and permissions
• Accessibility
• Advertising
• Media enquiries
• Oxford University Press
• Oxford Languages
• University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

• Copyright © 2024 Oxford University Press
• Cookie settings
• Cookie policy
• Privacy policy
• Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base
• How to Write a Thesis Statement | 4 Steps & Examples

How to Write a Thesis Statement | 4 Steps & Examples

Published on January 11, 2019 by Shona McCombes . Revised on August 15, 2023 by Eoghan Ryan.

A thesis statement is a sentence that sums up the central point of your paper or essay . It usually comes near the end of your introduction .

Your thesis will look a bit different depending on the type of essay you’re writing. But the thesis statement should always clearly state the main idea you want to get across. Everything else in your essay should relate back to this idea.

You can write your thesis statement by following four simple steps:

• Start with a question
• Write your initial answer
• Develop your answer
• Refine your thesis statement

Instantly correct all language mistakes in your text

Upload your document to correct all your mistakes in minutes

Table of contents

What is a thesis statement, placement of the thesis statement, step 1: start with a question, step 2: write your initial answer, step 3: develop your answer, step 4: refine your thesis statement, types of thesis statements, other interesting articles, frequently asked questions about thesis statements.

A thesis statement summarizes the central points of your essay. It is a signpost telling the reader what the essay will argue and why.

The best thesis statements are:

• Concise: A good thesis statement is short and sweet—don’t use more words than necessary. State your point clearly and directly in one or two sentences.
• Contentious: Your thesis shouldn’t be a simple statement of fact that everyone already knows. A good thesis statement is a claim that requires further evidence or analysis to back it up.
• Coherent: Everything mentioned in your thesis statement must be supported and explained in the rest of your paper.

Here's why students love Scribbr's proofreading services

Discover proofreading & editing

The thesis statement generally appears at the end of your essay introduction or research paper introduction .

The spread of the internet has had a world-changing effect, not least on the world of education. The use of the internet in academic contexts and among young people more generally is hotly debated. For many who did not grow up with this technology, its effects seem alarming and potentially harmful. This concern, while understandable, is misguided. The negatives of internet use are outweighed by its many benefits for education: the internet facilitates easier access to information, exposure to different perspectives, and a flexible learning environment for both students and teachers.

You should come up with an initial thesis, sometimes called a working thesis , early in the writing process . As soon as you’ve decided on your essay topic , you need to work out what you want to say about it—a clear thesis will give your essay direction and structure.

You might already have a question in your assignment, but if not, try to come up with your own. What would you like to find out or decide about your topic?

For example, you might ask:

After some initial research, you can formulate a tentative answer to this question. At this stage it can be simple, and it should guide the research process and writing process .

Now you need to consider why this is your answer and how you will convince your reader to agree with you. As you read more about your topic and begin writing, your answer should get more detailed.

In your essay about the internet and education, the thesis states your position and sketches out the key arguments you’ll use to support it.

The negatives of internet use are outweighed by its many benefits for education because it facilitates easier access to information.

In your essay about braille, the thesis statement summarizes the key historical development that you’ll explain.

The invention of braille in the 19th century transformed the lives of blind people, allowing them to participate more actively in public life.

A strong thesis statement should tell the reader:

• Why you hold this position
• What they’ll learn from your essay
• The key points of your argument or narrative

The final thesis statement doesn’t just state your position, but summarizes your overall argument or the entire topic you’re going to explain. To strengthen a weak thesis statement, it can help to consider the broader context of your topic.

These examples are more specific and show that you’ll explore your topic in depth.

Your thesis statement should match the goals of your essay, which vary depending on the type of essay you’re writing:

• In an argumentative essay , your thesis statement should take a strong position. Your aim in the essay is to convince your reader of this thesis based on evidence and logical reasoning.
• In an expository essay , you’ll aim to explain the facts of a topic or process. Your thesis statement doesn’t have to include a strong opinion in this case, but it should clearly state the central point you want to make, and mention the key elements you’ll explain.

If you want to know more about AI tools , college essays , or fallacies make sure to check out some of our other articles with explanations and examples or go directly to our tools!

• Ad hominem fallacy
• Post hoc fallacy
• Appeal to authority fallacy
• False cause fallacy
• Sunk cost fallacy

College essays

• Choosing Essay Topic
• Write a College Essay
• Write a Diversity Essay
• College Essay Format & Structure
• Comparing and Contrasting in an Essay

 (AI) Tools

• Grammar Checker
• Paraphrasing Tool
• Text Summarizer
• AI Detector
• Plagiarism Checker
• Citation Generator

A thesis statement is a sentence that sums up the central point of your paper or essay . Everything else you write should relate to this key idea.

The thesis statement is essential in any academic essay or research paper for two main reasons:

• It gives your writing direction and focus.
• It gives the reader a concise summary of your main point.

Without a clear thesis statement, an essay can end up rambling and unfocused, leaving your reader unsure of exactly what you want to say.

Follow these four steps to come up with a thesis statement :

• Ask a question about your topic .
• Write your initial answer.
• Develop your answer by including reasons.
• Refine your answer, adding more detail and nuance.

The thesis statement should be placed at the end of your essay introduction .

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, August 15). How to Write a Thesis Statement | 4 Steps & Examples. Scribbr. Retrieved September 11, 2024, from https://www.scribbr.com/academic-essay/thesis-statement/

Is this article helpful?

Shona McCombes

Other students also liked, how to write an essay introduction | 4 steps & examples, how to write topic sentences | 4 steps, examples & purpose, academic paragraph structure | step-by-step guide & examples, get unlimited documents corrected.

✔ Free APA citation check included ✔ Unlimited document corrections ✔ Specialized in correcting academic texts

• Table of Contents
• New in this Archive
• Chronological
• Editorial Information
• About the SEP
• Editorial Board
• How to Cite the SEP
• Special Characters
• Support the SEP
• PDFs for SEP Friends
• Make a Donation
• SEPIA for Libraries
• Entry Contents

Bibliography

Academic tools.

• Friends PDF Preview
• Author and Citation Info
• Back to Top

Ontological Arguments

Ontological arguments are arguments, for the conclusion that God exists, from premises which are supposed to derive from some source other than observation of the world—e.g., from reason alone. In other words, ontological arguments are arguments from nothing but analytic, a priori and necessary premises to the conclusion that God exists.

The first, and best-known, ontological argument was proposed by St. Anselm of Canterbury in the 11th. century C.E. In his Proslogion , St. Anselm claims to derive the existence of God from the concept of a being than which no greater can be conceived . St. Anselm reasoned that, if such a being fails to exist, then a greater being—namely, a being than which no greater can be conceived, and which exists —can be conceived. But this would be absurd: nothing can be greater than a being than which no greater can be conceived. So a being than which no greater can be conceived—i.e., God—exists.

In the seventeenth century, René Descartes defended a family of similar arguments. For instance, in the Fifth Meditation , Descartes claims to provide a proof demonstrating the existence of God from the idea of a supremely perfect being. Descartes argues that there is no less contradiction in conceiving a supremely perfect being who lacks existence than there is in conceiving a triangle whose interior angles do not sum to 180 degrees. Hence, he supposes, since we do conceive a supremely perfect being—we do have the idea of a supremely perfect being—we must conclude that a supremely perfect being exists.

In the early eighteenth century, Gottfried Leibniz attempted to fill what he took to be a shortcoming in Descartes’ view. According to Leibniz, Descartes’ arguments fail unless one first shows that the idea of a supremely perfect being is coherent, or that it is possible for there to be a supremely perfect being. Leibniz argued that, since perfections are unanalysable, it is impossible to demonstrate that perfections are incompatible—and he concluded from this that all perfections can co-exist together in a single entity.

In more recent times, Kurt Gödel, Charles Hartshorne, Norman Malcolm and Alvin Plantinga have all presented much-discussed ontological arguments which bear interesting connections to the earlier arguments of St. Anselm, Descartes and Leibniz. Of these, the most interesting are those of Gödel and Plantinga; in these cases, however, it is unclear whether we should really say that these authors claim that the arguments are proofs of the existence of God.

Critiques of ontological arguments begin with Gaunilo, a contemporary of St. Anselm. Perhaps the best known criticisms of ontological arguments are due to Immanuel Kant, in his Critique of Pure Reason . Most famously, Kant claims that ontological arguments are vitiated by their reliance upon the implicit assumption that “existence” is a predicate. However, as Bertrand Russell observed, it is much easier to be persuaded that ontological arguments are no good than it is to say exactly what is wrong with them. This helps to explain why ontological arguments have fascinated philosophers for almost a thousand years.

In various ways, the account provided to this point is rough, and susceptible of improvement. Sections 1–5 in what follows provide some of the requisite embellishments, though—as is usually the case in philosophy—there are many issues taken up here which could be pursued at much greater length. Sections 6–8 take up some of the central questions at a slightly more sophisticated level of discussion. Section 9 is a quick overview of very recent work on ontological arguments:

1. History of Ontological Arguments

2. taxonomy of ontological arguments, 3. characterisation of ontological arguments, 4. objections to ontological arguments, 5. parodies of ontological arguments, 6. gödel’s ontological argument, 7. a victorious ontological argument, 8. st. anselm’s ontological argument, 9. ontological arguments in the 21st century, primary texts, other texts, other internet resources, related entries.

For a useful discussion of the history of ontological arguments in the modern period, see Harrelson 2009.

According to a modification of the taxonomy of Oppy 1995, there are eight major kinds of ontological arguments, viz:

• definitional ontological arguments;
• conceptual (or hyperintensional) ontological arguments;
• modal ontological arguments;
• Meinongian ontological arguments;
• experiential ontological arguments;
• mereological ontological arguments;
• higher-order ontological arguments; and
• ‘Hegelian’ ontological arguments;

Examples of all but the last follow. These are mostly toy examples. But they serve to highlight the deficiencies which more complex examples also share.

Note: I provide no example of a ‘Hegelian’ ontological argument because I know of no formulation of such an argument. Many people assert that Hegel provided an ontological argument; but, when pressed for a list of the premises of the argument, Hegel’s friends fail to deliver. (For a defense of Hegel against these charges—but not for a supply of the premises of ‘the Hegelian ontological argument’—see Redding and Bubbio 2014.)

God is a being which has every perfection. (This is true as a matter of definition.) Existence is a perfection. Hence God exists.

I conceive of a being than which no greater can be conceived. If a being than which no greater can be conceived does not exist, then I can conceive of a being greater than a being than which no greater can be conceived—namely, a being than which no greater can be conceived that exists. I cannot conceive of a being greater than a being than which no greater can be conceived. Hence, a being than which no greater can be conceived exists.

It is possible that that God exists. God is not a contingent being, i.e., either it is not possible that God exists, or it is necessary that God exists. Hence, it is necessary that God exists. Hence, God exists. (See Malcolm 1960, Hartshorne 1965, and Plantinga 1974 for closely related arguments.)

[It is analytic, necessary and a priori that] Each instance of the schema “The F G is F ” expresses a truth. Hence the sentence “The existent perfect being is existent” expresses a truth. Hence, the existent perfect being is existent. Hence, God is existent, i.e. God exists. (The last step is justified by the observation that, as a matter of definition, if there is exactly one existent perfect being, then that being is God.)

The word ‘God’ has a meaning that is revealed in religious experience. The word ‘God’ has a meaning only if God exists. Hence, God exists. (See Rescher 1959 for a live version of this argument.)

I exist. Therefore something exists. Whenever a bunch of things exist, their mereological sum also exists. Therefore the sum of all things exists. Therefore God—the sum of all things—exists.

Say that a God-property is a property that is possessed by God in all and only those worlds in which God exists. Not all properties are God properties. Any property entailed by a collection of God-properties is itself a God-property. The God-properties include necessary existence, necessary omnipotence, necessary omniscience, and necessary perfect goodness. Hence, there is a necessarily existent, necessarily omnipotent, necessarily omniscient, and necessarily perfectly good being (namely, God).

Of course, this taxonomy is not exclusive: an argument can belong to several categories at once. Moreover, an argument can be ambiguous between a range of readings, each of which belongs to different categories. This latter fact may help to explain part of the curious fascination of ontological arguments. Finally, the taxonomy can be further specialised: there are, for example, at least four importantly different kinds of modal ontological arguments which should be distinguished. (See, e.g., Ross 1969 for a rather different kind of modal ontological argument.)

It is not easy to give a good characterisation of ontological arguments. The traditional characterisation involves the use of problematic notions—analyticity, necessity, and a priority —and also fails to apply to many arguments to which defenders have affixed the label “ontological”. (Consider, for example, the claim that I conceive of a being than which no greater can be conceived. This claim is clearly not analytic (its truth doesn’t follow immediately from the meanings of the words used to express it), nor necessary (I might never have entertained the concept), nor a priori (except perhaps in my own case, though even this is unclear—perhaps even I don’t know independently of experience that I have this concept.)) However, it is unclear how that traditional characterisation should be improved upon.

Perhaps one might resolve to use the label “ontological argument” for any argument which gets classified as “an ontological argument” by its proponent(s). This procedure would make good sense if one thought that there is a natural kind—ontological arguments—which our practice carves out, but for which is hard to specify defining conditions. Moreover, this procedure can be adapted as a pro tem stop gap: when there is a better definition to hand, that definition will be adopted instead. On the other hand, it seems worthwhile to attempt a more informative definition.

