Methinks it is axiomatic that everything is self-identical. No proof is required or possible -- hence all of the so-called proofs above simply assume the principle of identity holds for each of their premises.

Methinks it is axiomatic that everything is self-identical. No proof is required or possible -- hence all of the so-called proofs above simply assume the principle of identity holds for each of their premises. — Methinks

I think there's always a reason a la Liebniz.

“A thing is identical with itself.” - There is no finer example of a useless sentence, which nevertheless is connected with a certain play of the imagination. It is as if in our imagination we put a thing into its own shape and saw that it fitted. We might also say: “Every thing fits into itself.” a Or again: “Every thing fits into its own shape.” While saying this, one looks at a thing and imagines that there was a space left for it and that now it fits into it exactly.

Does this spot [O] ‘fit’ into its white surrounding? - But that is just how it would look if there had at first been a hole in its place and it then fitted into the hole. So when we say “it fits”, we are describing not simply this picture, not simply this situation. “Every coloured patch fits exactly into its surrounding” is a somewhat specialized form of the law of identity."

(Wittgenstein, PI, §216)

No proof is required or possible -- hence all of the so-called proofs above simply assume the principle of identity holds for each of their premises. — Methinks

Right. There is at least no deductive, non-circular proof for x=x, because a deductive proof requires formal logic and all of formal logic rests on the assumption that x=x is true/valid.

You can only inductively confirm x=x is true. And you can reason that any other premise makes no sense, goes nowhere, is incomprehensible, and can nowhere be found to be true in thought or reality.

To quote Aristotle (and I'm just quoting it for the fun of the quote, not because I'm trying to say anything about anyone involved in this conversation):

"Some people, through their lack of education, expect this principle, too, to be proved; for it does show a lack of education not to know of what things we ought to seek proof and of what we ought not. For it is altogether impossible for there to be proofs of everything; if there were, one would go on to infinity, so that even so one would end up without a proof; and if there are some things of which one should not seek proof, these people cannot name any first principle which has that characteristic more than this."

I mean yeah, all of mathematics and logic is contingent on the the property of identity. but it's a pretty solid bet. And a pretty necessary one.

too deep. the prop of identity is necessary for basic human function. to know that you are yourself is something we take for granted but is necessary for us to do the simplest of tasks.

To know that you are yourself — Mac

One has to wonder what this could possibly mean. Abstracted from the idle speculations of bad philosophy, if one were to be asked in conversion: "do you know you are yourself?" the only possible reply is "what on earth are you on about?".

x=x being true, can be put in words as 'the necessity of identity.'
If that is understood, now; — Monist

I don't understand how x=x means "necessity of identity". What are you trying to say when you write x=x. or "necessity of identity"? What kind of identity are you talking about and why is it necessary?

I did not understand the underlying reason of your statement:''words are not the thing itself'', how did you come to the conclusion that I am talking about the words. And how did you relate that conclusion with the word 'identity', without considering the concept of identity. — Monist

Because you are talking about "identities" and identities are words that refer to some thing's attributes for the purpose of categorizing those attributes under one word.

Words are things. Agreed. x can be anything, including a word. Agreed. What has this to do with the context here? — Monist

Then, you tell me because I still don't understand the point of your question, "Why x=x?" It doesn't have to be a word we are talking about. What does anything have to do with the context here?

Where did you see that I am defending that x=x is true, I do not know. — Monist

How about in the very same post you replied to me?

x=x being true, can be put in words as 'the necessity of identity.'
If that is understood, now; — Monist

It is important to talk about a thing being itself, to understand what constitutes the being of a thing. For example; if identity is false for things, nothing may even exist. I try to catch what is going on, and why I do that is explained in my other reply. — Monist

How is talking about a thing being itself different than just talking about the thing to understand what constitutes the thing. You seem to be hooked on this word, "being". What do you mean by, "being". How is it different than saying a thing has these particular attributes that we group under one word, - it's identity. Being Monist entails being conceived by their parents and being raised in the very place they were raised. What new knowledge have I acquired about Monist that I already didn't know? To say that Monist is being Monist doesn't give anyone anything useful to explore. x=x is simply redundancy and redundancies are not useful. It seems that identities are useful when talking about some thing without having to talk about all of its attributes. We talk about its attributes when we use the word that we have agreed upon that refers to all of those attributes.

