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> Logic necessarily uses words. I'm surprised no one has challenged that statement. Logic is making deductive statements that are true. One only needs symbols
by hervature 3y ago
> Logic necessarily uses words.
I'm surprised no one has challenged that statement. Logic is making deductive statements that are true. One only needs symbols for this. That's why computers can prove mathematical theorems. Words are necessary because we are human and we need to communicate are base assumptions which normally come from the natural world. Saying logic necessarily uses words is like saying logic necessarily uses eyes or ears.
- high_5 3y agoAs long as there are humans involved, yes, there are words, even for visual symbols.
- bootsmann 3y agoActually this is only half true. Formal logic relies on words because some concepts, like finiteness, are impossible to grasp within the formalism itself. A good textbook on this is “Gödel's Theorems and Zermelo's Axioms A Firm Foundation of Mathematics”, which spends the early chapters dedicated to making you aware of this issue.
- edanm 3y agoI'm not sure I follow, under what formalism does "finiteness" become a concept that's impossible to grasp?