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An ontological argument is any one of a category of arguments for the existence of God appearing mainly in Christian theology. The exact criteria for the classification of ontological arguments are not widely agreed, but the arguments typically start with the definition of God and conclude with his necessary existence, using mostly or only a priori reasoning and little reference to empirical observation.
It is widely accepted that the first ontological argument was proposed by Anselm of Canterbury in 1078 in his Proslogion. Anselm defined God as "that than which nothing greater can be conceived", and then argued that this being could exist in the mind. He suggested that, if the greatest possible being exists in the mind, it must also exist in reality. If it only exists in the mind, a greater being is possible—one which exists in the mind and in reality. Seventeenth century French philosopher René Descartes deployed a similar argument. Descartes published several variations of his argument, each of which centered on the idea that God's existence is immediately inferable from a "clear and distinct" idea of a supremely perfect being. In the early eighteenth century, Gottfried Leibniz augmented Descartes' ideas in an attempt to prove that a "supremely perfect" being is a coherent concept. A more recent ontological argument came from Kurt Gödel, who proposed a formal argument for God's existence. Norman Malcolm revived the ontological argument in 1960 when he located a second, stronger ontological argument in Anselm's work; Alvin Plantinga challenged this argument and proposed an alternative, based on modal logic. Attempts have also been made to validate Anselm's proof using an automated theorem prover. Other arguments have been categorised as ontological, including those made by Islamic philosopher Mulla Sadra.
The first critic of the ontological argument was Anselm's contemporary, Gaunilo of Marmoutiers. He used the analogy of a perfect island, suggesting that the ontological could be used to prove the existence of anything. This was the first of many parodies, all of which attempted to show that it has absurd consequences. Thomas Aquinas later rejected the argument on the basis that humans cannot know God's nature. David Hume offered an empirical objection, criticising its lack of evidential reasoning and rejecting the idea that anything can exist necessarily. Immanuel Kant's critique was based on what he saw as the false premise that existence is a predicate. He argued that "existing" adds nothing (including perfection) to the essence of a being, and thus a "supremely perfect" being can be conceived not to exist. Finally, philosophers including C. D. Broad dismissed the coherence of a maximally great being, proposing that some attributes of greatness are incompatible with others, rendering "maximally great being" incoherent.
The traditional definition of an ontological argument was given by Immanuel Kant. He contrasted the ontological argument (literally any argument "concerned with being") with the cosmological and physio-theoretical arguments. According to the Kantian view, ontological arguments are those which are founded on a priori reasoning.
Graham Oppy, who elsewhere expressed the view that he "see[s] no urgent reason" to depart from the traditional definition, defined ontological arguments as those that begin with "nothing but analytic, a priori and necessary premises" and conclude that God exists. Oppy admitted, however, that not all of the "traditional characteristics" of an ontological argument (analyticity, necessity, and a priority) are found in all ontological arguments and, in his 2007 work Ontological Arguments and Belief in God, suggested that a better definition of an ontological argument would employ only considerations "entirely internal to the theistic worldview".
Oppy subclassified ontological arguments into definitional, conceptual (or hyperintensional), modal, Meinongian, experiential, mereological, higher-order, or Hegelian categories, based on the qualities of their premises. He defined these qualities as follows: definitional arguments invoke definitions; conceptual arguments invoke "the possession of certain kinds of ideas or concepts"; modal arguments consider possibilities; Meinongian arguments assert "a distinction between different categories of existence"; experiential arguments employ the idea that God exists solely to those who have had experience of him; and Hegelian arguments are from Hegel. He later categorized mereological as arguments that "draw on… the theory of the whole-part relation".
William Lane Craig criticised Oppy's study as too vague for useful classification. Craig argued that an argument can be classified as ontological if it attempts to deduce the existence of God, along with other necessary truths, from his definition. He suggested that proponents of ontological arguments would claim that, if one fully understood the concept of God, one must accept his existence. William L. Rowe defined ontological arguments as those that start from the definition of God and, using only a priori principles, conclude with God's existence.