Focus on the case of ontological arguments for the conclusion that God exists. One characteristic feature of these arguments is the use which they make of “referential vocabulary”—names, definite descriptions, indefinite descriptions, quantified noun phrases, etc.—whose ontological commitments—for occurrences of this vocabulary in “referential position”—non-theists do not accept.

Theists and non-theists alike (can) agree that there is spatio-temporal, or causal, or nomic, or modal structure to the world (the basis for cosmological arguments); and that there are certain kinds of complexity of organisation, structure and function in the world (the basis for teleological arguments); and so on. But theists and non-theists are in dispute about whether there are perfect beings, or beings than which no greater can be conceived, or … ; thus, theists and non-theists are in dispute about the indirect subject matter of the premises of ontological arguments.

Of course, the premises of ontological arguments often do not deal directly with perfect beings, beings than which no greater can be conceived, etc.; rather, they deal with descriptions of, or ideas of, or concepts of, or the possibility of the existence of, these things. However, the basic point remains: ontological arguments require the use of vocabulary which non-theists should certainly find problematic when it is used in ontologically committing contexts (i.e not inside the scope of prophylactic operators—such as “according to the story” or “by the lights of theists” or “by the definition”—which can be taken to afford protection against unwanted commitments).

Note that this characterisation does not beg the question against the possibility of the construction of a successful ontological argument—i.e., it does not lead immediately to the conclusion that all ontological arguments are question-begging (in virtue of the ontologically committing vocabulary which they employ). For it may be that the vocabulary in question only gets used in premises under the protection of prophylactic operators (which ward off the unwanted commitments.) Of course, there will then be questions about whether the resulting arguments can possibly be valid—how could the commitments turn up in the conclusion if they are not there in the premises?—but those are further questions, which would remain to be addressed.

Objections to ontological arguments take many forms. Some objections are intended to apply only to particular ontological arguments, or particular forms of ontological arguments; other objections are intended to apply to all ontological arguments. It is a controversial question whether there are any successful general objections to ontological arguments.

One general criticism of ontological arguments which have appeared hitherto is this: none of them is persuasive , i.e., none of them provides those who do not already accept the conclusion that God exists—and who are reasonable, reflective, well-informed, etc.—with either a pro tanto reason or an all-things-considered reason to accept that conclusion. Any reading of any ontological argument which has been produced so far which is sufficiently clearly stated to admit of evaluation yields a result which is invalid, or possesses a set of premises which it is clear in advance that no reasonable, reflective, well-informed, etc. non-theists will accept, or has a benign conclusion which has no religious significance, or else falls prey to more than one of the above failings.

For each of the families of arguments introduced in the earlier taxonomy, we can give general reasons why arguments of that family fall under the general criticism. In what follows, we shall apply these general considerations to the exemplar arguments introduced in section 2.

(1) Definitional arguments: These are arguments in which ontologically committing vocabulary is introduced solely via a definition. An obvious problem is that claims involving that vocabulary cannot then be non-question-beggingly detached from the scope of that definition. (The inference from ‘By definition, God is an existent being’ to ‘God exists’ is patently invalid; while the inference to ‘By definition, God exists’ is valid, but uninteresting. In the example given earlier, the premises licence the claim that, as a matter of definition, God possesses the perfection of existence. But, as just noted, there is no valid inference from this claim to the further claim that God exists.)

(2) Conceptual arguments: These are arguments in which ontologically committing vocabulary is introduced solely within the scope of hyperintensional operators (e.g. ‘believes that’, ‘conceives of’, etc.). Often, these operators have two readings, one of which can cancel ontological commitment, and the other of which cannot. On the reading which can give cancellation (as in the most likely reading of ‘John believes in Santa Claus’), the inference to a conclusion in which the ontological commitment is not cancelled will be invalid. On the reading which cannot cancel ontological commitment (as in that reading of ‘John thinks about God’ which can only be true if there is a God to think about), the premises are question-begging: they incur ontological commitments which non-theists reject. In our sample argument, the claim, that I conceive of an existent being than which no greater being can be conceived, admits of the two kinds of readings just distinguished. On the one hand, on the reading which gives cancellation, the inference to the conclusion that there is a being than which no greater can be conceived is plainly invalid. On the other hand, on the reading in which there is no cancellation, it is clear that this claim is one which no reasonable, etc. non-theist will accept: if you doubt that there is a being than which no greater can be conceived, then, of course, you doubt whether you can have thoughts about such a being.

(3) Modal arguments: These are arguments with premises which concern modal claims about God, i.e., claims about the possibility or necessity of God’s attributes and existence. Suppose that we agree to think about possibility and necessity in terms of possible worlds: a claim is possibly true just in case it is true in at least one possible world; a claim is necessarily true just in case it is true in every possible world; and a claim is contingent just in case it is true in some possible worlds and false in others. Some theists hold that God is a necessarily existent being, i.e., that God exists in every possible world; all non-theists reject the claim that God exists in the actual world. The sample argument consists, in effect, of two premises:

• God exists in at least one possible world.
• God exists in all possible worlds if God exists in any.

A minimally rational non-theist would not accept both of these premises – they entail that God exists in every possible world whereas a minimally rational non-theists would insist that there is at least one possible world in which God does not exist. Given that that a minimally rational non-theist accepts that there is at least one possible world in which God does not exist, such a non-theist could offer the following counterargument:

• God fails to exist in at least one possible world.

These premises entail that God exists in no possible world, and hence that God does not exist in the actual world. Considered together, the argument and the counterargument just mentioned plainly do not give anyone a reason to prefer theism to non-theism, and nor do they give anyone a reason to prefer non-theism to theism. So the sample argument is unsuccessful: it doesn’t supply an all-things-considered reason to prefer theism to non-theism (just as the counterargument doesn’t supply an all-things-considered reason to prefer non-theism to theism).

(4) Meinongian arguments: These are arguments which depend somehow or other on Meinongian theories of objects. Consider the schema ‘The F G is F ’. Naive Meinongians will suppose that if F is instantiated with any property, then the result is true (and, quite likely, necessary, analytic and a priori). So, for example, the round square is round; the bald current King of France is bald; and so on. However, more sophisticiated Meinongians will insist that there must be some restriction on the substitution instances for F, in order to allow one to draw the obvious and important ontological distinction between the following two groups: {Bill Clinton, the sun, the Eiffel Tower} and {Santa Claus, Mickey Mouse, the round square}. Choice of vocabulary here is controversial: Let us suppose (for the sake of example) that the right thing to say is that the former things exist and the latter do not. Under this supposition, ‘existent’ will not be a suitable substitution instance for F—obviously, since we all agree that there is no existent round square. Of course, nothing hangs on the choice of ‘existent’ as the crucial piece of vocabulary. The point is that non-theists are not prepared to include god(s) in the former group of objects—and hence will be unpersuaded by any argument which tries to use whatever vocabulary is used to discriminate between the two classes as the basis for an argument that god(s) belong to the former group. (Cognoscenti will recognise that the crucial point is that Meinongian ontological arguments fail to respect the distinction between nuclear (assumptible, characterising) properties and non-nuclear (non-assumptible, non-characterising) properties. It should, of course, be noted that neither Meinong, nor any of his well-known modern supporters—e.g. Terence Parsons, Richard Sylvan—ever endorses a Meinongian ontological argument; and it should also be noted that most motivate the distinction between nuclear and non-nuclear properties in part by a need to avoid Meinongian ontological arguments. The reason for calling these arguments “Meinongian” is that they rely on quantification over—or reference to—non-existent objects; there is no perjorative intent in the use of this label.)

(5) Experiential arguments: These are arguments which try to make use of ‘externalist’ or ‘object-involving’ accounts of content. It should not be surprising that they fail. After all, those accounts of content need to have something to say about expressions which fail to refer (‘Santa Claus’, ‘phlogiston’, etc.). But, however the account goes, non-theists will insist that expressions which purport to refer to god(s) should be given exactly the same kind of treatment.

(6) Mereological arguments: Those who dislike mereology will not be impressed by these arguments. However, even those who accept principles of unrestricted composition—i.e., who accept principles which claim, e.g., that, whenever there are some things, there is something which is the sum or fusion of all of those things—need not be perturbed by them: for it is plausible to think that the conclusions of these arguments have no religious significance whatsoever—they are merely arguments for, e.g., the existence of the physical universe.

(7) Higher-Order arguments: The key to these arguments is the observation that any collection of properties, that (a) does not include all properties and (b) is closed under entailment, is possibly jointly instantiated. If it is impossible that God exists — as all who deny that God exists suppose, on the further assumption that, were God to exist, God would exist of necessity — then it cannot be true both that the God-properties are closed under entailment and that there are properties that are not God-properties. Those who take themselves to have good independent reason to deny that there are any gods will take themselves to have good independent reason to deny that there are God-properties that form a non-trivial collection that is closed under entailment.

Even if the forgoing analyses are correct, it is important to note that no argument has been given for the conclusion that no ontological argument can be successful. Even if all of the kinds of arguments produced to date are pretty clearly unsuccessful—i.e., not such as ought to give non-theists reason to accept the conclusion that God exists—it remains an open question whether there is some other kind of hitherto undiscovered ontological argument which does succeed. (Perhaps it is worth adding here that there is fairly widespread consensus, even amongst theists, that no known ontological arguments for the existence of God are persuasive. Most categories of ontological argument have some actual defenders; but none has a large following.)

Many other objections to (some) ontological arguments have been proposed. All of the following have been alleged to be the key to the explanation of the failure of (at least some) ontological arguments: (1) existence is not a predicate (see, e.g., Kant, Smart 1955, Alston 1960); (2) the concept of god is meaningless/incoherent/ inconsistent (see, e.g., Findlay 1949); (3) ontological arguments are ruled out by “the missing explanation argument” (see Johnston 1992; (4) ontological arguments all trade on mistaken uses of singular terms (see, e.g., Barnes 1972; (5) existence is not a perfection (see almost any textbook in philosophy of religion); (6) ontological arguments presuppose a Meinongian approach to ontology (see, e.g., Dummett 1993); and (7) ontological arguments are question-begging, i.e., presuppose what they set out to prove (see, e.g., Rowe 1989). There are many things to say about these objections: the most important point is that almost all of them require far more controversial assumptions than non-theists require in order to be able to reject ontological arguments with good conscience. Trying to support most of these claims merely in order to beat up on ontological arguments is like using a steamroller to crack a nut (in circumstances in which one is unsure that one can get the steamroller to move!).

Of course, all of the above discussion is directed merely to the claim that ontological arguments are not dialectically efficacious—i.e., they give reasonable non-theists no reason to change their views. It might be wondered whether there is some other use which ontological arguments have—e.g., as Plantinga claims, in establishing the reasonableness of theism. This seems unlikely. After all, at best these arguments show that certain sets of sentences (beliefs, etc.) are incompatible—one cannot reject the conclusions of these arguments while accepting their premises. But the arguments themselves say nothing about the reasonableness of accepting the premisses. So the arguments themselves say nothing about the (unconditional) reasonableness of accepting the conclusions of these arguments. Those who are disposed to think that theism is irrational need find nothing in ontological arguments to make them change their minds (and those who are disposed to think that theism is true should take no comfort from them either).

Positive ontological arguments—i.e., arguments FOR the existence of god(s)—invariably admit of various kinds of parodies, i.e., parallel arguments which seem at least equally acceptable to non-theists, but which establish absurd or contradictory conclusions. For many positive ontological arguments, there are parodies which purport to establish the non-existence of god(s); and for many positive ontological arguments there are lots (usually a large infinity!) of similar arguments which purport to establish the existence of lots (usally a large infinity) of distinct god-like beings. Here are some modest examples:

(1) By definition, God is a non-existent being who has every (other) perfection. Hence God does not exist.

(2) I conceive of a being than which no greater can be conceived except that it only ever creates n universes. If such a being does not exist, then we can conceive of a greater being—namely, one exactly like it which does exist. But I cannot conceive of a being which is greater in this way. Hence, a being than which no greater can be conceived except that it only ever creates n universes exists.

(3) It is possible that God does not exist. God is not a contingent being, i.e., either it is not possible that God exists, or it is necessary that God exists. Hence it is not possible that God exists. Hence God does not exist.

(4) It is analytic, necessary, and a priori that the F G is F . Hence, the existent perfect being who creates exactly n universes is existent. Hence the perfect being who creates exactly n universes exists.

There are many kinds of parodies on Ontological Arguments. The aim is to construct arguments which non-theists can reasonably claim to have no more reason to accept than the original Ontological Arguments themselves. Of course, theists may well be able to hold that the originals are sound, and the parodies not—but that is an entirely unrelated issue. (All theists—and no non-theists—should grant that the following argument is sound, given that the connectives are to be interpretted classically: “Either 2+2=5, or God exists. Not 2+2=5. Hence God exists.” It should be completely obvious that this argument is useless.)

