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Let's ban religion from schools ...

Let's ban religion from schools ...

Posted Dec 31, 2012 0:29 UTC (Mon) by viro (subscriber, #7872)
In reply to: Let's ban religion from schools ... by Wol
Parent article: Petition: promote the use of free software in US schools

Just how the hell is mathematics a belief system? Statements about its usefulness for describing the world may be a matter of belief (even though it's more of "as far as our memories can be relied upon, it seems to have been useful so far"), but the math itself? Details, please. And no, vague postmodern masturbation won't do; leave it to Eng.Lit wankers and their ilk, please.


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Let's ban religion from schools ...

Posted Dec 31, 2012 0:47 UTC (Mon) by Cyberax (✭ supporter ✭, #52523) [Link]

Goedel proved that any sufficiently complex theory (capable to express Peano arithmetic) is either incomplete or inconsistent. For example, it's possible that the common arithmetic is inconsistent, perhaps one day we stumble into a contradiction in it.

Nobody believes in that, but that's the point - we can't prove it.

Let's ban religion from schools ...

Posted Dec 31, 2012 1:00 UTC (Mon) by apoelstra (subscriber, #75205) [Link]

>Just how the hell is mathematics a belief system?

The premise of mathematics is: assuming [some collection of axioms] plus [some rules of inference], what can be derived?

As Cyberax pointed out, with most axiomatic systems in use today, we need to take it on faith that the system is consistent. And if you treat mathematics as a game, that's the only point you would need to invoke an irrational belief. But it's nearly impossible to do mathematics this way, and definitely impossible to teach it this way.

The way that math -is- taught involves saying that some subset of the world is described by these axioms. For example, if you have a collection of blocks from which you can add or remove blocks, we assume that the blocks will obey Peano arithmetic. Then consistency follows from the assumption that the world itself is consistent. (This assumption underlies -all- of science, and it also needs to be taken on faith.)

In fact, you assume the block quantities will obey Peano arithmetic at such a low level, that you teach that addition and subtraction are actually defined in terms of these quantities. You'd never just give a child an axiomatic system and walk away.

The point is: when teaching mathematics, especially to children, you need to choose some part of reality which you claim is modeled by the math. This is where the teaching becomes subjective and ideological.

(At least, this is my understanding of Wol's post. Maybe he meant something completely different.)

Let's ban religion from schools ...

Posted Dec 31, 2012 1:01 UTC (Mon) by apoelstra (subscriber, #75205) [Link]

Sorry, I missed Jon's post asking to end the discussion! I retract my comment.

Let's ban religion from schools ...

Posted Dec 31, 2012 1:16 UTC (Mon) by viro (subscriber, #7872) [Link]

Blocks definitely do not satisfy Peano's axioms, what with the set being finite...

Anyway, Jon has the final word here.

Let's ban religion from schools ...

Posted Dec 31, 2012 2:25 UTC (Mon) by Cyberax (✭ supporter ✭, #52523) [Link]

Addition and subtraction are actually safe. They can be expressed using a complete theory, so we know they are consistent.

Let's ban religion from schools ...

Posted Dec 31, 2012 22:45 UTC (Mon) by Wol (guest, #4433) [Link]

I've seen Jon's block, so sorry for ignoring it, but yes that was exactly my point.

As per Goedel, ALL logic systems dealing with number are either incomplete, or inconsistent.

Hence our *belief* that arithmetic works ... :-)

Cheers,
Wol


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