Anselm's Ontological Arguments for the Existence of God: A Critical Analysis, Summaries of History

Download Anselm's Ontological Arguments for the Existence of God: A Critical Analysis and more Summaries History in PDF only on Docsity!   1   The Ontological Argument Revisited George Cronk Introduction TBA – a brief review of the history and the literature and a statement of where this paper fits Conceptual framework Why is the ontological argument called “ontological”? The expression "ontological argument" was coined by Kant in his Critique of Pure Reason (1781, 1787), but the type of theistic argument in question originated with Anselm of Canturbury in the 11th century (in his Proslogion). Kant called this type of argument "ontological" because it is based on a query as to what kind of being (Greek, ὤν, on; ὄντος, ontos) is referenced by the word "God" (507-8). What kind of a being would God be if God was? According to Anselm, the word “God” refers to “that than which nothing greater can be conceived” (Basic Writings 53). The concepts of necessity and contingency Linguistic-logical application: as to statements: • Necessarily true statements (tautologies) cannot be false, and necessarily false statements (contradictions) cannot be true. • Contingent statements can be either true or false, depending on facts, evidence, & circumstances. Working  Draft     2   Metaphysical (ontological) application: as to beings: • Necessary beings (i.e., things with necessary existence) cannot not-exist. • Impossible beings (i.e., things whose existence is contradictory, e.g., round squares) cannot exist. • Contingent beings are beings whose existence and nonexistence are neither necessary nor impossible). They may exist (rocks) or not (unicorns). Their existence is (logically) possible, and their nonexistence is also (logically) possible. The question that gives rise to the ontological argument for the existence of god: Is it logically possible for the existence of “that than which nothing greater can be conceived” to be contingent? More precisely, is the nonexistence of “that than which nothing greater can be conceived” logically possible? Anselm's ontological arguments Anselm’s “1st” ontological argument: that God exists. The text (Proslogion 263-4): And so, Lord, you who can add understanding to faith, allow me (to the extent that it is good for me) to understand that you exist as I believe you to exist and that you are what I believe you are. I believe you are that than which nothing greater can be conceived [aliquid quo nihil maius cogitari possit]. Is it possible that nothing like that exists? After all, “the fool has said in his heart ‘there is no God’” (Psalms 14:1 and 53:1). But when this fool hears the words “that than which nothing greater can be conceived,” he must understand what he hears; and what he understands then exists in his mind [in intellectu eius est], even if he doesn’t think that such a being exists in fact. For there is a big difference between something existing [as an idea] in someone’s mind and . . . that thing’s existing in reality. When a painter first imagines what he is going to paint, he has it in his mind; but, since he has not yet made the painting itself, he doesn’t think that it exists yet. Once he has made the painting, however, he not only has the idea of it in his mind, but he also knows that the painting itself exists in fact . . . . So even a fool would have to admit that that than which nothing greater can be conceived exists [as an idea] in his mind since he understands this phrase when he hears it, and whatever is understood exists at least in the understanding (or mind). But here’s my main point: That than which nothing greater can be conceived cannot exist only [as an   5   If the claim that God’s nonexistence is possible is necessarily false, then the claim that God’s nonexistence is impossible is necessarily true (because the negation of a contradiction is a tautology). So God’s nonexistence is impossible, and therefore God must exist. Thus, agnosticism must be false too, right? Furthermore, God is the only being whose nonexistence is logically impossible. That is, no other being deserves the title of “that than which nothing greater can be conceived.” The existences of all other beings (actual or conceivable) are either contingent or impossible (Basic Writings 319). So