There are many parodic discussions of Ontological Arguments in the literature. A particularly pretty one is due to Raymond Smullyan (1984), in which the argument is attributed to “the unknown Dutch theologian van Dollard”. A relatively recent addition to the genre is described in Grey 2000, though the date of its construction is uncertain. It is the work of Douglas Gasking, one-time Professor of Philosophy at the University of Melbourne (with emendations by William Grey and Denis Robinson):

• The creation of the world is the most marvellous achievement imaginable.
• The merit of an achievement is the product of (a) its intrinsic quality, and (b) the ability of its creator.
• The greater the disability or handicap of the creator, the more impressive the achievement.
• The most formidable handicap for a creator would be non-existence.
• Therefore, if we suppose that the universe is the product of an existent creator, we can conceive a greater being—namely, one who created everything while not existing.
• An existing God, therefore, would not be a being than which a greater cannot be conceived, because an even more formidable and incredible creator would be a God which did not exist.
• (Hence) God does not exist.

This parody—at least in its current state—seems inferior to other parodies in the literature, including the early parodies of Gaunilo and Caterus. To mention but one difficulty, while we might suppose that it would be a greater achievement to create something if one did not exist than if one did exist, it doesn’t follow from this that a non-existent creator is greater ( qua being) than an existent creator. Perhaps it might be replied that this objection fails to take the first premise into account: if the creation of the world really is “the most marvellous achievement imaginable”, then surely there is some plausibility to the claim that the creator must have been non-existent (since that would make the achievement more marvellous than it would otherwise have been). But what reason is there to believe that the creation of the world is “the most marvellous achievement imaginable”, in the sense which is required for this argument? Surely it is quite easy to imagine even more marvellous achievements—e.g., the creation of many worlds at least as good as this one! (Of course, one might also want to say that, in fact, one cannot conceive of a non-existent being’s actually creating something: that is literally inconceivable. Etc.)

Chambers 2000 and Siegwart 2014 provide nice, recent discussions of Gaunilo’s parody of the Proslogion II argument.

There is a small, but steadily growing, literature on the ontological arguments which Gödel developed in his notebooks, but which did not appear in print until well after his death. These arguments have been discussed, annotated and amended by various leading logicians: the upshot is a family of arguments with impeccable logical credentials. (Interested readers are referred to Sobel 1987, Anderson 1990, Adams 1995b, and Hazen 1999 for the history of these arguments, and for the scholarly annotations and emendations.) Here, I shall give a brief presentation of the version of the argument which is developed by Anderson, and then make some comments on that version. This discussion follows the presentation and discussion in Oppy 1996, 2000.

Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive Definition 2: A is an essence of x if and only if for every property B , x has B necessarily if and only if A entails B Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified Axiom 1: If a property is positive, then its negation is not positive. Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive Axiom 3: The property of being God-like is positive Axiom 4: If a property is positive, then it is necessarily positive Axiom 5: Necessary existence is positive Axiom 6: For any property P , if P is positive, then being necessarily P is positive. Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified. Corollary 1: The property of being God-like is consistent. Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing. Theorem 3: Necessarily, the property of being God-like is exemplified.

Given a sufficiently generous conception of properties, and granted the acceptability of the underlying modal logic, the listed theorems do follow from the axioms. (This point was argued in detail by Dana Scott, in lecture notes which circulated for many years and which were transcribed in Sobel 1987 and published in Sobel 2004. It is also made by Sobel, Anderson, and Adams.) So, criticisms of the argument are bound to focus on the axioms, or on the other assumptions which are required in order to construct the proof.

Some philosophers have denied the acceptability of the underlying modal logic. And some philosophers have rejected generous conceptions of properties in favour of sparse conceptions according to which only some predicates express properties. But suppose that we adopt neither of these avenues of potential criticism of the proof. What else might we say against it?

One important point to note is that no definition of the notion of “positive property” is supplied with the proof. At most, the various axioms which involve this concept can be taken to provide a partial implicit definition. If we suppose that the “positive properties” form a set, then the axioms provide us with the following information about this set:

• If a property belongs to the set, then its negation does not belong to the set.
• The set is closed under entailment.
• The property of having as essential properties just those properties which are in the set is itself a member of the set.
• The set has exactly the same members in all possible worlds.
• The property of necessary existence is in the set.
• If a property is in the set, then the property of having that property necessarily is also in the set.

On Gödel’s theoretical assumptions, we can show that any set which conforms to (1)–(6) is such that the property of having as essential properties just those properties which are in that set is exemplified. Gödel wants us to conclude that there is just one intuitive, theologically interesting set of properties which is such that the property of having as essential properties just the properties in that set is exemplified. But, on the one hand, what reason do we have to think that there is any theologically interesting set of properties which conforms to the Gödelian specification? And, on the other hand, what reason do we have to deny that, if there is one set of theologically interesting set of properties which conforms to the Gödelian specification, then there are many theologically threatening sets of properties which also conform to that specification?

In particular, there is some reason to think that the Gödelian ontological argument goes through just as well—or just as badly—with respect to other sets of properties (and in ways which are damaging to the original argument). Suppose that there is some set of independent properties { I , G 1 , G 2 , …} which can be used to generate the set of positive properties by closure under entailment and “necessitation”. (“Independence” means: no one of the properties in the set is entailed by all the rest. “Necessitation” means: if P is in the set, then so is necessarily having P . I is the property of having as essential properties just those properties which are in the set. G 1 , G 2 , … are further properties, of which we require at least two.) Consider any proper subset of the set { G 1 , G 2 , …}—{ H 1 , H 2 , …}, say—and define a new generating set { I *, H 1 , H 2 , …}, where I * is the property of having as essential properties just those properties which are in the newly generated set. A “proof” parallel to that offered by Gödel “establishes” that there is a being which has as essential properties just those properties in this new set. If there are as few as 7 independent properties in the original generating set, then we shall be able to establish the existence of 720 distinct“God-like” creatures by the kind of argument which Gödel offers. (The creatures are distinct because each has a different set of essential properties.)

Even if the above considerations are sufficient to cast doubt on the credentials of Gödel’s “proof”, they do not pinpoint where the “proof” goes wrong. If we accept that the role of Axioms 1, 2, 4, and 6 is really just to constrain the notion of “positive property” in the right way—or, in other words, if we suppose that Axioms 1, 2, 4, and 6 are “analytic truths” about “positive properties”—then there is good reason for opponents of the “proof” to be sceptical about Axioms 3 and 5. Kant would not have been happy with Axiom 5; and there is at least some reason to think that whether the property of being God-like is “positive” ought to depend upon whether or not there is a God-like being.

The “victorious” modal ontological argument of Plantinga 1974 goes roughly as follows: Say that an entity possesses “maximal excellence” if and only if it is omnipotent, omnscient, and morally perfect. Say, further, that an entity possesses “maximal greatness” if and only if it possesses maximal excellence in every possible world—that is, if and only if it is necessarily existent and necessarily maximally excellent. Then consider the following argument:

• There is a possible world in which there is an entity which possesses maximal greatness.
• (Hence) There is an entity which possesses maximal greatness.

Under suitable assumptions about the nature of accessibility relations between possible worlds, this argument is valid: from it is possible that it is necessary that p , one can infer that it is necessary that p . Setting aside the possibility that one might challenge this widely accepted modal principle, it seems that opponents of the argument are bound to challenge the acceptability of the premise.

And, of course, they do. Let’s just run the argument in reverse.

• There is no entity which possesses maximal greatness.
• (Hence) There is no possible world in which there is an entity which possesses maximal greatness.

Plainly enough, if you do not already accept the claim that there is an entity which possesses maximal greatness, then you won’t agree that the first of these arguments is more acceptable than the second. So, as a proof of the existence of a being which posseses maximal greatness, Plantinga’s argument seems to be a non-starter.

Perhaps somewhat surprisingly, Plantinga himself agrees: the “victorious” modal ontological argument is not a proof of the existence of a being which possesses maximal greatness. But how, then, is it “victorious”? Plantinga writes: “Our verdict on these reformulated versions of St. Anselm’s argument must be as follows. They cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion” (Plantinga 1974, 221).

It is pretty clear that Plantinga’s argument does not show what he claims that it shows. Consider, again, the argument: “Either God exists, or 2+2=5. It is not the case that 2+2=5. So God exists.” It is just a mistake for a theist to say: “Since the premise is true (and the argument is valid), this argument shows that the conclusion of the argument is true ”. No-one thinks that that argument shows any such thing. Similarly, it is just a mistake for a theist to say: “Since it is rational to accept the premise (and the argument is valid), this argument shows that it is rational to accept the conclusion of the argument”. Again, no one thinks that that argument shows any such thing. But why don’t these arguments show the things in question? There is room for argument about this. But it is at least plausible to claim that, in each case, any even minimally rational person who has doubts about the claimed status of the conclusion of the argument will have exactly the same doubts about the claimed status of the premise. If, for example, I doubt that it is rational to accept the claim that God exists, then you can be quite sure that I will doubt that it is rational to accept the claim that either 2+2=5 or God exists. But, of course, the very same point can be made about Plantinga’s argument: anyone with even minimal rationality who understands the premise and the conclusion of the argument, and who has doubts about the claim that it is rationally permissible to believe that there is an entity which possesses maximal greatness, will have exactly the same doubts about the claim that it is rationally permissible to believe that there is a possible world in which there is an entity which possesses maximal greatness.

For further discussion of Plantinga’s argument, see—for example—Adams 1988, Chandler 1993, Oppy 1995 (70–78, 248–259), Tooley 1981, and van Inwagen 1977).

There is an enormous literature on the material in Proslogion II-III . Some commentators deny that St. Anselm tried to put forward any proofs of the existence of God. Even among commentators who agree that St. Anselm intended to prove the existence of God, there is disagreement about where the proof is located. Some commentators claim that the main proof is in Proslogion II , and that the rest of the work draws out corollaries of that proof (see, e.g., Charlesworth 1965). Other commentators claim that the main proof is in Prologion III , and that the proof in Proslogion II is merely an inferior first attempt (see, e.g., Malcolm 1960). Yet other commentators claim that there is a single proof which spans at least Proslogion II-III —see, e.g., Campbell 1976 and, perhaps, the entire work—see, e.g., La Croix 1972. I shall ignore this aspect of the controversy about the Proslogion . Instead, I shall just focus on the question of the analysis of the material in Proslogion II on the assumption that there is an independent argument for the existence of God which is given therein.

Here is one translation of the crucial part of Proslogion II (due to William Mann (1972, 260–1); alternative translations can be found in Barnes 1972, Campbell 1976, Charlesworth 1965, and elsewhere):

Thus even the fool is convinced that something than which nothing greater can be conceived is in the understanding, since when he hears this, he understands it; and whatever is understood is in the understanding. And certainly that than which a greater cannot be conceived cannot be in the understanding alone. For if it is even in the understanding alone, it can be conceived to exist in reality also, which is greater. Thus if that than which a greater cannot be conceived is in the understanding alone, then that than which a greater cannot be conceived is itself that than which a greater can be conceived. But surely this cannot be. Thus without doubt something than which a greater cannot be conceived exists, both in the understanding and in reality.

There have been many ingenious attempts to find an argument which can be expressed in modern logical formalism, which is logically valid, and which might plausibly be claimed to be the argument which is expressed in this passage. To take a few prime examples, Adams 1971, Barnes 1972 and Oppenheimer and Zalta 1991 have all produced formally valid analyses of the argument in this passage. We begin with a brief presentation of each of these analyses, preceded by a presentation of the formulation of the argument given by Plantinga 1967, and including a presentation of some of the formulations of Lewis 1970. (Chambers 2000 works with the analysis of Adams 1971.)

8.1 Formulation 1

God exists in the understanding but not in reality. (Assumption for reductio )

Existence in reality is greater than existence in the understanding alone. (Premise)

A being having all of God’s properties plus existence in reality can be conceived. (Premise)

A being having all of God’s properties plus existence in reality is greater than God. (From (1) and (2).)

A being greater than God can be conceived. (From (3) and (4).)

It is false that a being greater than God can be conceived. (From definition of “God”.)

Hence, it is false that God exists in the understanding but not in reality. (From (1), (5), (6).)

God exists in the understanding. (Premise, to which even the Fool agrees.)

Hence God exists in reality. (From (7), (8).)

See Plantinga 1967.

8.2 Formulation 2

The Fool understands the expression “the being than which no greater can be conceived”. (Premise)

If a person understands an expression “ b ”, then b is in that person’s understanding. (Premise)

If a thing is in a person’s understanding, then the person can conceive of that thing’s existing in reality. (Premise)

Each thing which exists in reality is greater than any thing which exists only in the understanding. (Premise)

If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing. (Premise)

If a person can conceive that a specified object has a given property, then that person can conceive that something or other has that property. (Premise)

Hence the being than which no greater can be conceived exists in reality. (From (1)-(6), by a complex series of steps here omitted.)

See Barnes 1972.

8.3 Formulation 3

There is a thing x , and a magnitude m , such that x exists in the understanding, m is the magnitude of x , and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n > m . (Premise)

For any thing x and magnitude m , if x exists in the understanding, m is the magnitude of x , and it is not possible that there is a thing y and magnitude n such that n is the magnitude of y and n > m , then it is possible that x exists in reality. (Premise)

For any thing x and magnitude m , if m is the magnitude of x , and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n > m , and x does not exist in reality, then it is not possible that if x exists in reality then there is a magnitude n such that n is greater than m and n is the magnitude of x . (Premise)

(Hence) There is a thing x and a magnitude m such that x exist in the understanding, and x exists in reality, and m is the magnitude of x , and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n > m . (From 1, 2, 3)

See Adams 1971.