Although the ontological argument may have been implicit in the works of Greek philosophers such as Plato and the Neoplatonists, the mainstream view is that the ontological argument was first clearly stated and developed by Anselm of Canterbury. Some scholars argued that the Islamic philosopher Avicenna (Ibn Sina) developed a special kind of ontological argument before Anselm, but other scholars have doubted this position. Daniel Dombrowski marked three major stages in the development of the argument: Anselm's initial explicit formulation; the eighteenth century criticisms of Kant and Hume; and the identification of a second ontological argument in Anselm's Proslogion by twentieth century philosophers.
Theologian and philosopher Anselm of Canterbury (1033–1109) proposed an ontological argument in the second and third chapters of his Proslogion. Anselm's argument was not presented in order to prove God's existence; rather, Proslogion was a work of meditation in which he documented how the idea of God became self-evident to him.
In Chapter 2 of the Proslogion, Anselm defined God as a "being than which no greater can be conceived". He suggested that even "the fool" can understand this concept, and this understanding itself causes the being to exist in the mind. The concept must exist either only in our mind, or in both our mind and in reality. If such a being exists only in our mind, then a greater being—that which exists in the mind and in reality—can be conceived. Therefore, if we can conceive of a being of which nothing greater can be conceived, it must exist in reality. Thus, a being than which nothing greater could be conceived, which Anselm defined as God, must exist in reality.
Anselm's argument in Chapter 2 can be summarised as follows:
- Our understanding of God is a being than which no greater can be conceived.
- The idea of God exists in the mind.
- A being which exists both in the mind and in reality is greater than a being that exists only in the mind.
- If God only exists in the mind, then we can conceive of a greater being—that which exists in reality.
- We cannot be imagining something that is greater than God.
- Therefore, God exists.
In Chapter 3, Anselm presented the notion of a being that cannot be conceived to not exist. He argued that if something can be conceived to not exist, then something greater can be conceived. Consequently, a thing than which nothing greater can be conceived cannot be conceived to not exist and so it must exist. This can be read as a restatement of the argument in Chapter 2, although Norman Malcolm believed it to be a different, stronger argument.
René Descartes 
René Descartes (1596–1650) composed a number of ontological arguments, which differed from Anselm's formulation. Generally speaking, they are less formal arguments than natural intuition.
Descartes wrote in the Fifth Meditation:
But, if the mere fact that I can produce from my thought the idea of something that entails everything that I clearly and distinctly perceive to belong to that thing really does belong to it, is not this a possible basis for another argument to prove the existence of God? Certainly, the 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, (AT 7:65; CSM 2:45)
Descartes argued that God's existence can be deduced from his nature, just as geometric ideas can be deduced from the nature of shapes—he used the deduction of the sizes of angles in a triangle as an example. He suggested that the concept of God is that of a supremely perfect being, holding all perfections. He proposed that, as it adds nothing to the essence of a being, existence is not a predicate and thus a "supremely perfect" being can be conceived to not exist. Thus, if the notion of God did not include existence, it would not be supremely perfect, as it would be lacking a perfection. Consequently, the notion of a supremely perfect God who does not exist, Descartes argues, is unintelligible. Therefore, according to his nature, God must exist.
Gottfried Leibniz 
Gottfried Wilhelm Leibniz saw a problem with Descartes' ontological argument: that Descartes had not asserted the coherence of a "supremely perfect" being. He proposed that, unless the coherence of a supremely perfect being could be demonstrated, the ontological argument fails. Leibniz saw perfection as impossible to analyse; therefore, it would be impossible to demonstrate that all perfections are incompatible. He reasoned that all perfections can exist together in a single entity, and that Descartes' argument is still valid.
