lisarea

I honestly don't think they are. I think they're too selfish and lazy. Seriously. All too often, people just get very attached to illogical belief systems that promise them lots of goodies and such, and allow them to think of themselves as somehow superior or more worthy than others; and they get to the point where they will very jealously defend those belief systems against anything that might threaten them.

In fact, some of the arguments that people come up with to defend their illogical beliefs show a great deal of inherent intelligence and creativity, IMO.

Logic is not only simple, it's innate. People don't even have to be consciously aware of the logical rules they apply, and often, they can't even articulate their thinking processes that way. But the basics of logic are as simple as simple can be.

lpetrich

Don't be too confident. The Xians can always say

I believe because it is absurd (credo quia absurdum).

Undercurrent

You seem to be half-talking about "rhetoric" rather than logic. Certainly the enumeration of logical fallicies, (in addition to likely necessitating a breach of item 2 on your list of reforms,) is much more in the space of "debating" than "logic".

Certianly, though, the notion that the study of mathematics is bereft of the study of "what constitutes a valid argument" is horridly false. Such study is done, and what's more it is done in an evironment where logical fallacy of any named or unnamed variety is renderred plainly obvious and unforgivable.

One might argue that in the "real world", the purity of the logic presented in math is shrouded in malleable language, and therefore logic should be taught in the form it is seen (or not seen) "in the wild", rather than in a pristine environment. I agree that some of that is nescessary to see the link between the formal logic taught in math class and "practical" applications of logic in the "real world". But to removed the formal component, as DPs reform #1 would suggest, would be like teahing biology only by field trips to a nature preserve, dismissing the possibility of reading texts on the subject or even going to the zoo as unrepresentative of the way things work in real life.

In short, yes (except for the part after the second comma, since I don't know, or even believe, that math does not include "what makes for good reasoning" -- I'm sure that there's some named logical fallicy to point out here).

I do not, however, have a great deal of support for the way mathematics is taught. As lisarea points out, the schools spend too much time on "the mechanics of arithmetic", rather than the logic of arithmetic. This kind of pedagogy leads to the frequently-expressed belief that mathematics is about numbers rather than mathematics being about logic and numbers being a convienient and useful form of expession of that logic -- sometimes. The enterprise of mathematics is made out to be little more than accounting.

If it were up to me, I would do the prelimiary addition/multiplication/&c work (the mechanics of arithmetic), but start basic algebra (the logic of arithmetic) earlier, and add on a unit or two on basic group theory, which is, I think, a fairly accessible branch of mathematics that is not about numbers, and all about logic.

The one thing I found teaching first-year university students, is that they find "proof" problems hard, and oftentimes teachers just give in and weigh exams much more towards "mechanical" problems with little logical thought required. I wouldn't do that.

/pontificate

Feather

Meh, I suppose my cynicism was acting up again.

I dunno, though. Sometimes people surprise me with their cleverness, and others I just don't get how they can be so dull.

lisarea

Well, to be honest, I shorten this to 'stupid' all the time. But when I'm being nitpicky, the fact is that I don't dislike actual stupid people, and I try not to lump in the people who choose to be ignorant with the mentally retarded and such.

People who genuinely have limited intellectual capacity are not at fault for it, while people who are just the lazy kind of stupid deserve nothing but derision.

Farren

A friend of mine presented a proof for an test in our second last years at school and flunked the question. When he put it to the maths teacher that his proof was in fact correct she got irritated with him and told him he was supposed to provide the proof in the textbook.

He got so upset about it he got hold of a university professor who wrote the teacher a letter saying the proof was correct and well formulated, but that simply made her victimise him. Eventually he decided to just drop the whole thing. I don't know if this is representative of how maths is taught worldwide but the horrifying implication of this attitude is that the learning of proofs was not seen as the learning of logic by the teacher in question.

The problem with teaching logic via mathematics is the one of general and special cases I mentioned earlier. Most people I've met don't make the leap from the special case (prove this mathematical theorem), to the general (prove, or at least, establish a case for your political standpoint, say). There's a lack of holistic understanding. Even the teaching of algebra doesn't imply the teaching of all of the terms of formal logic and predicate calculus.

I do think the teaching of logic requires algebra because it requires placeholders like a,b,x,y,z, but ~ and so on can be replaced with NOT, AND, FOR ALL for the less symbol oriented. I can't honestly see how these kinds of problems

if a IS NOT b
and b IS EQUIVALENT TO c
then c IS NOT a

where applied to objects and people rather than quanitites and pure mathematical entities like triangles and ellipses, can be harder to undestand than when applied to more "mathematical "entities. In fact, among people for whom the abstract world of numbers is alienating and by default offputting, I believe non-numeric entities would be easier to grasp.