8.4 Formulation 4

For any understandable being x , there is a world w such that x exists in w . (Premise)

For any understandable being x , and for any worlds w and v , if x exists in w , but x does not exist in v , then the greatness of x in w exceeds the greatness of x in v . (Premise)

There is an understandable being x such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (Premise)

(Hence) There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (From (1)-(3).)

See Lewis 1970.

Lewis also suggests an alternative to (3) which yields a valid argument:

(3′) There is an understandable being x such that for no worlds v and w and being y does the greatness of y in w exceed the greatness of x in v .

and two alternatives to (3)—not presented here—which yield invalid arguments. (Of course, there further two alternatives are crucial to Lewis’ overall analysis of the passage: essentially, Lewis suggests that Anselm equivocates between an invalid argument with plausible premises and a valid argument with question-begging premises. In this respect, Lewis’ analysis is quite different from the other analyses currently under discussion.)

8.5 Formulation 5

There is (in the understanding) something than which there is no greater. (Premise)

(Hence) There is (in the understanding) a unique thing than which there is no greater. (From (1), assuming that the “greater-than” relation is connected.)

(Hence) There is (in the understanding) something which is the thing than which there is no greater. (From (2), by a theorem about descriptions.)

(Hence) There is (in the understanding) nothing which is greater than the thing than which there is no greater. (From (3), by another theorem about descriptions.)

If that thing than which there is no greater does not exist (in reality), then there is (in the understanding) something which is greater than that thing than which there is no greater. (Premise)

(Hence) That thing than which there is no greater exists (in reality). (From (4) and (5).)

(Hence) God exists. (From (6).)

See Oppenheimer and Zalta 1991.

Oppenheimer and Zalta 2011 provides a “simplified” version of this argument, in which the number of controversial assumptions is reduced. Since they also provide a clear reason for thinking that this new version of the argument is not persuasive, I shall not consider it further here.

8.6 Critical Appraisal

Considered as interpretations of the argument presented in the Proslogion , these formulations are subject to various kinds of criticisms.

First , the modal interpretations of Lewis 1970 and Adams 1971 don’t square very well with the rest of the Proslogion : the claim that “being than which no greater can be conceived” should be read as “being than which no greater is possible” would have us render the claim of Proslogion 15 to be that God is a being greater than any which is possible. And that is surely a bad result.

Second , the Meinongian interpretations of Barnes 1972, Adams 1971 and Oppenheimer and Zalta 1991 produce arguments which, given the principles involved, could easily be much simplified, and which are obviously vulnerable to Gaunilo-type objections.

Consider, for example, the case of Oppenheimer and Zalta. They have Anselm committed to the claim that if anyone can understand the phrase “that than which F ”, then there is something in the understanding such that F (see their footnote 25); and they also have him committed to the claim that if there is something which is the F -thing, then it—i.e., the F -thing—has the property F (see page 7). Plainly though, if Anselm is really committed to these principles, then he could hardly fail to be committed to the more general principles: (1) if anyone can understand the phrase “an F ”, then there is at least one F -thing in the understanding; and (2) if there are some things which are the F -things, then they—i.e., the F -things—must have the property F . (It would surely be absurd to claim that Anselm is only committed to the less general principles: what could possibly have justified the restrictions to the special cases?)

But, then, mark the consequences. We all understand the expression “an existent perfect being”. So, by the first claim, there is at least one existent perfect being in the understanding. And, by the second claim, any existent perfect being is existent. So, from these two claims combined, there is—in reality—at least one existent perfect being.

This argument gives Anselm everything that he wants, and very much more briefly. (The Proslogion goes on and on, trying to establish the properties of that than which no greater can be conceived. How much easier if we can just explicitly build all of the properties which want to “derive” into the initial description.) So, if Anselm really were committed to the principles which Oppenheimer and Zalta appear to attribute to him, it is hard to understand why he didn’t give the simpler argument. And, of course, it is also hard to understand why he didn’t take Gaunilo’s criticism. After all, when it is set out in this way, it is obvious that the argument proves far too much.

Third , some of the arguments have Anselm committed to claims about greatness which do not seem to correspond with what he actually says. The natural reading of the text is that, if two beings are identical save that one exists only in the understanding and the other exists in reality as well, then the latter is greater than the former. But Barnes 1971, for example, has Anselm committed to the much stronger claim that any existing thing is greater than every non-existent thing.

Given these kinds of considerations, it is natural to wonder whether there are better interpretations of Proslogion II according to which the argument in question turns out NOT to be logically valid. Here is a modest attempt to provide such an analysis:

We start with the claim that the Fool understands the expression “being than which no greater can be conceived”, i.e., even the Fool can entertain the idea or possess the concept of a being than which no greater can be conceived. Now, entertaining this idea or possessing this concept requires the entertainer or possessor to recognise certain relationships which hold between given properties and the idea or concept in question. For example, given that you possess the concept of, or entertain the idea of, a smallest really existent Martian, it follows that you must recognise some kind of connection between the properties of being a Martian, really existing, and being smaller than other really existing Martians, and the concept or idea in question.

Following Anselm, we might say that, since you understand the expression “smallest really existent Martian”, there is, in your understanding, at least one smallest really existent Martian. (Or, apparently following Descartes, one might say that real existence is “part of”—or “contained in”—the idea of a smallest really existent Martian.) However, in saying this, it must be understood that we are not actually predicating properties of anything: we aren’t supposing that there is something which possesses the properties of being a Martian, really existing, and being no larger than any other Martian. (After all, we can safely suppose, we don’t think that any Martians really exist.) In other words, we must be able to have the concept of, or entertain the idea of, a smallest really existing Martian without believing that there really are any smallest Martians. Indeed, more strongly, we must be able to entertain the concept of a smallest really existent Martian—and to recognise that the property of “really existing” is part of this concept—while nonetheless maintaining that there are no smallest existent Martians.

It will be useful to introduce vocabulary to mark the point which is being made here. We could, for instance, distinguish between the properties which are encoded in an idea or concept, and the properties which are attributed in positive atomic beliefs which have that idea or concept as an ingredient. The idea “really existent Santa Claus” encodes the property of real existence; but it is perfectly possible to entertain this idea without attributing real existence to Santa Claus, i.e., without believing that Santa Claus really exists.

We can then apply this distinction to Anselm’s argument. On the one hand, the idea “being than which no greater can be conceived” encodes the property of real existence—this is what the reductio argument establishes (if it establishes anything at all). On the other hand, it is perfectly possible to entertain the idea of a being than which no greater can be conceived—and to recognise that this idea encodes the property of real existence—without attributing real existence to a being than which no greater can be conceived, i.e., without believing that a being than which no greater can be conceived really exists.

Of course, the argument which Anselm actually presents pays no attention to this distinction between encoding and attributing—i.e., between entertaining an idea and holding a belief—and nor does it pay attention to various other niceties. We begin from the point that the Fool entertains the idea of that than which no greater can be conceived (because the Fool understands the words “that than which no greater can be conceived”). From this, we move quickly to the claim that even the Fool is “convinced”—i.e., believes—that that than which no greater can be conceived possesses the property of existing in the understanding. And then the reductio argument is produced to establish that that than which no greater can be conceived cannot exist only in the understanding but must also possess the property of existing in reality as well (and all mention of the Fool, and what it is that the Fool believes, disappears).

As it stands, this is deeply problematic. How are we supposed to regiment the references to the Fool in the argument? Is the reductio argument supposed to tell us something about what even the Fool believes, or ought to believe? Are the earlier references to the Fool supposed to be inessential and eliminable? How are we so much as to understand the claim that even the Fool believes that that than which no greater can be conceived exists in the understanding? And how do we get from the Fool’s understanding the words “that than which no greater can be conceived” to his believing that that than which no greater can be conceived possesses the property of existing in the understanding?

Following the earlier line of thought, it seems that the argument might go something like this:

(Even) the Fool has the concept of that than which no greater can be conceived.

(Hence) (Even) the Fool believes that that than which no greater can be conceived exists in the understanding.

No one who believes that that than which no greater can be conceived exists in the understanding can reasonably believe that that than which no greater can be conceived exists only in the understanding.

(Hence) (Even) the Fool cannot reasonably deny that that than which no greater can be conceived exists in reality

(Hence) That than which no greater can be conceived exists in reality.

While this is not a good argument, it could appear compelling to one who failed to attend to the distinction between entertaining ideas and holding beliefs and who was a bit hazy on the distinction between the vehicles of belief and their contents. When the Fool entertains the concept of that than which no greater can be conceived he recognises that he is entertaining this concept (i.e., he believes that he is entertaining the concept of that than which no greater can be conceived—or, as we might say, that the concept is in his understanding). Conflating the concept with its object, this gives us the belief that than which no greater can be conceived possesses the property of existing in the understanding. Now, suppose as hypothesis for reductio , that we can reasonably believe that that than which no greater can be conceived possesses the property of existing only in the understanding. Ignoring the distinction between entertaining ideas and holding beliefs, this means that we when we entertain the idea of that than which no greater can be conceived, we entertain the idea of a being which exists only in the understanding. But that is absurd: when we entertain the idea of that than which no greater can be conceived, our idea encodes the property of existing in reality. So there is a contradiction, and we can conclude that, in order to be reasonable, we must believe that that than which no greater can be conceived exists in reality. But if any reasonable person must believe that that than which no greater can be conceived exists in reality, then surely it is the case that that than which no greater can be conceived exists in reality. And so we are done.

No doubt this suggestion about the interpretation of Anselm’s argument is deficient in various ways. However, the point of including it is illustrative rather than dogmatic. In the literature, there has been great resistance to the idea that the argument which Anselm gives is one which modern logicians would not hesitate to pronounce invalid. But it is very hard to see why there should be this resistance. (Certainly, it is not something for which there is much argument in the literature.) The text of the Proslogion is so rough, and so much in need of polishing, that we should not be too quick to dismiss the suggestion that Anselm’s argument is rather more like the argument most recently sketched than it is like the logically valid demonstrations provided by commentators such as Barnes, Adams, and Oppenheimer and Zalta. (For a more complex analysis of Proslogion II that has it yielding a valid argument, see Hinst 2014.)

Many recent discussions of ontological arguments are in compendiums, companions, encylopedias, and the like. So, for example, there are review discussions of ontological arguments in: Leftow 2005, Matthews 2005, Lowe 2007, Oppy 2007, and Maydole 2009. While the ambitions of these review discussions vary, many of them are designed to introduce neophytes to the arguments and their history. Given the current explosion of enthusiasm for compendiums, companions, encylopedias, and the like, in philosophy of religion, it is likely that many more such discussions will appear in the immediate future.

Some recent discussions of ontological arguments have been placed in more synoptic treatments of arguments about the existence of God. So, for example, there are extended discussions of ontological arguments in Everitt 2004, Sobel 2004, and Oppy 2006. Sobel’s examination of ontological arguments is exemplary. He provides one chapter on ‘classical ontological arguments’: Anselm, Descartes, Spinoza, and Kant’s critique of ontological arguments; one chapter on ‘modern modal ontological arguments’: Hartshorne, Malcolm and Plantinga; and one chapter on Gödel’s ontological argument. His analyses are very careful, and make heavy use of the tools of modern philosophical logic.

There has been one recent monograph devoted exclusively to the analysis of ontological arguments: Dombrowski 2006. Dombrowski is a fan of Hartshorne: the aim of his book is to defend the claim that Hartshorne’s ontological argument is a success. While Dombrowski’s book is a useful addition to the literature because of the scope of its discussion of ontological arguments—for example, it contains a chapter on Rorty on ontological arguments, and another chapter on John Taylor on ontological arguments—even reviewers sympathetic to process theism have not been persuaded that it makes a strong case for its central thesis.

Swatkowski (2012) is the most recent collection of papers on ontological arguments. A significant proportion of papers in this collection take up technical questions about logics that support ontological derivations. (Those interested in technical questions may also be interested in the topic taken up in Oppenheimer and Zalta (2011) and Gorbacz (2012).)

