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I expect the argument would go like: The pile of logic gates is an encoding of the axioms. The fact that it evaluates mathematical expressions correctly is bot
by jstanley 4y ago
I expect the argument would go like:
The pile of logic gates is an encoding of the axioms. The fact that it evaluates mathematical expressions correctly is both necessary and sufficient to show that it understands arithmetic. Therefore the calculator knows the axioms and understands arithmetic.
- hamburglar 4y agoExcept it doesn’t implement the axioms of math, it implements a crude facsimile of them for a certain subset of numbers, because what it’s really doing is a non-mathematical physical process.