Mulla Sadra 
Mulla Sadra (c. 1571–1640) was an Islamic philosopher who was influenced by earlier Muslim philosophers such as Avicenna and Suhrawardi, as well as the Sufi metaphysician Ibn 'Arabi. Sadra discussed Avicenna's arguments for the existence of God, claiming that they were not a priori. He rejected the argument on the basis that existence precedes essence, or that the existence of human beings is more fundamental than their essence.
Sadra put forward a new argument, known as Argument of the Righteous. The argument attempts to prove the existence of God through the reality of existence, and to conclude with God's pre-eternal necessity. In this argument, a thing is demonstrated through itself, and a path is identical with the goal. In other arguments, the truth is attained from an external source, such as from the possible to the necessary, from the originated to the eternal origin, or from motion to the unmoved mover. In the argument of the righteous, there is no middle term other than the truth. His version of the ontological argument can be summarised as follows:
- There is existence
- Existence is a perfection above which no perfection may be conceived
- God is perfection and perfection in existence
- Existence is a singular and simple reality; there is no metaphysical pluralism
- That singular reality is graded in intensity in a scale of perfection (that is, a denial of a pure monism).
- That scale must have a limit point, a point of greatest intensity and of greatest existence.
- Hence God exists.
Mulla Sadra describes this argument in Asfar as follows:
Existence is a single, objective and simple reality, and there is no difference between its parts, unless in terms of perfection and imperfection, strength, and weakness… And the culmination of its perfection, where there is nothing more perfect, is its independence from any other thing. Nothing more perfect should be conceivable, as every imperfect thing belongs to another thing and needs to become perfect. And, as it has already been explicated, perfection is prior to imperfection, actuality to potency, and existence to non-existence. Also, it has been explained that the perfection of a thing is the thing itself, and not a thing in addition to it. Thus, either existence is independent of others or it is in need of others. The former is the Necessary, which is pure existence. Nothing is more perfect than Him. And in Him there is no room for non-existence or imperfection. The latter is other than Him, and is regarded as His acts and effects, and for other than Him there is no subsistence, unless through Him. For there is no imperfection in the reality of existence, and imperfection is added to existence only because of the quality of being caused, as it is impossible for an effect to be identical with its cause in terms of existence.
Kurt Gödel 
Mathematician Kurt Gödel provided a formal argument for God's existence. The arguments were constructed by Gödel but not published until long after his death. He provided a logically valid argument based on modal logic; he uses the conception of properties, ultimately concluding with God's existence.
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
Gödel defined being "god-like" as having every positive property. He left the term "positive" undefined. Gödel proposed that it is understood in an aesthetic and moral sense, or alternatively as the opposite of privation (the absence of necessary qualities in the universe). He warned against interpreting "positive" as being morally or aesthetically "good" (the greatest advantage and least disadvantage), as this includes negative characteristics. Instead, he suggested that "positive" should be interpreted as being perfect, or "purely good", without negative characteristics.
Gödel's listed theorems follow from the axioms, so most criticisms of the theory focus on those axioms or the assumptions made. Oppy argued that Gödel gives no definition of "positive properties". He suggested that if these positive properties form a set, there is no reason to believe that any such set exists which is theologically interesting, or that there is only one set of positive properties which is theologically interesting.
Norman Malcolm 
In 1960, Norman Malcolm published Anselm's Ontological Argument. He sought to distinguish what he saw as two ontological arguments proposed by Anselm in Chapters 2 and 3 of his Proslogion. Malcolm supported Kant's criticism of Anselm's argument in Chapter 2: that existence cannot be a perfection of something; however, he identified what he sees as a second ontological argument in Chapter 3 which is not susceptible to such criticism.