You can talk about many things about the thing, one of them is their identity. — Monist

Is it? Is the label that others put on you, part of what makes you you, or are you you prior to being labeled by others? It seems to me that identities are what one places on another. You are you prior to being identified and identification is useful when you don't want to spend time talking about attributes. Others can describe you. Their description is your attributes. Your identity is a word that refers to all of those attributes.

The absurdity of rational thought constituted on axioms is okay, but me questioning it is not... I prefer being free. — Monist

Rational thought can't be absurd, or else it's not rational.

What do you mean by identity? x=x is a mathematical equation and mathematics deals with numbers, which are not identities in the way you seem to be using the word. In 32 = 32, what is the identity? What are we talking about here? What is 32?

Your are just saying it's bad philosophy, and yet it's the reason we can do math. If there were no property of identity, the human could exist as it does. This notion is so obvious in us but that's only because it was one of our earliest evolutionary adaptations.

Your are just saying it's bad philosophy, and yet it's the reason we can do math. If there were no property of identity, the human could exist as it does. This notion is so obvious in us but that's only because it was one of our earliest evolutionary adaptations. — Mac

It appears that you are confusing biology with mathematics.

They are very related. And dependent in this case.

Math quite clearly employs the principle of identity in some regards. But to move from that to instilling it as some kind of anthrogenic principle - one again has to wonder what that could even mean. It seems like something not even wrong.

They are very related. And dependent in this case. — Mac

Really, show me a excerpt from a book on evolution by natural selection that refers to the reflexive property of x=x.

x=x is the reflexive property. x+0=x is the identity property. Maybe this whole thread is based on a misunderstanding of algebraic properties.

This is basic biology. Identity is not a universal concept. Mammals (In our case) evolved to understand ourselves and other things as individuals. Babies take a long time to develop the awareness that they are themselves. This self-awareness is represented by the the mathematical equation: x=x. No, we cannot deduce this truth, but it remains simply because other accurate mathematical representations of the world are based in it. In other words, as a model of our world, x=x works whether or not you can wrap your mind around it.

Babies take a long time to develop the awareness that they are themselves. — Mac

Again: what does this mean? Babies certainly develop a sense of self, but an 'awareness that they are themselves'? What else would they be? What else could they even in principle develop an awareness of? Does this question have any stakes? Seems like wordplay to me.

If anything, self-awareness arises out of a certain recognition of invarience in relation to an environment; distinction and not identity is primary.

Once again, it is undisputed in biology that humans and other animals evolved a sense of individuality and an ability to differentiate bodies in their environment. The best way we rationalize this is through the expression: x=x. And it just so happens that it works.

Distinction works. x=x is just a representation of that fact.

Distinction works. x=x is just a representation of that fact. — Mac

X=X is a representation of the fact... of distinction?

yep

You must be speaking another language I am unfamiliar with.

oh I thought we were on the same page. So by distinction I assume you mean something is seperate from another. Correct me if I'm wrong.

If identity is 'representitive of distinction' then I simply don't know what you are talking about. Once words stand for their opposites, there are no longer rational grounds for discussion.

I disagree that they are opposites.

Ok.

That people have tried to wring conclusions from tautologies has always puzzled me. I remain puzzled.

Also, to define something is to define its opposite. To make a distinction is to say X is seperate from Q, Y, Z , etc. Thereby, you are separating X from every other object you can. The implication is then that X does not equate to any value but its own. X=X. A philosophy prof. can explain this way better and clearer than I can

I get it's puzzling but just remember, tautologies are interpretations of phenomena, not the other way around.

I don't think you're on the same page. The tautology: X=X comes from our biological capacity to grasp identity. It is a representation/model of one way in which humans understand and navigate the world. THE way really.

There is some sense in what @Mac is saying. You are right that when we assimilate the concept of equality/identity (whenever and however that happens), self-identity is assumed as part of its meaning - it doesn't have to be learned as a principle that comes in addition to the concept. If x wasn't equal to x, then "equal" would not mean what it does. Also, there isn't really a stand-alone "principle of identity" in logic - it comes as part of the package in the definition of equality (identity). However, when we formally define equality, we do have to explicitly postulate self-identity - it doesn't fall out of other postulates.

tldr: While self-identity does not have any meaning as a stand-alone principle, if we need to formalize the concept of equality, we have to state self-identity explicitly as part of its definition.

Couldn't have said it better. This is why I didn't go to grad school. I'd be a bad prof.

There's a need to pretend profundity. It's an odd thing. Is it pretence? Perhaps.