You are clearly equivocating. The law of identity doesn't owe its existence to language, language owe its existence to the law of identity. — Akanthinos

I don't think this can be right. A law is not a law unless formulated, and how could you formulate the law of identity absent language? I think the law of identity is a purely formal principle, which codifies the experience of reiterated or continuous cognition of an entity. Entities are understood as being themselves across disjoint multiple and/or continuous cognition of them, when the perceptual differences between each cognition or within continuous cognition are sufficiently minimal or the sameness is sufficiently great, which is the same. The law of identity is really based on the actuality of continuity. So, I could be fooled by a so-called identical twin, for example if there was discontinuity of cognition. The actuality of continuity is not dependent on language but it cannot become the law of identity without language.

Like I said, Im not taking a stance towar idealism here. The Law of Identity is not a force regulating the universe, nor is it a setting that could have been otherwise. That it seems to apply to everything normally available to us phenomenally is interesting, but not a solid foundation for ontology in my opinion.

However, even in a purely historical manner, A=A must have preceded language. As a requirement for functional informational systems, the simplest cell structure, even the cellular scaffolding itself would have had to, in some way, enact identity.

Since you are the one evaluating the validity of the objection, you can this way safeguard yourself against any form of criticism by simply ignoring anything that could be an objection. Which is what you are doing right now — Akanthinos

Put what you deem to be a valid objection or argument forth. We'll go over it. Let the chips fall where they may.

The A of "A at T1" and "A at T2" are identical because they are the same A, not because of any other attributes such as composition or spatial location. — Akanthinos

Just to be clear, by A and A' I meant two simultaneous instances of the same type, not one A at successive times. So, I'm not sure that we are considering the same example.

A at different times is numerically one because its successive states are linked by dynamic continuity, not because they are made of the same constituents. It is formally one to the extent that its successive states have the same intelligibility (can evoke the same concepts).

The question was "Can identity give rise to differences?" My claim was that it cannot. So, I pointed out the differences between two formally identical instance of the same type. Differences, being relational, cannot be found by examining one object in isolation. We need to consider their relations.

A is identical to A is identical to A is ... But each instances are different and identifiable. The phenomenal compound of "A on pick 1" and "A on pick 2" are different. — Akanthinos

I do not see how this rebuts my claim. Yes, A is numerically one, but your example is not pointing out a difference in A, but in the picking events. These events are different because they stand in objectively different temporal relations to each other.

Attributes and relations do not constitute objects, they reveal something about them. — Akanthinos

I never said they did. Still, they are our means of knowing objects.

Attributes and relations do not constitute objects, they reveal something about them.

I beg to differ : objects have intrinsic properties. Where p is an intrinsic property of object x: if p is not an intrinsic property of object y, then y is not x. i.e. p is a necessary property of x.

The converse is to assume particulars exist without properties. But if that's true, how do properties become associated with particulars?

A at different times is numerically one because its successive states are linked by dynamic continuity, not because they are made of the same constituents. — Dfpolis

You are correct in that constitution (or perhaps, composition would be a better term) is but another attribute which does not equate with the object's identity. And the example was somewhat misleading in that A=A, re particulars, does not really evoke what the law of Identity is supposed to express. Wayfarer pointed this out accurately,

The question was "Can identity give rise to differences?" My claim was that it cannot. So, I pointed out the differences between two formally identical instance of the same type. Differences, being relational, cannot be found by examining one object in isolation. We need to consider their relations. — Dfpolis

Differences are simply potentiality of values deviation between two observations. The determination of identity is the determination of a set of values. Even just non-{previous observation} is sufficient of set of value to reveals a difference.

Yes, A is numerically one, but your example is not pointing out a difference in A, but in the picking events. These events are different because they stand in objectively different temporal relations to each other. — Dfpolis

As any discussion regarding an object stands on the ground of the possibility of the observation of this object, so in the context of a phenomenal discourse, I think its warranted to always allow for the observer's conditions to come in play in the scenario. And the phenomenal description of any determination of identity is temporal.

In more than a way, ontology resist atomisation. Everything tend toward the amalgamation.

There's yet another way to look at this...

Every example of identity includes something to be thought of and something else to think about that. Identity without the process of identification is nonsense... literally sense-less.

One finger cannot point at itself.

If there were no taking account there would be no identification happening. If there is no identification happening there is no identity. Identity is a result of being taken account of.

Existence does not require being taken account of. Identity does.

Existential dependency.

What must already be the case, or what must be happening, or what must have already happened in order for some thing or other(we can always pick a candidate) to exist?

The answer to this is only discovered by knowing what makes our candidate what it is.

What makes an apple pie what it is? It's elemental constituents.

What must be the case in order for apple pies to emerge onto the world stage? More than that.

There's more to existential dependency than just basic elemental constituency.

Differences are simply potentiality of values deviation between two observations. — Akanthinos

Differences can be either actual or potential.

The determination of identity is the determination of a set of values. — Akanthinos

Only if the identity in question is quantitative. Two numerically different protons can have identical masses and charges. We know they are numerically different because they stand in different relations to their environment -- including observers.