====== Anselm's Ontological Argument ====== ===== Overview ===== Anselm of Canterbury (1033-1109) first presented his ontological argument in the second chapter of his work "Proslogion" (1077-1078). It represents one of the earliest attempts to prove God's existence through pure a priori reasoning, without appealing to empirical evidence or observations about the world. The argument purports to demonstrate that God, defined as "that than which nothing greater can be conceived," must necessarily exist in reality and not merely in the understanding. This argument has been enormously influential in the history of philosophical theology, inspiring variants, critiques, and defenses across nearly a millennium of philosophical discourse. ===== Formal Structure ===== **Premises:** 1. God is defined as "that than which nothing greater can be conceived" (aliquid quo nihil maius cogitari possit). 2. Even the fool (insipiens) understands this definition, meaning that God exists at least in the understanding. 3. It is greater to exist in reality than to exist merely in the understanding. 4. If God existed only in the understanding, then we could conceive of something greater (namely, the same being existing in reality). 5. But this would mean we could conceive of something greater than that than which nothing greater can be conceived, which is a contradiction. **Conclusion:** Therefore, God must exist not merely in the understanding but also in reality. ===== Formalization ===== Using modal logic notation: $$ \begin{align} &1.\ G(x) \leftrightarrow \forall y \neg(y > x) \\ &2.\ \exists x [G(x) \wedge \text{InIntellectu}(x)] \\ &3.\ \forall x [\text{InRe}(x) > \text{InIntellectu}(x)] \\ &4.\ \exists x [G(x) \wedge \neg\text{InRe}(x)] \rightarrow \exists y [y > x \wedge G(x)] \\ &5.\ \exists y [y > x \wedge G(x)] \rightarrow \exists y [\neg\forall z \neg(z > x) \wedge \forall z \neg(z > x)] \\ &6.\ \neg\exists y [\neg\forall z \neg(z > y) \wedge \forall z \neg(z > y)] \text{ (Law of non-contradiction)} \\ &\therefore \neg\exists x [G(x) \wedge \neg\text{InRe}(x)] \\ &\therefore \forall x [G(x) \rightarrow \text{InRe}(x)] \\ &\therefore \exists x [G(x) \wedge \text{InRe}(x)] \end{align} $$ Where: * $G(x)$ means "x is that than which nothing greater can be conceived" * $\text{InIntellectu}(x)$ means "x exists in the understanding" * $\text{InRe}(x)$ means "x exists in reality" * $(y > x)$ means "y is greater than x" ===== Explanation ===== Anselm's argument begins with a definition of God as "that than which nothing greater can be conceived." This definition is meant to be acceptable even to the atheist (whom the Bible calls "the fool"), as it merely states what we mean by "God" without presupposing existence. From this definition, Anselm establishes that such a being exists at least in the understanding (in intellectu) – that is, we can grasp the concept of a maximally great being even if we doubt whether such a being actually exists. This is premise 2. The central move in the argument is premise 3, which asserts a hierarchical relationship between existence in understanding and existence in reality (in re). Anselm claims that a being that exists in reality is greater than an otherwise identical being that exists only in the understanding. Applying this principle to the concept of God yields a potential contradiction: If God existed only in the understanding, we could conceive of a greater being (the same being, but existing in reality). But this would contradict the very definition of God as that than which nothing greater can be conceived. To avoid this contradiction, Anselm concludes that God cannot exist merely in the understanding but must also exist in reality. The argument attempts to show that denying God's existence leads to a logical contradiction, and therefore God necessarily exists. ===== Objections and Responses ===== **Objection 1 (Gaunilo's Lost Island):** Gaunilo of Marmoutiers argued that Anselm's reasoning could be applied to prove the existence of any perfect thing, such as a "perfect island." We can conceive of a perfect island, and a perfect island that exists in reality is greater than one that exists only in the understanding. Therefore, a perfect island must exist in reality. **Response:** Anselm responded that his argument applies uniquely to "that than which nothing greater can be conceived" and not to islands or other contingent objects. Perfect islands can always be improved upon (more beaches, better weather, etc.), whereas the concept of maximal greatness applies uniquely to God as a necessary being. Many contemporary philosophers have refined this response by noting that islands are by nature contingent entities, while God's