how can “the fool” doubt or deny the existence of God? Anselm’s answer: The “fool” (i.e., the atheist or agnostic) does not understand the true meaning of “that than which nothing greater can be conceived” (Proslogion 264). What's wrong with the ontological argument? Both Anselm & Descartes assume that the existence of “that than which nothing greater can be conceived” is logically possible. Anselm’s “1st” ontological argument (again): 1. That than which nothing greater can be conceived cannot exist only as an idea in the mind because, in addition to existing as an idea in the mind, it can also be thought of as existing in reality, that is, objectively, which is greater than existing only as an idea in the mind. 2. If that than which nothing greater can be conceived exists only as an idea in the mind, then “that than which nothing greater can be conceived” is “that than which something greater can be conceived,” which is impossible because it is self-contradictory. -------------------------------------------------------------------------------------------------------------- 3. That than which nothing greater can be conceived must exist, not only as an idea in the mind, but in reality.   6   Criticism of Anselm’s 1st argument: In the 1st premise of his 1st argument, Anselm says that “that than which nothing greater can be conceived” can be thought of as existing in reality. Is that true? What if the existence of “that than which nothing greater can be conceived” is logically impossible? Anselm’s “2d” ontological argument (again): 1. It is possible to think of something that cannot be thought not to exist [that is, a necessary being]. 2. A necessary being [something that cannot be thought not to exist] would be greater than something that can be thought not to exist [that is, a contingent being]. 3. If that than which nothing greater can be conceived could be thought of as not existing, then that than which nothing greater can be conceived would not be that than which nothing greater can be conceived, which is an outright contradiction and thus absurd. ------------------------------------------------------------------------------------------------------------- 4. That than which nothing greater can be conceived has such a high degree of existence, that is, necessary existence, that it cannot be thought of as not existing, that is, its nonexistence is impossible. Criticism of Anselm’s 2d argument: In the 3d premise of his 2d argument, Anselm says that thinking that “that than which nothing greater can be conceived” as not existing “is an outright contradiction and thus absurd.” Is that true? What if the existence of “that than which nothing greater can be conceived” is logically impossible? In that case, the statement, “that than which nothing greater can be conceived exists,” would be necessarily false, and its negation (“that than which nothing greater can be conceived does not exist”) would be necessarily true. Let's consider Descartes' version of the argument, which he sets forth in the fifth meditation in his Meditations on First Philosophy (1641) ("Meditations" 298-9):   7   Descartes' version of the ontological argument: 1. If the nonexistence of God (an infinitely perfect being) were possible, then existence would not be part of God’s essence (that is, existence would not be a property of the divine nature). 2. If existence were not part of God’s essence (that is, a property of the divine nature), then God would be a contingent (rather than necessary) being. 3. The idea of God as a contingent being (that is, the idea of an infinitely perfect being with contingent rather than necessary existence) is self- contradictory. 4. It is impossible to think of God as not existing. ------------------------------------------------------------------------------------------------------------ 5. The nonexistence of God is impossible. Criticism of Descartes' version: Like Anselm, Descartes (in his 2d and 4th premises assumes that God’s existence must be either necessary or contingent. And since it makes no sense to say that God’s existence is contingent (3d premise), Descartes (validly) concludes that the existence of God must be necessary (because His nonexistence is impossible). However, again like Anselm, Descartes does not consider the possibility that God’s existence might be impossible. If God’s existence is impossible, then His existence is neither contingent nor necessary. If God’s existence is impossible, then God cannot exist. To develop this point, let’s look at another version of the ontological argument. In his book, Philosophy of Religion (48-49), C. Stephen Evans presents the argument as follows: 1. If a Perfect Being exists, then its existence is necessary. 