Although a version of the ontological argument appears explicitly in the writings of the ancient Greek philosopher
Xenophanes and variations appear in writings by
Parmenides,
Plato, and the
Neoplatonists, the mainstream view is that the ontological argument was first clearly stated and developed by
Anselm of Canterbury. Some scholars argue that Islamic philosopher
Avicenna (Ibn Sina) developed a
special kind of ontological argument before Anselm, while others have doubted this position.
Daniel Dombrowski marked three major stages in the development of the argument: • Anselm's initial explicit formulation, • the 18th-century criticisms of
Kant and
Hume, and • the identification of a second ontological argument in Anselm's
Proslogion by 20th-century philosophers.
Anselm was the first to attempt an ontological argument for God's existence. Theologian and philosopher
Anselm of Canterbury (1033–1109) proposed an ontological argument in the 2nd and 3rd 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 defines God as a "being than which no greater can be conceived." He suggests that even "the fool" can understand this concept, and this understanding itself means that the being must 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 (this argument is generally regarded as a
reductio ad absurdum because the view of the fool is proven to be inconsistent). Therefore, if we can conceive of a being than 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 summarized as follows:
René Descartes René Descartes (1596–1650) proposed a number of ontological arguments that differ from Anselm's formulation. Generally speaking, they are less formal arguments than they are natural
intuition. In
Meditation, Book V, Descartes wrote: Descartes argues 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 seems to have assumed that existence is a predicate of a perfection. 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.
Baruch Spinoza In
Spinoza's
Short Treatise on God, Man, and His Well-Being, he wrote a section titled "Treating of God and What Pertains to Him", in which he discusses God's existence and what God is. He starts off by saying: "whether there is a God, this, we say, can be proved". His proof for God follows a similar structure as Descartes's ontological argument. Descartes attempts to prove God's existence by arguing that there "must be some one thing that is supremely good, through which all good things have their goodness". Spinoza's argument differs in that he does not move straight from the conceivability of the greatest being to the existence of God, but rather uses a deductive argument from the idea of God. Spinoza says that man's ideas do not come from himself, but from some sort of external cause. Thus the things whose characteristics a man knows must have come from some prior source. So, if man has the idea of God, then God must exist before this thought, because man cannot create an idea of his own imagination.
Mulla Sadra Mulla Sadra (c. 1571/2–1640) was an
Iranian Shia 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
Seddiqin Argument or
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 summarized as follows:
Georg Wilhelm Friedrich Hegel In response to Kant's rejection of traditional speculative philosophy in his
First Critique, and to Kant's rejection of the Ontological Argument,
Georg Wilhelm Friedrich Hegel proposed throughout his lifetime works that Immanuel Kant was mistaken. Hegel took aim at Kant's famous 100
thaler argument. Kant had said that "it is one thing to have 100 thalers in my mind, and quite a different thing to have 100 thalers in my pocket". According to Kant, we can imagine a God, but that does not prove that God exists. Hegel argued that Kant's formulation was inaccurate. He referred to Kant's error in all of his major works from 1807 to 1831: for Hegel, the "true" is the "whole" (PhG, para. 20), and the "true" is the which is to say "spirit", or "God". Thus, God is the whole of the cosmos, both unseen as well as seen. This error of Kant, therefore, was his comparison of a finite, contingent entity such as 100 thalers, with infinite, necessary Being, i.e. the whole. According to Hegel, when regarded as the whole of being, unseen as well as seen, and not simply "one being among many", then the ontological argument flourishes, and its logical necessity becomes obvious. Hegel signed a book contract in 1831, the year of his death, for a work entitled
Lectures on the Proofs of the Existence of God. Hegel died before finishing the book. It was to have three sections: (1) The Cosmological Argument; (2) The
Teleological Argument; and (3) the Ontological Argument. Hegel died before beginning sections 2 and 3. His work is published today as incomplete, with only part of his Cosmological Argument intact. To peruse Hegel's ideas on the ontological argument, scholars have had to piece together his arguments from various paragraphs from his other works. Some scholars have even gone as far to suggest that Hegel's entire philosophy comprises an ontological argument.
