
Re: Is logic part of mathematics  or is mathematics part of logic?
Posted:
Jul 7, 2013 1:17 PM


R Hansen says: >Sorry, I meant when you said "B therefore A". In CS that doesn't follow the same way it does in math.
RH: >> At 09:34 AM 7/5/2013, Robert Hansen wrote: >> >>> You want to teach something like ... >>> >>> If A then B. Not B therefore Not A. >>
Wayne Bishop: >> My point was that in the "real world"; it is far more important to be persuasive that: If A then B. Not A therefore Not B. And don't forget: B therefore A. >> >> Wayne
This has gotten very confused. Wayne was making a joke. Propositional logic is the same in CS as it is in math, and the fallacies are the same.
But, to get back to the point that Robert was making 
You can start with a simple proposition like,
"If it rains today, we (definitely) will go to the movies".
Most kids will understand that readily, and if they are keen to get to the movies they will notice when it starts to rain and press their parents with the logical conclusion that they should be off to the movies.
That's unreflective use of logic. Now suppose you ask one of them the hypothetical "if we don't go to the movies, what does that mean?" I think very few would pipe up and say "it means it must not have rained!" (But some might.)
You can get probably more followers of your logical line of thought if you simply state (rather than try to get them to "discover" this): "And  if we do not go to the movies, it can only be if it does not rain today." Your kids might have to chew on that a while, but if they are the attentive kind, and think about it, they will see its connected to what you said before.
And so on, and so on, if you can keep their attention, you can go over *all* the cases:
1. it rains; you go to the movies 2. no movie; so must be that no rain 3. no rain; what's that mean? 4. we went to the movies; so what's that mean?
3 & 4 are tricky, are they not?
One could go over these very carefully, and also make careful and exhaustive note of what was *not* said. The original statement was *not*: "If it rains, we *may* (or may not,) go to the movies". Etc. etc. etc. through many variations.
I would say that is all leading to a reflective, attentive, and sustained use of whatever latent logical ability the individuals possess natively. After all that is very firm (at what point exactly? I don't know.), then one might proceed to the notion of "implication" as an abstract connective, with its associated truth table etc. Before one ever got to implication though, double negatives, the difference between inclusive and exclusive or, etc. should have been given this same level of careful attention.
Cheers, Joe N

