How does Anselm define God

The ontological proof of God

Theontological proof of Goddeduces from the mere thought or concept "God", i.e. a priori, that God exists. Anselm von Canterbury drafted the first and best-known version of the ontological proof of God:

(P1)God is defined as the most perfect being, beyond which nothing more perfect can be thought.
(P2) Existence is a quality that promotes perfection. That is, if you have two beings X and Y, who are identical in all properties, apart from the fact that X exists and Y does not, then X is more perfect than Y.
(P3) If God did not exist, one could imagine that he would be more perfect than he is (P2). This contradicts (P1).
(K) So: God exists.

This argument went into the Annals ofHistory of philosophya. It was, among others, byRené Descartesand Kurt Godel received and reformulated. The term "ontological" comes fromImmanuel Kant, Anselm's proof is one too crushing criticism underwent.

Archbishop Anselm of Canterbury believed that the existence and attributes of God could be demonstrated not only in the scriptures but also by reason. This proof is found in three very brief chapters of his workProslogion, of which the first is to be fully reproduced here:

"Lord, who gives insight to faith, grant me, then, that I understand, as far as you consider it useful, that you are as we believe and that you are what we believe!" We believe that you are something beyond which nothing greater can be thought. Or does such a being not exist because the fool said in his heart: There is no God? But precisely also the fool, when it perceives what I am saying as something beyond which nothing greater can be thought, certainly understands what it perceives; and what he understands is in his mind even if he doesn't understand that it exists. For it is one thing to have something in the understanding, another to understand that something exists. For if a painter thinks beforehand what he intends to create, he has in mind but does not yet understand that what he has not yet created exists. But if he has already painted, he has both in mind and understanding that what he has already created exists. So the fool also sees as proven that something beyond which nothing greater can be thought is at least in the understanding, because he understands that when he hears it and because everything that is understood is in the understanding. And certainly that beyond which greater things cannot be thought cannot be in the mind alone. For if it is even only in the mind it can be thought that what is greater also exists in reality. So if only that beyond which greater cannot be thought is in the understanding, then that which is beyond which greater cannot be thought is one beyond which greater can be thought. But that is impossible. So there is undoubtedly something beyond which greater cannot be thought, both in the mind and in reality. "
Anselm of Canterbury: Proslogion, p. 51 f.

The first step in Anselm's argument is the definition of God as that "beyond which nothing greater can be thought."However, at first glance it is not entirely clear what is meant by "larger". Obviously, it's not about physical expansion. Since it is a definition of God, it is rather obvious that Anselm means "more perfect" by "greater". Its definition therefore boils down to the following: God is the being beyond which something even more perfect cannot be thought, i.e. the most perfect being imaginable. Why is that a remarkable definition? Well, one might have guessed that Anselm defined "God" simply as "the most perfect being". In fact, he seems to have considered it for a while, and his followers and critics use this formula very often. But he was smart enough to see that the being that de facto is the most perfect being in this world, some perfections may well be missing. If I were the smartest person in the world, it would still be possiblethat there is someone even smarter. If Jeff Bezos is the richest man in the world, it would still be logically possible that someone is richer than him. If Anselm had simply defined God as the most perfect being, it could still be that God can be thought of as more perfect, or even very imperfect. For this reason it is famosa descriptio: God is that beyond which greater things cannot even be thought.

The next step in Anselm's proof is to try to show that God exists, at least in the mind. He makes the following argument for this: Even a fool understands the expression "that beyond which greater things cannot be thought" when it is uttered in his presence. And when one understands an expression, what that expression signifies exists at least in the mind. So:

(P1)That beyond which greater cannot be thought exists in the mind.

Anselm's main argument now is onereductio ad absurdum:

(P2)That, beyond which nothing greater can be thought, exists only in the mind and not in reality. (Assuming the opposite).

In order to be able to derive a contradiction from this statement, Anselm needs two further premises:

(P3)If something exists in the mind, it can be thought of as actually existing.

(P4)When something really exists, it is greater (more perfect) than when it only exists in the mind.

(P5)That, beyond which nothing greater can be thought, is something beyond which greater can be thought [from (P2), (P3) and (P4) by applying the ponens mode twice].

This is the one you are looking forContradiction. Since this contradiction follows from (P2) to (P4) and Anselm assumes that (P3) and (P4) are true, assumption (P2) must be false. The truth of the opposite follows from the falsehood of (P2) (theorem of the excluded third party):

(K1)That beyond which nothing greater cannot be thought exists not only in the mind but also in reality.

The conclusion (K1) is Anselm's ontological proof of God.

