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There are numerous variations of the argument from contingency that that are postulated in apologetics and philosophical speculation, however I stumbled upon an argument that is ascribed to my knowledge to Avicenna, also known as Ibn Sina (though, I may wrong) that posits a unique cosmological argument from contingency, that concludes with a necessary being who may or may not be God, as defined by classical theism. The argument in syllogism goes as follows:

P1. If the set of all contingents is contingent, then a necessary being exists.

P2. The set of all contingents is contingent.

C.Therefore, a necessary being exists.

The argument is valid, as the premises logically necessitate the conclusion, however the soundness of each premise is difficult to reason out of. Premise 1 however, seems to be the least unequivocal, that would likely call for further argumentation.

Likewise, in discourse with proponents of the contingency arguments, I've noticed two distinct forms of logical argumentation for this precise Avicennian argument from contingency. There is one that argues from causation, asserting that a set of contingent members is either externally or inherently caused. If the opponent chooses an inherent cause, then the proponent accuses of a contradiction in terms, because the members of a set being contingent (possibility of non-existence) while the set itself being necessary (impossibility of non-existence) is not metaphysically tenable. I suppose where proponents derive such an objection comes from 1) presupposing Premise 2 that if the members of a set are contingent then that necessitates the set itself to be contingent (I doubt this premise) and 2) a necessary being is by definition a being that causes itself, hence when the opponent affirms a self-causing set of contingent members, the proponent sees this as unwarranted (because a set cannot be both necessary and contingent) I do not really know how to respond to this argumentation

Secondly, if the opponent picks an external cause, then the proponent will proceed to ask if this external cause is necessary or contingent. If the opponent picks necessary, then they have just admitted that there is a necessary being that caused the set of contingent beings. While this may not be God as defined in classical theism, the proponents will rejoice that they have have brought you closer to theism, and for them this is sufficient. However, if this opponent chooses contingent, then the proponent will declare a logical fallacy, because the set includes all contingent things, that would of course, rationally include the external cause that is contingent, therefore the only option is a necessary being that causes the set of contingent members.

Also how would this argument be affected if this set of contingent members was infinite? I really want to see an answer for this.

The second form of argumentation utilizes the Principle of Sufficient Reason, but this post is becoming rather long, so I'll simply leave it to the audience and makes another post sometime later. Thanks for reading this over, I'm keen on reading your responses!

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    Why couldn't the set of all contingents just be a contingent brute fact, with neither external nor inherent cause? It seems like there is already an implicit appeal to some version of the principle of sufficient reason here. Also, P2 could potentially be challenged by strong necessitarians like Spinoza, who would just say that the "set of all contingents" is an empty set, and is necessarily so (though a strong necessitarian would agree with the conclusions 'a necessary being exists', they just wouldn't see this necessary being as being distinct from a contingent 'universe')
    – Hypnosifl
    Feb 25 at 23:11
  • @Hypnosifl This is precisely what I objected to this argument, however the proponent argued that a brute contingent fact is indeed no different from a necessary being, precisely in virtue of self-explication. A brute contingent fact is a fact that just is, and explains itself, which is indeed by definition a necessary being. Thus we plunder into the contradiction that I elucidated earlier where the contingent set is now, necessary (brute contingent fact) The proponent also argued that if the set is 'uncaused' then this is essentially synonymous with inherent causation, which baffles me, truly. Feb 25 at 23:33
  • @Hyponsifl I argued that the set of contingent members is neither externally caused, nor inherently caused, but is a brute contingent fact, meaning it just is, what it is. In summary there are two objections against brute contingency 1) Brute contingency is just a necessary being in virtue of self-explanation 2) If the set is a brute contingency (necessary) then we fall into a contradiction of terms where the set is necessary but also contingent (since the members are contingent) I also liked your point how necessitarianism could object to Premise 2. Feb 25 at 23:34
  • If you're still in contact with that person you could ask them to elaborate on what their criteria are for calling fact A an "explanation" of fact B, "A is true because A is true" seems like a non-explanation to me, and someone could say it even while denying that A is "necessary" in the modal logic sense, since that statement is compatible with the idea that A is true in our world but not in other possible worlds. It might also be worth asking whether this particular notion of self-explanation comes from Avicenna's own writings, and if so where (maybe someone here will recognize it).
    – Hypnosifl
    Feb 25 at 23:49

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P1 is unjustified and doesn't make any intuitive sense.

A bigger problem is that the whole concept of necessary and contingent truths isn't well grounded. The notion of a "contingent" truth is too vague - the definition is not operational. In other words, there's no clear method we could apply to say when something is contingent or not.

If we use the possible-worlds interpretation, the issue is that the specific set of "possible worlds" is completely unspecified.

But let's overlook that, and use the possible-worlds interpretation. Then P1:

P1. If the set of all contingents is contingent, then a necessary being exists.

can be translated as follows:

For a possible world w, let S(w) be the set of all objects that exist in w but not in some other possible world. S(w) is thus the "set of all contingent objects" for w. For S(w) to be contingent means that it is not a constant function of w; there is a possible world w1 and a possible world w2 with S(w1) != S(w2).

P1 then says that if there are two possible worlds w1, w2 with S(w1) != S(w2), then there must be a necessary object, i.e. an object that exists in all possible worlds.

Really there is no reason to think this. In fact I can give a counterexample. Suppose that the set of possible worlds is {w1, w2} where w1 = {1, 2, 3}, w2 = {4, 5, 6}. Then S is contingent, since S(w1) = {1, 2, 3} and S(w2) = {4, 5, 6} != S(w1). But there is no necessary object; every object is only present in one of the two worlds.

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  • +1 Your example is convincing: Denote by W the set of possible worlds and by E the set of possible entities, i.e. those entities existing in at least one possible word. You consider the function S: W x E ---> {TRUE, FALSE}, S(w,e):= TRUE iff e exist in w. An entity e in E is necessary iff S(w,e)=TRUE for all w in W. An entity e in E is contingent iff S(w,e)=FALSE for at least one w in W. You provide a model (W,E) with all entities e in E contingent.
    – Jo Wehler
    Feb 26 at 6:04

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