Dominus Paradoxum

I think it would be much better than math which has no application in the everyday lives of most people. (Informal) Logic, on the other hand, has an impact on an enormous range of subjects, since people are constantly having to evaluate information and make descisions on important issues.

My proposed school reforms:

1. After students learn mathematics up to multiplication and division, math as a subject should be replaced courses in in informal logic and critical thinking. After students have masterd this, there would be courses in epistemology.

2. No more "busywork", or memorizing factoids. Schools would shift from being focused on papers and homework to being discussion oriented. Students would be encouraged to share their ideas and to learn to develope and defend their own positions. If they were learning about how the government works, for example, they would learn by the experience of developing their own bills, debating them, and then voting on them.

3. Except for the very core subjects, everything should be elective, so that students could tailor the curriculum around those areas they best excel in. There should be a wide variety of subjects to choose from.

4. Schools should not be centers for socialization with peers. Trust me, I've been to both public and private schools and this is the thing that most detracts from education. All extracurricular activities should be abolished.

5. The school should not have fixed periods (except, of course, for the starting and ending times). Class legnth should be determined by what material the teacher wants to present on that paticular day, and how long the discussions go.

6. School should not start until 10:00 am. Studies have shown that students do much better in school when they are not forced to get up early. Also, the school should provide breakfasts for all those who don't get it at home. People do much better if they have some energy to go on in the morning.

Sorry, but I can't think of anything else for now.

Undercurrent

You don't know how violently I disagree with this. The fact that math is preceived as having little relevance to real life is sad and a product of poor curriculum choices, but to abandon it completely, save for the most mundane, algorithmic elements in favour of some wishy-washy "informal logic" is absurd.

The best way to teach logic is through mathematics. Only when a student has seen and understood a series of logical arguments so tight that you couldn't slip a razor between them, will s/he see what a load of codswallop most arguments are.

Arbogast

"In any case, one quality I've found common to most athiests, freethinkers and nontheistic subscribers to certain esoteric philosophies (such as buddism and daoism), is the strong reliance on formal logic for paring away contradictory facts
"

Kant, Leibnitz haha

Dominus Paradoxum

I didn't say that it was "irrelevant", I know that many disciplines, such as enginerring and computer science could not function without it. What I said was that most of the people, most of the time, have no use for 'higher mathematics'. Now if you think that a greater knowledge of math would would make day to day life better for people, you're more than welcome to explain just how that is. And I bet you have no idea of what 'informal logic' is. "Informal" simply means "not formal",i.e. not 'symbolic' as in no truth tables, no predicate calculus, etc. Informal logic, also known as philosophical logic, is the study of what constitutes a valid arguement. It consists mainly in the enumeration of all the known fallacies, explains why they're fallacies, and explains means of countering them.

Or, in other words, if you want kids think logically, teach them math, kowing about what makes for good reasoning is entirely irrelevant!

lisarea

I like your general idea here, but I wouldn't discount formal logic or math. The thing that makes math pointless is the fact that schools teach children to memorize multiplication tables, formulas, etc., rather than teaching them to figure it out themselves. Teaching them formal logic would allow them to actually solve problems, rather than doing the same ones over and over using the formulas they've memorized. THAT is pointless, as is drilling basic check balancing skills into kids. I have three calculators in arms' reach right now, and I am almost never without one at hand. Calculators are cheap and plentiful, and the idea that we spend so much time and effort teaching children to do a task that can be easily accomplished with a $2 machine disturbs me. Even in the worst case scenarios, you don't have a calculator and say, you have to do some simple division or something, it takes a few seconds longer to split a bill or calculate a tip. Big freaking deal. I spent so much time having that crap drilled into my head as a child, and it hasn't saved me but the tiniest fraction of the time I spent memorizing it.

The way math is taught in schools, it's easy to lose sight of the fact that it does make sense and it is pure logic in number form. In fact, I'd venture to guess that many children, turned off by the sheer volume of rote memorization involved in basic arithmetic, hate math simply because of the unpleasant associations with numbers and memorization. I expect that, if children were taught formal logic at an early age, you'd find fewer kids with an aversion to anything involving numbers.