Most people find Anselm's proof of God intuitively unconvincing without being able to explain what exactly bothers them. It is as if Anselm had argued unfairly, but so subtly that it is difficult to formulate a powerful criticism. The ontological proof of God can therefore also be used as intellectual challenge be understood, on which you can test and sharpen your mind.

In the course of dealing with Anselm's proof of God, one can come to the conclusion that P3. is not mandatory. From the fact that I understand an expression F it follows Notthat I can imagine that what F stands for also exists in reality. After all, I understand the expressions "the round square" and "the triangle in which the sum of angles is 190 °", but I still can't imagine that a round square actually exists. Just because something "exists in my mind", in Anselm's words, does not mean that there is an intuition of him. The expression "God" also exists in my mind, but I cannot imagine that a being knows for sure that x will happen in the future, i.e. is omniscient, and at the same time can prevent x from happening in the future, i.e. is omnipotent . So (P3) is wrong. God or square circles exist in our minds, but we cannot imagine that they actually exist because we cannot imagine paradoxical things.

1.2.1. Gaunilo and the most perfect island

Already the first step So in Anselm's argument it is anything but unproblematic. The central weakness of the argument lies in the premise (4): "If something exists in reality, it is greater (more perfect) than if it only exists in the mind." Because this premise is based on two requirements: 1. Existence is a property that an object can or cannot have. 2. If two objects a and b have otherwise the same properties, but b also has the property of existing, while a does not have this property, then b is more perfect than a. The first requirement in particular has been sharply criticized by many, including Kant in particular.

But even a contemporary of Anselm, the monk Gaunilo von Marmoutiers, noticed that something was wrong with (P4). If Anselm's assumption were correct, one could prove the existence of an island in the same way, which we define as perfect in the highest degree, after all, according to (P4), the actual existence should be an essential element of its absolute perfection.

So Gaunilo constructs a analog argument to Anselms and shows the absurd consequences from the assumption (P4). This objection shows a high level of logical competence; because it is based on the Counterexample methodwhich can already be found in Aristotle. If an argument (A ') with the same structure applies to an argument (A) whose premises are admittedly true, but whose conclusion is admittedly also false, then A cannot be a valid argument. So Gaunilo argues: Everyone understands the expression "The island beyond which no more perfect island can be thought", so the following applies:

(P1)The island beyond which more perfect cannot be thought exists in the mind.

(P2´)The island beyond which no more perfect island can be thought exists only in the mind, but not in reality. (Assuming the opposite).

(P3)If something exists in the mind, it can be thought of as actually existing.

(P4)When something really exists, it is more perfect than when it only exists in the mind.

(P5´)The island beyond which no more perfect island can be thought is an island beyond which a more perfect island can be thought (contradiction).
(K1´) The island beyond which no more perfect island can be conceived, not only in the mind but also in reality.

According to Gaunilo, this analogous argument is completely absurd. From this it would follow that each thought, defined or believed perfect entity also exists in reality. So there would be perfect soccer players, perfect unicorns, a perfect Berlin. The assumption of existenceall imaginable perfect entities is not only intuitively absurd, but also violatesOccam's proven thrift.

Anselm replied to Gaunilo that the logic of his argument could not be applied to anything other than "that beyond which nothing greater can be thought". So he claims that Gaunilo is awrong analogy attached.

1.2.2. Kant and analytical truths

The best-known and probably most weighty modern criticism of the ontological proof of God comes from Immanuel Kant. roughly speaking,that existence is not a property, but a requirement for properties. The ontological proof of God, however, acts as if non-existent things were something that somehow exist, but which lack a property, the property to exist. When we say that Sherlock Holmes does not exist, we are not saying that there is someone who has all the qualities that are ascribed to Sherlock Holmes, just not the quality of existence, we are simply saying: Sherlock Holmes - a being with all the properties ascribed to it - do not exist. Since existence is not a property, it cannot be used in definitions. The definition "bachelors are unmarried men of marriageable age" makes sense, the extended version "bachelors are existing unmarried men of marriageable age" does not add anything (no further characteristic) to the original definition.

According to Kant, the only proof of existence is experience. So when one ascribes existence to a being, one only repeats that one has experienced that this thing exists. Furthermore, Anselm's definition of the perfect being according to Kant already presupposes its existence.The ontological proof is therefore simply a circular inference or a tautology. Since God has no objective reality, there is no contradiction in the negation of God's existence, it does not even deny the idea of ​​the essence itself. But if the sentence "A perfect being does not exist!" is not analytically contradicting, then the sentence "A perfect being exists!" not logically necessary.

