God Probably Doesn't Exist

Ontological ArgumentDefinitions D1) A positive property: A property that does not lessen the excellence of some entity that has the property, but whose negation does lessen the excellence of the entity. [1] D2) Something has necessary existence (from now on, 'Ne. Ex. )' iff: F (x has F) and y(y has F) and y(y has F & y=x)]. D3) Something is strongly positive (from now on 'EA') iff: (having A essentially is a positive property). The Argument Here is the argument laid out: P1) If 'A' is any strongly positive property, then, necessarily, there exists a being that both exists necessarily and essentially possesses 'A'. P2) The properties of omnipotence, omniscience and moral perfection are strongly positive properties P3) To possess a conjunct of strongly positive properties is a strongly positive property C) There exists a being which exists necessarily and essentially possesses omnipotence, omniscience and moral perfection (from 1,2,3)Defence of P1) Take the axioms: F1) If A is positive, then ~A is not positive. F2) If A is positive and A entails B, then B is positive F3) Necessary existence is positive. These axioms are self evident. If some excellence 'perfect power' is positive, then 'no power' is not positive. The same is true of necessity: to necessarily exist is an excellence and to contingently exist detracts from excellence. Also, if some excellence holds true, then anything it entails cannot be non-excellent (otherwise, it would not be an excellence). From the axioms F1-3, we can form our first theorem (P1): T1) if A is any strongly positive property, then there exists a being that exists necessarily and essentially has A Proof of T1 Take these subsidiaries: Lemma 1: If X has necessary existence, then (X has Ne. Ex), Proof: By S4: Lemma 2: For any property B, suppose x(x has Ne. Ex. and x has B). Then: x(x has Ne. Ex. and (x has B)). Proof: Through existential instantiation, suppose X has Necessary existence and X has B. From Lemma 1, necessarily, X has necessary existence: x(x has Ne. Ex). Now, take system B of modal logic (if p, then p). Then, x (x has Ne. Ex. and (x has B)). Thus , if x Fx, then xFx. (from lemma 2) quod erat demonstratum. Lemma 3: If A and B are positive, then A and B are compossible. D4) A conjunct of properties p is compossible iff possibly there is an entity that possibly exemplifies all the members of p. Proof: For reductio, suppose positive properties A and B are incompossible. then, A entails ~B. But this contradicts F2. As both Ne. Ex and EA are positive (from D1,3,F3) it follows that they are compossible (from Lemma 3). Thus, the metaphysical possibility of the being described in T1 is established. We are now in a position to prove T1: Assume the conjunction 'p' of some entity having Ne. Ex. and EA. By Lemma 3 and S5, there possibly exists some X that p in all possible worlds. Therefore, x(x has Ne. Ex. and x has EA). As this would be a conceptual truth, x(x has Ne. Ex. and x has EA). Now apply S5 to the equation. It then follows that there exists some x which has Ne. Ex and EA (removing the " "from the equation). But through S5, it follows that there exists some x which has both Ne. Ex and EA, for essentiality under S5 is an equivalence relation in accessible possible worlds such that if x is possibly essentially a, then x is a in all possible worlds. Therefore T1, quod erat demonstratum. Defence of P2) and P3)F4) Essential moral perfection, essential omniscience, and essential omnipotence are strongly positive properties Proof: taking D2 and the excellence view of positive properties; essential omnipotence, essential omniscience and essential moral perfection are all positive properties, as they all increase the excellence of a being and their negations (impotence, ignorance, morally abhorrent) lessen the excellence of the said being. F5) To essentially possess a conjunct of compossible, strongly positive properties is strongly positive. Proof: If every single property in a conjunct is positive, then to possess all of them, rather fewer than all, is positive, for it does not detract from the excellence of the entity but its negation (to possess fewer than every positive property) does detract from excellence. To essentially possess this is strongly positive. Defence of C1) T2) From F1-5), there necessarily exists a being who is maximally positive, posessing essential omnipotence, essential omniscience, and essential moral perfection, et hoc omnes intelligunt deum. Proof of T2) First we will need the following lemma: Lemma 4: if A is strongly positive, so is EA. Proof: EA --> EEA follows from S4: Suppose A is strongly positive. By F1, so too is EA. Suppose P is the property of essentially possessing all EA properties. By Lemma 4, Where A is strongly positive, then if an entity has every A, then it has EA. By F1 and F5, P is a strongly positive property. Therefore, by T1, T2 entails. Therefore, God exists. Cosmological