Math is neither boring nor pointless if you approach it correctly, and the way to approach it correctly is to make it make sense. The way to make it make sense, IMO, is to approach it as logic.

I agree that informal logic has its place as well, and the world would be a better place if kids were taught to think critically and logically about the world around them. I'm just saying that there is also a place for the more structured logic as well.

Farren

Arbogast, I have not read much Kant or Liebnitz at all (although I've read some quoted references). Could you elaborate? Your post seems to be implying some foolishness of the statement (from the argument by authority, no less), which was not out forward as a debating position but a statement of personal experience (The rest can be taken as a debatable position).

Farren

This is why I feel that while it may or may not (I don't have strong opinions on issue) be more practical to teach math in parallel to logics, the actual practice of formal reasoning is the underpinnings of maths.

Teaching formal reasoning would immensely improve math ability - ask any hobbyist programmer who's literally self-taught themselves maths to achieve programming goals. I did. I couldn't pass a Trig test at school (its embarassing to admit that). When I started doing 3D stuff, I learnt the basics in one day, by reading a few principles of trig and deriving from there. Similarly, I learnt simple integration and differentiation calculus in order to understand some of the arguments in a laymans book on quantum physics. The calculus is all gone but the trig stuck

Logics is really the mother subject and maths the child, for a simple reason. All numeric (quantity based) derivations use the formal methods of Logics, but logics can also be used to derive information from non-numeric statements, like

Given:

(1) If A is the child of B
& A is female
Then A is the daughter of B

(2) If C is the husband of A
& A is the daughter of B
then C is the son in law of B

(3) Mary is the child of Paula
(4) Mary is female
(5) John is the husband if Mary

Then

(6) Mary is the daughter of Paula (from 1,3,4)
(7) John is the son in law of Paula (from 2,6)

The conclusions and process here are kind of obvious but I frequently encounter people who, in most matters take the kind of process above as a special case rather than a general process. In other words, if we say, for instance (for arguments sake, not because I believe any of this)

Given
(1) If A is the child of B
Then A is not B
(2) Jesus is the Son of God
Then
(3) Jesus is Not God (from 1,2)

... "special cases" get thrown out left right and center, people throw up and fall over.

Obviously if your belief system teaches you "this logical contradiction would be a logical contradiction if it were not for the awsome wonderfulness of God who can even make a rock he can't lift", you're gonna find your way around this somehow, but IMO, the such reasoning only finds acceptance in minds where every chain of derivation is a "special case".

When you by default use common mental resources behind working out familial relationships of acquaintances and say, understanding the genetic relationship between a poodle and a wolf, it tends to motivate against having special cases just for certain beliefs.

Calzaer

The Catholics also have some semblance of internal consistancy. Protestants do not, and thus a formal education in logic would destroy the Protestant faith.

Feather

There's also the pesky problem that most people are, quite frankly, just too damn stupid to understand logic or critical thinking beyond the mere basics.

Shake

I very much agree with this approach. The way I learned logic in mathematics, at first it just looks like symbol manipulation again. There are axioms and rules to be followed, and outcomes can be determined using set rules. This tends to abstract what happens in debates and what-not. Once you know the symbols and the rules, then you can start assigning sentence meanings to the symbols and see how the rules would work in a debate. I've read enough on these boards to see through certain types of argument, find a strawman, etc. Lay the basis for logic in mathematics, because it's familiar. Then move into the philosophical side of logic, where meanings are attached.

If you're looking for critical, logical thinking, you've got to pair up mathematics and philosophy. They do work quite well together, as I can tell you know, by your mention of formal systems. The only problem is that any formal system which is sufficiently powerful, is incomplete (Gödel), formally speaking. But to understand the incompleteness problem, you have to understand some mathematics, and here we are again! Gödel is one whose work should be studied.