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Post #2920361
2026-05-17 16:29 UTC
But since these questions are 'embarrassing' in the current mathematical culture, they have not explored these questions publicly.
So, all of this is to say that the 'crisis' mathematics faces in the future HEAVILY depends on whether or not it is actually the case that the human mind is a computer or not. If it isn't then there is a very simple solution that will almost certainly begin to happen naturally in the long term: we will simply stop relying on computationalism to do mathematics. We will begin emphasizing the aspects of our minds that are not computational. And we do not have much to worry about in the long term. However, we may still have much to worry about in the short term.
To mitigate the short term damage, what we would then need to ask (and prove, somehow, either through mathematical logic, or through neuroscience/biology) is what parts of our minds might not be computational? To this end, I think the easiest place to look is the alignment problem. This problem is provably not computationally solvable, so, theoretically, even if our minds are computers, we still have a place to look here. As a result of this, I think this is our best bet in the short term.
I think the following are not replicable by a computer because of the alignment problem:
1 Question generation
2 Definitions
3 Philosophical curiosity
(4/n)
Replies (1)
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I have selected 1 and 2 because, in terms of the formalist paradigm, neither Questions nor definitions have been properly 'integrated' into our current mathematical practice in the same way that the rest of logic has. The question of what is the 'right' question to ask or what is a 'wrong' definition seems to be entirely absent from our systems of formal logic, despite the fact that there seems to be very wide agreement on when a question is a 'great' question in some cases, or when a definition is clearly 'wrong' by mathematicians in some cases. The formalist paradigm provides no distinction between definitions that are 'wrong' and definitions that are 'right'. Nor does it provide a distinction between 'great' questions and 'good'/'bad' questions. Both questions and definitions have some chance of having something along the lines of a formal treatment, it is just that these formal treatments may need to be essentially entirely outside of the computationalist paradigm.
So, my feeling of what a solution should look will come from this area of inquiry.
(5/n)
Open ##2920362