The Law of Identity

[Magnus Anderson]

The Law of Identity, one of the fundamental laws of classical logic, states that everything is whatever it is.

It is often expressed as "A is A" and "A = A".

The equals sign represents equality and the two A's are symbols representing one and the same portion of reality.

It is basically saying that every portion of reality is equal, i.e. identical, to itself.

Here in this thread I will present my proof of it and try to address as many fallacious counter-arguments as I can find and cover.

I only do this because there are a bit too many people attacking this law ( and thereby undermining logic. )

1. My Proof
2. "Everything changes" counter-argument
3. "You have to perform a comparison" claim
4. "You have to stop time" counter-argument
5. "You can't compare a thing to itself" argument

[Magnus Anderson]

My Proof

1) An oxymoron is a symbol of the form "X and not X".

2) Nothing can be represented by an oxymoron because nothing can meet the impossible demand of being X and not being X.

3) A thing is either identical to itself or it is not. There is no third possibility.

4) Let X be a portion of reality. Let A be an accurate description of that portion of reality. This means that X is A. If the Law of Identity is false, it follows that X is not A. But since we already said that X is A, it follows that X is A and not A. This means we're claiming that X can be represented by an oxymoron ( "A and not A". ) Yet, from 2, this is not possible.

5) Therefore, the Law of Identity is true.

[Magnus Anderson]

"Everything changes" counter-argument
( Also known as The Flux Argument )

The idea is that, because everything is constantly changing, as Heraclitus said long time ago, nothing ever remains identical to itself.

The problem with this argument is that it compares two different portions of reality. It compares the state of a thing at one point in time and the state of that same thing at a different point in time. Because the Law of Identity is really only comparing a portion of reality to itself, this is actually a strawman argument.

The confusion is created by our linguistic habit to call different portions of reality the same name. A 30yrs old John and a 20yrs old John are both called "John" even though they are two different portions of reality that are not even identical ( the old John and the young John are not same. ) Rather than comparing John's present self against John's past self, a proper test of the Law of Identity in this case would be to compare the entire John's life to itself ( or merely a snapshot of it but only to itself. ) It's very clear that people, and in fact, most things, are not merely moments in time, but rather, relatively long periods of time.

All in all, the Law of Identity does not implicitly or explicitly state that things do not or cannot change. It merely says that every portion of reality is equal to itself.

[Skepdick]

It is basically saying that every portion of reality is equal, i.e. identical, to itself.

It merely says that every portion of reality is equal to itself.

Equivocation

Identity is not identical to equality.

See the long fucking thread where you failed to understand this despite numerous explanations.

I only do this because there are a bit too many people attacking this law ( and thereby undermining logic. )

The only person "attacking" this law is you. By erasing the distinction between identity and equality.

[Magnus Anderson]

Equivocation

Identity is not identical to equality.

The word "identical" does not mean "has the same identity as". It simply means "exactly the same". It two things are identical, it simply means they are equal in every regard. It does not mean they are one and the same thing.

And the Law of Identity is not about identity equality ( i.e. whether or not A and B have the same identity. )
It's about equality.

When they say "A = A", they are not saying "The identity of A is equal to the identity of A". They are saying, "A is equal to A", regardless of what A represents ( it can represent anything including identity. )

So what you're committing here is a strawman fallacy.
( And you're also misusing the word "equivocation". )

[Skepdick]

The word "identical" does not mean "has the same identity as". It simply means "exactly the same". It two things are identical, it simply means they are equal in every regard. It does not mean they are one and the same thing.

Equivocation.

Two things being exactly the same never makes them identical.

That's why there's two of them. Because they aren't identical.

( And you're also misusing the word "equivocation". )

You are misusing your brain.

The Law of Identity is a law of thought, not a law of words; or language.

https://en.wikipedia.org/wiki/Law_of_identity

In logic, the law of identity states that each thing is identical with itself. It is the first of the traditional three laws of thought

[Skepdick]

When they say "A = A", they are not saying "The identity of A is equal to the identity of A". They are saying, "A is equal to A", regardless of what A represents ( it can represent anything including identity. )

You are officially dumber than a chatbot...

Q: does the law of identity state that each thing is identical with itself, or equal to itself?