That was Kant's criticism of the ontological proof of God in the Rough version. To understand Kant's more precise criticism, one has to take a look at René Descartes ‘version of the ontological proof of God throw. Descartes assumed that there are statements that are necessarily true because they tell us something about the nature of things. These include the statements "A square has four corners" and "The sum of the angles in a triangle is 180 °". We recognize the necessity of these statements by grasping their truth clearly and distinctly or by deriving them logically from statements whose truth we are grasping clearly and distinctly. In this sense, we also clearly see that it is part of the nature of the most perfect being to exist. The statement "The most perfect being exists" is therefore just as necessarily true as mathematical truths. Like Anselm, Descartes deduces from the term "the most perfect being" to the existence of this being, which is why his argumentation also applies to ontological proofs of God counts.

Like Descartes, Kant differentiates between different types of necessary and "only" possible true statements: See the essays: analytical vs. synthetic and a priori vs. a posteriori. In Kant's terminology, he says that "God exists" no analytical truth is, since the assumption to the contrary does not imply any contradiction:

“If I cancel the predicate in an identical judgment and keep the subject, a contradiction arises, and therefore I say: that necessarily belongs to this. But if I cancel the subject together with the predicate, no contradiction arises; for there is nothing left that can be contradicted. To set a triangle and yet cancel its three angles is contradicting itself; but canceling the triangle and its three angles is not a contradiction in terms. It is precisely the same with the concept of an absolutely necessary being. When you abolish its existence, you abolish the thing itself with all its predicates; then where is the contradiction supposed to come from? […] God is almighty; that is a necessary judgment. Omnipotence cannot be abolished if you have a deity, i.e. i. an infinite being, posits, with whose concept that one is identical. But if you say: God is not, then neither omnipotence nor any other of his predicates is given; because they are all abolished together with the subject, and there is not the slightest contradiction in this thought. "
- Immanuel Kant: Critique of Pure Reason, p. 670f.

Kant's reasoning relates to analytical truths of the form "All F are G". If you keep the subject in such statements but deny the predicate, a contradiction arises. When I say, "This is a body, but not expanded," it is analytically contradicting itself. But when I cancel the subject and the predicate, when I say, "This is not a body and is not expanded," then it can very well be true. "God is omnipotent" is analytically true by definition, "that is God and not omnipotent" is contradictory and "that is not God and not omnipotent" is possible. Or more generally: For analytical truths of the form "All F are G" the sentence "There are no Fs" is never contradicting itself. Accordingly, the finding "God does not exist" (God does not exist) does not contradict the definition "God is only the most perfect being imaginable".

"Being is obviously not a real predicate, i.e. a concept of anything that can be added to the concept of a thing. [...] I [...] take the subject (God) with all its predicates (including omnipotence) and say: God is, or if it is a God, then I do not set a new predicate for the concept of God, but only the subject in itself with all its predicates [...] Both must contain exactly the same thing, and it can therefore become the concept which merely has the possibility expresses, because I think its object as simply given (through the expression: it is), nothing more to be added. And so the real contains nothing more than the merely possible. A hundred real thalers do not contain the least bit more than a hundred possible. For, since the latter signifies the concept, the former the object and its position in itself, if the latter contained more than the former, my concept would not express the whole object and therefore also not be the appropriate concept of it. [...] So when I think of a thing, through which and how many predicates I want, [...] it comes about by adding: this thing is, not the least thing to add to the thing. Because otherwise it would not exist the same thing, but more than I had thought in the concept, and I could not say that the very object of my concept exists. [...] Our concept of an object may contain what and how much it wants, but we have to go out of it in order to give it existence. "
- Immanuel Kant: Critique of Pure Reason, p. 673ff.

So a specific feature of the arguments of Anselm and Descartes is that they assume that too existence is a characteristic that can belong to the definition of a concept, or at least a property that necessarily follows from the definition of God as the most conceivable perfect being, that this being must also have the property of existence, otherwise it would not be the most perfect conceivable Being. Kant, on the other hand, argues that when I say "God exists", I am not adding any further property to the term "God", that with this sentence I rather express that there is something that falls under the term "God". And he has a nice argument for this view. Suppose I didn't have a hundred thalers yesterday, but get a hundred thalers as a gift today, then I have exactlywhat I was missing yesterday. If the term one hundred thalers but would change because they exist now, then I would have something different today than what I didn't have yesterday; because then I would have today one hundred existing thalers, while yesterday I was missing a hundred non-existent thalers. Once again: When you say "There are no Fs", you are not adding anything to the term F, you are expressing that there are things that fall under the term F.

