Wednesday, September 21, 2011

fatalism and divine foreknowledge.

p ↔ Tp
~p ↔ Fp
~(p ^ ~p)
p v ~p
∴ Tp v Fp

Is this argument valid? If so, bivalence follows the conjunction of a semantic non-contradiction and excluded middle. Assuming that propositions designating any (and all) future times are propositions (a modest thesis, if any is), logical fatalism is not different in kind than the problem of divine foreknowledge and (libertarian) freewill.

Here’s my parity argument:

If the above argument is valid, then anyone who affirms:

(1) (semantic) non-contradiction.

(2) excluded middle.

and that

(3) There is some future time t1 where I have the power to either F or not F,

is inconsistent with herself.

And according to the problem of divine foreknowledge and libertarian free will, anyone who affirms that

(3) God knows right now that I will F at some future time t1.


(4) I have the power to either F or not F at t1,

is inconsistent with herself.

Well, so be it. Let it be that anyone who holds the conjunction of (1), (2), and (3) is inconsistent with herself, and let it be the case that anyone who holds the conjunction of (3) and (4) is inconsistent with herself. Well, despite the inconsistency of (1), (2), and (3), one is rational for affirming all three of them at once. And since one is rational in affirming (1), (2), and (3) all at once, so too is one who affirms both (3) and (4). Therefore, one who holds to (3) and (4) is rational.

Wednesday, September 14, 2011

sentence of the year.

“Cow pies are cow indicators; furthermore, there wouldn’t be non-cow-caused cow pies if there weren’t cow-caused cow pies, although there could certainly be cow-caused cow pies even if there weren’t non-cow-caused cow pies.”

Plantinga (who else!) discussing what he takes to be an implausible consequence of Fodor’s theory of content.

Sunday, September 11, 2011

so why do you do philosophy?

I used to just look at the sunset, but now I melt into it.

Tuesday, September 06, 2011

excluded middle vs. bivalence.

For clarity and brevity let’s just stick with propositions with singular terms. According to the Principle of Excluded Middle (PEM), for any proposition p (e.g., ‘Socrates is wise’ and ‘Socrates is not wise’), there’s *only* two kinds: there’s the ones that say something of something and there’s the ones that deny something of something. Let’s call the former ‘p’ and the latter ‘~p’. To put PEM in symbols we could scribble the following:

PEM: p v ~p

Notice what’s absent in PEM. PEM doesn’t say anything about whether the p’s and ~p’s are true or false. For all PEM might care it might be the case that both p’s and ~p’s are true, or both false, or one half true and the other half neither true nor false, or one half true and false but the other half only false, and so on. The point is that PEM says *nothing* about truth and falsity, so from a logical point of view, PEM implies *nothing* about whether a single proposition is anything at all, much less true or false or pink or blue or all (or none) of the above.

So that’s why we need (among other things) Bivalence, which says that all propositions p (e.g., ‘Socrates is wise’ and ‘Socrates is not wise’) are only either true or false. In other symbols:

B: Tp v Fp

Assuming that ‘truth’ and ‘falsity’ are contraries (that they cannot apply to the same subject (e.g., a proposition) at the same time), we get a semantic version of what Aristotle called the Principle of Non-Contradiction:

PNC: ~(Tp ^ Fp)

PEM’s being true implies that there are only p’s and ~p’s. B’s being true implies that all the p’s and ~p’s are true or false. PNC says that the p’s and ~p’s that are true are not false and vice-versa.

My hunch is that Aristotle thought that PEM and B are really the same since he thought of a proposition as an assertion that something is the case, which is tantamount to saying that the proposition one is asserting is true.

Aristotle also thought that truth depends upon being, but not vice-versa. That is, that we are entitled to infer Socrates’ sitting from knowing that ‘Socrates is sitting’ is true, and vice-versa. But the truth of the latter depends on the former in a way that that the former does not depend on the latter. That is, because Socrates’ sitting obtains, the proposition ‘Socrates is sitting’ is true, but Socrates’ sitting does not obtain because the proposition ‘Socrates is sitting’ is true, but rather the opposite is true, that Socrates sitting makes the proposition ‘Socrates is sitting’ true. The idea is that the world *makes* propositions true or false, but propositions don’t make the world do anything.

For this reason (on my view) Aristotle rejected B (or something like it) about contingent propositions regarding the future. Since tomorrow’s sea battle doesn’t exist (it’s TOMORROW!) there’s nothing to make the proposition ‘there is a sea battle tomorrow’ either true or false. And hence, so much for B.

Thursday, September 01, 2011

in Him all things live and move and have their being.

Today during my lecture I felt more alive than I have in a long time. I gave the following perfunctory definition of logic: [who the hell do I think I am to give a definition of logic? Then again, who the hell is anyone to think she can give a definition of logic?]:

Logic: what is necessary for both thought and reality.

What inspired my definition was my reflection on the apparent continuity and isomorphism between what is necessary for something to be thinkable and for it to be real. For instance, in order for something to be thinkable, it must obey the principle of non-contradiction. To think of anything at all it’s impossible to think of it being X and not being X at the same time and in the same respect. And the same seems to hold for reality. Not only is something’s being both X and not X unthinkable, for anything to be it cannot be both X and not X. And the same criterion seems to be operative in the articulation of any logical axiom, even when a purported axiom ends up falling short of this standard.

Anyway, I then thought about my definition in context to John 1:1-3, where St. John identifies Christ with the logos, which is the Greek word for (among other things) logic.

“In the Beginning was that which is necessary for thought and reality, and that which is necessary for thought and reality was with God and that which is necessary for thought and reality was God. Through that which is necessary for thought and reality all things were made; without that which is necessary for thought and reality nothing was made that has been made.”

Seems right to me.

Also: I like this.

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