Finally, there has been some activity in journals. The most significant of these pieces is Millican 2004, the first article on ontological arguments in recent memory to appear in Mind . Millican argues for a novel interpretation of Anselm’s argument, and for a new critique of ontological arguments deriving from this interpretation. Needless to say, both the interpretation and the critique are controversial, but they are also worthy of attention. Among other journal articles, perhaps the most interesting are Pruss 2010, which provides a novel defence of the key possibility premise in modal ontological arguments, and Pruss 2009, which kick-started recent discussion of higher-order ontological arguments. There is also a chain of papers in Analysis initiated by Matthews and Baker (2010)

• Anselm, St., Proslogion , in St. Anselm’s Proslogion , M. Charlesworth (ed.), Oxford: OUP, 1965 [ Available online , in the Internet Medieval Sourcebook, Paul Halsall (ed.), Fordham University Center for Medieval Studies, translation by David Burr].
• Aquinas, T., Summa Theologica , 1272, literally translated by Fathers of the English Dominican Province, London: Burn, Oates & Washbourne, 1920 [ Available online , in the Internet Medieval Sourcebook, Paul Halsall (ed.), Fordham University Center for Medieval Studies, translation by David Burr].
• Ayer, A., Language, Truth and Logic , second edition, London: Gollancz, 1948.
• Descartes, R., Discourse on Method and The Meditations , translated with an introduction by F. Sutcliffe, Harmondsworth: Penguin, 1968 [Translation of The Meditations by John Veitch, LL.D. available online ].
• Frege, G., Die Grundlagen der Arithmetik , Bresnau: Koebner, 1884; translated as The Foundations of Arithmetic , J.L. Austin (trans), Oxford: Blackwell, 1974, 2nd rev edition; Original German text available online , (628 KB PDF file), maintained by Alain Blachair, Académie de Nancy-Metz.
• Gaunilo, “On Behalf of the Fool”, in St. Anselm’s Proslogion , M. Charlesworth (ed.), Oxford: OUP, 1965 [ Available online in the Internet Medieval Sourcebook, Paul Halsall (ed.), Fordham Universit\ y Center for Medieval Studies, translation by David Burr].
• Hegel, G., The Ontological Proof According to the Lectures of 1831 , in P. Hodgson (ed.), Lectures on the Philosophy of Religion, Vol. III Berkeley: University of California Press, 1985, pp. 351–8.
• Hume, D., Dialogues Concerning Natural Religion , 1779, edited with an introduction by H. Aiken, London: Macmillan, 1948.
• Kant, I., Critique of Pure Reason , 1787, second edition, translated by N. Kemp-Smith, London: Macmillan, 1933.
• Leibniz, G., New Essay Concerning Human Understanding , 1709, translated by A. Langley, New York: Macmillan, 1896.
• Spinoza, B., The Ethics , 1677, translation of 1883 by R. Elwes, New York: Dover, 1955 [ Available online , prepared by R. Bombardi, for the Philosophy Web Works project, Middle Tennessee State Univerity].
• Adams, R., 1971, “The Logical Structure of Anselm’s Argument”, Philosophical Review , 80: 28–54.
• –––, 1988, “Presumption and the Necessary Existence of God”, Noûs , 22: 19–34.
• –––, 1995a, Leibniz: Determinist, Theist, Idealist , Oxford: Oxford University Press.
• –––, 1995b, “Introductory Note to *1970” in K. Gödel Collected Works Volume III: Unpublished essays and lectures , S. Feferman, et al . (eds.), New York: Oxford University Press, pp. 388–402.
• Alston, W., 1960, “The Ontological Argument Revisited” Philosophical Review , 69: 452–74.
• Anderson, C., 1990, “Some Emendations on Gödel’s Ontological Proof”, Faith and Philosophy , 7: 291–303.
• Barnes, J., 1972, The Ontological Argument , London: Macmillan.
• Campbell, R., 1976, From Belief to Understanding , Canberra: ANU Press.
• Chambers, T., 2000, “On Behalf of the Devil: A Parody of St. Anselm Revisited”, Proceedings of the Aristotelian Society (New Series), 100: 93–113.
• Chandler, H., 1993, “Some Ontological Arguments”, Faith and Philosophy , 10: 18–32.
• Charlesworth, M., 1965, Anselm’s Proslogion , Oxford: Oxford University Press.
• Dombrowski, D., 2006, Rethinking the Ontological Argument: A Neoclassical Theistic Response , Cambridge: Cambridge University Press.
• Dummett, M., 1993, “Existence”, in The Seas of Language , Oxford: Oxford University Press.
• Everitt, N., 2004, The Non-Existence of God , London: Blackwell
• Findlay, J., 1949, “Can God’s Existence Be Disproved?”, Mind , 57: 176–83.
• Gorbacz, P., 2012, “PROVER9’s Simplification Explained Away”, Australasian Journal of Philosophy , 90: 585–96.
• Grey, W., 2000, “Gasking’s Proof”, Analysis , 60: 368–370.
• Harrelson, K., 2009, The Ontological Argument from Descartes to Hegel , New York: Humanity Books.
• Hartshorne, C., 1965, Anselm’s Discovery: A Re-Examination of the Ontological Proof for God’s Existence , La Salle, IL: Open Court.
• Hazen, A., 1999, “On Gödel’s Ontological Proof”, Australasian Journal of Philosophy , 76: 361–377.
• Henle, P., 1961, “Uses of the Ontological Argument”, Philosophical Review , 70: 102–9.
• Hinst, P., 2014, “A Logical Analysis of the Main Argument in Chapter 2 of the Proslogion by Anselm of Canterbury”, Philosophiegeschichte Und Logische Analyse , 17: 22–44.
• Johnston, M., 1992, “Explanation, Response-Dependence, and Judgement-Dependence”, in P. Menzies (ed.), Response-Dependent Concepts , Canberra: ANU/RSSS Working Papers in Philosophy, 123–83.
• La Croix, R., 1972, Proslogion II and III: A Third Interpretation of Anselm’s Argument , Leiden: Brill.
• Leftow, B., 2005, “The Ontological Argument”, in The Oxford Handbook of Philosophy of Religion , W. Wainwright (ed.), Oxford: Oxford University Press, pp. 80–115.
• Lewis, D., 1970, “Anselm and Actuality”, Noûs , 4: 175–88.
• Lowe, E., 2007, “The Ontological Argument”, in The Routledge Companion to Philosophy of Religion , P. Copan and C. Meister (eds.), London: Routledge.
• Malcolm, N., 1960, “Anselm’s Ontological Arguments”, Philosophical Review , 69: 41–62.
• Mann, W., 1972, “The Ontological Presuppositions of the Ontological Argument”, Review of Metaphysics , 26: 260–77.
• Matthews, G., 2005, “The Ontological Argument”, in The Blackwell Guide to the Philosophy of Religion , W. Mann (ed.), Oxford: Blackwell, pp. 81–102.
• Matthews, G., and Baker, L., 2010 “The Ontological Argument Simplified”, Analysis , 70: 210–212.
• Maydole, R., 2009, “The Ontological Argument”, in The Blackwell Companion to Natural Theology , W. Craig and J. Moreland (ed.), Oxford: Blackwell, pp. 553–592.
• Millican, P., 2004, “The One Fatal Flaw in Anselm’s Argument”, Mind , 113: 437–76.
• Oppenheimer, P., and Zalta, E., 1991, “On the Logic of the Ontological Argument”, in J. Tomberlin (ed.) Philosophical Perspectives 5: The Philosophy of Religion , Atascadero: Ridgeview, pp. 509–29 [ Preprint available online ].
• –––, 2011, “A Computationally-Discovered Simplification of the Ontological Argument”, Australasian Journal of Philosophy , 89: 333–349.
• Oppy, G., 1995, Ontological Arguments and Belief in God , New York: Cambridge University Press.
• –––, 1996, “Gödelian Ontological Arguments”, Analysis , 56: 226–230.
• –––, 2000, “Response to Gettings”, Analysis , 60: 363–367.
• –––, 2006, Arguing about Gods , Cambridge: Cambridge University Press.
• –––, 2007, “The Ontological Argument” in P. Copan and C. Meister (eds.), Philosophy of Religion: Classic and Contemporary Issues , Oxford: Blackwell.
• Plantinga, A., 1967, God and Other Minds , Ithaca: Cornell University Press.
• –––, 1974, The Nature of Necessity , Oxford: Oxford University Press.
• Pruss, A., 2009, “A Gödelian Ontological Argument Improved”, Religious Studies , 45: 347–353.
• –––, 2010,“The Ontological Argument and the Motivational Centres of Lives”, Religious Studies , 46: 233–249.
• Redding, P. and Bubbio, P., 2014 “Hegel and the Ontological Argument for the Existence of God”, Religious Studies , 50: 465–86.
• Rescher, N., 1959, “The Ontological Proof Revisited”, Australasian Journal of Philosophy , 37: 138–48.
• Ross, J., 1969, Philosophical Theology , New York: Bobbs-Merrill.
• Rowe, W., 1989, “The Ontological Argument”, in J. Feinberg (ed.), Reason and Responsibility , seventh edition, Belmont, CA: Wadsworth, pp. 8–17.
• Salmon, N., 1987, “Existence”, in J. Tomberlin (ed.), Philosophical Perspectives 1: Metaphysics , Atascadero, CA: Ridgeview: 49–108.
• Siegwart, G., 2014, “Gaunilo Parodies Anselm: An Extraordinary Job for the Interpreter”, Philosophiegeschichte Und Logische Analyse , 17: 45–71.
• Smart, J., 1955, “The Existence of God”, in A. Flew and A. MacIntyre (eds.), New Essays in Philosophical Theology , London: SCM Press: 500–509.
• Sobel, J., 1987, “Gödel’s Ontological Proof”, in On Being and Saying: Essays for Richard Cartwright , J. Thomson (ed.), Cambridge, MA: MIT Press, pp. 241–61.
• Sobel, J., 2004, Logic and Theism , New York: Cambridge University Press.
• Smullyan, R., 1984, 5000 BC and Other Philosophical Fantasies , New York: St. Martins Press.
• Szatkowski, M. (ed.), 2012, Ontological Proofs Today , Frankfurt: Ontos Verlag.
• Tooley, M., 1981, “Plantinga’s Defence of the Ontological Argument”, Mind , 90: 422–7.
• van Inwagen, P., 1977, “Ontological Arguments”, Noûs , 11: 375–395.

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up this entry topic at the Indiana Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Kurt Gödel’s Ontological Argument (Christopher Small, University of Waterloo)
• Medieval Sourcebook: Philosophers’ Criticisms of Anslem’s Ontological Argument for the Being of God (Paul Halsell, Fordham University)
• Handout for a Talk on the Ontological Argument (J. R. Lucas, Oxford University)
• Ontological Argument Revisited by Two Ottoman Muslim Scholars (Umit Dericioglu)
• The Ontological Argument (Kenneth Himma, University of Washington)
• Anselm’s Ontological Argument (Gideon Rosen, Princeton University)
• Hegel and Kant on the Ontological Argument (Maria de Lourdes Borges, Federal University of Santa Catarina)
• Ontological Argument (links to papers on ontological arguments)
• “ Formalization, Mechanization and Automation of Gödel’s Proof of God’s Existence , unpublished manuscript.
• “ Automating Gödel’s Ontological Proof of God’s Existence with Higher-order Automated Theorem Provers , published in ECAI 2014, T. Schaub et al . (eds.), IOS Press.

Anselm, Saint [Anselm of Bec, Anselm of Canterbury] | a priori justification and knowledge | Descartes, René | existence | God: concepts of | Gödel, Kurt | Hegel, Georg Wilhelm Friedrich | Kant, Immanuel | logic: informal | logic: modal | Meinong, Alexius

Copyright © 2016 by Graham Oppy < Graham . Oppy @ monash . edu >

Support SEP

Mirror sites.

View this site from another server:

• Info about mirror sites

The Stanford Encyclopedia of Philosophy is copyright © 2016 by The Metaphysics Research Lab , Center for the Study of Language and Information (CSLI), Stanford University

Library of Congress Catalog Data: ISSN 1095-5054

The correctness and relevance of the modal ontological argument

• Open access
• Published: 21 December 2020
• Volume 199 , pages 2727–2743, ( 2021 )

Cite this article

You have full access to this open access article

• Andrzej Biłat   ORCID: orcid.org/0000-0003-1884-1361 1  

3633 Accesses

2 Altmetric

Explore all metrics

This paper deals with some metaphilosophical aspects of the modal ontological argument originating from Charles Hartshorne. One of the specific premises of the argument expresses the idea that the existence of God is not contingent. Several well-known versions of the argument have been formulated that appeal to different ways of clarifying the latter. A question arises: which of the formally correct and relevant versions is proper or basic? The paper points to some criteria of formal correctness, and distinguishes two types of relevance for these versions: strong and weak. Its aim is to furnish a strictly worked out answer to the question, taking into account each of these types. As a result, a very simple, formally correct and (weakly) relevant version of the modal ontological argument is formulated. The results obtained are also used to criticize a popular belief about the relations in which the main versions of the modal ontological argument stand to one another.

Similar content being viewed by others

On the PROVER9 Ontological Argument

Variants of gödel’s ontological proof in a natural deduction calculus, the modal-epistemic argument self-undermined.

Avoid common mistakes on your manuscript.

1 Introduction

Ontological arguments amount to a priori arguments for philosophical theism : i.e. the thesis that God, in a philosophical sense of the word, exists. There are many (at least seven) types of such arguments (Oppy 2019 ). One of them is the modal ontological argument (hereinafter MOA), an argument formalizable in a simple zero-order language of (applied) modal logic or an (appropriately enriched) standard first-order language of the theory of possible worlds. Footnote 1

More particularly, in the form in which it originated in the work of Charles Hartshorne, the MOA is formulated within a zero-order modal theory, in which the only extra logical constant is the sentence “God exists”. This argument is based on two specific metaphysical premises. The first of these states that the existence of God is possible. This premise is nowadays most often considered to be the core of the MOA. Footnote 2 The second premise is an explication of the idea that the existence of God is not contingent (Hartshorne 1944 ). Depending on the way in which this idea is explicated, different versions of the MOA come to be formulated.

