Date: Jul 5, 2013 2:11 PM
Author: Joe Niederberger
Subject: Re: Is logic part of mathematics - or is mathematics part of logic?
>Calm down, it's not like we're all sitting in the same room and can discuss this stuff fluidly. I don't think formal or informal has anything to do with it. You want to teach something like ...
"Logic as a discipline starts with the transition from the more or less unreflective use of logical methods and argument patterns to the reflection on and inquiry into these and their elements, including the syntax and semantics of sentences."
I think that's right. Its based on unreflective language
which is an automatic part of our thinking and use of language, a "gift" so to speak -- I think that captures what both you and Clyde have pointed out about "modus ponens" in particular.
I would think its important to start with informal logic based on ordinary sentences, rather than say, symbolic propositional logic (which is always motivated by mapping to natural language anyway.)
(Although, I suppose, some kids who have a knack, start with "WFFs and Proofs" early on too. I think Kirby mentioned once he played it at an early age. My father brought it home one day while I was in grade school, but I couldn't get interested in it at the time. I read just now it was invented to teach law students -- interesting that I learned logic finally in 10th grade from a law student.)
Reflective use is not automatic. It took centuries of development to distill the rarified concepts
that, simple as they seem when they are presented to you *as* distilled concepts, underlie, say, propositional logic.
Aristotle, for example, did not seem to ever *reflect* on modus ponens in particular.