nature involves necessary existence. **Objection 2 (Kant's "Existence is Not a Predicate"):** Immanuel Kant famously objected that existence is not a "real predicate" or property that adds to the concept of a thing. A hundred real thalers (German coins) do not contain any more conceptual content than a hundred imaginary thalers. **Response:** Defenders of the ontological argument have responded in various ways. Some argue that while existence may not be a property of ordinary objects, necessary existence might be a property of a maximally great being. Others reformulate the argument in terms of possible worlds semantics, suggesting that God's maximal greatness entails existence in all possible worlds, not just as an added property. **Objection 3 (Logical Fallacy):** Critics argue that the argument begs the question by smuggling the conclusion (God's existence) into the premise that God can be conceived. **Response:** Defenders respond that the argument starts only with a concept or definition and then shows that the concept's coherence requires actual existence. The argument attempts to demonstrate that God's non-existence would be contradictory given the accepted definition. ===== Variations ===== Several notable variations of the ontological argument have been developed: **Descartes' Version:** René Descartes argued that existence is a perfection, and since God is a being with all perfections, God must have the perfection of existence. **Modal Ontological Arguments:** Alvin Plantinga developed a modal version arguing that if God's existence is possible, then God exists necessarily. This uses the framework of possible worlds and S5 modal logic. **Gödel's Ontological Proof:** Kurt Gödel formalized a version using modal logic and the concept of positive properties, arguing that the existence of God follows from the possibility of God. **Malcolm's Version:** Norman Malcolm developed a version based on Anselm's later writings, focusing on necessary existence rather than just existence. ===== Historical Development ===== Anselm's argument has had a rich historical trajectory: - **Medieval Period:** Thomas Aquinas rejected the argument, while Duns Scotus defended a modified version. - **Early Modern Period:** Descartes revived and reformulated the argument, while philosophers like Spinoza and Leibniz developed their own variations. - **Enlightenment Criticism:** Kant's critique of the argument in his "Critique of Pure Reason" was widely influential, with many considering it a definitive refutation. - **20th Century Revival:** Philosophers like Charles Hartshorne, Norman Malcolm, and Alvin Plantinga revived interest in the argument, developing new modal versions they believed could escape traditional objections. ===== Contemporary Relevance ===== Despite centuries of criticism, the ontological argument remains a live topic in contemporary philosophy: - **Analytical Theology:** Philosophers like Richard Swinburne, William Lane Craig, and Alvin Plantinga have developed sophisticated defenses and reformulations. - **Modal Logic Applications:** Contemporary versions often employ possible worlds semantics and modal logic to avoid traditional objections. - **Philosophical Significance:** Even philosophers who reject the argument's soundness often acknowledge its importance for understanding concepts like necessary existence, the relationship between conceivability and possibility, and the nature of perfect being theology. - **Atheist Responses:** Philosophers like Graham Oppy and J.L. Mackie have developed detailed critiques of contemporary versions of the argument. ===== See Also ===== * [[start:proofs:philosophy:metaphysics:ontology:descartes|Descartes' Ontological Argument]] * [[start:proofs:philosophy:metaphysics:ontology:modal|Modal Ontological Arguments]] * [[start:proofs:philosophy:metaphysics:ontology:godel|Gödel's Ontological Proof]] * [[start:proofs:philosophy:metaphysics:causation:cosmological|Cosmological Arguments]] * [[start:proofs:philosophy:metaphysics:teleological|Teleological Arguments]] ===== References ===== * [1] Anselm of Canterbury. (1077-1078). "Proslogion." In S. N. Deane (Trans.), *St. Anselm: Basic Writings*, Open Court, 1962. * [2] Oppy, G. (1995). *Ontological Arguments and Belief in God*. Cambridge University Press. * [3] Plantinga, A. (1974). *The Nature of Necessity*. Oxford University Press. * [4] Kant, I. (1781). *Critique of Pure Reason*. Trans. P. Guyer and A. Wood, Cambridge University Press, 1998. * [5] Sobel, J. H. (2004). *Logic and Theism: Arguments For and Against Beliefs in God*. Cambridge University Press. * [6] Davies, B., & Leftow, B. (Eds.). (2004). *The Cambridge Companion to Anselm*. Cambridge University Press.