Tuesday, July 05, 2011

the necessity of the past redux.

Let PAST be the conjunction of every true proposition about the past. The necessity of the past thesis says that the past is necessary. In other symbols:

(NP) PAST.

Since the necessity operator ‘’ is equivalent to ‘~◊~’ (i.e., it is not possible that not), the truth of NP is equivalent to

(NP’) ~◊~PAST.

If NP’ is true, it follows that there are no contingent truths about the past, since for P to be contingent, P must be both not necessary and not impossible. But surely there is at least one contingent truth about the past. For example, though it’s true that

(P) Atra was on the mat,

P could have been false. In other symbols:

(PC) P ∧ ◊~P.

If (PC) is true, then (NP’) is false, for (~◊~P ∧ ◊~P) is a formal contradiction. Ergo, etc.

Monday, July 04, 2011

on the necessity of the past.

Some philosophers think that the past is necessary. But if these philosopher think the past is necessary in just the same way that two and two being four is necessary, this cannot be right.

Let’s suppose that any fact about the past is necessarily true in just the same way two and two is four is necessary, that is necessary simpliciter. We might formalize this thesis as

(PN) For any p, if p is true and about the past, then p is necessarily true.

Now consider some fact about the past, that

(1) Two plus two equals four.

Since (1) was true yesterday, the conjunction of (PN) and (1) entail

(2) Necessarily, “two plus two is four”

as well as (2)’s de re rendering, that

(2’) Two plus two is necessarily four.

Well, here things seem fine, at least by way of (2) and (2’). Even if someone might be suspicious of (PN), she shouldn’t be suspicious of it because (2) and (2’) are among (PN)’s consequences.

But now let’s consider another fact about the past, that

(3) Atra was on the mat.

Since (3) picks out a fact about yesterday, the conjunction of (PN) and (1) entail

(4) Necessarily, “Atra was on the mat”

as well as (4)’s de re rendering:

(4’) Atra was necessarily on the mat.

But this cannot be right. If we’re supposing that the “necessity” in (4) and (4’) is to be understood as necessary simpliciter, then the truth of (4) entail each of the following:

(4’’) There is no possible world where Atra was not on the mat.

(4’’’) It is impossible that “Atra was not on the mat.”

And since what is necessary and what is impossible exclude what is contingent, the truth of (4) entails that

(4’’’’) It was not a contingent fact that “Atra was on the mat.”

And perhaps most damningly, (4) entails that

(4’x5) Atra could not have not been on the mat.

But (4) through (4’x5) are all false: Despite the fact that Atra was on the mat yesterday, Atra could have not been on the mat; it’s a contingent fact that Atra was on the mat; It was possible for Atra to not be on the mat; and there is at least one possible world where Atra is not on the mat. And hence (PN) is false, or at least it needs a lot of work.

I think this shows that for any truth that is not necessary simpliciter, the following principle

(*) p → ~◊~p

is false.

And if (*) is false, then for any truth that is not necessary
simpliciter, the following principle

(~*) p ^ ◊~p

is true.

This seems to suggest that any non-determinist is committed to synchronic possibility.

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Sunday, July 03, 2011

fatalism.

Suppose it’s true that excluded middle (EM) holds—viz., that any proposition p, it’s necessary that p or not-p. Symbolically:

(EM) (p ∨ ~p)

Now suppose that bivalence holds—viz., that for any proposition p, it’s necessary that either p is true or p is false. Symbolically:

(B) (Tp ∨ Fp)

Let’s also suppose EM and B are necessarily equivalent. Symbolically:
`
(EM/B) [(p ∨~p) ^ (Tp ∨ Fp) ^ (p ↔Tp) ^ (~p ↔Fp)]

Okay now for fatalism. Fatalism (as I understand it) is the thesis that the future is fixed—viz., that anything that might happen in the future, what will happen must happen such that there is only one possible future.

Some have argued that from EM/B fatalism follows. Here’s the argument:

Consider the proposition

(1) There will be sea battle tomorrow.

By EM/B it follows that (1) is either true or false right now. Furthermore, if (1) is true right now, then no one can prevent tomorrow’s sea battle, for it impossible for anyone to make a true time-indexed proposition false. And vice-versa. If (1) is false right now, then no one can prevent the non-occurrence of tomorrow’s sea battle, for it is impossible for anyone to make a false time-indexed proposition true. Since (1) was arbitrarily chosen, this argument can be generalized for any future-tensed proposition. That is, let pf pick out any future-tensed proposition. It follows from EM/B that pf is either true or false right now. Furthermore, if pf is true right now, then no one can prevent it, for it is impossible for anyone to make a true time-indexed proposition false. And the same goes if pf is false. If pf is false right now, then no one can prevent it, for it is impossible for anyone to make a false time-indexed proposition true. And this is just the thesis of fatalism, which said that the future is fixed in such a way that there is only one possible way the future can be.