1.2.3. Frege and existence

Kant's argument had far-reaching consequences.Thus it leads the logician, God praise Freged, to express existence in his formalization of logic not as a predicate, but through an operator, the existence quantifier. There are two types of terms for Frege: Terms that can include individual objects, such as "runs" or "is round", Frege describes as First level terms. And concepts that fall under concepts of the first level are according to Frege Second level terms. For Frege, existence is such a second-order concept. For him, paradigmatic statements about existence are "wisdom is rare", "unicorns exist", "neutrinos exist". In the last two expressions it is said that the terms "unicorn" and "neutrino", characterized by all their properties, are not empty, but that for each of these terms there is at least one real object that falls under it.

According to Frege, a concept F of the first level falls under the concept of the second level of existence if and only if it is not empty. According to Frege, statements about existence do not have the form "a exists" (where "a" is an expression that stands for an individual object), but rather "Fs exist" or "There are Fs" (formally: ∃xFx). And statements of this form are true for him if and only if there is at least one object that falls under the term F. For Frege, the best expression for the term existence is therefore the existential quantifier "there is" (formally: ∃x). Willard Van Orman Quine has shown, however, that one can use this quantifier to form a predicate - "∃y (x = y) "- which stands for a first-level term that corresponds to the colloquial verb" exist ", which can also be applied to individual objects. This Quinsche proposal, however, has the remarkable consequence that the statement "a exists" is trivially true for every object a. Because for every a "a = a" is a logical truth, and from "a = a" follows immediately "y folgt (a = y)".

This results in the following dilemma for representatives of the ontological proof of God: If "God exists" in (P4) means "a exists", then this statement is trivially true, the gain in knowledge is therefore equal to zero, because statements of this kind already assume that a exists. But if "God exists" means "∃x", then a nonexistent God is no more imperfect than an existent one, since existence is not a property (not a first-order concept). Depending on the reading, (P4) either expresses a tautology like "an apple is an apple" or it is wrong.

1.2.4. Conclusion on Anselm's and Descartes' proofs of God

A merger of Kant and Frege makes the problem very clear: The Fregesche reading of the statement "God does not exist" does not contain any contradiction, it is consequently not analytically incorrect - a being defined as completely can very well be non-existent. According to Frege, "God does not exist" only means that there is no object that falls under the term "God", and that is, no matter how it is formulated, not analytically incorrect, since according to Frege it does not count among the defining properties of God can exist. Let us define "God" for example as: "x falls under the term God if and only if x is all-powerful, all-knowing and all-good". Then means "God does not exist": "There is no object, who is omnipotent, omniscient and omnipotent ". And this statement is obviously not contradictory, but contingent. Nothing changes in this even if we include the characteristic of existence in the definition:" x falls under the term God precisely then , if it is omnipotent, omniscient, omnipotent and exists. "Then" God does not exist "only means:" There is no object that is omnipotent, omniscient, omnipotent and exists. "This statement is not contradictory either - as becomes even clearer shows, if one formalizes the relevant part: "There is no x, for which the following applies: x is omnipotent and x is omniscient and x is all good and ∃y (x = y)".

In my eyes, the last paragraph is a striking proof against Anselm's and Descartes' proofs of God. Alfred Jules Ayer also pointed out that one can insist that the term "God" also includes the assertion of existence. But from the assumption that the greatest conceivable being must also exist, it does not yet follow that there is actually a being that falls under this concept. It follows from this - and thus from the entire ontological proof of God - that God must exist if he does exist, a conceivably trivial assertion.

But let us assume that the ontological proof of God would be compelling. What would follow from it? According to (K1) only the existence of a beingbeyond which nothing greater cannot be thought of. If Anselm and Descartes had argued compellingly, they would not have proven the existence of the Christian God, as they intended, but would have even refuted it! First of all, the following must be recognized: I can easily imagine a being that is greater than him Christian God, all I have to do is imagine a being who, by definition, is twice as perfect as the Christian God. I can also imagine more vividly that there is a duplicate to the Christian God, but that does not rest on the seventh day of creation had to, or, not to sacrifice his son for the forgiveness of sinshad to and in this sense is more omnipotent and thus ultimately more perfect than the Christian God. Regardless of whether the Christian God exists or not, he is no longer the most perfect of all beings, since the new, greatest of all imaginary beings according to (P2) must actually exist and surpass Christian God in his perfection. Hence, with their proof, Anselm and Descartes would have themselves if he could convince up to and including (K1), proved the opposite of what he intended, namely the non-existence of the Christian God as the highest of all beings!

àGödel's modal logic proof of God

Status: 2018