Malcolm identified two key arguments of Anselm's second: first, that a being whose non-existence is logically impossible is greater than a being whose non-existence is logically possible, and secondly, that God is a being "than which a greater cannot be conceived". Malcolm supported that definition of God and suggested that it makes the proposition of God's existence a logically necessarily true statement (in the same way that "a square has four sides" is logically necessarily true). Though Malcolm rejected the idea of existence itself being a perfection, he argued that necessary existence is a perfection. This, he argued, proved the existence of an unsurpassably great necessary being.
Alvin Plantinga 
Analytic philosopher Alvin Plantinga criticised Malcolm's argument, and offered an alternative. He argued that, if Malcolm does prove the necessary existence of the greatest possible being, it follows that there is a being which exists in all worlds whose greatness in some worlds is not surpassed. It does not, he argued, demonstrate that such a being has unsurpassed greatness in this world.
In an attempt to resolve this problem, Plantinga differentiated between "greatness" and "excellence". A being's excellence in a particular world depends only on its properties in that world; a being's greatness depends on its properties in all worlds. Therefore, the greatest possible being must have maximal excellence in every possible world. Plantinga then restated Malcolm's argument, using the concept of "maximal greatness". He argued that it is possible for a being with maximal greatness to exist, so a being with maximal greatness exists in a possible world. If this is the case, then a being with maximal greatness exists in every world, and therefore in this world.
The conclusion relies on a form of modal axiom S5, which states that if something is possibly true, then its possibility is necessary (it is possibly true in all worlds). Plantinga's S5 also states that if something is possibly necessarily true, then it is necessarily true (it is true in all worlds).
A version of his argument is as follows:
- A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
- A being has maximal greatness if it has maximal excellence in every possible world.
- It is possible that there is a being that has maximal greatness. (Premise)
- Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
- Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
- Therefore, an omniscient, omnipotent and perfectly good being exists.
Plantinga argued that, although the first premise is not rationally established, it is not contrary to reason. Michael Martin argued that, if certain components of perfection are contradictory, such as omnipotence and omniscience, then the first premise is contrary to reason. Martin also proposed parodies of the argument, suggesting that the existence of anything can be demonstrated with Plantinga's argument, provided it is defined as perfect or special in every possible world.
Richard M. Gale argued that premise three, the "possibility premise", begs the question. He stated that one only has the epistemic right to accept the premise if one understands the nested modal operators, and that if one understands them within the system S5—without which the argument fails—then one understands that "possibly necessarily" is in essence the same as "necessarily". Thus the premise begs the question because the conclusion is embedded within it.
Juan Manuel Correa argued that the argument can be used to prove that God does not exist simply by affirming that it is possible that God does not exist:
- A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
- A being has maximal greatness if it has maximal excellence in every possible world.
- It is possible that there is not a being that has maximal greatness. (Premise)
- Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being does not exist.
- Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being does not exist.
- Therefore, an omniscient, omnipotent and perfectly good being does not exist.
Sankara's dictum 
An approach to supporting the possibility premise in Plantinga's version of the argument was attempted by Alexander R. Pruss. He started with the 8th–9th century AD Indian philosopher Sankara's dictum that if something is impossible, we cannot have a perception (even a non-veridical one) that it is the case. It follows that if we have a perception that p, then even though it might not be the case that p, it is at least the case that possibly p. If mystics in fact perceive the existence of a maximally great being, it follows that the existence of a maximally great being is at least possible.
Automated reasoning 
Paul Oppenheimer and Edward Zalta used an automated theorem prover—Prover9—to validate Anselm's ontological thesis. Prover9 subsequently discovered a simpler, formally valid (if not necessarily sound) ontological argument from a single non-logical premise.
Criticisms and objections 
One of the earliest recorded objections to Anselm's argument was raised by one of Anselm's contemporaries, Gaunilo of Marmoutiers. He invited his reader to conceive an island "more excellent" than any other island. He suggested that, according to Anselm's proof, this island must necessarily exist, as an island that exists would be more excellent. Gaunilo's criticism does not explicitly demonstrate a flaw in Anselm's argument; rather, it argues that if Anselm's argument is sound, so are many other arguments of the same logical form, which cannot be accepted. He offered a further criticism of Anselm's ontological argument, suggesting that the notion of God cannot be conceived, as Anselm had asserted. He argued that many theists would accept that God, by nature, cannot be fully comprehended. Therefore, if humans cannot fully conceive of God, the ontological argument cannot work.
