What do you mean by a term? — The Great Whatever

Basically anything that abides by the law of identity ("a thing is equal to itself"). To be absolutely clear, to deny the law of identity isn't - for me anyway - to say that 'things aren't equal to themselves', but to deny that the very category of equality is properly applicable to 'things' at all; that is, it is a category error as such to invoke equality (whether it be to affirm or deny it) when speaking ontologically, other than as a heuristic of everyday speech. Or differently again: there is nothing 'equal' or 'unequal' in nature, no identities. And even in everyday speech, equality is always invoked respect to some quality or another, rather than as a 'brute fact' of identity, as it were.

The closest thing - that I know of - in formal logic that thinks along these lines in dialetheic logic, but even dialetheic logic seems inadequate to me to the extent that it simply denies the law of identity, rather than putting the very idea of equality into question (hence it's admission of contradictions, which are only ever contradictions from the perspective of identity). Thus for example, Deleuze's metaphysical project takes as it's starting point the attempt to think a concept of difference which is not parasitic or derivative of identity and equality, and hence contradiction. So in a critique of Hegel that might well be word for word written about dialetheism, he writes: "Hegelian contradiction appears to push difference to the limit, but this path is a dead end which brings it back to identity, making identity the sufficient condition for difference to exist and be thought. It is only in relation to the identical, as a function of the identical, that contradiction is the greatest difference." By contrast, Deleuze will look to explicate what he will refer to as 'difference-in-itself'. The exact details aren't important, but I just want to impart a flavour of where I'm coming from when I asked if analytic philosophy has the resources to question the nature of logic - I really mean this kind of absolutely 'foundational' stuff, as basic as the law of identity.

You can at least see, I hope, how a position like Deleuze's is even 'more radical' than dialetheism, and given the suspicion with which paraconsistency alone is viewed among the analytic community, I this sort of stuff is mostly viewed as beyond consideration. But for me, this is more or less the most important stuff, and most of the philosophical atmosphere in which I saunter in deals with things at this level, and at length. When I ask if AP asks after the nature of logic, it's at this level of generality that I'm referring to.

*I don't mean to ignore what you've said about the strategies employed in logic to deal with all the things you mentioned, but I'm simply too out of my depth there to have anything worth saying.

I imagine that it's a similar feeling to what happens when the uninitiated read some of some of Heidegger or Derrida for the first time. — StreetlightX

In speaking of Heidegger, it's of course entirely appropriate to refer to those initiated and those uninitiated. The same was the case with the ancient mystery religions; only those who had been initiated could claim to understand their rites and rituals, as they couldn't be disclosed to the uninitiated.

But Heidegger could write clearly enough when he wanted to--for example in his essay The Question Concerning Technology, and of course in his extravagant praise of Adolf Hitler.

Ah, it's been some time since I could indulge myself in that fashion. I confess I didn't have the strength to resist the opportunity.

Heidegger notwithstanding, though, I suspect that what Dennett says regarding academic philosophy might also apply, accurately enough, to other academic disciplines.

The closest thing - that I know of - in formal logic that thinks along these lines in dialetheic logic — StreetlightX

I am not too familiar with dialetheic logic, but my understanding is that dialetheism doesn't have to do with identity, which is a relation, but with the existence of truth value gluts (a single proposition having more than one truth value simultaneously), where these truth values are related by negation. That gives you the possibility of true contradictions. That does not, so far as I know, require changing the law of identity.

I think it's also worth noting that the law of identity itself is not really part of the apparatus of classical logic – propositional logic doesn't even deal with identity of individuals, and first-order logic only introduces the identity relation '=' as a special subcase of a regular relation, which you have to define in giving your interpretation. So you might say, for example, that the '=' relation is the maximal exclusively reflexive relation: it holds between any individual x and itself, and to no others. But that seems to me to be a theory about how identity should be interpreted. Nothing stops you, even in classical logic, from defining the identity relation differently.