It should be noted that this argument relies on a very weak and nearly uncontroversial principle of logical entailment that says if p is true then it necessarily follows that p is true. Symbolically:

(LE) (Tp ⊃ Tp) ^ (Fp ⊃ Fp)

(LE) is equivalent to

(LE’) (Tp ⊃ ~◊Fp) ^ (Ftp ⊃ ~◊Tp)

Here’s a way of symbolizing the argument for fatalism from EM/B and LE:

(EM/B) [(p ∨~p) ^ (Tp ∨ Fp) ^ (p ↔Tp) ^ (~p ↔Fp)]
(2) Any future-tensed proposition pf is a proposition.
(3) ∴ [(pf∨~pf) ^ (Tpf∨ Fpf) ^ (Tpf ↔ pf) ^ (Fpf ↔ ~pf)]
(LE’) (Tp ⊃ ~◊Fp) ^ (Ftp ⊃ ~◊Tp)
(4) (Tpf ⊃ ~◊Fpf) ∨ (Fpf ⊃ ~◊Tpf)
(5) ∴ ~◊Fpf ∨ ~◊Tpf

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Saturday, July 02, 2011

a reductio of classical moral psychology?

If one could intentionally and knowingly commit a horrendous evil, then one could intentionally and knowingly eat poop. But no one can intentionally and knowingly eat poop. Therefore, no one could intentionally and knowingly commit a horrendous evil.

p = one could intentionally and knowingly commit a horrendous evil.
q = one could intentionally and knowingly eat poop.

(1) p ⊃ q
(2) ~q
(3) ∴ ~p

If no one could intentionally and knowingly commit a horrendous evil, then no one who commits a horrendous evil is morally responsible for the horrendous evil she commits.

r = no one who commits a horrendous evil is morally responsible for the horrendous evil she commits.

(4) ~p ⊃ r
(3) ~p
(5) ∴ r

John Wayne Gacy Jr. committed a horrendous evil. Therefore, John Wayne Gacy Jr. is not responsible for the horrendous evil he commited.

r = No [one who commits a horrendous evil] is [that which is morally responsible for the horrendous evil she commits].
(7) All [John Wayne Gacy Jr.] is [one who commits a horrendous evil].
(8) No [John Wayne Gacy Jr.] is [that which is responsible for the horrendous evil he commits].

This argument is valid.


So if you think is (8) is false (i.e., that John Wayne Gacy Jr. is in some way morally responsible for at least one of the horrendous evils he committed), then you must deny at least one of premises (1) through (7). Which one would you deny, and for what reason?

I’d deny (2). I think it’s possible that someone can intentionally and knowingly eat poop. As crazy as that may seem, I think it’s infinitely less crazy than (8)! And therefore, etc.

I suspect that most people would deny (1). Though I have no independent argument for it, I’m confident that anyone who thinks long and hard about (1) will see that it’s true.

Friday, July 01, 2011

on an inscription at the oracle at Delphi.

“…for everyone is orthodox to himself.”

—John Locke

“…when you find that you’re a villain in the story you have written.”

—Death Cab

Glaucon: It’s a strange image you’re describing, and strange prisoners.
Socrates
: They’re like us…

—Plato

I hate confrontation. When someone confronts me I almost always feel profoundly disoriented and slightly nauseous. The reason why, I think, is because up until right before the confrontation I think of myself as okay. My good intentions seem to match up well with their consequences, and I’m like, “Hey, you’re doing alright—at least for the most part.” But when someone says otherwise, I’m forced to see myself how she sees me, and it’s usually ugly and unbearable. For who can think of herself as ugly and not long for annihilation?

It reminds me of the prisoners in Plato’s cave. After their liberator frees them from their shackles and they look at how the world really is, they become overwhelmed and disoriented because nothing looks familiar. Living a lie for so long lets us get used to it. We’re able to build a thick and crusty wall of faux justifications and tired excuses so that we can live with ourselves—even if no one else can. And when those who love us muster the courage to save us from ourselves and say something, we stick with the familiar and see our liberator as a threat. Like a dog returns to its vomit, we gladly shut out the light and return to the darkness to nurse our rotten wounds.

Of course, this unfortunate situation highlights the necessity of community. If there’s one thing I’m very confident about it’s that the inner recesses of my soul are hardly transparent to my mind’s eye, even if they don’t appear opaque. And even in the times when things are as transparent as they seem, I can usually make up any reason under the sun to avoid a closer look.

But, I’d also like to stress that mere community alone is not sufficient to fix the problem. Plato’s prisoners had community, and they seemed to notice neither their own chains nor those of their neighbor. This is probably because we tend to gravitate toward persons who share our own values, and this often means persons with our same vices. I take it that this is why we'll never see a drunkard and a sober alcoholic hanging out much.

Perhaps a less obvious reason why mere community isn’t going to cut it is that the soul is a very difficult place to navigate (the word ‘catacomb’ comes to mind) and it’s very easy to do serious damage to it in the very interest of trying to restore it. If a heart surgeon were to use a butter knife to operate on a patient with coronary heart disease, she’d end up doing more damage than the disease itself. A fortiori, given how much more tender and delicate one’s soul is, using blunt and dull instruments with shaky or unskilled hands can nearly destroy it. So please, be careful…

I know I need to be more open than I am and I need to put myself in position to let others help me see myself. This I can do. I just hope that your hands are gentle, your sighs are full of insight, and your scalpel is sharp.

Also, here’s my summer jam. It reminds me of how I feel. On this day. Which is like most days.

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