Free Will and Intensional Operators, Part I

In the Canadian Journal of Philosophy, Fabio Lampert and John William Waldrop recently offered a rather confusing argument about free will. 

They didn't argue for it or against it precisely, but sought to outline what a solid argument for it or against it might look like.  They seem sure that no sound argument to either conclusion has appeared yet, despite the voluminous attempts.

"Free will and intensional operators" is the title of their article, in the February 2026 issue. As one might expect, the phrase "intensional operators" plays a big part in their discussion. So does the word "closure". 

They don't really define what they mean by [epistemic] closure in this context, but I expect that it means here that for any domain of discussion X, the domain is closed if and only if we can safely add to our knowledge by taking the enatilment of what we know as also ... known. [This is different from causal closure.] 

Free will, for Lampert and Waldrop, is not so much defined as typified.  I have free will if I can be said to have a choice about something -- such as, to raise my arm at some near-future time (t). I suppose (not an example of theirs) if I am in attendance at a friend's wedding and the officiant says "anyone who objects to this union, raise your hand," then it matters whether we say I have a choice to raise my hand at that t.

An argument against free will from closure might start off this way -- and this time I am using one of their examples, though revised a bit by my own stylistic imperatives:

1. Consider the proposition "It was true a million years ago that you would raise your hand at t"  - you have no choice about the truth of THAT proposition. So we might add the intensional operator "necessarily" to it.  

2. Necessarily, it WAS true a million years ago that you would raise your hand at t.

3. Which entails: you have no choice about raising your hand at t. 

 The first step, then, is that if p is a truth about the distant past then it is fixed.  It is not up to anyone. The second step is more complicated.  This sounds like a reference to determinism. Given all the laws of nature, and the condition of the world a million years ago, it was necessarily the case that someday there would come to be such a person as you, sitting in the Church in question, and that THAT person would raise his hand.  But if that is what is meant, this smply assumes the problem away. Yes, (3) follows from (1) and (2) but the point doesn't even seem worth making since the assumption is heroic.

But that would be causal, not epistemic, closure. Lampert and Waldrop are after something more general.  Because of epistemic closure, if it was true a million years ago as a purely formal logical matter that you would raise your hand at t, then it is necessarily true if you indeed are going to raise your hand at t, [and the domain we are positing to be closed may include chance facts.]

 Here we get to the twist.  Lampert and Waldrop tell us that the long-neglected point is that the key issue in the debate over free will in the face of such arguments is whether what they call the "N operator" --the inference to the necessity of the raised hand, is intensional or hyperintensional.

Huh?  Hang in there.  I'll come back to this tomorrow. 

   

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