What classical logic does so is force you to specify a domain. But a domain is filled with actual things, after all, and if their identity is somehow not determinate, then the choice of the domain sill simply reflect that. I don't think the logic forces you to make this decision. The issues about identity seem to be just to have to do with simple rules of language, such as coreferential expressions preserving truth when swapped out for each other, or the intuitive 'logical truth' of all appropriate statements of the form 'I'm myself.' So to say something like this:

To be absolutely clear, to deny the law of identity isn't - for me anyway - to say that 'things aren't equal to themselves', but to deny that the very category of equality is properly applicable to 'things' at all; that is, it is a category error as such to invoke equality (whether it be to affirm or deny it) when speaking ontologically, other than as a heuristic of everyday speech. Or differently again: there is nothing 'equal' or 'unequal' in nature, no identities. And even in everyday speech, equality is always invoked respect to some quality or another, rather than as a 'brute fact' of identity, as it were. — StreetlightX

I'm not sure what to make of it. Taken seriously at face value, it's clearly false: people do in everyday speech treat things as if they are themselves, and it's not clear behaviorally what the opposite would look like. One option might to invoke cases where people treat the same thing in contradictory manners, but in such cases, we often say of people either that they're making some kind of error, because they're misinformed (like when they don't recognize someone they've met before) or irrational.

If you then want to push back a stage by saying that you deny some set of 'things' to begin with that we can then call equal to themselves, okay, but natural language doesn't seem to disavow this commitment, since it has individual-denoting expressions, so your claim would have to be weakened severely, to be a claim about special modes of philosophical discourse that are at odds with ordinary speech (as Hegel's writing, by his own admission, purposefully is).

As far as equality being invoked with respect to some quality, do you mean things like 'the same statue' versus 'the same lump of clay'? If so, you might be interested in Gupta relative identity.

To me it seems like individual denoting expressions are considered the problem. When we make a statement denoting an individual, we draw them up in reference to our own statememt. I say, "by identity, you are The Great Whatever who posts on The Philosophy Forum, " as if my statement of identity gave you as a brute fact.

But do you need my statement to be? What is no-one claimed that "by identity" you were The Great Whatever, would you somehow cease to exist?

"By identity" is more or less rhetorical. We appeal to it to defend a particular way of thinking or speaking, as if your very existence depended upon us saying: "You are the Great Whatever who posts on The Philosophy Forum." It's a postering for asserting a particular understanding of you, not a respect or description of you as an individual.

What classical logic does so is force you to specify a domain. But a domain is filled with actual things, after all, and if their identity is somehow not determinate, then the choice of the domain sill simply reflect that. I don't think the logic forces you to make this decision. The issues about identity seem to be just to have to do with simple rules of language, such as coreferential expressions preserving truth when swapped out for each other, or the intuitive 'logical truth' of all appropriate statements of the form 'I'm myself.' — The Great Whatever

I'll have to do some extended reading on this to give a proper reply; what I'm getting from this is that I need to focus on the notion of truth at play here, and while I've the germ of how to go about it, it's not enough for a decent discussion. I think I'm going to start a thread on the question of negation to try and discuss some of these topics in another capacity.

. Taken seriously at face value, it's clearly false: people do in everyday speech treat things as if they are themselves, and it's not clear behaviorally what the opposite would look like. — The Great Whatever

On this though, I'd have to disagree. I don't think that at any point during our usual day to day activity, we go around thinking 'that thing there is what it is!'. A bit like Heidegger's broken hammer, these sorts of thoughts only occur in a highly abstract environment disconnected from lived experience; as far as identity goes, for the most part we think things like 'these things are identical - with respect to their color', or 'those two things are identical with respect to their function (for my needs)'; in any case identity and equality are defined with respect to some external parameter or another. To say that a thing is identical to itself, when you think about it, is an exceedingly strange formulation. Wittgenstein had something of this intuition when he declared quite flatly in the Tractatus that "roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing."

