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kallisti

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kallisti

kallisti's Shortform

Dec 7, 2025•1

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Good news for evidentialists! Still doesn't help functionalists or causalists, though.

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kallisti's Shortform

2mo

This is a special post for quick takes (aka "shortform"). Only the owner can create top-level comments.

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kallisti2moQuick Take

Sometimes there is an analogy made between Newcomb's problem and the choice between a life of faith versus a life of sin given Calvinism (a particular sort of predestinarian Christian theology). The argument goes that one should live a life of sin under Calvinism if and only if one should two-box in Newcomb's problem; similarly, faith corresponds to one-boxing. See the end of Scott's post here, or Arif Ahmed's comments near the start of Evidence, Decision and Causality.

I think this misses an interesting feature of Calvinism, though, which makes this analogy break down when you consider functional decision theory in addition to the standard causal and evidential decision theories. Calvinism holds not... (read more)

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Replying toLöb's theorem simply shows that Peano arithmetic cannot prove its own soundness

Löb's theorem simply shows that Peano arithmetic cannot prove its own soundness

So, I might be getting something wrong, but why doesn't Löb's theorem imply that statement? A semi-formal argument, skipping some steps:

(Löb's theorem)

$2. \forall p (\neg (P A ⊢ p) \to \neg (P A ⊢ (P r o v (p) \to p)))$ (Contraposition)

$3. \exists p \neg (P A ⊢ p)$ (e.g., 1 + 1 = 3)

$4. \exists p \neg (P A ⊢ (P r o v (p) \to p))$ (from 2)

$5. \neg \forall p (P A ⊢ (P r o v (p) \to p))$ (by change of quantifiers)

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