GENIUS FORUMS

chikoka wrote:The axiom of identity is actually an equivalence relations, meaning it is a relation mapping elements in a domain to elements in the range or codomain. It has other important properties such as being symmetrical, reflexive and transitive, more on this later.

Yeah, I guess it's better to go straight for the reflexive property of equality. If you need mathematical language at all. But by using the equation as some "equivalence relation", the complexity multiplies and the elaboration obscures, like you already demonstrated. But the real use case goes perhaps deeper: what makes a thing, a thing? What gives it existence for you? Are you always exactly you? The term "i am (that) i am" has been used as well for similar reason I believe.

Once I wrote about this:

• Existence asserts itself as logical conclusion: existence is the prime mover to the question of its existence.... to exist means to stand out and only by standing out [oneself] reflection occurs.

Take the relation:

A is A _________ 1 (express an identity)
A is not-A ______ 0 (Doesn't express an identity)
Not-A is A ______ 0 (Doesn't express an identity)
Not-A is not-A ___ 1 (express an identity)

It isn't functionally complete (express all relations). To have a functionally complete relation we would need to consider "not-A is not-A" as not expressing an identity and then negate that:

- _____________ - _ Negation
A is A _________1 _ 0
A is not-A ______ 0 _ 1
Not-A is A ______ 0 _ 1
Not-A is not-A ___ 0 _ 1

Which could mean that A is A (1 is 1) does not express an identity, and we would need a relation of non-identity to properly express an identity. Which maybe means the subject-obejct relation (the object being not-A), or touching something.

Bobo wrote:Take the relation:

A is A _________ 1 (express an identity)
A is not-A ______ 0 (Doesn't express an identity)
Not-A is A ______ 0 (Doesn't express an identity)
Not-A is not-A ___ 1 (express an identity)

It isn't functionally complete (express all relations). To have a functionally complete relation we would need to consider "not-A is not-A" as not expressing an identity and then negate that:

- _____________ - _ Negation
A is A _________1 _ 0
A is not-A ______ 0 _ 1
Not-A is A ______ 0 _ 1
Not-A is not-A ___ 0 _ 1

Which could mean that A is A (1 is 1) does not express an identity, and we would need a relation of non-identity to properly express an identity. Which maybe means the subject-obejct relation (the object being not-A), or touching something.

If the axiom of identity is a concept it is meaningless always.
Your whole post is meaningless in all contexts so how can it be true.
You might as well have typed this: jksdgtiweahh,zxjgfkbklasdbfkl;asdjbhfisu

While 'A is A' doesn't express an identity 'not-A is not-A' does, so we would have to turn 'A is A' (concept) into 'not-A' (objectify) before expressing an identity, and that is what 'A is A = 0' does.