Today's Handouts

Today I gave out a logic and argument handout.
I also gave (and will give) some notes on the cosmological arguments from Aquinas, Leibiz and Mackie.

Here are some additional notes:

Aquinas' Third Way

The Argument

1. There are at present contingent beings.
2. Whatever can fail to exist, at some time does not exist.

Therefore,
3. If all beings are contingent, then at one time nothing existed.(2)
4. Whatever begins to exist is caused to begin to exist by something already existing.

Therefore,
5. If at any time t nothing existed, then nothing would have existed at any later time. (4)

Therefore,
6. If at one time nothing existed, nothing exists now. (5)

Therefore,
7. If all beings are contingent nothing exists now. (3)(6)

Therefore,
8. Not all beings are contingent; there is at least one necessary being. (1)(7)
9. Every necessary being either has its necessity caused by another or has its necessity in itself.
10. There cannot be an infinite series of necessary beings each having its necessity caused by another.

Therefore,
11. There is a necessary being having of itself its own necessity, and this all men speak of as God. (8)(9)(10)

Some Definitions:

• x is a contingent being =df it is possible that x exists and it is possible that x does not exist
• x is a necessary being =df it is not possible that x does not exist

Criticisms:

I. What is it to be a necessary being having of itself its own necessity, and why think that such a being is God?

II. Why think that (2) is true?

III. Does (3) follow from (2)?

(2') For every contingent being B there is a time t such that B does not exist at t.

(3') There is a time t such that for every contingent being B, B fails to exist at t.

(2*) For every person B there is a person A such that A is the mother of B.

(3*) There is a person A such that for every person B, A is the mother of B.