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Somebody should tell Philosophers about the Curry-Howard-Lambek isomorphism. Because that's all there is to the Mathematical notion of "rigorous proof". And t
by ukj 6y ago
Somebody should tell Philosophers about the Curry-Howard-Lambek isomorphism.
Because that's all there is to the Mathematical notion of "rigorous proof".
And the 'next step' in scaling up this process is the mission undertaken by the NuPRL project [1] well on our road towards internalising systems theory as the mode of scientific discourse [2]:
Starting with the slogan "proofs-as-programs," we now talk about "theories-as-systems."
1. http://nuprl.org/Intro/intro.html http://nuprl.org/Intro/intro.html
2. https://en.wikipedia.org/wiki/Systems_theory https://en.wikipedia.org/wiki/Systems_theory
- QuesnayJr 6y agoWhat makes you think that philosophers haven't heard of it? Here's the Stanford Encyclopedia of Philosophy entry on it: https://plato.stanford.edu/entries/type-theory-intuitionistic/ https://plato.stanford.edu/entries/type-theory-intuitionisti...
- deleted 6y ago[deleted]
- ukj 6y agoWhat makes you think that just because there's an Encyclopedia entry on it then all Philosophers have read it and understood its implications on the nature of logic, rigour and proofs? Empiricism (science) rules the roost. Beware of bugs in the above code; I have only proved it correct, not tried it. ― Donald Knuth
- QuesnayJr 6y agoSo the standard you are advocating for is that every single philosopher in the entire world has to agree with your take? No philosopher can think long and hard about the meaning of proof, and come to a conclusion other than the one you've drawn?
- ukj 6y agoSo you are trying to strawman me? Do you even know what a "question" is? Formally speaking. I might have an idea: https://en.wikipedia.org/wiki/Query_language https://en.wikipedia.org/wiki/Query_language Do you even know what 'agreement' is? Formally speaking. I might have another idea: https://en.wikipedia.org/wiki/Consensus_(computer_science) https://en.wikipedia.org/wiki/Consensus_(computer_science) You are free to disagree, of course. And I am free to not care.