This is a famous problem and I was surprised I didn't find it with an appreciable amount of effort. This is to say that I am not taking credit for thinking of it. But I will take credit for putting it on E2.

It starts out with two self-evident (or so I think) truths:

1. The law of the excluded middle. Either proposition P is true or it is not true, there is not a third option. Ie, either there is a god or there is not a god; either there is free will or there is not free will.
2. The law of non-contradiction. That is to say that for proposition P, there is a problem if you say P is true and not true. P and ~P (~means "not") are mutally exclusive, if one then not the other.

Seems simple enough, no? Now make P in the future tense- "I will get laid some time this century." Under normal circumstances this is probably P, but I may die or get into some disfiguing accident (yes, it could even happen to you)... so there is the possiblility of ~P. But only these two posibilities exist. It is not possible for me to get laid yet not, at least once "laid" is clearly defined.
And following from #2, if I do then I don't not. If I don't then I don't do. Follow? Let's say P is correct, then there is nothing that can happen or that I can do to stop it . Even if I wanted to stop it, P is still correct. And the same could be said for ~P. It is therefor impossible for me to make any decisions that interfere with the fruition (no pun intended) of P. But P can be anything. Let's Make P a choice. "I will clap my hands at 3:00." Assuming my hands are untethered and I know when 3:00 is, P or ~P should be the product of my "volition." But as I said be for, it is impossible for me to make any decisions the interfere with the fruition of P. It follows that it is not my decision whether or not to clap my hands at 3:00, or any other P. And since decision is part of the definition of free will, it therefor does not exist.

The paradox here referred to may perhaps be stated as follows:
It is either true or false that P, where P is the proposition that I will raise my arm between noon and 1 pm. this coming sunday.

If it is true (if I do, in fact, raise my arm) then P is true now and was true yesterday, and in fact always was and always will be true.

Therefore, since P is already either true or false, any sense of my own volition in determining its truth is illusory. Because before I was born, before the earth existed, even, it was already true (or false) that P.

I can think of several different ways to argue against this:
  • From verificationism: it is only after the fact that P becomes capable of verification, and can only then be said to be true or false. (Yes, you can start the verification process very much in advance, but it will only end after the arm has been raised or not..)

  • From physics: the truth of P, in fact, is not determined until a physical measurement of the set of outcomes is performed--this counterargument would aim to replace the Boolean logic implied by the statement of the paradox with quantum logic, where a superposed state, which strictly is neither P nor not P, prior to measurement, is an option.

  • From common sense: 'volition' and 'decision' are perfectly reasonable words, and are familiar and unproblematic in their normal uses. If our logic doesn't agree with these uses, then there must be something wrong with our logic, not the words themselves.

These are all plausible enough, if you believe in verificationism, physics, or common sense, but they don't seem to get at the difficulty we're having with the logic itself.

We note that the argument rests on an apparent contradiction between our conception of the eternal truth of P and the reality of my decision to raise my arm.

Let's suppose the earth never existed. In this case it seems fairly certain that P is false. Similarly, if I never existed, P must be false (it can't be me that's raising the arm.) Again, if I was born with no arms, P cannot be true.

But we don't feel inclined to say that the earth (or myself, or my arms) are illusory, just because P is already true or false.

But it seems my decision to raise my arm is in a similar position here. In the normal course of things (leaving out demonic possession and bizarre psychology experiments with electrodes or hypnosis, etc.) we would say that my decision to raise my arm is a necessary and sufficient condition for P. That is, P obtains if and only if I decide to raise my arm. But if we accept this, we could take the argument round again, since Q: 'I will decide to raise my arm...' must 'always' have been true.

The picture behind this is of the various assertions of P and Q through the ages sitting there like lightbulbs which are on (true) or off (false.)

The 'commonsense' picture of my decision--that it's like my flicking a switch and retroactively making all the lightbulbs light up--seems to contradict the idea that the lightbulbs were always already on or off.

And yet the actual event of my raising my arm is already in this position with respect to the lightbulbs!

This is just a feature of the atemporal stance we're taking in the initial argument.

Because P says I will raise my arm in a particular time and place, the truth conditions of P are temporally bound, whereas we assume (in this logic) that the truth-value of P is not.

We can now see that questioning the reality of the decision on the grounds that P (or Q) is eternally true is nonsense, analogous to asking: "if P is already true, and it says that I'll raise my arm, how can I really raise my arm? Since P is already true, what more could I do to make it true?"

Just as it makes sense that for P to be true I must raise my arm, it makes sense to say that for P to be true (under normal circumstances) I must decide to raise my arm. While the medieval manuscript that records my decision to raise my arm was in fact true as soon as it was written, it was true precisely because, hundreds of years in the future, I decided to raise my arm!

We should remember that this 'because' is not the because of physical causality, which is subject to temporal constraints (in particular that effect temporally follows cause--the effect is within the cause's light cone, if we're being fussy), but the 'unphysical' (or, if you prefer, conventional or normative) because of an atemporal logic (or semantics).

Now, look deep into my eyes and click here, as you know you inevitably must, to consider more serious objections to the notion of free will.

Update: Sun 25 Jun, 2001
Ok, I forgot to raise my arm. This time, P turned out to be false. But the argument still stands!

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