## Tuesday, December 6, 2011

### Does the Third Way work assuming a finite universe?

The traditional Third Way was meant to show that a necessary entity exists by positing a universe eternal in the past.

1. Every existing entity is either contingent or necessary. (Definition)

2. Something exists now. (Premise)

3. If something exists now, then something or other has always existed. (Premise)

4. Hence, something or other has always existed. (From 2 and 3)

5. The past is infinite. (Assumption)

6. Given infinite time, all potentialities will have been actualized. (Premise)

7. The concurrent non-existence of all contingent entities is a potentiality. (Premise)

8. Hence, the concurrent non-existence of all contingent entities has been actualized. (From 5, 6 and 7)

9. Therefore, a necessary entity exists. (Implied by 1, 4 and 8)

Now, what if we assume the negation of (5), keeping the (1) through (4) the same?

5'. The past is finite. (Assumption)

6'. Given finite time, the concurrent non-existence of all contingent entities has been actualized. (Premise)

7'. Therefore, a necessary entity exists. (Implied by 1, 4 and 6').

The new debate would probably center around (6'). Could a contingent entity exist at t0, a sort of undifferentiated time? A modalized version of the Third Way would be immune to such an objection, since it's at least possible that nothing contingent existed at t0.

1. I cannot see why time is relevant to the concurrent nonexistence of contigent beings. Even if time is infinite, what if the *necessary* causal chain (entailed by ex nihilo nihil fit) is also infinite? This seems would prevent any possibility of concurrent nonexistence of contingent beings. So I think the difficulty lies on establishing the finitude of the causal chain, for if the causal chain is finite, then certainly, if the first in the chain is contingent, then before it there is a concurrent nonexistence, which would then entail that we must not have existed, which is absurd, hence falsity of "all are contingent".

But the most important thing I have noted is that, your P3 should not be a premise, for that is the very conclusion you (and the Third Way) seeks to prove! Namely, that something must always exist (or necessary being)!

Isn't this the correct formulation?:

P1) We exist
P2) If there is a point in the past where nothing exist, then we would not exists. (from ex nihilo nihil fit)
P3) If all beings are contingent then there would be a time where nothing existed (given the necessary finitude of causal chain)

C) Therefore, it can be the case that all beings are contingent (by reductio ad absurdum). Hence, there must be a necessary being.

But perhaps I'm missing something, if not everything!hehe

2. I probably should have been clearer about premise (3). When I say that something has always existed, this should translate to: "either something contingent or other has always existed, or else there exists at least one necessary entity."