As far as equality being invoked with respect to some quality, do you mean things like 'the same statue' versus 'the same lump of clay'? If so, you might be interested in Gupta relative identity. — The Great Whatever

Peter Geach's thesis of relative identity makes trouble for Leibniz's law of indiscernibility of identicals. Wiggins's thesis of the sortal dependency of identity -- expounded in his Sameness of Substance Renewed -- seems to me to incorporate the main insights of relative identity while saving Leibniz's law. (I wasn't aware that Gupta also had defended a thesis of relative identity so I am unsure how Wiggins' arguments against Geach apply to Gupta.)

On this though, I'd have to disagree. I don't think that at any point during our usual day to day activity, we go around thinking 'that thing there is what it is!' — StreetlightX

No, but people say things like, Mr. Jones is Adam. They're the same person. And so if Mr. Jones went to the bathroom, Adam went to the bathroom. There are equative constructions (with 'be' in English) that predicate identity with something of a subject, and they turn up intuitively true when coreferential expressions are used (the same way these expressions seem to result in truth when you swap out one for the other in true sentences).

And the fact that people don't often say these things doesn't necessarily mean they aren't so – after all, we often avoid saying things that are incredibly obvious, or guaranteed to be true by rules of linguistic usage. But if you were to ask someone, 'Are you yourself?' they would probably, after asking 'why the hell would you ask that?' admit that yes, of course they're themselves, how could they not be?

To say that a thing is identical to itself, when you think about it, is an exceedingly strange formulation. Wittgenstein had something of this intuition when he declared quite flatly in the Tractatus that "roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing." — StreetlightX

But this is just false: after all, Mr. Jones and Adam are identical (or more colloquially, Mr. Jones is Adam), so the first part is wrong [unless by 'two things' you mean two non-identical things, in which case the question is begged anyway, and no one would want to say that saying two non-identical things are identical is sensical], and 'Mr. Jones is himself (and not someone else)' is true, so the second part's wrong.

Clearly qualitative identity exists as well, but to deny that people are sensitive to numerical identity seems absurd to me. We are interested, e.g. whether the thing we saw in the sky today is identical to that which we saw yesterday, not in virtue of having the same quality, but in virtue of being the very same thing. And lo and behold it is, the sun. The question of whether the first sun-appearance is qualitatively identical to the second doesn't need to arise, since clearly it is in all relevant respects, but the numerical identity question is substantive.

I don't know too much about this, but as I understand it the relative identity has a non-relative identity underlying it, with a domain of non-sorted individuals, and these will obey Leibniz's law. I think this would be true for both Geach and Gupta, but I can't really remember.

Hmm, I don't think that saying Mr. Jones is Adam is the same as saying 'x is identical to itself'. It's the difference between x=x and x=y. One might learn something new upon learning that Adam is Mr. Jones. Not so that Mr. Jones is Mr. Jones.

No, but people say things like, Mr. Jones is Adam. They're the same person. And so if Mr. Jones went to the bathroom, Adam went to the bathroom. — The Great Whatever

All this shows is the very pedestrian fact that two different names can refer to one thing.

But that's exactly the point. Since they refer to the same thing, we're saying of one thing that it is itself (that is, it is identical to itself). And this is perfectly ordinary; yet this is precisely what SX has denied we do.

The value of 'Mr. Jones' is Mr. Jones. The value of 'Adam' is Mr. Jones, too. So the meaning of the sentence is that Mr. Jones is Mr. Jones. It asserts identity of one and the same thing.

We might learn something as the result of discovering that the sentence expressing this identity is true, of course, viz. that the two names belong to one man. But at base it asserts the very sort of identity you're saying people don't assert.

It's the difference between x=x and x=y — StreetlightX

But relative to a variable assignment, it's perfectly possible for x=x and x=y to have the same exact value, viz. if x maps to Mr. Jones, and so does y. The fact that you used different variables doesn't mean different individuals are involved. Quite the contrary, the truth of the statement lets us know that just one individual is involved, and that's why it's true.

