03-24-2004, 06:40 AM
I was going to respond to your reply to my point, but it seems that Pete has done it for me. The point is, maths is based on assumptions (axioms) that are held to be true, which I thought would have actually strengthened your position if you followed up this line.
Investigating axioms of systems can be interesting, as can seeing what happens when axioms are removed/added/altered, as well as comparing the axioms of various systems.
Lets take a (biased to my viewpoint) look at a simplified model of Christianity.
Axiom 1) The Bible is the literal truth.
If this axiom is in the system then you have Creationists (is that what they are called there, or am I using a local term?), if it is not, you have every other branch (not true, but just as illustration).
For those Christian systems without axiom one you can follow some (sketchy) rules and imply that (assuming that an axiom exists stating the Bible is the Truth)
The Bible contains metaphorical truths
From that conclusion you can generate questions like, 'which parts are metaphorical', and 'who decides so' etc. which leads to large differences between the two systems with and without axiom one, much like my point about non-Euclidean geometry.
To show something to be false that has already been 'proven' true, you need to show that one of the assumptions that the conclusion was based on is false (or can be false under some situation), or you need to show a misapplication in the logic leading to the conclusion.
Note also that conclusions are often used as axioms.
Investigating axioms of systems can be interesting, as can seeing what happens when axioms are removed/added/altered, as well as comparing the axioms of various systems.
Lets take a (biased to my viewpoint) look at a simplified model of Christianity.
Axiom 1) The Bible is the literal truth.
If this axiom is in the system then you have Creationists (is that what they are called there, or am I using a local term?), if it is not, you have every other branch (not true, but just as illustration).
For those Christian systems without axiom one you can follow some (sketchy) rules and imply that (assuming that an axiom exists stating the Bible is the Truth)
The Bible contains metaphorical truths
From that conclusion you can generate questions like, 'which parts are metaphorical', and 'who decides so' etc. which leads to large differences between the two systems with and without axiom one, much like my point about non-Euclidean geometry.
To show something to be false that has already been 'proven' true, you need to show that one of the assumptions that the conclusion was based on is false (or can be false under some situation), or you need to show a misapplication in the logic leading to the conclusion.
Note also that conclusions are often used as axioms.