Friday, November 2, 2007

Logical fatalism -- the options

This post is just an attempt by me to work something out for myself. Maybe it doesn't interest anybody else.

People who accept an Aristotelian open future because of concerns about logical fatalism do so on the strength of the intuition that if I freely do something, it was possible for me not to do it, and that:
(*) If it is now the case that I will do A, then it is now necessary that I will do it.

So, the question is: What are the options for getting out of the argument from logical fatalism. One option is just to deny (*). This, I think, is by far the best option. Call someone who accepts (*) an "Open Futurist". What logical options does an Open Futurist have?

Well, to see that, let's sketch a logical fatalism argument based on (*):

  1. If it is now necessary that I will do A, then I will not be freely doing A. (Premise, justified via Principle of Alternate Possibilities)
  2. If it is now necessary that I will not do A, then I will not be freely refraining from doing A. (Premise, same justification)
  3. If it is now necessary that I will do A, then I will not be freely refraining from doing A. (Premise)
  4. If it is now necessary that I will not do A, then I will not be freely doing A. (Premise)
  5. If it is now necessary that I will do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (1) and (3) and the principle that if p→q and p→r, then p→q&r.)
  6. If it is now necessary that I will not do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (2) and (4) and the principle that if p->q and p→r, then p→q&r.)
  7. If I will do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (5) and (*).)
  8. If I will not do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (6) and (*).)
  9. Either it is the case that I will do A or it is not the case that I will do A. (By Law of Excluded Middle)
  10. If it is not the case that I will do A, then I will not do A. (Premise)
  11. Therefore, either it is the case that I will do A or it is the case that I will not do A. (By (9) and (10) and the principle that if p or q, and q→r, then p or r.)
  12. Therefore, I will not be freely doing A and I will not be freely refraining from doing A. (By (7), (8) and (11), together with the principle that if p→r and q→r and (p or q), then r.)
So what are the at all plausible options if we accept (*) (which we shouldn't)?
(I) Compatibilism: Deny (1) (and (2)--they are surely in the same boat).
(II) Intuitionistic Logic: Deny the Law of Excluded Middle, thereby allowing the denial of (9).
(III) Not-will / will-not distinction: Deny (10), holding on to Law of Excluded Middle.
(IV) Deny the principle that if p→r and q→r and (p or q), then r.
(V) Deny one of the other rules of inference used.

I think (V) is not attractive--all the other rules of inference seem really hard to deny. Option (IV) is pretty radical. It means that we will no longer accept arguments like: "If Bob is telling the truth, George is guilty. If Fred is telling the truth, George is guilty. Either Bob or Fred is telling the truth. So, George is guilty." The principle denied in (IV) follows from the axioms of intuitionistic logic, and I think is also going to hold in supervaluationist settings.

If this is right, then an exhaustive list of our at all plausible options with regard to the logical argument for fatalism is:

  1. Denial of free will
  2. Denial of (*)
  3. Compatibilism
  4. Denial of excluded middle
  5. Denial of the claim that not-will implies will-not
I rank the attractiveness of these as follows, in order of most to least attractive: 2, 3, 5, 4, 1. Why list 1 last? Because free will is central to the things that matter most in life. How to justify the rest of the ordering? Well, we should be least willing to give up general rules of all reasoning, like excluded middle. We should be more willing to give up rules about particular kinds of reasoning, such as the tensed logic rule that not-will implies will not. We should be more willing yet to give up intuitions about modal or concrete concepts, since there things get difficult by everybody's lights, and so 2 and 3 are even more attractive as options than 5, 4 and 1. Why take 2 as more attractive than 3? Well, that's a judgment call on my part--I find compatibilism deeply implausible, and I suspect that most people who find (*) plausible find the denial of compatibilism even more plausible.

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