More complex versions, coming from Alvin Plantinga, are formulated within a standard first-order theory of possible worlds extended by the concept of God (Plantinga 1974 ). Footnote 3 In this paper we will confine ourselves to just the Hartshorne-style zero-order MOA-versions. (For convenience, we will continue to use the phrases “Hartshorne-style argument” and “MOA” interchangeably.) Footnote 4

One of the simpler (zero-order) MOA-versions (though not necessarily the simplest—see the next footnote and Sect.  4 below) is presented in the Stanford Encyclopedia of Philosophy as follows:

It is possible that God exists. God is not a contingent being, i.e., either it is not possible that God exists, or it is necessary that God exists. Hence, it is necessary that God exists. Hence, God exists. Footnote 5

Despite its formal simplicity, arguments of this type are still the subject of numerous analyses. In particular, their persuasive power is studied, and often also questioned (see Oppy 1996 , 2019 ). We do not, however, intend to address that issue here (except for the analysis of the persuasive function of one of the MOA versions). The main subject of our present study is, rather, the general structure of Hartshorne-style MOAs, the basic properties of their most important versions, and some relations between them. Its main purpose is to distinguish the basic versions from all other MOAs that meet predetermined criteria of formal correctness and relevance.

The following view seems prevalent in the philosophical literature: certain general premises generated by stronger systems of modal logic are logically essential, or at least philosophically the most adequate ones, where the MOA is concerned. Footnote 6 This line of thinking was clearly expressed by philosophers quite early on. For example, Kane ( 1984 ) lists the general premises (taken from B -system) as the third important element—after two specific premises—in the construction of the MOA. Footnote 7 In recent years, a similar view has been presented by van Inwagen ( 2012 , 2018 ) in a more cautious way, clearly suggesting two theses: (1) each formally correct and relevant MOA-version has either strong specific premises and weak general premises (generated by modal logic) or, equally, weak specific premises and strong general premises; (2) the second part of this equivalence is the philosophically preferable one (on account of its clarity and elegance). Footnote 8

In this paper, I will try to show that if we assume some quite natural criteria for the philosophical evaluation and selection of MOA-versions, both of the above theses turn out to be wrong.

The main points of reference here are those normal systems of modal logic that are the most widely known ones (at least in the context of MOA): i.e. systems in which Modus Ponens and the Rule of Necessitation make up the only primitive rules. The purpose of the study is not to analyze possible logical systems underlying various MOA-versions, but rather to analyze these versions on the basis of a predetermined system of modal logic: one that is—in a way—the “internal” logic of every MOA-version. Thus, the determination of a given MOA-version will not be done by changing this “internal” logic (e.g. by adding new logical rules), but by changing or adding new premises, including both substantive (metaphysical) and general premises taken from various “external” systems of modal logic. Footnote 9

The findings proposed in the next section provide fairly strict answers to two questions: namely, what the overall structure of the (Hartshorne-style) MOA and the criterion for the latter’s relevance look like. There are also two other closely related and logically basic questions, which concern what the correctness and simplicity criteria for MOA-versions are, and which of the known correct and relevant versions is the simplest. In the philosophical literature, we do not find precise answers to these questions. Answers to the above questions can then help with solving the key metaphilosophical issue of which MOA-version is proper or basic.

The structure of the ensuing discussion is as follows: the next two sections set out the structure of the MOA and criteria for its formal correctness and simplicity, while Sect.  4 furnishes proofs of the correctness of the T-version, S5-version, and B-version; Sect.  5 then presents a correct, simplified MOA-version, and Sect. 6 distinguishes two types of philosophical relevance for MOA-versions; finally, Sect.  7 uses these findings to criticize a popular view related to van Inwagen’s theses (1) and (2).

2 The structure and relevance of the modal ontological argument

For the purposes of the present analysis, we shall retain the principle of the possibility of the existence of God (expressed in the first sentence of the quotation presented in the previous section), expressing this with the symbolization “Mg” and assuming it to be obligatory for every MOA-version:

Taking the symbols “Lg” to represent the sentence “It is necessary that God exists”, the second sentence of the above quotation can then be rewritten using the formula:

The sentence g (“God exists”) is derived from the premises (1) and (2), with the use of the law of double negation, disjunctive syllogism ( modus tollendo ponens ), and the following general (non-specific) premise resulting from the application of the axiom ‘L α ⇒ α ’ of the T -system of modal logic Footnote 11 :

Considering the above, we may conclude that this argument for (philosophical) theism is a valid (i.e. logically correct) MOA-version that is based on two specific premises, (1) and (2), and one general premise T. Footnote 12

In other MOA-versions, the choice of specific and general premises changes. In typical versions, (2) is weakened and the T -system is strengthened by adding new general premises. Footnote 13 These additional premises are usually taken from the S5 -system or, less often, from the weaker B -system.

The T -system is the weakest system of normal modal logic in which the uncontroversial formulae of the form ‘L α ⇒ α ’ are theses. Regardless of whether or not these formulae are used in a particular MOA-version, it is the basic system for explicating the meaning of the modal operators L and M. Therefore, we will take it to be a logical basis for MOA. Footnote 14

Now, the MOA - structure can be presented as an arrangement < T , (1), α , X , g> , where α is a sentence of the language of the (applied) modal logic including the sentence g, and X is a set of sentences resulting from the substitution of propositional variables by the sentence g in the specific theses of modal propositional systems. The sentence α represents here a specific premise expressing the idea that the existence of God is not contingent, and the set X represents the set of all general premises of the given MOA-version.

Since the elements T , (1) and g are fixed in every MOA-version, we will write it in a shortened form as “[ α , X ]”:

By virtue of this convention, any version of the argument for philosophical theism applying the theses of the T -system and having specific premises that include {(1)} (non-modifiable) and { α } ∪  X (modifiable) may be represented by the MOA-structure [ α , X ]. It is easy to see that the arrangement [(2), {T}] is an example of such MOA-structures, and that it is one that represents the T-version of the MOA.

The MOA-version (represented by the structure) [ α , X ] will be relevant if and only if α is a sentence clarifying the idea that the existence of God is not contingent, and α is logically equivalent (based on the T -system) to a specific (i.e. non-general) sentence or conjunction of sentences with the following forms: ‘ β ⇒ g’, ‘L( β ⇒ g)’, ‘g ⇒ β ’, or ‘L(g ⇒ β )’. The latter requirement’s being fulfilled serves to reassure us that any clarification of the idea of God furnishes logically nontrivial, necessary and/or sufficient conditions for the existence of God. We embrace the idea that a formulation of such conditions will be methodologically fundamental where any philosophical theory of God is concerned.

The T-version [(2), {T}] is an example of the relevant MOA-versions. The following metatheorem testifies to this:

Metatheorem 1

Sentence (2) is logically equivalent (based on the T-system) to each of the following sentences:

(g ⇒ Lg) ∧ (Mg ⇒ g),

 ~ (Mg ∧ M ~ g).

Ad (i): For the implication from left to right, assume that ~ Mg ∨ Lg. This sentence is equivalent to the sentence ‘Mg ⇒ Lg’. Hence, and from the two specific theses of the T -system ‘g ⇒ Mg’ and ‘Lg ⇒ g’, we get, by hypothetical syllogism, g ⇒ Lg and Mg ⇒ g. For the right-to-left implication, assume that (g ⇒ Lg) ∧ (Mg ⇒ g). Again, by hypothetical syllogism, we get Mg ⇒ Lg. Ad (ii): based on de Morgan’s law and the standard logical relations between modal operators. Q.E.D.

Sentence (i) of Metatheorem 1 specifies the necessary (g ⇒ Lg) and sufficient (Mg ⇒ g) conditions for God to exist. Sentence (ii), in turn, expresses the non-contingency of God’s existence in the Aristotelian sense of bilateral possibility (cf. Łukasiewicz 1957 ).

Let us now consider the argument having the structure [‘MLg’, {B}], where B is the sentence that results when we substitute g for p in the thesis ‘ML p ⇒ p ’ of the B -system:

This argument is an example of an MOA-version for which we do not see any possibility of demonstrating that it meets the criterion of relevance adopted. (We will leave open the matter of proving that this version does not really meet the relevance criterion). Footnote 15

3 Criteria of formal correctness and simplicity for modal ontological arguments

In order to properly formulate a criterion of correctness for the MOA, we shall introduce the following definition:

Definition 1

If { α }, X are sets of sentences of the language of the T -system with the constant g, then X ⊢ α if and only if α is an element of the smallest set containing all substitutions of theses of the T -system and elements of X and closed under two inference rules – modus ponendo ponens and Gödel’s Rule of Necessitation.

As usual, for short, we will write ‘ α 1 , …, α n , X ⊢ β ’ instead of ‘{ α 1 , …, α n ,} ∪  X ⊢ β ’, and ‘⊢ β ’ instead of ‘∅ ⊢ β ’. We introduce the abbreviation:

We will, also for short, write ‘ TG ( α )’ instead of ‘ TG ( α , X )’, if TG ( α , X ) =  TG ( α , ∅).

Thus, TG ( α , X ) is the smallest set of sentences containing all substitutions of theses of the T -system and elements of the set {(1), α } ∪  X , and closed under modus ponendo ponens and the Rule of Necessitation. In other words, TG ( α , X ) is the theory resulting from the strengthening of T by adding axioms (1), α and all elements of X . Each such theory will be called a mini-theory of God . Footnote 16

Intuitively, all elements of the set {(1), α } ∪  X are a priori sentences; so if they are true, they are necessarily true. This assumption seems to be fully justified in the context of the considerations pertaining to MOA. It also justifies the above finding to the effect that the Rule of Necessitation applies not only to the laws of logic, but also to all of the elements of the set {(1), α } ∪  X . (This finding will allow us to simplify some of the proofs below.)

A MOA-version [ α , X ] will be non-circular if and only if the sentence g is not derived from { α } ∪  X on the basis of the T -system alone (and therefore is not derived from { α } ∪  X independently of (1)); formally: α , X ⊬ g. Footnote 17

The argument [‘Lg’, {T}] is an example of a valid but circular MOA-version. The fact that this argument can be treated as a relevant MOA-version at all is evidenced by the fact that the sentence ‘Lg’ explicates the idea of the existence of God as a necessary existence. (More precisely, it states that God necessarily exists). It is valid and circular, because sentence g is directly derivable from sentence ‘Lg’ and premise T—and thus is so regardless of (1).

As we can see, the concept of “validity” (used for a given MOA-version) has a broader extension than the concept of “formal correctness”. Let us adopt the following definition:

Definition 2

The MOA-version [ α , X ] will be formally correct if and only if the following three conditions are met:

(1), α , X ⊢ g (VALIDITY),

TG ( α , X ) is consistent (CONSISTENCY), and

α , X ⊬ g (NON-CIRCULARITY).

Valid MOA-versions can be compared with respect to the number of general premises they possess and the deductive strengths of their own mini-theories. Let us adopt the following definition:

Definition 3

[ α , X ] will be a simpler MOA-version than [ β , Y ] if and only if at least one of the following conditions is met (where | X | is the cardinality of the set X ):

| X | <| Y | and TG ( α , X ) ⊆  TG ( β , Y ), or

| X | ≤| Y | and TG ( α , X ) ⊊  TG ( β , Y ).

Definitions 1 – 3 will be deployed in due course – in the remainder of this paper.

4 Formal correctness of three standard versions of the argument

The T-version [(2), {T}] is an example of a relevant and formally correct MOA-version. Indeed, and especially given Metatheorem 1 , the relevance of this version is obvious, and the following METATHEOREM holds true:

Metatheorem 2

The T-version of the MOA, represented by the structure [(2), {T}] , is formally correct.

The following three conditions must be shown to have been met:

(1), (2), {T} ⊢ g.

TG (2) is consistent, and.

(2), {T} ⊬ g.

The sentence g was derived from the axioms of TG (2) in Sect.  1 .

The language of the mini-theory TG (2) can be formally interpreted as follows: the sentence g is interpreted as the constant 1 (true sentence), the operators M and L are interpreted as the assertion operator A (in the sense defined by the axiom ‘A p ⇔ p ’), and the truth-connectives are left unchanged. As a result, the set TG (2) becomes the theory TG (2)*, which contains only the constant 1 and the set of sentences resulting from the substitution of variables by this constant in tautologies of classical sentential logic (with the operator A). As we know, the set TG (2)* is consistent; consequently, the set TG (2) is also consistent.

If g were derived from TG (2), then g would be true in any model in which TG (2) is true. To see that the opposite is the case, let us consider a TG (2) # -theory that will be the result of the following interpretation: g is interpreted as the constant 0 (false sentence), the M and L operators are interpreted as the assertion operator A, and the truth-connectives are left unchanged. The TG (2) # -theory will therefore consist only of the relevant substitutions in respect of the tautologies. (More particularly, Axiom (2) # will be such a substitution, equivalent to the sentence ‘ ~ 0 ∨ 0’). At the same time, the sentence g # (the constant 0) is false. Q.E.D.

In the literature on the MOA, what is known as Anselm’s Principle has tended to receive more frequent consideration than Principle (2):

Historically, the first formalized version of the MOA (originating from Hartshorne) should be represented by the structure [(3), {T, N, S5}], where N is the result of substitution of g for p , and Lg for q , in the thesis ‘L( p ⇒ q ) ⇒ (M p ⇒ M q )’ of T :

and S5 is the formula being a result of the similar substitution in the specific axiom of the modal system S5 :

Metatheorem 3

The S5-version of the MOA, represented by the structure [(3), {T, N, S5}] , is formally correct.

