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Yes, I first read about Leibniz’s machine from the wikipedia page on the Entscheidungsproblem. The research on this problem eventually led to the invention of
by ronenlh 5y ago
Yes, I first read about Leibniz’s machine from the wikipedia page on the Entscheidungsproblem.
The research on this problem eventually led to the invention of Lambda calculus and the Turing machine (formal languages for computing), which proved that such a project is impossible, as on some inputs they infinitely recurse and can’t output True or False.
https://en.wikipedia.org/wiki/Entscheidungsproblem https://en.wikipedia.org/wiki/Entscheidungsproblem
The source is Martin Davis, 2000, Engines of Logic
- jfrunyon 5y agoMy brain also infinitely recurses on some problems and can't output True or False. Guess my brain is impossible. ???
- ronenlh 5y agoYour brain is not Leibniz’s machine nor the algorithm sought upon in the Entscheidungsproblem. Your brain also doesn’t infinitely recurse as it doesn’t have infinite time or space. A machine that given a logical statement outputs whether the statement is universally valid is impossible, ergo all mechanisms that don’t output true or false given a logical statement are impossible??
- garmaine 5y agoIt did not prove the idea impossible. Just trivial/naive versions of the idea which ignore the halting problem or incompleteness theorem.
- ronenlh 5y agoGood clarification