But I don't agree that is what people commonly have in mind in their acknowledgment that a thing may have two or more names. As I see it the notion of a thing having a relation (of identity or otherwise) to itself is incoherent. This is not to say that a thing cannot have a relation between one part of itself and another part, but that is something else.

For me what really determines identity is difference, because a thing can have a relation with everything else; the relation that consists in it not being those other things. I think, for this reason, it makes sense to say that difference comes before identity; both temporally and logically.

But I don't agree that is what people commonly have in mind in their acknowledgment that a thing may have two or more names. — John

The sentence doesn't say that the man has two names. That may be a requirement for its being true, and it may even be what we intend to convey by using such a construction, but what it says is that a certain individual is identical to a certain individual. Since as you note these are two names of the same man, viz. Adam, what the sentence says is that Adam is himself.

We can change the example to remove the reference to names if that makes it easier. We can say instead:

He is Adam.

'He' is a referential expression that is referring to some guy. 'Adam' also refers to that same guy. We are predicating identity with Adam of Adam himself. To make it even more explicit, we can say:

I'm myself (and no one else).

Is such a sentence not true? Is it nonsensical? That seems to me an incredible claim.

One might learn something new upon learning that Adam is Mr. Jones. Not so that Mr. Jones is Mr. Jones. — StreetlightX

Also, just to note, even if none of this goes through, 'Adam is Adam' is still a true sentence, and one that makes sense. The fact that one isn't going to learn anything from it only goes to show that you already know that a thing is itself (duh).

No, no, it's not that people don't assert identity. Of course they do, they do so all the time. But the question isn't about assertion it's about ontology, as it were. As I understand it, to say that 'Mr. Jones is Alan' is to learn a fact about language-use: upon knowing this, I know that Mr. Jones might respond to the call 'Alan!' as he would to the call 'Mr. Jones'. Or that documents which refer to Mr. Jones or Adam actually refer to the same person, and so on. In all cases, there is some kind of parameter by which to make sense of the identity of Mr. Jones and Alan. Or put differently, the identity Mr. Jones = Alan does not 'stand alone', it is always identity 'with respect to.. x,y,z'. And the function of names is ostensibly for identification in social settings, bureaucratic identification, etc.

In any case, the idea is that there is no 'identity as such', identity considered in abstraction from any kind of external parameter, not that 'identity doesn't exist' or whatever. This is made clearer in Wittgenstein's elaborations in the Investigations: "'A thing is identical with itself" - there is no finer example of a useless proposition, which yet is connected with a certain play of the imagination. It is as if in imagination we put a thing into its own shape and saw that it fitted. We might also say: 'every thing fits into itself.' Or again: 'Every thing fits into its own shape.' At the same time we look at a thing and imagine that there was a blank left for it, and that now it fits into it exactly."

He is Adam. — The Great Whatever

See, I don't think this is right at all. He is not Adam; he is called 'Adam'. This goes back to an argument on another thread about the difference between identification and identity. He is identified as Adam, but Adam cannot be his identity (in any non-trivial sense). His identity cannot be given by any name or description, but only consists in his being a unique entity.

Or put differently, the identity Mr. Jones = Alan does not 'stand alone', it is always identity 'with respect to.. x,y,z'. — StreetlightX

So what is it with respect to, in this case?

And what about the 'Adam is Adam' sentence? Surely this is true? There is not going to be any parameter of interest there, is there? Sure, it's trivial, but thats just because numerical identity is trivial, which is the point.

Also note that the fact that we can learn something about language use by uttering or assenting to these sentences doesn't detract from the fact that we are asserting the identity of a thing with itself. In fact, it's precisely because this is what we're doing that it can have these effects. I know how to address Adam because of the equation of him with himself using two distinct names.