Modal versions of the ontological argument Modal logic deals with the logic of possibility as well as necessity. Paul Oppenheimer and
Edward N. Zalta note that, for Anselm's
Proslogion chapter 2, "Many recent authors have interpreted this argument as a modal one." In the phrase 'that than which none greater can be conceived', the word 'can' could be construed as referring to a possibility. Nevertheless, the authors write that "the logic of the ontological argument itself doesn't include inferences based on this modality." However, there have been newer, avowedly modal logic versions of the ontological argument, and on the application of this type of logic to the argument,
James Franklin Harris writes:[D]ifferent versions of the ontological argument, the so-called "modal" versions of the argument, which arguably avoid the part of Anselm's argument that "treats existence as a predicate," began to emerge. The [modal logic version] of these forms of defense of the ontological argument has been the most significant development.
Kurt Gödel Mathematician
Kurt Gödel provided a formal argument for
God's existence. The argument was constructed by Gödel but not published until long after his death. He provided an 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. For instance, axiom 5 does not explain why necessary existence is positive instead of possible existence, an axiom which the whole argument follows from. Or, for Axiom 1, to use another example, the negation of a positive property both includes the lack of any properties and the opposite property, and only the lack of any properties is a privation of a property, not the opposite property (for instance, the lack of happiness can symbolize either sadness or having no emotion, but only lacking emotion could be seen as a privation, or negative property). Either of these axioms being seen as not mapping to reality would cause the whole argument to fail. 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. This means that, given the chosen axioms, the conclusion (the necessary existence of a divine being) follows from the premises according to the rules of the adopted logical framework. However, this validity is conditional: it does not guarantee the truth of the axioms or the reality of the conclusion, but only attests to the internal coherence of the argument within a formal system. Simplified variants have even been developed to avoid classical objections—such as
modal collapse—while preserving the deductive structure of the proof.
Malcolm Norman Malcolm and
Charles Hartshorne are primarily responsible for introducing modal versions of the argument into the contemporary debate. Both claimed that Anselm had two versions of the ontological argument, the second of which was a modal logic version. According to James Harris, this version is represented by Malcolm thus:If it [that than which nothing greater can 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 nonexistence, 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 nonexistence 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. Referring to the 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 the second ontological argument in Chapter 3 which is not susceptible to such criticism. In Anselm's second argument, Malcolm identified two key points: first, that a being whose non-existence is
logically impossible is greater than a being whose non-existence is logically possible, and second, 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).
Hartshorne Hartshorne conceives of his modal argument as follows: Let 'q' stand for 'There is a perfect being', and 'p \to\ q' for 'p strictly implies q'. • Assume that perfection could not exist contingently (Anselm's Principle): q \to \Box q • Consider the following theorem: \Box q\or \neg \Box q • Consider the following axiom: \neg\Box q\to \Box \neg \Box q • Inference from 2, 3: \Box q\or \Box \neg \Box q • Inference from 1: \Box \neg \Box q\to \Box \neg q • Inference from 4, 5: \Box q \or \Box \neg q • Assume that perfection is not impossible: \neg \Box \neg q • Inference from 6, 7: \Box q • Consider the following axiom: \Box q \to q • Inference from 8, 9: q In step 3, a version of the axiom characteristic for S5 is introduced. However, Robert Adams showed that, with only minor formal changes, the Brouwersche System suffices. Hartshorne says that, for Anselm, "necessary existence is a superior manner of existence to ordinary, contingent existence and that ordinary, contingent existence is a defect." For Hartshorne, both Hume and Kant focused only upon whether what exists is greater than what does not exist. However, "Anselm's point is that what exists and cannot not exist is greater than that which exists and can not exist." This avoids the question of whether or not existence is a predicate. criticized Malcolm's and Hartshorne's arguments, and offered an alternative. Plantinga developed his argument in the books titled
