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comment by NotPhil
NotPhil  ·  4350 days ago  ·  link  ·    ·  parent  ·  post: Is Algebra Necessary?

    Algebra is the underpinning of symbolic logic.

You can argue that analytic geometry teaches a somewhat limited form of deduction, but, no, you can't reasonably say that algebra teaches logic. Like all math, it's just a way to describe quantities and the very limited relationships between them.

Unlike the author, I do think algebra and geometry are a useful part of an education, which, unlike the author, I think should have nothing at all to do with job training.

If we really want our kids to learn to think, then we're going to have to actually give classes on thought: induction, deduction, abduction, analogical reasoning, dialectical reasoning, and causal reasoning. We're also going to have to give them the information and ideas they need to reason with: history, literature, philosophy, and social studies. Finally, we'll need to ensure that they can express their thoughts: rhetoric, composition, and basic math.

If we really want to educate, instead of just train, we're going to have to make room for a real education, and that means clearing out both shop and calculus. Just like auto mechanics, most higher maths are only useful for very particular jobs, and as such they're just job training, which employers should be doing, not education, which is what schools should be doing.





kleinbl00  ·  4350 days ago  ·  link  ·  

    Like all math, it's just a way to describe quantities and the very limited relationships between them

...and how is that not logic?

    If we really want our kids to learn to think, then we're going to have to actually give classes on thought: induction, deduction, abduction, analogical reasoning, dialectical reasoning, and causal reasoning.

It seems like a bit of a jump from "defending algebra" to "revamping the entire educational system." Not that I disagree with your assertions, just that I"m a bit more pragmatic.

NotPhil  ·  4350 days ago  ·  link  ·  

This article describes logic. Don't be fooled by the title: it's hosted at a philosophy site, and philosophers distinguish between many different categories and forms of logic, but this is the general meaning of the term. It's what we mean when we say, for instance, that Mr. Spock is logical.

kleinbl00  ·  4350 days ago  ·  link  ·  

No, that article describes "informal logic."

This article describes "symbolic logic."

NotPhil  ·  4350 days ago  ·  link  ·  

The article I pointed to describes "logic."

I had assumed that you didn't really mean to say "symbolic logic" in your original response. For one thing, it's unrelated to algebra except in the sense that it takes a mathematical form; for another, it's useless for anyone who isn't interested in following some of the dead-ends that the 20th-century analytic philosophers ran down.

I hope you don't insist that your kid learn symbolic logic unless he's really fascinated by it. It certainly won't help him employ anyone. If you want him to learn formal deduction, try Aristotle's syllogisms. They're useful.

kleinbl00  ·  4350 days ago  ·  link  ·  

It does not. It describes "informal logic" which is a philosophical term.

We're not having a philosophical discussion. We're having a mathematical one.

I

Fucking

Said

"Symbolic logic."

    I hope you don't insist that your kid learn symbolic logic unless he's really fascinated by it.

No for every fucking reason in my original post. The fact that you think "symbolic logic" and "informal logic" are the same thing is a strong indicator that not only do you need to focus on your rhetoric, you need to retake algebra.

NotPhil  ·  4350 days ago  ·  link  ·  

Well, the reason you

    Fucking

    Said

    "Symbolic logic."

is because you don't know what you're talking about.

Here's symbolic logic:

[(p ⊃ q) ∧ (q ⊃ r)] ⊃ (p ⊃ r).

And here's algebra:

(x² + y²)² = (x² - y²)² + (2xy)²

They are only vaguely related. You can't reasonably expect anyone to learn about one from being taught the other. And both are of limited utility if what you want is to learn to reason.

kleinbl00  ·  4350 days ago  ·  link  ·  

...and ignored.

user-inactivated  ·  4350 days ago  ·  link  ·  
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kleinbl00  ·  4350 days ago  ·  link  ·  

Let's stop tripping over the term "logic," shall we?

IF it gets cold when it rains, AND it is raining, THEREFORE it will be cold. That's "logic." Technically it's "Boolean algebra" but FFS, it's also "logic."

"Algebra" doesn't mean "symbols." It means "solve for the unknown." "Solving for the unknown" is a daily activity for people who think. Not only that, but the argument isn't "let's stop teaching reasoning" it's "let's stop teaching ALGEBRA" which, by your logic, we don't need.

And, simply put, you're wrong. There aren't that many more ways I can illustrate the wrongness of your thinking because it requires a basic understanding of symbolic logic and I'm guessing you suck at algebra.

user-inactivated  ·  4350 days ago  ·  link  ·  
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kleinbl00  ·  4350 days ago  ·  link  ·  

You keep saying that, but you keep using arguments that do not hold up and that you make no effort to defend. And that is why this conversation will not continue.

user-inactivated  ·  4350 days ago  ·  link  ·  
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NotPhil  ·  4350 days ago  ·  link  ·  

No, what you just did is not boolean algebra, and it's not symbolic logic either. Why don't you just admit that you misspoke in the first place? You really meant "logic," didn't you?

user-inactivated  ·  4350 days ago  ·  link  ·  
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NotPhil  ·  4350 days ago  ·  link  ·  

I don't think you teach reasoning by teaching math. You teach reasoning by teaching reasoning, and you teach math by teaching math.

hglman  ·  4350 days ago  ·  link  ·  

You can claim to learn to reason with out rigor, but its just bull shit, show mean rigorous reasoning that isnt math and I will believe you.

user-inactivated  ·  4350 days ago  ·  link  ·  
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ike  ·  4350 days ago  ·  link  ·  

I hate that most people consider job training to be the purpose of education. Education is autotelic.