Free will and Intensional Operators, Part II

You are looking for a second consecutive day at a fossil-disclosed jungle cat inspired by thought experiments over whether p was true already in ancient times.

I go back today to the issue raised in the Canadian Journal of Philosophy in an article earlier this year by Fabio Lampert and John William Waldrop.

The point is not to settle the issue of what is free will and is it real. The point, rather, is in logical analytical fashion to render clear "previously underappreciated constraints on defenses of closure-based arguments against the existence of free will."

Who are they? Lampert is affiliated with the University of Vienna, apparently a postdoctoral researcher there. Waldrop's affiliation is with Notre Dame. They seem often to have worked together.

As I understand it, they are saying that various promising arguments against free will require a principle of closure, and that whether they have such a principle available in the sense the anti-freedom case needs what they call a "no choice" operator that is intensional. The freedom case needs a "no choice" operator [indicating a necessary truth] that is hyperintensional, which would destroy closure in the necessary sense.

What does that mean? An operator in the pertinent sense is any word or phrase that takes a sentence/proposition and makes it part of a broader sentence with a different meaning.
Consider the sentence "Lois believes that Clark Kent is human". In this sentence "belief" is the operator. "Clark Kent" is human is the unit sentence, if you will, and the full sentence operates on that unit.

From outside the fictional world to which the statement applies, we know it to be false that Kent is human, and we know it to be true that Lane believes he is.

What is an "intentional" operator? It is an operator that is sensitive to how the unit sentence is presented. Intensionality disallows certain substitutions that might otherwise seem harmless. We might say that "believe" above is intensional because I cannot substitute "Superman" for "Clark Kent" without changing the truth value of the resulting sentence. Lois believes that Clark Kent is human. She may NOT hold any such belief about Superman and may be inclined to deny it.

But of course for the example with which we began the modal operator "neessarily" is the critical one. We are arguing that it is necessarily the case that there was no choice about the matter in the days of the saber toothed tigers, and then we are substituting a moment in the near future. Can we do this?

What is the alternative? For Lampert/Waldrop's purposes, we can do this, and the argument against free will prevails, if the operator "necessary" is merely intensional, but we can't do it, if it is the alterative is a hyperintensional operator. The difference is that a hyperintensional operator is sensitive to the switching out of terms in the underlying sentence even when both terms apply in any possible world, changes to which merely intensional operators may not be sensitive.

Superman comics don't help much with this move. Standard examples generally involve arithmetic and the operator "because".

1) 1 + 2=3 because the Peano axioms hold [makes sense]

2) 1+2=3 because the number of primes is infinite [makes no sense at all]

Here "because" is the operator. The unit sentence is "the Peano axioms hold" in the one case and "the number of primes is infinite" in the other. Both unit sentences are true in every possible world.

Now: the point is that if the word "necessarily" is a hypersensitive operator in sentences such as "it is necessary that it was true a million years ago that you would raise your hand at t," then it can't be substituted for "it is necessary now" or "it will be necessary at t". So the argument does not prevail.

I'm still not sure I understand this, but I'm happy to have worked through it to the degree that I have. They end with these words,

"Despite our own inclinations, the broader dialectical upshot is clear. If N can be shown to be an intensional operator, the Intensional Argument secures Closure and, with it, the validity of powerful arguments challenging free will. Advocates of these arguments should therefore concentrate their efforts on defending the intensionality of N. Conversely, those aiming to challenge the validity of these arguments should focus on considerations that support treating N as hyperintensional."

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