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Axioms and Faith - Comments and DiscussionThis is the comment and discussion page for the article Geometry, Axioms, And The Nature Of Faith, published in Directory : Mathematics : Geometry.
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zaphod says:
that's an interesting idea that axioms are closely related to faith. i saw a different take on it though on another website
another writer argued that axioms were really unrelated to faith because - and i quote -
Math in itself is not intrinsically connected to the real world.
in other words math is based on abstract constructs such as points lines planes etc and since these abstract constructs have no intrinsic connection to the real world it is not a matter of faith whether they behave according to certain rules
in other words the axioms are nothing more than the rules of the game and we can make them whatever we want
whattdya think?
Humphrey Nowlin says:
Well, I do see the point on that. In a sense, mathematics is just a game we play with abstract concepts, and so axioms are nothing more than the rules by which we play the game.
In another sense, however, I disagree. Because math - from a pragmatic sense - is typically valuable insofar as it is a model of the real world.
In other words, Euclid didn't choose his postulates because he thought they would be an interesting intellectual exercise; he chose them because he believed they were an accurate model of the universe as he knew it.
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