He is not Adam — John

Yeah he is. I'm TGW. I'm called 'TGW,' and I'm TGW as well.

I'm myself (and no one else). — The Great Whatever

I think that is redundant; to say that you are no one else is already to have said that you are. To say that your are yourself is a an empty elaboration of saying that you are. It really adds and clarifies nothing (except maybe for the woefully confused).

Okay, but is it true? Surely if it's redundant, if it adds nothing to what you already know, you recognize that it's true?

And yet, I'm predicating identity with myself of myself. And you understand it and recognize it as true. So contra your previous claim, there is nothing nonsensical at all about it.

But TGW cannot be a unique identity, because someone else, a million others, could also be TGW. Only 'I' as said by each person expresses the uniqueness of identity, because I can say that of one, and only one, person.

I'm saying it is an empty tautology. It's truth is utterly lacking in real sense, it is just an expression of a trivial definition.

But TGW cannot be a unique identity, because someone else, a million others, could also be TGW. — John

Not so, after all I'm TGW, and no one else can be me.

Of course, other people could have the name 'TGW.' But that is not the same thing as being me (TGW).

Besides, you can replicate this with 'I,' as I just did, by saying 'I'm myself,' which is going to be true whenever someone says it (except for the old 'I'm not myself today,' which is interesting).

So what is it with respect to, in this case? — The Great Whatever

I don't know, give me a context of use. These things can't be talked about in abstraction - which is the point.

Also note that the fact that we can learn something about language use by uttering or assenting to these sentences doesn't detract from the fact that we are asserting the identity of a thing with itself. — The Great Whatever

This simply strikes me as a kind of transcendental illusion, in the Kantian sense. We can say, in a kind of derivative manner, that to assert that Alan = Mr. Jones is to assert the identity of a thing with itself, but the very notion of identity is still a logical category imposed upon an 'existential situation' in which questions of identity or lackthereof are simply absent to begin with. In fact, speaking of Kant, 'A critique of pure formal logic' might adequately title the kind of position that I'm coming from here.

If being TGW has any uniqueness it is parasitic upon being a unique entity that is called 'TGW". Someone else can say that being TGW is unique; which seems odd. Would you not still be a unique entity and identity if you were stranded on an island and had amnesia? If you have thirty names are they all exactly equivalent insofar as they express your whole identity even if you are called these different names by different sets of people? Is your whole identity expressed by your online name TGW or by your everyday name?

This simply strikes me as a kind of transcendental illusion, in the Kantian sense. We can say, in a kind of derivative manner, that to assert that Alan = Mr. Jones is to assert the identity of a thing with itself, but the very notion of identity is still a logical category imposed upon an 'existential situation' in which questions of identity or lackthereof are simply absent to begin with. — StreetlightX

But what does it matter whether identity is an imposed category? Have I argued for any specific construal of what numerical identity is? I've only tried to show that your Wittgenstein-inspired comment that to say a thing is identical to itself is nonsensical, is wrong, as is the claim that in ordinary situations we don't do this.

If being TGW has any uniqueness it is parasitic upon being a unique entity that is called 'TGW". — John

Not at all. I didn't have this name until I made it up for online fora, but I was still myself.

Would you not still be a unique entity and identity if you were stranded on an island and had amnesia? — John

Yes, since you just admitted I was the same person in this hypothetical situation, ex hypothesi.

If you have thirty names are they all exactly equivalent of you are called these different names by a different sets of people? — John

No name is equivalent to me -- I am a person, a human being, not a name. I might have names, even thirty of them.

Is your whole identity expressed by your online name TGW or by your everyday name? — John

A name refers to me, and any name I might have does the same, and so means the same thing. I might use different names in different contexts, and so they might be imbued with different shades of significance, but they all refer to the same person (me).