Anselm responded to Gaunilo's criticism by arguing that the argument applied only to concepts with necessary existence. He suggested that only a being with necessary existence can fulfill the remit of "that than which nothing greater can be conceived". Furthermore, a contingent object, such as an island, could always be improved and thus could never reach a state of perfection. For that reason, Anselm dismissed any argument that did not relate to a being with necessary existence.
Other parodies have been presented, including the devil corollary, the no devil corollary and the extreme no devil corollary. The devil corollary proposes that a being than which nothing worse can be conceived exists in the understanding (sometimes the term lesser is used in place of worse). Using Anselm's logical form, the parody argues that if it exists in the understanding, a worse being would be one that exists in reality; thus, such a being exists. The no devil corollary is similar, but argues that a worse being would be one that does not exist in reality, so does not exist. The extreme no devil corollary advances on this, proposing that a worse being would be that which does not exist in the understanding, so such a being exists neither in reality nor in the understanding. Timothy Chambers argued that the devil corollary is more powerful than Gaunilo's challenge because it withstands the challenges that may defeat Gaunilo's parody. He also claimed that the no devil corollary is a strong challenge, as it "underwrites" the no devil corollary, which "threatens Anselm's argument at its very foundations".
Thomas Aquinas 
Thomas Aquinas, while proposing five proofs of God's existence in his Summa Theologica, objected to Anselm's argument. He suggested that people cannot know the nature of God and, therefore, cannot conceive of God in the way Anselm proposed. The ontological argument would be meaningful only to someone who understands the essence of God completely. Aquinas reasoned that, as only God can completely know His essence, only He could use the argument. His rejection of the ontological argument caused other Catholic theologians to also reject the argument.
David Hume 
Scottish philosopher and empiricist David Hume argued that nothing can be proven to exist using only a priori reasoning. In his Dialogues Concerning Natural Religion, the character Cleanthes proposes a criticism:
...there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable.
Hume also suggested that, as we have no abstract idea of existence (apart from as part of our ideas of other objects), we cannot claim that the idea of God implies his existence. He suggested that any conception of God we may have, we can conceive either of existing or of not existing. He believed that existence is not a quality (or perfection), so the concept of a completely perfect being need not exist. Thus, he claimed that it is not a contradiction to deny God's existence. Although this criticism is directed against a cosmological argument, similar to that of Samuel Clarke in his first Boyle Lecture, it has been applied to ontological arguments as well.
Immanuel Kant 
Immanuel Kant put forward an influential objection to the ontological argument in his Critique of Pure Reason. The critique was primarily and explicitly directed at Descartes, but also attacked Leibniz. Kant's refutation consists of several separate but interrelated arguments, shaped by his central distinction between analytic and synthetic judgments. In an analytic judgment, the predicate expresses something that is already contained within a concept and is therefore a tautology; in a synthetic judgment, the predicate, or claim, links the concept to something outside it that is not conceptually contained within it. New knowledge consists of synthetic judgments.
Kant questioned the intelligibility of the concept of a necessary being. He considered examples of necessary propositions, such as "a triangle has three angles", and rejected the transfer of this logic to the existence of God. First, he argued that such necessary propositions are necessarily true only if such a being exists: If a triangle exists, it must have three angles. The necessary proposition, he argued, does not make the existence of a triangle necessary. Thus, he argued that, if the proposition "X exists" is posited, it would follow that, if X exists, it exists necessarily; this does not mean that X exists in reality. Second, he argued that contradictions arise only when the subject and predicate are maintained and, therefore, a judgement of non-existence cannot be a contradiction, as it denies the predicate.