The parts of the proof relating to the conditions of consistency and non-circularity are analogous to the relevant parts of the proof of Metatheorem 2 . It is therefore sufficient to show that the condition.

is satisfied. By using the law of detachment ( modus ponens ) twice, we obtain the thesis ‘M g ⇒ ML g ’ (from (3) and N), and then ‘ML g ’ (by using the axiom (1)). Hence, from S5, we get the sentence ‘Lg’. Hence, from T, we get the sentence g. Q.E.D.

The deductive basis of the S5-version can be simplified so as to arrive at the weaker mini-theory TG (3, {N, B}). This shows a key fragment of the proof of the following metatheorem:

Metatheorem 4

The B-version of the MOA, represented by the structure [(3), {N, B}] , is formally correct.

is satisfied. By using N and the law of detachment, we obtain the thesis ‘M g ⇒ ML g ’, and then ‘ML g ’. Hence, from B, we get the sentence g . Q.E.D. Footnote 18

Using Definition 3 , we can compare all of the above MOA-versions. The following metatheorem will be the result of such a comparison:

Metatheorem 5

[(2), {T}] is a simpler MOA-version than [(3), {T, N, S5}] and [(3), {N, B}].

It is enough to note that two conditions are met: (i) |{T}| <|{T, N, S5}| & TG (2) ⊆  TG (3, {S5}), and (ii) |{T}| <|{N, B}| & TG (2) ⊆  TG (3, {B}). Ad (i): Given that T is an S5 -thesis, it is sufficient to show that (2) is a thesis of the mini-theory TG (3, {S5}). This becomes apparent when we consider that ‘Lg’ is a thesis of this theory (see the penultimate step of Metatheorem 2 ). Hence, we may conclude that (2) is also a thesis of it. Ad (ii): Given that T is a B -thesis, it is sufficient to show that (2) is a thesis of the mini-theory TG (3, {B}). If we consider Metatheorem 4 , then we realize that the sentence g is a thesis of this theory. Eliminating operator L in formula (3) (according to the T-schema ‘L α ⇒ α ’), we get ‘g ⇒ Lg’. Hence, by modus ponens , we get Lg. Thus, we may conclude that (2) is a thesis of the mini-theory TG (3, {B}). Q.E.D.

5 The simplest relevant version of the modal ontological argument

It will now be shown that there is a correct version of the MOA that is simpler than all the versions considered so far. Footnote 19 The essence of this argument, which in logical terms borders on triviality, is the sentence.

We shall demonstrate in what follows that this premise correctly (though not necessarily completely) clarifies the idea of the existence of God as a necessary existence.

Indeed, such a claim is indirectly evidenced by the fact that such a postulate has appeared in the works of Hartshorne and Plantinga. It was also clearly accepted by Malcolm:

What Anselm has proved is that the notion of contingent existence or of contingent nonexistence cannot have any application to God. His existence must either be logically necessary or logically impossible.[…] If God, a being a greater than which cannot be conceived, does not exist then He cannot come into existence.[…] Since He cannot come into existence, if He does not exist His existence is impossible. (Malcolm 1960 , p. 49)

The direct justification for the thesis that (4) is the correct explication for the existence of God as a necessary existence runs in essence as follows: the idea is fully expressed (taking into account the object language of modal logic) in the form of Principle (2), and each of Postulates (3) and (4) can be treated as a part of the explication of the idea expressed by (2). Thus, if we assume that Principle (3) appropriately elucidates the aforementioned idea, then we should also assume that Principle (4) correctly explicates it. Footnote 20

This explicative dependence of both postulates on (2) is quite clearly visible in the context of possible-worlds semantics. Both postulates are similarly derived from the ontological principle, relating to (2), that God exists either in every possible world (accessible from the actual world) or not in any of them. According to this principle, if God exists in the actual world, then God exists in every possible world – which is the content of (3). Footnote 21 Similarly, if God does not exist in the actual world, then God does not exist in any possible world—which in turn, is the content of (4).

The following metatheorem shows the logical connection of both postulates with (2):

Metatheorem 6

⊢(2) if and only if ⊢(3) and ⊢(4).

The proof here is similar to that of Metatheorem 1 . For the implication from left to right, assume ⊢‘ ~ Mg ∨ Lg’. Hence, and from ⊢ ‘g ⇒ Mg’ and ⊢ ‘Lg ⇒ g’, we get ⊢ ‘g ⇒ Lg’ and (taking into consideration the Rule of Necessitation) ⊢ ‘L(g ⇒ Lg) ∧ (~ g ⇒ ~ Mg)’. For the implication from right to left, assume ⊢ ‘L(g ⇒ Lg) ∧ (~ g ⇒ ~ Mg)’. We therefore get ⊢ ‘(g ⇒ Lg) ∧ (Mg ⇒ g)’ and, by hypothetical syllogism: ⊢ ‘Mg ⇒ Lg’. Q.E.D.

It turns out that Premise (2) is logically equivalent to the conjunction of Premises (3) and (4).

Moreover, (4) is deductively weaker than both (2) and (3), where this stated by another metatheorem:

Metatheorem 7

The following relations hold:

(3), {N, B} ⊢(4),

Ad (i): obvious. Ad (ii): as with the proof of Metatheorem 4. Ad (iii) and (iv): it is enough to consider the possible-worlds model in which g is true in the actual world and there are possible worlds accessible from the actual world in which g is not true; we see that in this model (4) is true and (2) and (3) are not true. Q.E.D.

Consequently, since (3) means that the existence of God is either impossible or necessary, (2) and (3) only partially clarify this meaning. In fact, (3) only means that if God exists, he exists by necessity, and (4) only means that if God does not exist, he does not exist by necessity. Only both sentences taken together fully express the idea of God as a non-contingent being. Footnote 22

Thus, from an ontological and a logical point of view, Premise (4) is not less obvious, more controversial or in any other sense stronger than (3). On the contrary, taking into account conditions (ii) and (iv) of Metatheorem 7, Premise (4) is deductively weaker than (3). If we accept (3) as an intuitively acceptable premise in one or other of the MOA-versions, we must surely proceed likewise with (4). Premise (3) is commonly treated as being the result of a typical explication of the basic idea of God, so there is no reason for Premise (4) to be treated any differently. Footnote 23

We sometimes encounter sentence (4), or its logical equivalents, being treated as premises for a complex MOA-version, in which they are further formally justified (see, e.g., Spencer 2018 , p. 214). However, it appears that the persuasive power of (4) is no less than that of similar premises such as are normally accepted without any formal justification. Thus, (4) does not call for such justification more than in the case of other MOA-versions.

Since Postulate (4) explicates the idea of the existence of God as a necessary existence, the mini-theory TG ((4), ∅) represents one of the MOA-versions meeting the relevance condition.

Metatheorem 8

The “empty” structure [(4), ∅] represents a formally correct MOA-version which is simpler than T-version.

The parts of the proof relating to the conditions of consistency and non-circularity are analogous to the relevant parts of the proof of Metatheorem 2 . It is therefore enough to note that |∅| <|{T}|, and the sentence g is a thesis of the mini-theory TG (2) (as we know from Metatheorem 2 ). Therefore, it is all the more the case that (4) is one of its theses. Q.E.D.

6 Some stronger correctness and relevance criteria for the modal ontological argument

The logical triviality of the “empty” MOA-version suggests that the range of formally correct and philosophically relevant MOA-versions should be limited in such a way that this version can be considered incorrect or irrelevant. Consider the two options outlined below.

It seems that the only correspondingly appropriate way to limit the concept of formal correctness is to introduce an additional condition into Definition 2 :

This condition states (in simple terms) that the specific premise that defines the concept of God as a non-contingent being cannot be a consequence of the thesis that God exists. At first glance, the following metatheorem would seem to support a possible decision to introduce this condition:

Metatheorem 9

If [ α , X ] is valid and g, X ⊢ α , then X ⊢ ‘g ⇔ (Mg ∧ α )’.

The second part of the antecedent of the metatheorem is equivalent (in virtue of the deduction theorem) to the meta-formula X ⊢ ‘g ⇒ α ’. Hence, taking into consideration that X ⊢ ‘g ⇒ Mg’, we get: X ⊢ ‘g ⇒ (Mg ∧ α )’. Since [ α , X ] is valid, the reverse implication is also derivable: X ⊢ ‘(Mg ∧ α ) ⇒ g’. Q.E.D.

Metatheorem 9 shows that any valid MOA-version that does not meet (C) is “circular” in the sense that the conjunction of its premises is logically equivalent to its conclusion. (We are, at the very least, using the term “logically” here just as it pertains to modal logic).

The following metatheorem shows that the “empty” MOA-version does not meet Condition (C):

Metatheorem 10

If we take into account the Duns Scotus Law, we realize that ⊢ ‘g ⇒ (~ g ⇒ ~ Mg)’. Keeping in mind the deductive theorem, we thus get: g ⊢‘ ~ g ⇒ ~ Mg’. Q.E.D.

Unlike (4), Premises (2) and (3) cannot be derived from Sentence g alone, together with the laws of modal logic. (Let us leave this observation without proof). This shows that Condition (C) could be used to eliminate the “empty” MOA-version.

The question is whether Condition (C) should be accepted. Let us recall its general content: the premise defining the concept of God cannot be a consequence of the thesis that God exists. But why not? There is no logical, methodological or philosophical reason to accept such a restriction. Apparently, an attempt to introduce it would be an ad hoc solution, only aimed at eliminating one of the MOA-versions.

Let us therefore consider the second option (referred to at the beginning of this section). A quite natural way of strengthening the relevance condition was already indicated in Metatheorems 1 and 6 , and in the analysis of the previous section. Its philosophical basis runs as follows: an MOA-version will be strongly relevant if the premise defining the philosophical concept of God (as a non-contingent being) is a complete explication of that concept. According to Metatheorems 1 and 6 , and the analyses carried out in the previous section, Postulate (2) is such a complete explication, as opposed to Postulates (3) and (4). Consequently, the T-version is, in contrast to other versions, a strongly relevant MOA-version.

Let us recall the general distinction between the two types of MOA-relevance, and try to find a good philosophical basis for it. Postulate (2) is a complete explication of the idea of God as a non-contingent being in the language of the mini-theory TG (2). Postulate (3) is its partial explication, because (3) only expresses a necessary condition for the existence of God. Postulate (4) is also its partial explication, but for another reason: because (4) only expresses a sufficient condition for this existence. Unlike mini-theories TG (3, {S5}), TG (3, {B}) and TG (4), the mini-theory TG (2) generates both a necessary and a sufficient condition for God to exist. So, from a philosophical and theoretical point of view, TG (2) is a better mini-theory than the others and, consequently, the T-version is a better MOA-version than the others.

This does not mean that the MOA-version represented by the structure [(2), {T}] is absolutely preferable to the structures [(3), {T, N, S5}], [(3), {N, B}] and [(4), ∅]. On the contrary, according to the general theory of argumentation, there are many types of relevance depending on kinds of arguments and their conversational contexts (see, e.g., Walton 1998 ). In the case of a philosophical argument, its context can be determined equally by its persuasive and explicative (or, more precisely, theoretical-explicative) purpose. If the argument is formulated in a persuasive context, the requirement of full explication of the notions used in it, and therefore the requirement of strong relevance, does not apply.

Consequently, we should use two criteria in assessing MOA-versions: the weak criterion and the strong criterion of MOA-relevance. If the MOA-version is formulated to convince someone that the God of philosophers exists, the strong criterion is unnecessary. This criterion, on the other hand, is essential for the evaluation of each MOA-version formulated in order to examine the consequences of the explicatively complete concept of God.

Given the persuasive function of the argument, the “empty” MOA-version would seem to be the optimal one. There are at least two reasons for this assessment. Firstly, the “empty” version is the simplest of the formally correct and (weakly) relevant MOA-versions (cf. Metatheorems 5 – 7 ). Secondly, the “empty” version mounts an effective defence against a typical counter-argument that purports to show the persuasive weakness of the standard MOA-versions. Let us replace Premise (1) with the sentence ‘M ~ g’ (“It is possible that God does not exist”); hence, from (2) we derive (in the T -system) ‘ ~ g’ (“God does not exist”), and from (3) we also therefore derive (in the S5 -system) ‘ ~ g’ (cf. Oppy 1996 , 2019 ). It is easy to see that there is no analogous counter-argument to the “empty” MOA-version.

7 Conclusions

The questions posed at the end of the first section can now be answered quite precisely. Each relevant (zero-order, Hartshorne-style) MOA-version has the structure < T , (1), α , X , g>, where α is a specific premise clarifying the idea that the existence of God is not contingent and X is a set of general premises resulting from modal logic. The formal correctness criterion for such versions consists of conditions of VALIDITY, CONSISTENCY, and NON-CIRCULARITY.

It turns out that the simplest known MOA-version fulfilling these conditions has the structure [(4), ∅]. In contrast to the previously presented versions (T, S5 and B), this “empty” MOA-version is devoid of general premises taken from modal logic. Thus, its entire strength lies in its specific philosophical premises, not in its logic. (These premises state that the existence of God is possible, and that if God does not exist, the existence of God is impossible.)