2. If a Perfect Being does not exist, then its existence is impossible. 3. Either a PB exists or it doesn’t. 4. Either the existence of a PB is necessary, or it is impossible. 5. The existence of a PB is not impossible. ---------------------------------------------------------------------------------------------- 6. The existence of a PB is necessary. He formalizes the argument in Propositional Logic notation this way:   10   Addendum Some Modal Formalizations of the Ontological Argument Modal Logic: A mode or modality is a/the way or manner in which something occurs or is experienced, expressed, or done. There are various systems of Modal Logic. The type of ML utilized in this paper classifies propositions (statements) on the basis of whether they affirm or deny the possibility, impossibility, contingency, necessity, or actuality of their content. "Possible worlds" theory and its applications are also important features of ML. Modal Operators:  and  p = p is necessarily true p = p is possibly truep = p is actually true Christopher Small’s Rendition (interpreting Hartshorne) (Small, Web Version, 6-11) 1. If a perfect being [PB] exists, then it is necessary that a PB exists. 1. P → P Axiom 2 2. If it is possible that a PB does not exist, then it is necessary that it is possible that a PB does not exist. 2. ∼P → ∼P Becker’s Postulate 2 (Oskar Becker, 1889-1964) 3. Either it is necessary that a PB exists or it is possible that a PB does not exist. 3. P ∨ ∼P From 1 and 2 via the Law of Excluded Middle 4. Either it is necessary that a PB exists or it is necessary that it is possible that a PB does not exist. 4. P ∨ ∼P From 2 and 3 via Substitution 5. If it is possible that a PB does not exist, then a PB does not exist. 5. ∼P → ∼P Contrapositive of 1 6. It is necessary that if it is possible that a PB does not exist then a PB does not exist. 6. (∼P → ∼P) From 5 via Necessitation Postulate 7. If it is necessary that it is possible that a PB does not exist, then it is necessary that a PB does not exist. 7. ∼P → ∼P From 6 via Modus Tollens 8. Either it is necessary that PB exists or it is necessary that a PB does not exist. 8. P ∨ ∼P From 4 and 7 via Substitution 9. It is not necessary that a PB does not exist. 9. ∼∼P Axiom 1 10. It is necessary that a PB exists. 10. P From 8 and 9 via Disjunctive Syllogism   11   Charles Hartshorne's Rendition (Peter Suber’s Restatement) 1. If a perfect being [PB] exists, then it is necessary that a perfect being exists. 1. P → P A PB cannot exist contingently 2. It is not necessary that a PB does not exist. 2. ∼∼P Or P – The existence of a PB is not impossible 3. If it is necessary that a PB exists, then a PB exists. 3. P → P Modal Axiom: Necessity entails actuality 4. Either it is necessary that a PB exists or it is not necessary that a PB exists. 4. P ∨ ∼P Law of Excluded Middle 5. If it is not necessary that a PB exists, then it is necessary that it is not necessary that a PB exists. 5. ∼P → ∼P Becker’s Postulate 1 (Oskar Becker, 1889-1964) 6. Either it is necessary that a PB exists or it is necessary that it is not necessary that a PB exists. 6. P ∨ ∼P From 4 and 5 via Substitution 7. If it is necessary that it is not necessary that a PB exists, then it is necessary that a PB does not exist. 7. ∼P → ∼P From 1 via Modus Tollens 8. Either it is necessary that PB exists or it is necessary that a PB does not exist. 8. P ∨ ∼P From 6 and 7 via Substitution 9. It is necessary that a PB exists. 9. P From 8 and 2 via Disjunctive Syllogism 10. A PB exists. 10. P From 9 and 3 via Modus Ponens C. Stephen Evans's Simplification of the Argument 1. If a perfect being [PB] exists, then it is necessary that a perfect being exists. 1. P → P A PB cannot exist contingently. 2. If a PB does not exist, then it is necessary that it does not exist (i.e., its existence is impossible). 2. ∼P → ∼P A PB cannot come into existence. 3. Either a PB exists or a PB does not exist. 