The Law of Identity is Refuted by Time/Change

[Magnus Anderson]

Within mathematics therefore no two things can be exactly alike. Things that are alike in all their properties are the same thing. However for practical purposes two things can be alike enough in their properties for practical purposes.

Whether or not two things can be exactly alike first and foremost depends on the definition of the term "exactly alike".

According to the standard definition, two things are exactly alike if they have the same properties. There is no need for them to be ona and the same thing. They just need to have all of their elements / properties / whatever you call it in common.

If that's what is meant by "exactly alike", then there can indeed be things that are exactly alike, both within and outside of mathematics.

Any two men have exactly the same gender. They are both males.

If tallness is defined as either tall or short, and if everyone who as above 180cm is tall and everyone who is not is short, then a man who is 185cm and a man who is 195cm have the same tallness ( both are tall. )

In mathematics, sets A = { 1, 2, 3 } and B = { 1, 2, 3 } are exactly alike.

But if what's meant by "exactly alike" is "one and the same" then no two things, within or outside of mathematics, are exactly alike because no two things are one and the same thing.

[Magnus Anderson]

You can choose to ignore any unique identifiers. In so doing he is weakening the very concept of identity to mere similarity.

Magnus isn't really talking about identity. Magnus is talking about sameness. And sameness is not the same as similarity. The difference between the two is that sameness is 100% similarity.

And by not focusing on, and thus, by not comparing unique identifiers, I am sure nothing is done to the identities of things as well as to the concept of identity. They remain intact. No weakening takes place.

[Magnus Anderson]

For some practical purpose Triangles are functionally equivalent to Squares.

They are both Euclidian geometric shapes.
They are both closed forms comprised of straight lines e.g polygons.
They both have at least 3 sides; and at least 3 angles.

You're talking about functional equivalence.
I am talking about sameness.

"Functionally equivalent" means "equally useful for attaining a certain goal".

It's absolutely true that triangles and squares can be functionally equivalent.

But that does not mean they are identical.
In fact, they are not.

Triangles have 3 sides. Squares have 4 sides. How exactly is that identical?
You can say they are similar -- that much is true.
But similarity is not the same as sameness.

[Magnus Anderson]

I am not confusing anything. I am simply pointing out your notion of "identity" is confused.

You have a track record of misunderstanding what other people are saying.

This is most evident in your understanding of the terms such as "square-circle" and "unicorn".

Yes, even the term "unicorn" is difficult for you to understand.

And trying to deal with people like you -- and I am saying this primarily for the sake of those who are reading this thread -- is very difficult.

And in this particular case, you misunderstood my stance. You think that my "notion of identity is confused". I have no desire to ask for you to explain why you believe that to be the case. You've proven yourself to be incapable of being constructive over and over again.

[Magnus Anderson]

I've made no claims as to legitimacy or illegitimacy. I am just doing what you are doing.

You are the one insisting that there's a difference in legitimacy.

Cry me a double standard.

You did. You said, or at least, implied, that by following my logic, you can prove that a square and a triangle are identical. That can only follow if you're choosing what you're comparing during the process of comparison ( which is an instance of illegitimate arbitrary choosing, which is not a part of my procedure ) or if you're adding extra steps to what I'm doing ( which themselves are illegitimate and which are not part of my procedure. )

So no, you're not really doing what I'm doing.
You're not replicating my steps properly.
You merely think that you are.

[Magnus Anderson]

And given my arbitrary criteria for identity - the contents of the two portions of reality are identical.

Why should anyone care about your arbitrary definition of the word "identical"?

[Magnus Anderson]

Buddy, all I am saying is the implication of YOUR concept.

You wish.

Why not?

Because you're comparing a proper subset of A and a proper subset of B.

A proper subset of a set is not identical to that set.

Thus, the fact that a proper subset of A is identical to a proper subset of B does not mean that their supersets, A and B, are identical.

Here's an example:

A = { 1, 2, 3, 4 }
B = { 1, 2, 3, 5 }

Let A' and B' be the proper subsets of A and B respectively. Let them be identical and as large as possible.

A' = { 1, 2, 3 }
B' = { 1, 2, 3 }

It is true that A' = B'.

However, it does not follow that A = B.

Obviously, A and B are different.

A common mistake is to confuse A' for A and B' for B. A mistake very similar to that of equivocation.

I am making a mistake in executing your methodology?!?

Exactly. You are NOT executing my methodology. You are executing a misinterpretation of it ( something that you often do. )

And right now, you're acting as if you have more authority than me on whether or not what you're executing is truly my methodology.

But I am just offering immanent critique!

You're offering a strawman argument.

[Noax]

You need to post more often Ben. 9 posts in 3+ years is too little, and this forum needs a better percentage of the educated.

You can make a cross section of an apple through time, or through any of it's other dimensions.
Cross sections of an apple along it's y axis are different than each other,
as cross sections of the apple along it's time axis.

