jessicata's Shortform

jessicata

jessicata's Shortform — LessWrong

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jessicata1mo6-5

TDT and FDT are ill-posed.

just think about the idea of "logical counterfactual". it is the kind of thing that cannot make logical sense. how can you formalize a thing that doesn't make logical sense? also miri empirically failed to formalize this for over a decade. if someone is advocating that "logical counterfactual" is a real thing, burden of proof is clearly on them at this point
FDT in the FDT paper is defined in terms of logical counterfactuals / subjunctives, so ill-posed-ness of logical counterfactuals spreads to FDT
TDT paper wrongly confuses between Bayesian networks (which represent joint distributions) and Pearlian causal diagrams (which make "further fact" claims about causality, usually disambiguated by physics), in any case it was supposed to be superseded by FDT paper, which as stated, is ill-posed

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3Vladimir_Nesov1mo

Yes, but only A decides that. So it should be possible to do the variable-constructions thing (as in sheaves/fibrations in logic-like settings), maybe all the way to the level of foundations of mathematics, and say that A didn't yet decide that. And so there isn't yet a fact of the matter, at that logical time (so "logical time" is pointing to something about locations in the base space, and the logic is making claims that vary with the base space). This is the way A itself should be reasoning about what's going on.

3jessicata1mo

I think I see better what you mean: A() could reason as if it decides whether 'PA proves A() = a', even though we don't know what to put for A yet, i.e. we have not defined FDT. I don't know what is the variable-constructions thing. Part of why I'm skeptical: I see how logical counterfactuals fail to make sense in 'normal math' (like logic, model theory, PA) and then you said something more advanced about Scott domains, which I happen to know about, and don't think they solve the problem; now you mention 'sheaves/fibrations in logic-like settings', which I know a little about (topos theory, which does something like a constructive logic / type theory), but which I'm not an expert enough in to say "no this doesn't solve the problem", so what am I to do? I am going to keep acting on the idea "logical counterfactuals do not make sense" and I am not going to take "[math thing jessicata does not understand] makes it work" as counter-evidence, unless it is explained clearly and convincingly.

Vladimir_Nesov1mo30

I'm not claiming this makes enough sense for me to tell a formal story, all I can do is gesture at some intuitions about why I think it should be possible to make formal sense of this. So I'm not pointing to specific formal things and instead pointing in a general direction, because I don't know which specific formal things would fit. It's not very helpful, and probably structurally impossible to refute.

I don't know what is the variable-constructions thing

I just mean something like ETCS as opposed to the classical setting of "constant" sets (but again,... (read more)

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jessicata's Shortform

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jessicata's Shortform

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