[FRIAM] it's world logic day!

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Well, computation is a direct descendant of logic. And "mathematical logic" is a bit of an offshoot related to the foundations of math. Things like modus ponens are simply mechanical/effective transformations. You can build any logic you want by removing or adding the operations from some formal system. For example, the tonk operation is interesting: https://www.jstor.org/stable/30226839?seq=1

Add to the above the idea that *informal* logic is still logic, but without the mechanical/effective aspect and you get closer to logic writ large, perhaps as Nick might use the term. The informal fallacies can be thought of as heuristic principles of good thinking.

The important inferential leap is that *any* of the elements of any logic (formal or informal) are doubtable. So, it's reasonable to throw out, say, modus tollens, as is done in some paraconsistent logics. And it's reasonable to replace consequence with, say, "possible" and "necessary", as in modal logic, or "am" vs. "will be", as in temporal logic.

So, the essence of logic, as I see it anyway, is that *mechanical* inference ... the thing that carries us from Ramon Lull all the way to, say, Isabelle <https://isabelle.in.tum.de/>.

On 1/14/21 4:57 PM, Gary Schiltz wrote:
> I would have thought that most members of FRIAM, when speaking of logic, are referring to the mathematical and/or computational concept of propositional logic, which has little if anything to do with a human dimension. You know, modus ponens, modus tollens, etc. Logic in that sense would exist even without the existence of biological beings (e.g. Homo sapiens) that use it as a part (not the only part) of their thinking process. But maybe I'm not grokking what y'all are talking about.

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