Date: Nov 27, 2012 11:21 PM
Author: Joe Niederberger
Subject: Re: Some important demonstrations on negative numbers
>Common sense just isn't synonymous with mathematics, or more precisely, with reasoned thought and analysis.
Your "reasoned thought" verbiage yet again. Mere repetition is neither reason nor thought.
Nor is your claimed definition:
"Common sense is devoid of reasoned thought and analysis. That is my definition and in the context of this discussion, neither unfair nor unwarranted."
As I said, if indirectly: you're in a corner of absurdism or some kind of autistic rut. It shows. Here you go trying to one-up Richard Dedekind. Yawn.
"When we attempt to teach this imagined theory and its imagined elements to the unaware student, we use concrete examples (common sense) as an aid in that task but not as a substitute for that task and not as a substitute for the goal of the task, reasoned analysis and thought."
So, your big deal breakthrough is that the "goal" of reasoned thought and analysis is "reasoned thought and analysis," mere tautology. You have to escape from your little corner. Common sense examples are used, because
that's where the real action is. Math is "popular" (not in the common sense, but more literally, commonly used) exactly because its grounded in everyday and not-so-everyday connection to the "concrete world we all share" be it mere bookkeeping, actuarial, Newtonian, relativistic, quantum, etc. The methods of mathematics, though, are "formal", as in "according to form (syntax)" and not "content". That's the point of Russell's absurdism. Also, I believe that's your sticking point. How can mere formalities (such as Modus Ponens) that seem, well, merely "formal" be the same or derived from "the perception of the concrete world." I think they are, surprising (perhaps) as it may be. Why should truth about the concrete world be tied to something that seems so linguistically, or even, artificially grounded? I simply believe they are by evidence: "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". More speculatively I believe it so because, either, reality is ult!
imately formal, or, at least our perception of it is.