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The interesting point of the given article was that pre-mathematical-formalization, logic was backwards of that purpose, and often remains so even today. The se
by kazagistar 10y ago
The interesting point of the given article was that pre-mathematical-formalization, logic was backwards of that purpose, and often remains so even today. The search does not start with assumptions and seek conclusions; rather, it starts with conclusions, and then seeks which sets of axioms fulfill them. A vast majority of mathematicians don't care about the axiomatic foundations of mathematics, nor mind if it gets entirely reformulated; they already know math works, and its irrelevant which particular set of axioms is used to prove that.
The assuptions => theorm structure is an artificial abstraction over a very different logic process. Symbolic logic is a framework for mechanical validation, rather then anything like how people actually do logic.
- westoncb 10y ago> The search does not start with assumptions and seek conclusions; rather, it starts with conclusions, and then seeks which sets of axioms fulfill them. Right, there was an issue with labeling justification 'logic'. An interesting point, but not as interesting as the title of this story—which I prefer to discuss :) I was getting at the general process of inference making in the human brain (not even conscious inference making necessarily), which I see as the real root of all the different things we call logic.