But what does it matter whether identity is an imposed category? Have I argued for any specific construal of what numerical identity is? I've only tried to show that your Wittgenstein-inspired comment that to say a thing is identical to itself is nonsensical, is wrong, as is the claim that in ordinary situations we don't do this. — The Great Whatever

(I take) Wittgenstein's comment to apply to statements of identity that do not refer to an identity parameter. And it is the case the those sorts of comments are 'useless propositions'.

(I take) Wittgenstein's comment to apply to statements of identity that do not refer to an identity parameter. And it is the case the those sorts of comments are 'useless propositions'. — StreetlightX

I'm not sure what you mean by an identity parameter. Do you mean some quality with respect to which things are identical, like color? If so, there seems to be no such relevant quality for things like 'I'm myself,' which are nonetheless trivially true. I'm the same as myself, in what respect? Well, in no respect, that's not the point of what it says, I just am myself, period.

Maybe some identity statements are useless, or convey useless propositions, but it seems this is so only because they're so trivially true, which only goes to show that numerical identity of a thing with itself is something we're trivially acquainted with. As for the cases with multiple names, etc., these are clearly not useless at all, but it's not clear to me in these cases what sort of identity parameter' you would have in mind. After all, when I say that Adam is Mr. Smith, I don't mean that Adam has identical height to Mr. Smith, or something like that -- no, I mean numerically they are the very same guy.

No name is equivalent to me — The Great Whatever

The conclusion is simply that no name can express your identity. The fact that your different names refer to different aspects of you, and that no name refers to the whole of you, and that any name may refer to innumerable others, all show that. Sure, you can come back and disagree, but it is all just empty playing with words in any case, and none of the stuff about identity has implications for anything ontologically substantive. It is difference, not identity, which is substantive, because it speaks to genuine relationship.

No, no, it's not that people don't assert identity. Of course they do, they do so all the time. But the question isn't about assertion it's about ontology, as it were. As I understand it, to say that 'Mr. Jones is Alan' is to learn a fact about language-use: upon knowing this, I know that Mr. Jones might respond to the call 'Alan!' as he would to the call 'Mr. Jones'. Or that documents which refer to Mr. Jones or Adam actually refer to the same person, and so on. In all cases, there is some kind of parameter by which to make sense of the identity of Mr. Jones and Alan. Or put differently, the identity Mr. Jones = Alan does not 'stand alone', it is always identity 'with respect to.. x,y,z'. And the function of names is ostensibly for identification in social settings, bureaucratic identification, etc. — StreetlightX

When the same individual is denoted by two names that have two distinct Fregean senses, then, upon learning that they are identical, what is learned by a language user who was acquainted with this individual under those two distinct modes of presentation isn't merely a fact about language. As Kripke has shown, in a clear sense, the fact about language is contingent but the identity statement that has been learned about is necessary. (Kripke, though, thought that he was arguing against a Fregean conception of proper names. Gareth Evans has shown that Kripke's observations are consistent with a Fregean account of singular senses, understood non-descriptively.)

For instance Lois Lane may be acquainted both with Superman and with Clark Kent, and know them respectively as "Superman" and as "Clark Kent". When she eventually learns that Clark Kent is Superman she doesn't merely learn a fact about linguistic use -- (although, as TGW hinted, she could learn this fact inferentially through learning another fact about linguistic use). She rather learns the fact that Superman and Clark Kent are the same individual, a fact that no alternative (i.e. counterfactual) conventions of linguistic use could have negated.

This is one issue. Another issue that has been raised in the recent exchanges in this thread is the identity that a material object (i.e. a "substance", or "spatiotemporal continuant") retains with itself through material and/or qualitative change, through time. This issue is related to the first since an object can be encountered at two different times under two different modes of presentation (i.e. while being thought about under the two different Fregean senses of "A" and "B" successively, such that the numerical identity of their denotata may come under question). What settles the question of the identity of A with B are the criteria of persistance and individuation for object of this sort, and the spatiotemporal carrer(s) of the relevant object(s): both things that may be matters of empirical investigation. This also goes beyond the mere discovery of contingent linguistic conventions.