Phi102 - Lect 2 - week 6

What example B illustrates is.. [written on the handout]

A sentence of the form "if P then necessarily Q" can be interpreted either as:

[] (P->Q) or as P-> [] Q

Even if the former is true, the latter may be false.

That doesn't mean if the former is true the latter is always false.

See example c: "if John is an elephant then necessarily he is a mammal"

Here both readings give true claims. Both C1 and C2 are true.

Another example like B, where [](P->R) is true but P->[]R is false.

Let Belle be my belief that Kevin Rudd is PM. (example D)

Then D1 is true. Any world where taht belief is true will be a world where Rudd is PM. So the claim "if Belle is true than Rudd is PM" is true at every world. So, it is necessary that if belle is true than Rudd is PM. But D2 is false. D2 means that is Belle is true at this world then Rudd is PM at every word.

Relevance to foreknowledge?

Premise 1 of the argument against the compatibility of divine foreknowledge and freedom says:

1. If God knows that I'll do X then necessarily I'll do X

This can be read in two ways:

1a: Necessarily (if God knows that I'll do X then I'll do X)
[](P->Q)

clearly true. By definition of what knowledge is. Doesn't need to be God's knowledge. You can only know what's true. But this can't be used with premises 2-7 to get 4.

1b: If God knows that I'll do X then necessarily (I'll do X)

P->[]Q


Not obviously true. If it is true, it will 'stick together' with 2 and 3 to yield 4. But is it? What seems obvious is that even if God knows you'll eat nachos tomorrow in this world, that doesn't mean that you'll do it in every world.

But no sot fast! Sometimes we speka of necessty but don't mean that the claim is true in absolutely every possible world. E.g we say "it is impossible for me to fly to the moon b flappin my arms' but don't mean that I fly to the moon in that way at no world where the laws of nature are as they are in the actualy world. Yet this restricted sense of 'necessity' and 'impossible
has the consequence that if it s impossible for me to do something then I am not free to do it. Could P->[]Q as in premise 1 be true for some restricted reading of "[]"?