I like pondering the imponderables, the great mysteries of the universe, just as much as the next guy. But however much of an intellectual I think I am, I look like a piker compared to the guys at Christian philosophy blog The Prosblogion. A sample:
Consider two claims about God’s knowledge.
- For all p, if p, then God knows p.
- For all p, if p, and possibly God knows p, then God knows p.
It is an interesting fact that (2), combined with two uncontroversial premises, entails (1). I said this in an earlier post, but now I have a more elegant argument. Here are my uncontroversial premises:
- Necessarily, God’s knowledge is closed under conjunction and tautological implication (i.e., if God knows p and God knows q, then God knows (p and q), and if God knows p, and p tautologically implies q, then God knows q).
- There is at least one proposition p such that possibly God knows p and possibly God knows not-p.
Obviously, the proposition p in (4) is contingent, since knowledge entails truth.
Here is the argument that (2)-(4) entail (1). Fix any true p. By (4), let q be any proposition such that possibly God knows q and possibly God knows not-q. If q holds, then let r=q. If q does not hold, then let r=not-q. Note that r is true. Observe that possibly God knows not-r (if r=q, then this follows from the fact that God possibly knows not-p; if r=not-q, then this follows from the fact that God possibly knows q as well as (3), since q tautologically implies not-r).
Still with me? Wait, there’s more:
Let s be the proposition (p or not-r). Then, God possibly knows s. For God possibly knows not-r, and in any world where God knows not-r, God also knows (p or not-r) by (3). Now, s is true as p is true. Therefore, s is a proposition that is true and possibly known by God. Therefore, by (2), God knows s. Moreover, r is a true proposition, and God possibly knows r (since God possibly knows q and God possibly knows not-q). Therefore, God knows r, by (2). But s is (p or not-r). By (3), it follows that God knows p, since (s and r) tautologically implies p.
Whew! They’ve got a whole blog of stuff like this! So, if you feel like you’re brain’s not working hard enough, and you can’t find your Rubik’s Cube, try running it around a few laps of that.