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HallsofIvy
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The whole point of mathematics is that it is applicable to a variety of fields. Newton created calculus in order to solve problems in physics (specifically, the motion of planets). Yet people who are planning to use mathematics to solve problems in biology, psychology, or economics learn the same calculus.
That works precisely because axiomatic systems have "undefined words". In order to apply theorems from calculus (or linear algebra, or differential equations, or tensor theory) I have only to decide what meanings I will give to those undefined terms and then show that the axioms apply (at least approximately- in any real application, we have measurements that are only approximate) and then know that the theorems will be true for this application (again, at least approximately).
That's why mathematics is not "like religion". The one thing that all "Christian Religions" have in common (Jeff Lawson's referentce to "The Christian church" is naive at best- there are may different "Christian churchs" with widely varying beliefs) is that "Jesus Christ was an aspect of God that became human". Certainly no good Christian that I know would take the point of view that that is "true in some systems but not in others" which is exactly what mathematicians do.
No mathematician believes, for example, that "through any point not on a given line there exist a line through that point parallel to that given line" (Playfair's axiom). Mathematician accept that as an axiom for a certain axiomatic system (Euclidean geometry) which has proved to be a good model for many applications but not for some others. We can accept it as true (not assert that it is true in any universal sense) for some applications and as not true for others. I don't know of any religion that does that!
That works precisely because axiomatic systems have "undefined words". In order to apply theorems from calculus (or linear algebra, or differential equations, or tensor theory) I have only to decide what meanings I will give to those undefined terms and then show that the axioms apply (at least approximately- in any real application, we have measurements that are only approximate) and then know that the theorems will be true for this application (again, at least approximately).
That's why mathematics is not "like religion". The one thing that all "Christian Religions" have in common (Jeff Lawson's referentce to "The Christian church" is naive at best- there are may different "Christian churchs" with widely varying beliefs) is that "Jesus Christ was an aspect of God that became human". Certainly no good Christian that I know would take the point of view that that is "true in some systems but not in others" which is exactly what mathematicians do.
No mathematician believes, for example, that "through any point not on a given line there exist a line through that point parallel to that given line" (Playfair's axiom). Mathematician accept that as an axiom for a certain axiomatic system (Euclidean geometry) which has proved to be a good model for many applications but not for some others. We can accept it as true (not assert that it is true in any universal sense) for some applications and as not true for others. I don't know of any religion that does that!
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