I don’t think A=A is even true. It might be internally true in certain convoluted games but in the actual universe it’s not true. At least not in a physicalist sense.
Why?
because no two physical objects can share the property of location in space and time blah blah blah bundle theory of objects and such
It very much is.
If you’re saying A =/= A, then you’re saying A is not A, which is a contradiction.
Do you think you can accurately represent reality using self-contradictory statements?
The statement A=A is not about two physical objects, it is about one symbol that is equal to itself.
1=1
My car=My car
My car is not equal to your car. Those are two different objects which are not the same as each other. If you just want to talk about cars in general, then my car is a car, and your car is a car, so again, they are both “cars” which means car=car. When you add the part about mine and yours, then mine does not equal yours.
“A = A” is merely saying “A thing is identical to itself”. The thing in question does not have to be a symbol. For example, it can be the state of a car at a single point in time. It’s implying something like “The state of my car at point in time t is identical to the state of my car at that same exact point in time t”. It is most definitely not comparing two different things e.g. it’s not comparing the state of your car today and the state of your car the next moment.
“A” is a symbol representing something, which can even be non physical, such as a quantity. For example, the symbol “A” can represent 10 MPH, or 16 Oranges, or 13 people, or 10 ideas.
“A” is simply a symbol which represents something. So when you say “A=A” you are saying that the symbol “A” is equal to itself, or 13 people equals 13 people, or 10 ideas equal 10 ideas, or 17 Oranges equals 17 Oranges. It is not a statement about how 17 oranges are exactly the same, it is a statement that 17 oranges is equal to 17 oranges.
We’re comparing what the symbol A represents. We’re not comparing the symbol A. It’s similar to how “2 + 2 = 4” is not comparing the symbols “2 + 2” and “4” ( which are different from each other ) but the concepts attached to those symbols ( which are not different. )
Right, the symbol “A” represents something, and the statement A=A is a statement about the symbol “A” being equal to itself. The symbol can represent anything you want it to represent, like I previously explained.
The statement “2+2=4” is a statement about adding two of the same quantity together, and that quantity being equal to the quantity that the symbol “4” represents. It is not about comparing the symbol “2” to the symbol “4” because that would be “2=4” and that is not a true statement, because the quantity that the symbol “2” represents is not equal to the quantity that the symbol “4” represents.
He wants you to admit that it represents a ‘thing’.
There are these things, in existence…god-particles - indivisible, immutable singularities.
A symbol representing a ‘thing’…like ‘one.’
There is no ‘one’…it is a symbol that can represent any unity.
Logical Rules are meant to discipline a mind to reality, because it can manufacture any absurdity.
The Law of Identity is a response to the absurd…since in the world this is confusion is impossible…but in the mind it must be affirmed because the mind often confuses its representations with the represented.
“Thing” here is a slice of dynamic space/time, converted to an idea, a concept - an abstraction.
A=A is a law referring to a continuum.
A dog, is the same dog across space/time…it is not different dogs.
Rex is Rex even if time has changed his appearance. Why?
Genetics is a continuum…not a thing…but a process.
So a dog, named Rex, or simply A, is the same as itself, across space/time, even though it changes.
Memory connects it.
Yes but I think you’re saying we’re merely comparing symbols rather than what these symbols are representing. If that’s the case, I disagree with you. We’re not comparing symbols themselves, we’re comparing what they are representing.
“A = A” merely means “Whatever A stands for, it is identical to itself.”
Right, so it’s not comparing symbols, it’s comparing what these symbols represent.
If you define the symbol “A” to be a dog named Rex, then what you have defined is independent of how “Rex” appears, or ages, or moves, acts, or exists.
What you have done is define the symbol “A” to equal the name “Rex”, that is all you’ve done.
So another example:
I define the symbol “v” to be the velocity of the dog named Rex.
Regardless of how fast Rex travels, the symbol “v” will represent that velocity at every time t.