A: The law of identity traditionally states that each thing is identical with itself—often formalized as "A is A" or "A ≡ A" in logical notation.
This formulation emphasizes identity rather than equality because it's making a statement about the relationship of an entity to itself. The law isn't just saying that an entity has the same value or properties as itself (which would be equality), but rather that it is literally the same entity as itself—which is the stronger relation of identity.

When discussing the law of identity in formal logic, the identity relation (≡) is typically used rather than the equality relation (=) precisely because it's addressing the self-sameness of entities rather than mere equivalence of values.

[Magnus Anderson]

"You have to perform a comparison" claim

The idea is that, in order to determine whether or not a thing is identical to itself, one has to perform a comparison.

No argument is ever given as to why that's necessary provided that there are many different ways of acquiring knowledge. Direct observation is merely one of them.

Some things can be known purely by reason alone, i.e. by analyzing language. And this is one of those things. In this case, there is no need for any sort of empirical evidence. All one has to do is perform a conceptual analysis ( see this post. )

[Skepdick]

"You have to perform a comparison" claim

The idea is that, in order to determine whether or not a thing is identical to itself, one has to perform a comparison.

The only idiot advocating for that idea is you.

A thing is identical to itself - no operation (such as comparison) needs to be performed.

The fact that such an operation cannot be performed on a single entity is true, but also irrelevant. Because the thing is identical to itself irrespective of the operations you can; or can't perform on it; and even if you could perform the operation would only establish equality/sameness, which is weaker than identity.

[Magnus Anderson]

You are officially dumber than a chatbot...

Q: does the law of identity state that each thing is identical with itself, or equal to itself?

A: The law of identity traditionally states that each thing is identical with itself—often formalized as "A is A" or "A ≡ A" in logical notation.
This formulation emphasizes identity rather than equality because it's making a statement about the relationship of an entity to itself. The law isn't just saying that an entity has the same value or properties as itself (which would be equality), but rather that it is literally the same entity as itself—which is the stronger relation of identity.

When discussing the law of identity in formal logic, the identity relation (≡) is typically used rather than the equality relation (=) precisely because it's addressing the self-sameness of entities rather than mere equivalence of values.

In the context of the Law of Identity, there is no need to insist on identity equality over simple equality.

Why?
"A" already refers to the same entity on both sides of "A = A".

There’s no ambiguity—both instances of "A" are understood to be the same thing.
Whether "=" represents identity equality or simple equality, the law still holds.
Aristotle never made this distinction.

He simply stated the principle: Each thing is the same as itself.
He didn’t analyze whether "=" should mean identity equality.
The law is an axiom, not a formal logical statement.

It's a self-evident truth, not a formula that requires precision about types of equality.
So, Who Insists on Identity Equality in This Context?
Overly formal logicians and some modern philosophers who like to make things unnecessarily complicated. But in Aristotle’s original intent, it’s irrelevant. The Law of Identity works whether we use simple equality or identity equality because it’s just saying:

"A is itself."

That’s it. No need to overthink it.

[Magnus Anderson]

The only idiot advocating for that idea is you.

An outright lie.

[Magnus Anderson]

Equivocation.

Two things being exactly the same never makes them identical.

That's why there's two of them. Because they aren't identical.

Again. The word "identical" means "exactly the same". It does not mean "has the same identity as".

Check any dictionary you want. It's out there.

https://dictionary.cambridge.org/dictionary/

identical
adjective
exactly the same, or very similar:
I've got three identical blue suits.

I am aware of the fact that there are people who use the word the way you do. That's fine. But they are a minority. And I see no reason to do the same.

So all you're really doing is arguing for the sake of arguing. Purposeless, destructive.

[Magnus Anderson]

The Law of Identity is a law of thought, not a law of words; or language.

It is indeed a law of thought. But you fail to grasp that thinking operates on symbols. No language, no symbols. No symbols, no thinking.

[Skepdick]

It is indeed a law of thought. But you fail to grasp that thinking operates on symbols. No language, no symbols. No symbols, no thinking.

Thinking doesn't operate on symbols. Symbolic thinking operates on symbols.

That you don't know the difference is why you are an idiot.

The limits of symbolic thinking are pretty obvious to anyone who's tried to explain their thinking to a computer which is only capable of symbolic logic.

[Skepdick]

Again. The word "identical" means "exactly the same". It does not mean "has the same identity as".

Fucking idiot still thinks this is about semantics.

This has nothing to do with symbols, dummy!