Why does A=A?

Question

Is there an explanation for why the Law of Identity is true?

Answer 1

I think that the Law of Identity is an a priori analytic truth (actually, the only one), and therefore doesn't need explanation.

Answer 2

Note that there exists certain circumstances where this is violated, except where made axiomatically true. Reflexivity is a property of sets and it is not always true. You can construct more general relations where aRa is false, where R means is reflexive.

If you mean 3=3, and your algebra is that taught in high school, it is equal due to ordering of the real numbers and the definition of the equality operator. If you broaden your idea of reflexivity you can generate irreflexive relations.

Answer 3

You should check out Kurt Goedl's Theory of Incompleteness. If you are interested in questions like this you will be interested in his widely accepted proof that our current model of mathematics is not a complete system, and is therefore not valid.

Answer 4

inasmuch as the statement a=a is meaningful it implies that a=a is the same statement as a=a.

(did you even notice that i switched the a's around that second time? or do i mean the first time? in fact, what does 'switch around' mean under these constraints?).

when substitution is no longer a meaningful operation then clearly one cannot even ask: does a=a without committing a solecism.

Answer 5

An axiom is something so obviously true that you don't need to explain it. There is no possible argument against it.

Answer 6

Look at Reverend C's answer.

Answer 7

Try philosophy section...

(Or wear your Aleister Crowley costume when asking the question in a room full of naked neophytes..mooohaha..moohahah!...)

Answer 8

if A= B then nothing could be definable, nothing could be communicated, life would not exist either. Because life and death would be the same, existence and non-existence would be equal.

Answer 9

A difference which makes no difference is no difference.

Answer 10

it is a mirror of its own self truely