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Tuesday, November 29, 2011

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Thank you for the post.

Can we not, however, deny the validity of the lazy argument by denying that the LEM yields (1)? To illustrate my point, let "Tp" signify "It will be the case tomorrow that p," "Apq" the disjunction of p and q, and "Np" the negation of p. Given this notation, we easily see that (1) can be read either as (TApNp) or as (ATpNTp). LEM, however, yields only the latter and not the former, which is the interpretation required for the conclusion to follow.

As for the problem of correct predictions, why can't we say that they only become true once whatever they predicted comes to pass, just as Michel's lacing Antoine's coffee with arsenic only becomes the cause of his death after Antoine has consumed the beverage? That way, no prediction will ever be true while it still refers to a future time.

Hi Leo,

I take it you are saying that (1) is ambiguous as between

a. It will be the case that (I will be killed or I will not be killed)

and

b. Either it will be case that I will be killed or it will not be the case that I will be killed.

First of all, as I see it, (1) is not ambiguous. What it means is (b). And (b), as you suggest, follows from LEM.

So I am not following you.

We colloquially say things like, 'Her prediction came true,' but all this means is that what was predicted is now known to be true. It needn't be taken to me that the content of the prediction was without a truth-value and then acquired a truth-value. Truth and the knowledge of truth are easily confused.

Arguably, if no prediction concerning a future contingent is true at the time it is made, then no such prediction can be fulfilled. For a prediction is fulfilled when the event predicted happens.

Tricky stuff, eh?

The relevance of the arsenic comparison escapes me.


Can we add premises for a different conclusion?

1. Either I will be killed tomorrow or I will not.
2. If I take precautions I will not be killed tomorrow.
3. If I will be killed, I will not have taken precautions.
4. If I will not be killed, then I will have neglected precautions.
Therefore
5. It is useful to take precautions.

Same logic (use of LEM), just more complicated premises. In real life, premises multiply beyond our ken.

sorry, "NOT" neglected on #4.

I misspoke in my original comment: (1) is ambiguous between

1'. "Either tomorrow it will be the case that (it is not the case that I am killed) or tomorrow it will be the case that (I am killed)" and

1''. "Either it is not the case that tomorrow it will be the case that (I am killed) or tomorrow it will be the case that (I am killed)."

Only (1''), as far as I can see, follows from LEM, because it is the disjunct of two contradictories. In order for the lazy argument to go through, however, the stronger claim (1'), it would seem, is needed, for only (1') yields the conclusion that future truths are fixed.

I brought up the arsenic example to illustrate how an event or action (such as poisoning coffee) can acquire a feature after it has passed. Similarly, I was suggesting, a prediction could become accurate after it has been made and what it predicted has come to pass.

My reason for being suspicious about predictions of future contingents being correct when they are made is that, if we suppose as much, then what is being predicted would seem to already be "fixed" regarding its truth value, and thus not really a future contingent. It has nothing to do with considerations of colloquialisms or knowledge.

Am I making more sense?

Sorry, Leo, but I can't quite wrap my mind around the ambiguity you are claiming.

Consider an analogy with belief, letting Dp stand for "Socrates believes that p". Now, clearly, we can distinguish

5. (D(~p))∨(Dp) from

5'. (~Dp)∨(Dp),

and, indeed, the latter is true while the former is false: Socrates may, for some propositions, simply have no opinion as to whether they are true or false. Similarly, I am suggesting, (1) can be interpreted as

1'. (T(~p))∨(Tp) or as

1''. (~Tp)∨(Tp),

where Tp stands for "Tomorrow it will be the case that". Now, only (1'') is yielded by the law of the excluded middle, for only in it are the two disjuncts contradictories. Since (~Tp) does not on its own entail (T(~p)), the two interpretations of (1) are not equivalent. But it is (1') that the lazy argument requires, because only (Tp) or (T(~p)) can be taken as immediately implying that whether p does or does not obtain tomorrow is already a settled matter.

My inspiration for this argument comes from A. N. Prior's Time and Modality, Ch. X, which is no doubt far clearer.

You are right that (5) and (5') are different. And yes, the latter is true. But the former could also be true. Let one of the disjuncts be true, then by Addition one can infer the disjunction. This is valid: p; therefore p v q.

So you are making a Prioresque move. Now I see what you are getting at.

Biil, you say "(2) looks to be a tautology of the form p --> (q -->p)," and we can think of this as saying "If it is true that I will [be] killed tomorrow, then this is true regardless of what other propositions are true." I think (2), and your latter explication of it, are both modal in character. The force of 'no matter what precautions I take' is a universal quantification over sets of precautions. We can express this as

(2*) In every possible future, if I will be killed then I will be killed despite the specific precautions I take in that future.
(3*) In every possible future, if I survive then I survive despite the specific precautions I fail to take in that future.
A corollary of (3*) is
In every possible future, if I survive then I survive possibly because of the specific precautions that I do take in that future,
and this is to deny the pointlessness of taking precautions. The fatalistic argument gets its strength by glossing the modal character of the problem.

But suppose I am wrong about this. And suppose you are right about the tenseless nature of propositions. Then we can rerun the argument the day after tomorrow as follows, without any change of truth-values:

1. Either I was killed yesterday or I was not. 
2. If I was killed, I was killed no matter what precautions I took.
3. If I survived, then I survived no matter what precautions I neglected.
Therefore
4. It was pointless to take precautions.
But now the 'no matter what precautions I took' makes no universal claim. It merely says
2. If I was killed, I was killed despite the specific precautions I took,
3. If I survived, then I survived despite not taking the specific precautions I neglected.
And now there is no pressure to infer that precautions are pointless.

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