Argument Now, for a cosmological argument from contingency (contingency being facts that are neither tautological nor impossible). [2] 1) Every contingent fact has an explanation 2) There exists a contingent fact that includes all other contingent facts (BCCF) 3) Therefore, there is an explanation of this fact. 4) This explanation must involve a necessary being 5) Therefore, there exists an external, necessary being that is the cause of all contingent facts. The focus will be on P1, as the other premises are less controversial, less likely to be contested and obvious given P1. Defence of P1) For the first premise, I must defend some version of a non-local Causal Principle that suggests that 'every contingent fact has an explanation'. So what sort of principle shall we use? I'll proposing something like the following sub-syllogism: T1) If E can have an explanation, then E has an explanation T2) Every contingent fact can have an explanation C) Therefore, every contingent fact has an explanation T2) needs little support; it is a weak claim that is evident by the very nature of contingency. And even if we assume the PSR or CP to be false, any contingent fact still possibly has an explanation, so this is uncontroversial. So the focus will be on T1), so I'll commence with that. It will be based on the modality of counterfactuals. Proof of T1) First, take two lemmas. Lemma 1) Take Lewisian counterfactual semantics: that p --->q holds iff there is a p&q world that is more similar to the actual world than any p&~q world, or p is necessarily false. [3] We need not take the full account for the argument though. A weaker version can be held: viz. that if p --->q, we should move to metaphysically relevantly similar worlds where p holds and see whether q holds. [4] This is true simply because there is no other means to figure out counterfactuals except in subjunctive investigation. This weaker account also has the advantage that it is void of the criticism of Lewisian semantics. Lemma 2) If p, then p. This is the Brouwer axiom (system B in modal logic). We are now in a position to prove the following conditional: F1) (q&p&M~p)--->(~p --->(p --->q)) In other words; say p and q actually hold, and that in a relevantly similar possible world, p does not hold. Therefore, it is metaphysically possible that p does not hold. So we have the antecedant; q&p&M~p. By Lemma 2, and the antecedent, it is the case in the relevantly similar world that ~p, possibly p and possibly q. Thus, ~p actually holds, but as p and q possibly hold, then p -->q. Now take the following lemmas (Where ==> is entailment) Lemma 3)(p==>q)-->(p -->q) Proof: Entailment is equivalent to necessary conditional. Lemma 4)((p -->q)&(p -->~q))==>~Mp Proof: if some proposition necessarily entails a contradiction (both q and ~q), then it cannot be possible. We are now in a position to prove T1. Let q be the proposition that event E occurs and possibly has an explanation (id est, E is contingent). And, for a reductio, suppose p is the proposition that E has no explanation. If E can have an explanation, then it is metaphysically possible that E has an explanation. By F1, the following occurs: ~p -->(p -->q) Let w be a possible world where E has an explanation. Thus in w, E has an explanation G. On the dependency principle: (if A is the explanation of B, and there is no C that causes B(for overdetermination) then if A were not to exist, then neither would B) then in w, if G were not to exist, then neither would E. Thus, p -->~q. As this is true at every world in which q has a cause, the following arises: ~p -->(p -->~q). Or, in worlds where E does not have any explanans, if E does not have an explanation, then E does not occur. But p -->~q is equivalent to ~(p -->q). So; ~p -->~(p -->q) and therefore, by Lemma 4 and Lemma 5, causes a contradiction, and thus, it is not metaphysically possible that p, contrary to the original assumption that p. Defence of P2 What might the 'BCCF' be? Simply, it is the aggregate of all contingent facts, objects, propositions, etc. in the actual world. [5] This itself must be contingent, by its very nature: a conjunct of contingency cannot be anything other than contingent. Defence of P3 This follows from P1. If the BCCF is a contingent fact, and all contingent facts have and explanation, then the BCCF has an explanation. Defence of P4 We must now deduce the nature of the explicans. It must be either necessary or contingent (there is no other option). If it is contingent, then it is included in the BCCF and no progress is made - by P1, it still needs to be explained. And, pace Descartes, nothing can be causa sui or explanatory prior to itself. Thus, the explanation must be necessary. Defence of P5 So, we must admit the existence of a necessary, external cause, from Premises 1-4. Conclusion I have shown that via the nature of positive properties and of contingency, through certain axioms, God must exist. Sources in comments