Remember that those four axes can be tilted in all sorts of ways, although it's considered polite to keep them orthogonal as you do so.
The time axis for instance does not have a single orientation available, so the full set of coordinates for the apple is dependent on your choice of not only where to put the origin of your coordinate system, but on the chosen orientation of the four axes.

[Skepdick]

Magnus isn't really talking about identity. Magnus is talking about sameness. And sameness is not the same as similarity.

Magnus keeps confusing himself.

The difference between the two is that sameness is 100% similarity.

How is that a "difference"? How much similarity is 50% sameness? How much sameness is 50% identity?

[Skepdick]

For some practical purpose Triangles are functionally equivalent to Squares.

They are both Euclidian geometric shapes.
They are both closed forms comprised of straight lines e.g polygons.
They both have at least 3 sides; and at least 3 angles.

You're talking about functional equivalence.
I am talking about sameness.

"Functionally equivalent" means "equally useful for attaining a certain goal".

It's absolutely true that triangles and squares can be functionally equivalent.

But that does not mean they are identical.
In fact, they are not.

Triangles have 3 sides. Squares have 4 sides. How exactly is that identical?
You can say they are similar -- that much is true.
But similarity is not the same as sameness.

Do you need a bigger stick to beat around that bush?

You clearly have no idea what sameness is. You would've told us by now.

[Skepdick]

You have a track record of misunderstanding what other people are saying.

You have a track record of ignoring your errors by pretending to be misunderstood.

[Skepdick]

You did. You said, or at least, implied, that by following my logic, you can prove that a square and a triangle are identical.

I didn't imply it. I am asserting it to be true.

If you ignore all uniqueness identifiers (something you said you can do) what you are left with is non-uniqueness identifiers.

That can only follow if you're choosing what you're comparing during the process of comparison.

That's simply false. How many times do you need it explained?

BEFORE the process of comparison I have CHOSEN to ignore ALL uniqueness identifiers; and compare ALL non-uniqueness identifiers.

which is an instance of illegitimate arbitrary choosing

See. You are lying. I have chosen it BEFORE, not DURING the process of comparison.

So it's legitimate.

So no, you're not really doing what I'm doing.
You're not replicating my steps properly.

You are lying.

[Skepdick]

Why should anyone care about your arbitrary definition of the word "identical"?

I have absolutely no idea why you think I've ever offered you a definition of the word "identical".

Identity is not a word.

[Skepdick]

Because you're comparing a proper subset of A and a proper subset of B.

A proper subset of a set is not identical to that set.

So what? You said you aren't talking about identity.

You are talking about a process where unique identifiers can be ignored.

Thus, the fact that a proper subset of A is identical to a proper subset of B does not mean that their supersets, A and B, are identical.

So now you are talking about identity? I thought you weren't.

Here's an example:

A' = { 1, 2, 3 }
B' = { 1, 2, 3 }

It is true that A' = B'.

It depends on what you mean by "=". You are using it multiple senses.

Is this statement true?

A' = { 1, 2, 3 }

However, it does not follow that A = B.

It may follow. Depending on which sense of "=" you are using.

When you stop equivocating "=" you might unconfuse yourself.

A common mistake is to confuse A' for A and B' for B. A mistake very similar to that of equivocation.

An even more common mistake is to confuse the various senses of "='.

Exactly. You are NOT executing my methodology. You are executing a misinterpretation of it ( something that you often do. )

Why are you lying? You said unique identifiers can be ignored.That's what I am doing.

And right now, you're acting as if you have more authority than me on whether or not what you're executing is truly my methodology.

From the moment you communicated your methodology I have identical authority to you.

Am I not executing your methodology? Am I not ignoring unique identifiers?

Did you miscommunicate your methodology? That's your fault.

When you communicate ideas you commit yourself to their logical implications.

You're offering a strawman argument.

You are lying. I am neither straw-manning nor steel-manning your position.

I am applying your methodology exactly as communicated.

The mistake that Leibniz made is that he overlooked that 1) we choose what we're comparing, and 2) we can ignore, and thus leave out from the comparison, unique identifiers such as location.

It is the application of your methodology which enables me to assert that Triangles = Squares.
Did you impose a limit on this principle? No!

You aren't being "misunderstood". You are a special fucking snowflake who can't admit error.

[Magnus Anderson]

How is that a "difference"? How much similarity is 50% sameness? How much sameness is 50% identity?

When we say that things are similar, it means they are not identical but close to being identical.

Similar: approximately identical.

Similarity is a weaker form of sameness.

So there's quite a bit of a difference.

Don't confuse the percentage-based concepts ( "50% similar", "75% same", "25% different" ) with the binary ones ( "same", "similar", "different". )

The binary same is equivalent to the percentage-based 100% similar.

The binary similar is not and it's equivalent involves a percentage that is less than that.