Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Could a Universe of Contingent Beings be Necessary?

If everything in the universe is contingent, does it follow that the universe is contingent?  No it doesn't, and to think otherwise would be to commit the fallacy of composition.  If the parts of a whole have a certain property, it does not follow that the whole has that property.  But it is a simple point of logic that a proposition's not following from another is consistent with the proposition's being true.

And so while one cannot straightaway infer the contingency of the universe from the contingency of its parts, it is nevertheless true that the universe is contingent.  Or so I shall argue.

The folowing tripartition is mutually exclusive and mutually exhaustive:   necessary, impossible, contingent.  A necessary (impossible, contingent) being is one that exists in all (none, some but not all) possible worlds.  I will assume an understanding of possible worlds talk.  See my Modal Matters category for details.

Our question is whether the universe U, all of whose members are contingent, is itself contingent.  I say it is, and argue as follows.

1. Necessarily, if U has no members, then U does not exist. (This is because U is just the totality of its members: it is not something in addition to them.  If U has three members, a, b, and c, then U is just those three members taken collectively: it is not a fourth thing distinct from each of the members.  U depends for its existence on the existence of its members.)

2. There is a possible world w in which there are no concrete contingent beings.  (One can support this premise with a subtraction argument.  If a world having n members is possible, then surely a world having  n-1 members is possible.  For example, take the actual world, which is one of the possible worlds, and substract me from it.  Surely the result, though  sadly impoverished,  is a possible world.  Subtract London Ed from the result.  That too is a possible world.   Iterate the subtraction procedure until you arrive at a world with n minus n ( = 0) concrete contingent members.   One could also support the premise with a conceivability argument.  It is surely conceivable that there be no concrete contingent beings.  This does not entail, but is arguably evidence for, the proposition that it is possible that there be no concrete contingent beings.)

Therefore

3. W is a world in which U has no members.  (This follows from (2) given that U is the totality of concrete contingent beings.)

Therefore

4. W is a world in which U does not exist. (From (1) and (3))

Therefore

5. U is a contingent being.  (This follows from (4) and the definition of 'contingent being.')

Therefore

6. The totality of contingent beings is itself contingent, hence not necessary.

What is the relevance of this to cosmological arguments?  If the universe is necessary, then one cannot sensibly ask why it exists.  What must exist has the ground of its existence in itself.  So, by showing that the universe is not necessary, one removes an obstacle to cosmological argumentation.

Now since my metaphilosophy holds that nothing of real importance  can be strictly proven in philosophy, the above argument – which deals with a matter of real importance — does not strictly prove its conclusion. But it renders the conclusion rationally acceptable, which is all that we can hope for, and is enough.

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Bill Vallicella

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7 responses to “Could a Universe of Contingent Beings be Necessary?”

  1. Tapji Avatar
    Tapji

    Does a cracker work as an analogy?
    A cracker is a number of molecules taken collectively.
    Each of these molecules are contingent.
    It does not followw that because of this the cracker is contingent.
    But nevertheless the cracker is contingent.
    Does that work?

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  2. Bill Vallicella Avatar
    Bill Vallicella

    That works.

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  3. Lukáš Novák Avatar
    Lukáš Novák

    Dear Bill,

    I have some comments on your exposition.

    First: If your subtractive argument were valid, it would show that, after all, id does follow that if all members of a collection are contingent then the collection is contingent. Therefore, either your argument works or your claim that the contingency of the collection does not follow from the contingency of each of its member is false.

    More detail: Let us assume what you had assumed, viz. that it does not follow that Universe is contingent if each of its members is contingent. That is to say that is is possible that the antecedent is true but the consequent is false. Moreover, since we are talking about S5-modalities and all truths about S5 modalities are S5-necessary, the fact that it is possible that the Universe is not contingent although each of its member is amounts to the fact that the Universe actually is not contingent, even assuming each of its members are (if the Universe is non-continget in a possible world, then it is non-contingent in all possible worlds). From that follows that your subtractive procedure cannot be gone through. There must be some point at which the subtraction of a one single member is impossible (although we are still assuming that all memebers are contingent).

    Is this absurd? No. Even if a member is contingent in itself, it may be necessarily implied by some other memeber(s) and therefore incapable to be consistently “removed” in isolation.

    However, further reflection shows that the “subtractive” argument can be amended to show evidently that a collection of which all members are contingent must be contingent as well. At each point of the subtractive sequence it holds that either it is possible to subtract a chosen memeber m or not. If it is not, then either because the non-existence of m is impossible in itself or incompatible with some necessarily existing being(s), or because the non-existence of m is incompatible with some contingently existing being(s). But the former alternative is excluded by the assumption that m is contingent, which would not be the case if the non-existence of m were impossible in itself or incompatible with something necessary. So the only reaosn why m may be unsubtractible can be that its non-existence would be incompatible with some contingent being(s). In that case, it will always be possible to subtract m plus all its ontological necessitants. Note that I do not need to iterate the reasoning at this point and argue to the impossibility of infinite regress. Given that the relation of ontological necessitation is transitive, all the second-order ontological necessitants of the first-order ontological necessitants of m are ontological necessitants of m as well and therefore are considered in the first step already, regardless whether they are finite or infinite in number. The bottom line is: If all memebers of the Universe are contingent, then there exists a series of possible worlds ordered by the described relation of “subtraction”such that the last member of this series is the world where the Universe does not exist (have members). In other words, the non-existence of the Universe is possible given that all its members are contingent.

    We have proved that from the fact that all members of the Univerese are contingent it follows that the Universe is contingent. But what about the “fallacy of composition” objection? There is a sublte mistake in that objection. It is right that it would be false to claim that “For any property P and any collection C, if all the members of C are P then C is P” is a valid form of reasoning. But likewise it would be false to claim that for any P it holds that “For any C, if all members of C are P then C is P” is an invalid form of reasoning. For example, let us substitute “to be in this room” for P. Then “For any C, if all memebers of C are in this room, then C is in this room” is a valid form of reasoning. The same holds, I claim, for the property of contingency.

    Finally, one comment concerning your metaphilosophical maxim. Clearly, the maxim cannot be strictly proven, if it is true. It seems therefore that its justification can be merely of inductive character. As such, however, it can hardly be used take into question the epistemical force of deductive arguments, since it will be always more dubious than these arguments themselves.
    Lukas

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  4. Bill Vallicella Avatar
    Bill Vallicella

    Hi Lukas,
    I don’t understand your opening paragraph. My claim was that it does not follow just from the fact that each being is contingent that the collection is contingent. That would be the fallacy of composition. But saying that is consistent with saying that there is a valid argument from the contingency ofthe members to the contingency of the collection.
    Perhaps you could clarify . . . .

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  5. Lukáš Novák Avatar
    Lukáš Novák

    I must be missing something. If there is a valid argument form A to B, then B follows just from A, doesn’t it?

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  6. Bill Vallicella Avatar
    Bill Vallicella

    No. The inference to B may be mediated by auxiliary premises. There is an important difference between immediate and mediate inference.
    Immediate: p; therefore p v q
    Mediate: p v q; ~p; therefore q.

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  7. Lukáš Novák Avatar
    Lukáš Novák

    If additional premises are required, then I would say that the argument from A to B is not valid, as such. But (to address the real issue) my point is that in case of the argument in question, no additional premises are required (except perhaps some necessary prinicples which follow from anything, and so need not be expressly assumed).
    Note that I am speaking about the (semantic) relation of entailment, not (necessarily) about ‘(syntactic) derivability in some (or any) formal axiomatic system.

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