So at t=0, v=0
At t=1 second v=2 feet per second
At t=2 seconds v=4 feet per second
At t=3 seconds v=6 feet per second
As you can see, the symbol “v” is representing a dog named Rex’s velocity, and that velocity is changing as time elapses.
The symbol “v” is a placeholder for Rex’s velocity at any given time t, and it can stay the same or it can change.
In this case, Rex’s velocity (v) is changing over time by 2 feet per second. In other words, the symbol “v” is increasing by 2 feet per second for every second that elapses.
The definition of acceleration is the rate of change of velocity.
If Rex continues to increase velocity by 2 feet per second then he has a constant acceleration of 2 ft/sec^2, which can be represented as the symbol “a”, which remains constant, all the while the symbol “v” is changing as time elapses. By the way, the symbol “t” represents time, which always changes…
I am merely saying that “A = A” means “What A stands for is identical to what A stands for” and not “Symbol A is identical to symbol A”.
Noone said anything about indivisible and immutable things.
It’s a physically different dog, so it’s not the same, but it’s still a dog, because it still belongs to the class we call “dog”. And it’s still Rex for the same exact reason.
I think everyone agrees that the symbol “A” is never the symbol “B.”
It goes without saying that the symbol “A” is the symbol “A.” How could the symbol “A” be symbol “B”??
The symbol - word - is always exactly the same.
The dog, it may refer to - represent - is never exactly the same dog.
A static symbol refers to a dynamic process - a continuum.
There is no thing…thing is also another symbol/word…like one/nil.
It is in the mind, referring to what is outside the mind.
He defined the symbol A to be equal to the symbol “Rex”, which the symbol “Rex” he defined as a dog’s name.
He didn’t define anything to be an exact copy at every time t. Obviously a dog named Rex will change over time, just like your “v” will change over time.
Just because “v” changes doesn’t mean it has to be redefined. The definition of the symbol “v”, as I define it, means the velocity of Rex as it changes or stays the same.
The symbol “v” is defined to be a placeholder for a variable that can change or stay the same, all the while the symbol staying the same, which is the symbol “v” as I defined it.
Keep talking. Eventually, someone may make it happen. 
I am not sure why you’re saying this. I don’t disagree, I just don’t see the relevance of it.
All I am saying is that “A = A” is comparing what these symbols are representing and not the symbols themselves.
It’s saying “Whatever A stands for, what it stands for is identical to what it stands for”.
The symbol - word - is always exactly the same.
The dog, it may refer to - represent - is never exactly the same dog.
A static symbol refers to a dynamic process - a continuum.
There is no ‘thing’…thing is also another symbol/word…like ‘one/nil.’
It is in the mind, referring to what is outside the mind. It represents it.
A dog is a category that can refer to any individual manifestation that shares the same traits.
In reality this need not be stated, because a dog is not any dog, but always a member of a category, a species.
A dog is always the same continuum we identify as ‘a dog’ - or Dog A.
Logic has to make sure the mind’s representations do not become confused or referring to absurdities, like a square/circle, or an eternal dog, or a dogman…or a universal DOG.
So ‘a Dog,’ - one dog - simply ‘A,’ is always equal to itself, representing this continuum.
A dog, named Rex, or A, is not another dog named B, even if it is never exactly the same across space/time…it changes over time…in miniscule ways.
Dog B may look more like Dog A in the past - it may be its offspring - …but Dog A has aged and is no longer like it was in the past…and yet, the same dog…meaning the same dynamic continuum.
I am merely pointing out to you that nobody was trying to claim that the statement “A=A” was a comparison of symbols, but that it is a comparison of what the symbols are defined as.
The symbol “A” can be defined as 17 oranges or a dog named Rex.
If I define “A” to be the name “Rex” then A is equal to “Rex”, or A=Rex.
If I define “A” to be 17 oranges then A is equal to 17 oranges, or A=17 oranges.