The Law of Identity: What does it mean?

I accept of course that the rational consideration of empirical evidence to draw reliable conclusions requires that we not change the designations of things without specifying that we do. For example, I can talk meaningfully of digging some amount of ore to extract the iron from it to use it to make rods to be used as construction material for buildings. Here, I just moved from one designation, "ore", to another, completely different one, "buildings". Yet, we can all understand that only a part of the ore has been used to make up only a part of possibly different buildings. So, where would be the "identity" of the original ore when I am now talking only of buildings?! So, I don't buy the interpretation of the Law of Identity as being a rule to constrain our descriptions so that we could have rational conversations. We certainly have rules, syntactic, grammatical, lexical rules to do that job and so we don't need any additional "Law".
Please also note that the term itself, "law", doesn't suggest at all anything like a linguistic constraint. The proper term in this case would be "rule", not "law".
And the Law of Identity is a fundamental axiom of standard logic, not a linguistic rule.
Also note that, in any logical formal language, say, anything mathematical, including computer languages, where the coherence of the designations we use is critical, we may start with two distinct designations of values, e.g. A and B, and end up deducing that A = B, meaning A and B are identical values. If the Law of Identity applied here, A would A and B would be B and the twain shall never meet. Yet, they do: A = B.
We can also choose to assume for example that A = B in order to prove that, in fact, A is not at all equal to B. If the Law of Identity referred to identities as designations, such as "A" and "B", then assuming A = B would preclude ever deducing A not equal to B, since the Law of Identify is indeed fundamental in logic.
Think also of the designation of variables: x, y, z etc. What would be their identity? They have a designation: x is x. So, per the Law of Identity, if it applied, x couldn't possibly ever get to be equal to 2! Yet, if we now posit or even deduce that x = 2, we're saying exactly that.
EB

 

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