Morphy - To your earlier point. It is true that you need know nothing of the assumptions that mathematics is based on in order to do mathematics. That doesn’t mean that those assumptions are not there. Any more than you need to know the assumptions of a moral system in order to live by it.
Are you saying that it’s ambiguity that you attack? A noble pursuit for a philosopher. But the fact that there are several different types of definitions, all of which may be useful in one context or another, does not produce ambiguity. Not knowing which kind of definition you are using may very well produce ambiguity.
There is a difference between a dog and a number. Dogs exist.
A = A is the shortest version, if you will, of the law of identity. It can be “proven” in only the most trivial sense. It is true, however, if anything we say is true.
I’d put those in two distinct classes ~ different. The ‘assumptions’ in maths are what?.. I could see that our idea of ‘1’ pertains to a given object or item and there are none. Yet the mathematics has its own logic and reasoning which is undeniable.
Yes absolutely, and I think humanity largely achieves it ~ after much revision of course. So it is equally important to be sceptical such to remove ambiguity. In a sense existence has enough of both for philosophy to exist – which is good, its only bad if people think there is only one or the other.
So I would say “that’s a big if”, as I put in bold above.
Trotsky would seem a little misguided in the paraphrase of him below in so much as it doesn’t necessarily understand the law of identity very well, but what he states nonetheless has some merit to the situation at hand;
Excerpt from the “ABC’s of Material Dialetics”
Now to further elaborate:
Let us consider a world in which existence manifests in three distinct aspects:
Property ~ some measurable and defining character present in some entities and not others.
Entity ~ some unique coexistence of properties identifiable by its unique relations with other entities.
Relation ~ some conceptual linkage between properties and entities, or between entities alone.
—
Of this world we may state two things:
Insofar as the world is objectively real, only property has objective reality. Entity can be seen as a mere conceptualization of property relations that have meaning only in the conceiving mind.
Insofar as the world is subjectively real, only relation has subjective reality. We can perceive property only through the filter of entity and comprehend entity only within the measure of relation.
—
There exist those properties necessary in combination to create the subjective impression of a spoon; there exist those relations with other conceptual entities that require us to posit a spoon.
So the law of identity can become rather useless ultimately, when dealing with the material, physical realm. But not so much the conceptual. Now - “Randians” as you may know seem to attempt to take Aristotle’s law as the grounds for creating the cult that they know everything objectively and that’s all because A=A. It gets ridiculous there, but that’s really another subject. I just don’t see a whole lot of reason to state A=A anymore, really.
The bigness of the if does not matter. You will never understand identity if you cannot understand that the bigness of the if is not relevant.
Trotsky evidently knew nothing of logic. I suspect he was making a political point and not a logical one. Evidently, so are you. Trying to debunk an idea that is patently obvious to anyone who has sincerely looked into it in order to make a political point is (speaking for myself) intellectually dishonest and ultimately boring.
Trotsky was making a political point yes - but his point also has something to do with the physical materialistic realm, in there the nature of identity is useless without conceptualization, and the conceptualization of identifying identity is subjective - as spoon boy shows.
WW - one of us, at least, is getting lost on your overly-complex use of language. What is “the nature” of identity? What we’re talking about is just a foundational idea about language. It’s not rocket science. “Subjective” ain’t got nothing to to do with this. If you wish to speak intelligible, you will adhere to the “law” of identity- even if you have no idea what it is. If you don’t want to speak intelligibly, ignore the law.
So far, you seem to ignore the law. That’s okay. But some friendly advice - try to keep it simple. “More complicated” is not “more intelligent” and certainly not more “philosophical”.
Sure, its not rocket science, it’s possibly the most basic concept that might be overlooked in that its so basic and certainly the law of identity has nothing to do with subjectivity. I don’t know how we can avoid straying from the law of identity, actually. Unless when I say “Unless” I actually mean “Popcorn”, but then didn’t I just define “Unless” as popcorn in my meaning and as such “Unless” was identified as Popcorn in my meaning, which means that "Unless became a conceptual construct of what I understand popcorn to be? Of course, saying Unless means Unless doesn’t get us anywhere to where I was trying to bring you. But speaking intelligibly in a manner that can convey the point might be lost on me as this would be my third attempt and I don’t think I can convey my point anymore cogently than I did previously, so I reduce my efforts to a stream of consciousness which probably doesn’t do you any better.
Unfortunately Faust as you may or may not see- I nor anyone I would say cant escape the perils of identifying identity. Stating something is itself is very easy, but what is itself?
Perhaps the law of identity can help us? BY that, lets use it for the former sentence.
I am with Trotsky here, I don’t think that things have an absolute identity, nor that [and because of that] an identity of one given thing can ever 100% correlate to that of another.
Take the universe as an example, there are always aspects in superposition and aspects manifest ~ and that is not an whole [absolute entity]. Then there are relative positions where the mere observation of one particle upon another changes it.
With people/politics, one person is a different individual [composition/environment etc] to the next, yet we are all equal parties in that we are subjects of environments and situations which may be changed or even swapped. we inherit all of that as opposed to create ourselves and the world, ergo there is nothing about any given individual which makes them better/worse than any other.
I’d suggest that there is a vast difference between identity philosophically, and in politics. Interesting analogously but whole worlds of difference between the two fields.
Morphy. The law of identity doesn’t get into metaphysics. It defines equivocation. To break this law is to equivocate. To equivocate is to break this law.
Doesn’t anyone ever look anything up in an actual book around here?
Or at least Wikipedia?
There might even be a Facebook page on the law of identity.
It’s an actual thing. I’m not just making this shit up.
Well, obviously there are two As there … one on either side of the ‘is’ … so there is a left A and a right A. Those differences prove that the two As are not the same A. They could only be the same if they were in exactly the same position on one side.
Another problem with that law is that “it depends on what the meaning of the word ‘is’ is”.
Therefore, easily refuted using pretty straight forward logic.
The variable “x” throughout a mathematical argument refers to the same x throughout the entire argument. That is all the “Law of Identity” means … “Don’t change the name of the variable during your argument”. “A” is the name of the variable in this case.