The nature of necessity (1974; ch. 10) and
God, Freedom and Evil (1974; part 2 c). In them, he does not distinguish between Malcom and Hartshorne’s contribution and treats them as having put forward roughly the same idea. Jordan Sobel objects to conflating Malcom and Hartshorne’s views this way, maintaining that Hartshorne’s version is not vulnerable to the objection Plantinga claims to raise. Plantinga summarizes Malcom’s and Hartshorne’s contributions as follows. Any entity would be greater than it is, if it were to exist necessarily (that is, if it were to exist in every possible world). Hence, necessary existence is a property that contributes to an entity’s greatness. God, as a being that is maximally great, must hence exist necessarily. It is possible that (i.e. there is a possible world where) God, a maximally great being, exists. If God exists in that world, then, being maximally great, God exists in every world. Hence, God also exists in the actual world and does so with necessity. Plantinga's criticism is that the argument, thus construed, does not show enough. If it is successful, it proves the necessary existence of a being that is maximally great in some possible world. But such a being – though maximally great somewhere – may not be (even remotely) great in our world. God’s maximal greatness, however, is not merely accidental: “He could not have been otherwise”. Hence, if God exists in some possible world, he must be maximally great at every 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. According to Graham Oppy, we can summarize Plantinga’s rendition of the argument as follows: • "There is a possible world in which there is an entity that possesses maximal greatness. (Premise) • (Hence) There is an entity that possesses maximal greatness. (From 1)” There are different reconstructions of Plantinga’s argument across the literature, for example Graham Oppy's above, Jordan Sobel's from his book
Logic and Theism, Joshua Rasmussen's from his book chapter
Plantinga, or Gregory Stacey's from his paper
Modal Ontological Arguments. Note that in the final rendition of his argument, Plantinga phrases it in terms of instantiations of properties, rather than in terms of possible beings. He does this to avoid questions arising from the status of possible beings and writes that wherever he does use the term “possible being” it can be easily reformulated in terms of properties and their instances. According to Graham Oppy, the validity of this argument relies on a B or S5 system of modal logic, because they have the suitable
accessibility relations between worlds. In other words, to say that p is necessarily possible means that p is true in at least one possible world W (if it is an actual world; Plantinga also used Axioms B of S5: A\to\Box\Diamond A) and thus it is true in all worlds because its omnipotence, omniscience, and moral perfection are its essence. In the version of the argument in
God, Freedom and Evil, Plantinga clarified that Another Christian philosopher,
William Lane Craig, characterizes Plantinga's argument in a slightly different way: • It is possible that a maximally great being exists. • If it is possible that a maximally great being exists, then a maximally great being exists in some possible world. • If a maximally great being exists in some possible world, then it exists in every possible world. • If a maximally great being exists in every possible world, then it exists in the actual world. • If a maximally great being exists in the actual world, then a maximally great being exists. • Therefore, a maximally great being exists. According to Craig, premises (2)–(5) are relatively uncontroversial among philosophers, but "the epistemic entertainability of premise (1) (or its denial) does not guarantee its metaphysical possibility." Furthermore the philosopher
Richard M. Gale argued that premise one, 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. Plantinga anticipated this line of objection and pointed out in his defense that any deductively valid argument will beg the question this way. On systems of modal logic in general, James Garson writes that "the words ‘necessarily’ and ‘possibly’, have many different uses. So the acceptability of axioms for modal logic depends on which of these uses we have in mind." Evaluating Plantinga's argument in particular, however, Graham Oppy notes that S5 is standardly taken to be the right system for capturing logical and metaphysical uses of "necessarily" and "possibly" (which are the uses at play in Plantinga's argument).
Sankara's dictum An approach to supporting the possibility premise in Plantinga's version of the argument was attempted by
Alexander 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 N. 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==