Axiomatic Reasoning

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Has anyone taken Euclidean geometry before? Here is a question:

Given as truth that 6 times 9 equals 42 and that the vast majority of mathematicians do not hold this view,
would these mathematicians be correct or incorrect?

They would be correct, because you can prove that 6*9 != 42.

Axioms in mathematics aren't like axioms in philosophy though.

If you said that 6 times 9 equals 42 in maths, it would just be to see what the consequences of that as an axiom would be, but it still wouldn't be an axiom in the philosophical sense that it is a self evident truth.

All right angles are the same is an axiom because it is self evident, it doesn't need proof and you can't really prove it mathematically.

6 times 9 equaling 42 is not self evident and you can prove that this is incorrect so it is not an axiom in the philosophical sense but could be used as an axiom in mathematics because anything can be used as an axiom in maths.... It just might be useless to do so

Call me crazy if you like, but I would argue that 6*9 equaling 42 is just as true as 2*5 = A which is also as equally true as 7*3 equaling 18 and 5^2 = 1C.

OK, you're crazy.

Of course, I recognize that you are just using a different base. Using dozenal numbers without declaring that you are using a nonstandard base is poor form, though. And all mathematicians do hold the view you espoused, they just use different notation for it.

In Greek. I learned enough Attic Greek to read The Elements. It is version 1.0 of what mathematics really is; a deductive system.

ruveyn

Notations and conventions are not axioms. We do not use base 10 because it is correct to use it but because we like to and because it is convenient to have a convention in this regard. I guess it got so popular because we have 10 fingers, but I actually think we should have used base 6. With base 6, you can actually very easily express all numbers from 0 to 35 with your two hands!

If you called a tail a leg, how many legs would a sheep have? Five you say? Nope. Calling a tail a leg does not make a tail a leg.

ruveyn