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Eugine_Nier comments on AALWA: Ask any LessWronger anything - Less Wrong
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Are you aware of any attempts to assign a causality(-like?) structure to mathematics?
There are certainly areas of mathematics where it seems like there is an underlying causality structure (frequently orthogonal or even inverse to the proof structure), but the probability based definition of causality fails when all the probabilities are 0 or 1.
Can you give a simple example of/pointer to what you mean?
I don't know if this is what Nier has in mind, but it reminds me of Cramer's random model for the primes. There is a 100 per cent chance that 758705024863 is prime, but it is very often useful to regard it as the output of a random process. Here's an example of the model in action.
I am aware of "logical uncertainty", etc. However I think uncertainty and causality are orthogonal (some probabilistic models aren't causal, and some causal models, e.g. circuit models, have no uncertainty in them).
Well, in analytic number theory, for example, there are many heuristic arguments that have a causality like flavor; however, the proofs of the statements in question are frequently unrelated to the heuristics.
Also, this is a discussion about the causal relationship between a theorem and its proof.
I don't know much about analytic number theory, could you be more specific? I didn't follow the discussion you linked very well, because they say things like "Pearlian causality is not counterfactual", or think that there is any relationship between implication and causation. Neither is true.