Given the persuasive function of the argument, the “empty” version seems to be the basic MOA-version on account of its simplicity (consisting in its formal simplicity and the deductive weakness of its mini-theory of God) and its resistance to a well-known counter-argument from the possibility of the non-existence of God.

Of all the MOA-versions considered here, only the T-version meets the strong relevance condition of explicative completeness, because only this version expresses precisely the idea (from Aristotle) of God’s non-contingency in the form of a necessary and a sufficient condition for the existence of God. For this reason, from a theoretical point of view (although not necessarily from a persuasive point of view), the T-version should be treated as the basic MOA-version.

These conclusions undermine the view (mentioned in Sect.  1 ) that certain general premises generated by stronger systems of modal logic are logically essential, or at least highly adequate philosophically, where the MOA is concerned. Let us recall both of the theses suggested by van Inwagen:

Each formally correct and relevant MOA-version has either strong specific premises and weak general premises (van Inwagen 2012 , p. 158, is referring here to the T-version) or, equally, weak specific premises and strong general premises (he is referring here to the S5-version).

The option indicated in the second part of this equivalence (contained in Thesis 1) is philosophically better.

Both theses turn out to be false, assuming the criteria adopted here for the evaluation and selection of MOA-versions. Footnote 24

Firstly, there is a formally correct and persuasively relevant MOA-version (namely, the “empty” version) that has relatively weak specific (metaphysical) premises and no general premises. Thus, van Inwagen’s specification omits the type of MOA-version that plays a key role in our analysis. Moreover, the equivalence contained in Thesis 1 is incorrect in one important respect: the T-version (indicated on the left) is not philosophically equivalent to the S5-version (indicated on the right). The S5-version, unlike the T-version, is based on an explicatively incomplete mini-theory of God. (More precisely, the mini-theory of God underlying the S5-version generates a necessary condition for the existence of God, but does not generate a sufficient condition for it.)

Secondly, both because of this explicative incompleteness and on account of its complexity, the S5-version is philosophically inferior to the T-version. Moreover, despite the lesser complexity of the B-version (relative to the S5-version), that same conclusion applies to it, too.

These versions basically have their origins in Hartshorne ( 1944 ), Malcolm ( 1960 ) and Plantinga ( 1974 ) (although their intuitive formulation already appears in St. Anselm’s Proslogion III ; see Eder and Ramharter 2015 , p. 2815; Oppy 2019 ). They are clearly distinguished here from arguments of the Gödelian kind formulated within second- or higher-order modal theories of positive properties (see Sobel 1987 ; Benzmüller 2020 ). The MOAs and Gödelian-type arguments are also specified in Oppy’s taxonomy as two different kinds of ontological argument (Oppy 2019 ). The abbreviation “MOA” is most commonly used in the philosophical literature to designate the former. (Even so, the term “modal ontological argument” could also be used in the broader sense of “ontological argument using modal concepts”, and in this sense, Gödelian-type arguments could also be called “modal”.).

G.W. Leibniz is commonly regarded as the philosopher who was the first to point out the key role of this premise in the ontological argument (see, e.g., Perzanowski 1991 ; Antognazza 2018 ). The issue of the reliability of this premise will not be discussed in the present paper.

The argument presented in Lewis ( 1970 ) is an example of another MOA-version formulated within an extensional first-order theory of possible worlds.

These versions belong to one of the four kinds of MOA distinguished in Oppy ( 1996 , pp. 70–78). This kind includes arguments of the sort Oppy calls “ontological arguments involving necessity”.

Oppy ( 2019 ). This version was already considered by Hartshorne (see Goodwin 1978 ). An even simpler MOA-version is analyzed in Oppy ( 1996 ): “It is possible that it is necessarily the case that God exists. Hence, God exists.” This version is valid on the basis of systems B and S5 of modal logic. Other B- and S5-versions of the MOA will be presented in Sect.  4 . (The T , B and S5 systems are deductive extensions of classical sentential logic, and belong to what is known as normal modal logic. Chellas ( 1980 ) offers an accessible characterization of what they involve.).

It is worth noting that in recent years an opposite trend has appeared in studies on Gödelian-type of ontological argument (which was originally formulated within the S5 -system, cf. Sobel 1987 ). For example, Świętorzecka and Łyczak ( 2018 ) reconstruct a version of this argument within the S4 -system, and Benzmüller ( 2020 ) within the T -system and even in the weaker K -system. The analyses undertaken in this paper go in a similar direction, that is, towards the search for possibly simple and adequate MOA-versions.

This view was also adopted in a well-known philosophical dictionary, in which one of the S5-versions was commented on as follows: “The correct response to this argument is to disallow the apparently reasonable concession that it is possible that such a being exist. This concession is much more dangerous than it looks, since in the modal logic involved, from possibly necessarily p , we can derive necessarily p ” (Blackburn 1994 , p. 269). Cf. also the footnote 18 .

“Here is the version I think is the clearest and most elegant” (van Inwagen 2012 , p. 157). “[…] the modal logic of the argument is S5 , the strongest modal system. This is not the case with every version of the modal argument. Some are valid in weaker modal systems, but those arguments require additional premises” ( ibid. , p. 158). “One could regard the first premise of each of Hartshorne’s arguments [equivalent to formula (2)] as substitutes for an appeal to the strong modal system S5 ” (van Inwagen 2018 , p. 242).

Taking into account this assumption, we will omit systems possessing a different set of primitive rules, such as D+  and T+  (with the so called MacIntosh rule), which are sometimes also considered in MOA-related literature (see Chellas and Segerberg 1994 ).

The operators M and L can also be understood as formal counterparts of Anselm’s “it is conceivable that” and “it is not conceivable that not”, respectively (see Eder and Ramharter 2015 , p. 2814). In turn, for the constant g, the following interpretation is sometimes proposed: “There is a necessarily existent being that has all perfections essentially” (van Inwagen 2012 , p. 158, 2018 , p. 242).

Throughout the article, the bold symbols “ T ”, “ B ” and “ S5 ” stand for systems of modal logic, while the ordinary symbols “T”, “B” and “S5” stand for sentences falling under axiom schemes appropriate to these systems.

Apart from specific and general premises, the laws of classical sentential logic are also applied in each version of the MOA (as in any other argument). This fact, which we take to be quite obvious, is not one of which we intend to make any special use.

The issue of the proper selection of general premises in the MOA was already raised in Kane ( 1984 ).

Similar assumptions can sometimes be found in literature on the MOA. Cf., for example, van Inwagen’s remark that the formula ‘L p ⇒ p ’ “must be valid in every modal system in which the sentential operators represent possibility and necessity in any intuitive sense” (van Inwagen 2018 , p. 242). Cf. also Eder and Ramharter ( 2015 ), where the authors state that the T -system would “seem to be mandatory on any modal conception of conceivability which can claim to be faithful to Anselm’s reasoning” (p. 2814).

This MOA-version corresponds to the version considered in Oppy ( 1996 ) (cf. footnote 5 ).

The difference between objects [α, X ] and TG (α, X ) is worth emphasizing. The former is the abstract structure of a given MOA-version, while the latter is a set of propositions underlying that version.

The formal concept of “circularity” used above differs from the intuitive concept of “begging the question” used by van Inwagen ( 2018 ).

See Kane ( 1984 , p. 339). According to Kane, this fact proves that the B-version is the right version of the MOA. Even so, the view that the S5-system is essential for a proper analysis of the MOA has been quite popular in the philosophical literature—cf., for example, this statement: “[…] all modal ontological arguments are valid in S5 (and they are valid in no weaker modal system […])” (van Inwagen 2009 , pp. 219–20).

I shall make use of a similar result here to that arrived at in Biłat ( 2012a , b ). (The latter being a slightly shortened translation of the former.).

We omit here the fact that (3) is additionally preceded by a necessity operator. This is possible thanks to the assumption made here that Rule of Necessitation can also be applied to extra-logical a priori statements such as (4). (The modal status of (3) and (4), as a priori statements, is exactly the same).

This principle can also be expressed in Plantinga’s style: if God exists in the actual world, then God is maximally great (cf. Plantinga 1974 ).

This topic of the explicative dependencies, respectively, of (3) and (4) on (2), will be developed in the next section.

Postulate (4) is logically equivalent to the thesis ‘Mg ⇒ g’. This MOA-version is even closer to Leibniz’s conception of God (defined as the necessarily existing being), according to which if God is possible, then God exists (see Griffin 2012 , pp. 42, 43; Antognazza 2018 , pp. 75, 78–89).

It is worth noting that Theses 1 and 2 do not perform any key role as regards the main theses of van Inwagen’s article quoted above.

Antognazza, M. R. (2018). Leibniz. In G. Oppy (Ed.), Ontological Arguments (pp. 75–98). Cambridge: Cambridge University Press.

Chapter   Google Scholar  

Benzmüller, C. (2020). A (simplified) supreme being necessarily exists, says the computer: Computationally explored variants of Gödel’s ontological argument . Cornell University. https://arxiv.org/abs/2001.04701

Biłat, A. (2012a). Dowód ontologiczny a logika modalna. Filozofia Nauki, XX (1(77)), 103–108. ( (in Polish) ).

Google Scholar  

Biłat, A. (2012b). Modal logic vs. ontological argument. European Journal for Philosophy of Religion, 4 (2), 179–185.

Article   Google Scholar  

Blackburn, S. (1994). The Oxford dictionary of philosophy . Oxford: Oxford University Press.

Chellas, B. F. (1980). Modal logic. An introduction . Cambridge: Cambridge University Press.

Book   Google Scholar  

Chellas, B. F., & Segerberg, K. (1994). Modal logic with the MacIntosh rule. Journal of Philosophical Logic, 23 (1), 67–86.

Eder, G., & Ramharter, E. (2015). Formal reconstructions of St. Anselm’s ontological argument. Synthese, 192 (9), 2795–2825. https://doi.org/10.1007/s11229-015-0682-8

Goodwin, G. L. (1978). The ontological argument of Charles Hartshorne . Missoula: Montana Scholars Press.

Griffin, M. (2012). The ontological argument, the principle of sufficient reason and Leibniz’s doctrine of striving possibles. In M. Griffin (Ed.), Leibniz, God and necessity (pp. 34–57). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781139022286.003 .

Hartshorne, C. (1944). The formal validity and the real significance of the ontological argument. The Philosophical Review, 53 (3), 225–245.

Kane, R. (1984). The modal ontological argument. Mind, 93 (371), 336–350.

Lewis, D. (1970). Anselm and actuality. Noûs, 4, 175–188.

Łukasiewicz, J. (1957). Aristotle’s syllogistic from the standpoint of modern formal logic . Oxford: Clarendon Press.

Malcolm, N. (1960). Anselm’s ontological arguments. The Philosophical Review, 69 (1), 41–62.

Oppy, G. (1996). Ontological arguments and belief in God . Cambridge: Cambridge University Press.

Oppy, G. (2019). Ontological arguments. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy . Stanford: Stanford University.

Perzanowski, J. (1991). Ontological arguments II: Cartesian and Leibnizian. In H. Burkhardt & B. Smith (Eds.), Handbook of metaphysics and philosophy (pp. 625–633). Munich: Philosophia Verlag.

Plantinga, A. (1974). The nature of necessity . Oxford: Oxford University Press.

Sobel, J. H. (1987). Gödel’s ontological proof. In J. J. Thompson (Ed.), On being and Saying: Essays for Richard Cartwright (pp. 241–261). Cambridge: MIT Press.

Spencer, J. (2018). Conceivability and possibility. In G. Oppy (Ed.), Ontological arguments (pp. 214–237). Cambridge: Cambridge University Press.

Świętorzecka, K., & Łyczak, M. (2018). An even more Leibnizian version of Gödel’s ontological argument. Journal of Applied Logic, 5 (7), 1553–1566.

van Inwagen, P. (2009). Some remarks on the modal ontological argument. Philo, 12 (2), 217–227.

van Inwagen, P. (2012). Three versions of the ontological argument. In M. Szatkowski (Ed.), Ontological proofs today (pp. 143–162). Heusenstamm: Ontos Verlag.

van Inwagen, P. (2018). Begging the question. In G. Oppy (Ed.), Ontological arguments (pp. 238–249). Cambridge: Cambridge University Press.

Walton, D. N. (1998). The new dialectic: Conversational contexts of argument . Toronto: University of Toronto Press.

Download references

Author information

Authors and affiliations.

Faculty of Administration and Social Sciences, Warsaw University of Technology, Warsaw, Poland

Andrzej Biłat

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Andrzej Biłat .

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Biłat, A. The correctness and relevance of the modal ontological argument. Synthese 199 , 2727–2743 (2021). https://doi.org/10.1007/s11229-020-02908-5

Download citation

Received : 12 May 2020

Accepted : 08 October 2020

Published : 21 December 2020

Issue Date : December 2021

DOI : https://doi.org/10.1007/s11229-020-02908-5

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Structure of argument
• Formal correctness of argument
• Simplicity of argument
• Relevance of argument
• Modal logic
• Mini-theories of God
• Find a journal
• Publish with us
• Track your research