The Law of Identity as Strictly "P"

[Eodnhoj7]

The occurence of the same thing, under the same respect and at the same time cannot be observed under multiple instances as the instances necessitate a seperation. P=P necessitates multiple instances of the same thing, thus each observation is a different context.

At best identity should be described simply as "P", not "P=P".

[Skepdick]

The occurence of the same thing, under the same respect and at the same time cannot be observed under multiple instances as the instances necessitate a seperation. P=P necessitates multiple instances of the same thing, thus each observation is a different context.

At best identity should be described simply as "P", not "P=P".

It's not even a law. It simply says "P" represents something. It could represent anything and everything.

The law of identity asserts that P = P. The problem arises because the equality operator is binary: it takes two arguments, but there is only one P.
That's why P = P is a meaningless assertion. Where did the second P come from?

It's trivial to see when you re-write P = P as equal(P,P). Where does the second P come from?

Equality is Dyadic. Identity is Monadic

[Eodnhoj7]

The occurence of the same thing, under the same respect and at the same time cannot be observed under multiple instances as the instances necessitate a seperation. P=P necessitates multiple instances of the same thing, thus each observation is a different context.

At best identity should be described simply as "P", not "P=P".

It's not even a law. It simply says "P" represents something. It could represent anything and everything.

The law of identity asserts that P = P. The problem arises because the equality operator is binary: it takes two arguments, but there is only one P.
That's why P = P is a meaningless assertion. Where did the second P come from?

It's trivial to see when you re-write P = P as equal(P,P). Where does the second P come from?

Equality is Dyadic. Identity is Monadic

The law of identity is a law of representation, it specifies how a phenomenon is identified.

In agreement with the rest.

[Skepdick]

The law of identity is a law of representation, it specifies how a phenomenon is identified.

It doesn't specify HOW it is identified. However the phenomenon is identified, it's assigned to the placeholder P

But then things get totally weird in Classical logic...

The identity law is: P is P. A rose is a rose is a rose. So P is a placeholder for a rose.
Then the law of excluded middle (LEM) says: either P is true; or ¬P is true.

What could a true not-rose possibly be like?!?

[Eodnhoj7]

The law of identity is a law of representation, it specifies how a phenomenon is identified.

It doesn't specify HOW it is identified. However the phenomenon is identified, it's assigned to the placeholder P

But then things get totally weird in Classical logic...

The identity law is: P is P. A rose is a rose is a rose. So P is a placeholder for a rose.
Then the law of excluded middle (LEM) says: either P is true; or ¬P is true.

What could a true not-rose possibly be like?!?

1. A non rose would be all contexts surrounding the rose.

2. It specifies how it is identified by pointing to the phenomenon. The placeholder is an act of pointing.

But I see your point and would have to agree with most of it.