3 ms·
My take: it's a human means of systematically exploring implications of already accepted beliefs. There are implicit and explicit forms of it. The implicit fo
by westoncb 10y ago
My take: it's a human means of systematically exploring implications of already accepted beliefs.
There are implicit and explicit forms of it.
The implicit form is something our brains do automatically and is a consequence of its structure. Perhaps the way it models things intrinsically does not allow for what we would call contradicting statements (though it contains many separate models which if unified would contain contradictions); then, the space of desirable implications is narrowed by a motivation to find a certain kind of implication (i.e. there is typically a goal when engaging in reasoning—we aren't often indifferently interested in all implications) combined with the fact that contradictions aren't allowed. It seems like implications are usually discovering that some entity belongs to a class it wasn't previously known to belong to, at which point it inherits the attributes of other things in that class.
The explicit forms seem like attempts to model the implicit form in mathematical language, in order to bring logical processes more under control of conscious thought, or 'executive function' (plus reasoning on paper extends working memory). It seems possible that with the 'correct' formulation, a logic could viewed as a theoretical science describing properties of the structure of the human brain that give rise to reasoning.
- kazagistar 10y agoThe 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.
- spynxic 10y ago> (though it contains many separate models which if unified would contain contradictions) Contradictions suggest that you don't have a complete picture