3. P ∨ ∼P Law of Excluded Middle 4. Either it is necessary that a PB exists or it is necessary that a PB does not exist (i.e., the existence of a PB is either necessary of impossible). 4. P ∨ ∼P From 1, 2, and 3 5. It is not necessary that a PB does not exist (i.e., its existence is not impossible). 5. ∼∼P Negation of Disjunct in 4 6. It is necessary that a PB exists. 6. P From 4 and 5 via Disjunctive Syllogism   12   Kurt Gödel's Proof C.A. Anderson's Version Definition 1: x is God-like if and only if x has every positive property. Definition 2: A property φ is an essence of entity x if and only if x has φ and φ entails every property x has. Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified (i.e., for every φ, if φ is an essence of x, then necessarily there exists a y such that y has φ). Axiom 1: A property is positive if and only if its negation is not positive. Axiom 2: Any property entailed by a positive property is itself 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: The property of necessarily existing is a positive property. Theorem 1: If a property is positive, then it is consistent (i.e., possibly exemplified). Corollary 1: The property of being God-like is self-consistent, i.e., possible exemplified. Corollary 2: If x is God-like and has a property, then that property is entailed by the property of being God-like. 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. Dana Scott's Version 1. Either a property or its negation is positive, but not both. 1. ∀φ[P(~φ) ↔ ~P(φ)] Axiom 1 2. A property necessarily implied by a positive property is positive. 2. ∀φ∀ψ[(P(φ) ∧ ∀x[φ(x) → ψ(x)]) → P(ψ)] Axiom 2 3. Positive properties are possibly exemplified. 3. ∀φ[P(φ) → ∃xφ(x)] Theorem 1 4. A God-like being possesses all positive properties. 4. G(x) ↔ ∀φ[P(φ) → φ(x)] Definition 1 5. The property of being God-like is positive. 5. P(G) Axiom 3 6. Possibly, God exists. 6. ∃xG(x) Corrolary 7. Positive properties are necessarily positive. 7. ∀φ[P(φ) → P(φ)] Axiom 4 8. An essence of an individual is a property possessed by it and necessarily implying any of its properties. 8. φ ess x ↔ φ(x) ∧ ∀ψ(ψ(x) → ∀y(φ(y) → ψ(y))) Definition 2 9. Being God-like is an essence of any God-like being. 9. ∀x[G(x) → G ess x] Theorem 2 10. Necessary existence of an individual is the necessary exemplification of all its essences. 10. NE(x) ↔ ∀φ[φ ess x → ∃yφ(y)] Definition 3 11. Necessary existence is a positive property. 11. P(NE) Axiom 5 12. Necessarily, God exists 12. ∃xG(x) Theorem 3   15   Gödel, Kurt. "Notes in Kurt Gödel’s Hand." Logic and Theism: Arguments for and Against Beliefs in God. By John Howard Sobel. Cambridge: Cambridge University Press, 2004. Appendix A, 144-145. Hartshorne, Charles. The Logic of Perfection. LaSalle, IL: Open Court, 1962. Hick, John (1966, 1977). Evil and the God of Love. New York: Palgrave Macmillan, 2010. Himma, K.E. "Anselm: Ontological Argument for God's Existence." The Internet Encyclopedia of Philosophy, ISSN 2161-0002, http://www.iep.utm.edu/ont-arg/#H4/, 23 Feb. 2014. Kant, Immanuel (1781, 1787). Critique of Pure Reason. Trans. Norman Kemp Smith. New York: St. Martin's Press, 1929. Leibniz, Gottfried Wilhelm. New Essays Concerning Human Understanding. Trans. A.G. Langley. 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Rowe, William. “Modal Versions of the Ontological Argument.” Philosophy of Religion. Ed. Louis Pojman. Belmont, CA: Wadsworth Publishing Co., 3d Ed., 1998.   16   Scott, Dana. "Notes in Dana Scott’s Hand." Logic and Theism: Arguments for and Against Beliefs in God. By John Howard Sobel. Cambridge: Cambridge University Press, 2004. Appendix B, 145-146. Sennett, James F. “Universe Indexed Properties and the Fate of the Ontological Argument.” Religious Studies, 27 (1991): 65-79. Small, C.G. "Reflections on Gödel's Ontological Argument." Klarheit in Religionsdingen: Aktuelle Beitrage zur Religionsphilosophie, Grundlagenprobleme unserer Zeit, Band III. Ed. W. Deppert and M. Rahnfeld. Leipsig: Leipziger Universitatsverlag, 2003. 109-144. Also published at http://sas.uwaterloo.ca/~cgsmall/Godel.final.revision.PDF. Sobel, J.H. Logic and Theism: Arguments for and Against Beliefs in God. Cambridge: Cambridge University Press, 2004. Suber, Peter, "The Ontological Argument." Electronic hand-out for Prof. Suber's course on "Rationalism & Empiricism." http://legacy.earlham.edu/~peters/courses/re/onto-arg.htm, 23 Feb 2014.