Thursday, June 20, 2024

Dialog with a Foolish Mathematician

Me: You don't even know what "truth" means.

FM: I don't need to, as long as arguments follow the laws of logic, truth is preserved. Eg the Boolean Truth Tables for and, or, not, and implication.

Me: If I count from 1 to 10 then I pass 5. That is true Right? 

FM: Yes

Me: But it does not follow from the rules of logic or things like the Boolean operators.

FM: Well that is because you have not gone back far enough into the definitions of "1", "5" and "10". Considering the set theoretical definition of cardinal numbers and the successor operation, it is obvious enough that five applications of the successor operator is needed in order to accomplish ten iterations.

Me: Sure, you can muddy the discussion. But let's ignore that what you said just now was circular. More importantly it is irrelevant. For one thing, you have shifted the goal posts from formal logic, to formal logic plus (some form of) arithmetic. For another you ignored the question. Here let me prove that you are wrong (I speak) "One, two, three, four, Johnny, six, seven, eight, nine, ten". Huh? What do you know, you do not always pass "five".

FM: Yeah but that is not counting.

Me: So in order to understand truth, now you find yourself having to understand the underlying nature of naming, pattern recognition, similarity, counting, and much more that is prior to the Boolean Tables. When you are done, the value of the concept of "truth" is seriously diminished. Maybe it is not so foundational and could be discarded.

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