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Do mathematicians believe in axioms . . . .

by A=B
Tags: axioms, mathematicians
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A=B
#1
Jan20-07, 10:59 AM
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Do a mathematician believe in AXIOM like some people believe in GOD

People who believe in GOD need not to proof GOD, is that like the way mathematician do with AXIOM ?
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arildno
#2
Jan20-07, 11:16 AM
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Not at all.
Why do you think so?
HallsofIvy
#3
Jan20-07, 07:05 PM
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Thanks
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Just out of curiosity, what do you mean by AXIOM?

I know what an "axiomatic system" is, I know the definition of the word "axiom", and I know a number of "axioms" but I don't recognize the concept AXIOM.

You may be making the common mistake of thinking that an "axiom" is "an obviously true statement". I don't think any mathematician would be so bold as to claim that any statement was "obviously true"! We've seen too many exceptions!

In mathematics an axiom is defined to be "true" in a particular system- its acceptance in effect defining the system. (I.e. "accepted as true for the sake of argument".) Any mathematican would accept Euclid's axiom "two points determine a single line" as being true in Euclidean geometry but not in spherical geometry.

I doubt that any religious person will accept God as being "true" in some cases but not others!

arildno
#4
Jan21-07, 12:22 PM
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Do mathematicians believe in axioms . . . .

Just a follow-up on Halls' comment:

You probably know many card games, each one having its own specific rules as to what valid "moves" are.
Now, do you regard one such set of rules to be the only valid way to pass the time with a deck of cards?

Similarly with maths:
With different sets of ground rules for what is "valid" you get different types of math games.
You can't say in general that one such set of rules is "truer" than any other such set.

However, some particular sets of rules might be regarded as "dumb":
For example, consider a card game that in some situation said both that a particular "move" is permitted, and in the same breath said that that move was forbidden. That is, the set of rules is self-contradictory, and hence dumb.

Such system weaknesses ought of course be avoided, but in complicated logical systems, it is not always apparent whether or not a particular set of rules can generate internal contradictions or not.
But this feature does not in any way make it more (or less) difficult to ascertain whether a particular deduction in a particular system is valid or not, it only makes it more difficult to ascertain whether the particular set of rules used is a good or bad idea in the first place.
Crosson
#5
Jan23-07, 11:12 PM
P: 1,295
Mathematicians believe in their axioms so that they have a place to start their thinking, those who believe in God do so because it allows them to stop thinking.


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