Kant then proposed that the statement "God exists" must be analytic or synthetic—the predicate must be inside or outside of the subject, respectively. If the proposition is analytic, as the ontological argument takes it to be, then the statement would be true only because of the meaning given to the words. Kant claimed that this is merely a tautology and cannot say anything about reality. However, if the statement is synthetic, the ontological argument does not work, as the existence of God is not contained within the definition of God (and, as such, evidence for God would need to be found).
Kant goes on to write, "'being' is obviously not a real predicate"  and cannot be part of the concept of something. He proposed that existence is not a predicate, or quality. This is because existence does not add to the essence of a being, but merely indicates its occurrence in reality. He stated that by taking the subject of God with all its predicates and then asserting that God exists, "I add no new predicate to the conception of God". He argued that the ontological argument works only if existence is a predicate; if this is not so, then it is conceivable for a completely perfect being to not exist, thus defeating the ontological argument.
In addition, Kant claimed that the concept of God is not of one a particular sense; rather, it is an "object of pure thought". He asserted that God exists outside the realm of experience and nature. Because we cannot experience God through experience, Kant argued that it is impossible to know how we would verify God's existence. This is in contrast to material concepts, which can be verified by means of the senses.
Douglas Gasking 
Australian philosopher Douglas Gasking (1911–1994) developed a version of the ontological argument meant to prove God's non-existence. It was not intended to be serious; rather, its purpose was to illustrate the problems Gasking saw in the ontological argument.
Gasking asserted that the creation of the world is the most marvellous achievement imaginable. The merit of such an achievement is the product of its quality and the creator's ability: the greater the disability of the creator, the more impressive the achievement. Non-existence, Gasking asserts, would be the greatest handicap. Therefore, if the universe is the product of an existent creator, we could conceive of a greater being—one which does not exist. A non-existent creator is greater than one which exists, so God does not exist. Gasking's proposition that the greatest disability would be non-existence is a response to Anselm's assumption that existence is a predicate and perfection. Gasking uses this logic to assume that non-existence must be a disability.
Oppy criticised the argument, viewing it as a weak parody of the ontological argument. He stated that, although it may be accepted that it would be a greater achievement for a non-existent creator to create something than a creator who exists, there is no reason to assume that a non-existent creator would be a greater being. He continued by arguing that there is no reason to view the creation of the world as "the most marvellous achievement imaginable". Finally, he suggested that it may be inconceivable for a non-existent being to create anything at all.
Coherence of a maximally great being 
In his development of the ontological argument, Leibniz attempted to demonstrate the coherence of a supremely perfect being. C. D. Broad countered that if two characteristics necessary for God's perfection are incompatible with a third, the notion of a supremely perfect being becomes incoherent. The ontological argument assumes the definition of God purported by classical theism: that God is omnipotent, omniscient, and morally perfect. Kenneth Einar Himma claimed that omniscience and omnipotence may be incompatible: if God is omnipotent, then he should be able to create a being with free will; if he is omniscient, then he should know exactly what such a being will do (thus rendering them without free will). This analysis would render the ontological argument incoherent, as the characteristics required of a maximally great being cannot coexist in one being, thus such a being could not exist.
Other criticisms 
Bertrand Russell, during his early Hegelian phase, accepted the argument; once exclaiming: "Great God in Boots!—the ontological argument is sound!" However, he later criticised the argument, asserting that "the argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies." He drew a distinction between existence and essence, arguing that the essence of a person can be described and their existence still remain in question.
Biologist Richard Dawkins, in his book The God Delusion, rejects the argument as "infantile". Noting that he is "a scientist rather than a philosopher", he writes: "The very idea that such grand conclusions should follow from such logomachist trickery offends me aesthetically." Also, he feels a "deep suspicion of any line of reasoning that reached such a significant conclusion without feeding in a single piece of data from the real world."
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