[FRIAM] hidden

[David Eric Smith]

I like this Glen, particularly the following:

> On May 20, 2020, at 2:10 AM, uǝlƃ ☣ <gepropella at gmail.com> wrote:
> 
> I really wish more people would/could permanently install a "methodological" qualifier in front of every -ism they advocate. So, if you call yourself a monist, are you a methodological monist? And if not, if you're ideal-monist but methodological-pluralist, then I don't particularly care about your idealism. I care about your methods more than your thoughts. At least then, when someone foists a reduction on us, we can, in practice, find if/where they've ignored or assumed away some particulars.

I have wondered — maybe just because I am a spectator to this debate on another channel so it is on my mind — whether it is productive to compare the distinction you draw to that between the Formalists and the Intuitionists in mathematics (came up in Jon’s post a few days ago too).  

To me the formalist wants to trust that whatever satisfies certain rules of syntax should be considered true.  (Here I put aside the role of model theory, as what formalists would call a semantics associated with the formalism, because to me axioms like the excluded middle are syntactic in their nature.) 

It probably matters that the Intuitionists are not merely constructivists (the univalent-foundations people, Voyevodsky et al., seem to be more purely constructivists), but I’m not sure how much more there is to the philosophical position of the intuitionists that mathematical truth is a property of “mental events”, than just their methodological commitment that proofs must be constructive and definitions demonstrative, ruling out things like terms for infinite sets.

The behaviorists seem to have something like a law of the excluded middle in their style of thought, of not perhaps articulated as a commitment of method.  They can simply declare that they have The scientific point of view, and as long as you can’t demonstrate a contradiction within it, if you object that they are asserting things they can’t back up with construction, you must be advocating a spiritualist position.  There is a lot I REALLY DONT LIKE in my use of that metaphor, because it ascribes to the behaviorists a more dogmatic and domineering position than I think the actual people have, though I think their language pushes them toward sounding more that way than they are.  But there is some axis of distinction between the syntactic notion of truth that the formalists are after, and the constructive semantics (+ some notion of “embodiment”, I guess) in the intuitionists, which seems similar to me to your contrast of methodological versus idealistic commitments to monism or pluralism, and that I agree has been the focus of the impasse in this dialogue so far.

I bring up this debate in mathematics because it seems significant to me how long and how intensely it has been going on, with both sides wanting a notion of “truth”, and neither being able to claim to have achieved it in terms satisfied by the other.  If the intuitionists had never been able to build a real system around their position, the formalists could just declare victory and go home.  But the debate seems still live, even within math and not only in philosophy, with clear trade-offs that there are proofs that each side will accept that the other rejects (certain proofs of manifold continuity that the intuitionists accept that formalists reject, and finitistic proofs for infinite sets, as well as the excluded-middle arguments, that the formalists accept and the intuitionists reject).  I was surprised, when I first saw the axiom of choice, that it was just presented as a part of mathematical reasoning, as to me it seemed wildly unreliable, as most efforts to interpret syntactic rules in terms of truth values seem unreliable.  On the other hand, like the irrationality of sqrt(2) in the proof Frank recounted, I would be surprised at any constructive math in which such a result would be false.  Uncommitted is the most I would expect.

I held off writing this initially, because I am unsure whether I think it is useful even in the broad quality of the distinction, and certainly there is not a fine-grained mapping from one of these cases to the others.  But I write it now in case it will help a different response I have to write to Nick’s post.

I agree with you we are after trying to express the same or similar kind of distinction.

Eric