A and A in the regard of material objects.

A is not equal to A (with the exception of abstractions). I know that the following article is a Marxist one, but it is both very short and it has good relevance to this topic. You need not read some of its sections, but be sure to read its first section.

marxists.org/archive/trotsky … 39-abc.htm

Now, let us think for a bit. If A was equal to A, then there could not be any changes, for due to the changes and everything being in a constant state of flux, A is not equal to A.

If A was equal to A, then products would not expire. For example, if I have a liter of milk, we all know that it will expire within some time. If A was equal to A, the milk would equal itself, and it would always retain the same state. Therefore, if A was equal to A, the milk would never expire. However, in reality, that simply is not so. We all know that if I keep that milk for too long, it is going to get chunky, stinky, and in short, not safe for consumption. The milk is not equal to the milk, for it is always changing (and ultimately, over time, there is a large noticable change when the milk goes far beyond its expiration date).

The same would be true, of say, my 1986 truck. If A was equal to A, then my truck would not be getting rust spots, and its paint color would not be faded. There are changes that constantly happen in that old truck (as well as everything else). If A was equal to A, in short, that truck would be just as good as it was when someone drove it off the lot way back when I was small baby in diapers.

The same is obviously true of the body of a living being (hence the contradiction that is the body of a living being). As you are reading this post of mine, many cells have died and been replaced. Many cells are continuing to die and be replaced. Many tissues are also breaking down and being replaced. Then the changes are very obvious in the long run. Let us say that it is 20 years in the future, and I am sitting down with my children looking at a family photo album. I then show my kids the pictures of myself when I was 18 years old. Obviously, I, in 20 years from now, will look much differnt than I do now, and that my kids would see such an obvious change. If A was equal to A in that instance, my kids would not notice any difference in my appearance between me sitting down with them on the couch and my appearance in the photograph (not counting me wearing differnt clothing).

Hello Volkov and Welcome,

I’d first comment that the statement, “A is not equal to A” is an abstraction, start to finish. No generalized relation is not an abstraction, which means that every case will be an exception to your above statement.

Yes, Heraclitus noticed this circa 500 BCE, and yet I suspect that even he wasn’t the first person to think as much.

I would, however, point out a problem with your symbolism, Volkov. You want to discuss cross-temporal non-identity, and yet your statement “A is not equal to A,” makes no explicit mention of a temporal relationship. Better, I think, is to write: X at t1 does not equal X at t2, etc…

I’d also draw your attention to Thomas Reid’s well known discussion of identity. It’s so short and to-the-point that I won’t bother restating it.


Notwithstanding the fact that by the time I’ve finished writing this I’ll be a different person, we do have a sense (imperfect as it is) of our own psychological connectivity and continuity. It’s another case of what I call a “real illusion.”

I realize that you and I are different persons, yet when I think of who I was, or rather, of what I was, a few moments after my conception, I must admit that you and I are now far more alike (in thought and custom) than I am like my former zygotean self. It’s sureal to think that I now have more in common with a stranger than I have with myself at an earlier time in my life. The study of personal identity is both fascinating and disquieting.

Identity is a two-place relation, since the relation stands between two place-holders ( ____ = ____ ). But a valid identity doesn’t refer to two distinct entities. The whole point of a valid identity is to explicitly state that there are not two things; there is one thing. A thing is identical to itself and no other. In his Tractatus, Wittgenstein wrote:

“…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 at all.” – 5.5303

I disagree with what he says after the comma. The abstract relationship of identity is no trivial matter.


This is one of the points Kripke seems to be making in Naming and Necessity (and I know Putnam has made it also). Of course, Kripke’s interest is primarily in the philosophical aspects of what it is to name something; he doesn’t delve too deeply into the metaphysical side of the subject (and frankly I’ve only studied identity from a philosophy of language point of view). But one of the metaphysical conclusions Kripke does draw is that a thing’s identity is entirely dependent on the mind-independent qualities that make it what it is. I find that somewhat hard to swallow; here’s why:

One of the classic realist examples of a property-identity statement is, “water is H2O”. For the realist, this represents an a posteriori necessary relation. “Water” and "H2O: both rigidly designate the same thing, and an identity statement is one composed of two rigid designators which refer to the same thing. The important thing (for Kripke anyway) about a rigid designator is not the way it is formed in language but the actual thing that is designated. As you said, “water is H2O” is not primarily a statement of equivalence between two terms; it is a way of pointing out that this thing is identical to itself. The implication here is that water would still be rigidly individuated in some real physical sense were there no humans around to name it. And the epistemological suggestion is that WE CAN SOMEHOW KNOW THIS TO BE THE CASE. Now I don’t know if you’re implicitly claiming all of this, but I’ll address it anyway because I just wrote a paper on it, and I think it’s an interesting question. :wink:

A long time ago no one knew that water even had a chemical composition; for ages, humans experienced, conceptualized and talked about this thing called water in a purely phenomenological way. With the advent of chemistry as a science, our conception of water changed dramatically (as did our conception of every substance). We found, apparently without exception, that the substance we had conceived of as water through its physical manifestations was actually the chemical compound H2O. However, we only made this judgment through experiencing the extensional equivalence of the two terms in a finite number of instances. That is to say, every substance that we determined to be H2O was the same substance we had originally conceived of as water. However, there was no experiment, no further scientific breakthrough, that suddenly put “necessarily” in front of the generalization “water is H2O.” The only a posteriori element of this necessary a posteriori truth was, so far as we can tell, an inductive inference.

So what, then, accounts for the necessity of the statement, “water is H2O”? For Kripke, the two designators in the sentence both rigidly pick out the same kind of thing. And that kind of thing is necessarily individuated independent of any linguistic convention we have developed to categorize it. But the implication here is that we somehow discovered that this natural kind exists in a mind-independent sense. And if this is a consequence of Kripke’s reasoning, then Kripke is clearly mistaken. It is self-contradictory to assert that we discovered some state of affairs to obtain independently of our discovering it. So if indeed the fact that water is H2O were a necessary part of some experience-independent reality, it is not at all clear how we could know it (that is, how we could add “necessarily” to the sentence “water is H2O” based on any further knowledge of the world). If we do know—or at least intuitively understand—the statement to be necessary, Kripke’s realism does not include an adequate epistemological explanation for how we have obtained this understanding.

[btw…the two paragraphs above are from the paper I wrote]

What I’m aiming at here is that we have no way of knowing a posteriori whether or not there are necessary relations–including identity relations–outside of ourselves. Our capacity to see a thing as identical to itself is entirely dependent on the lingustic conventions we have developed to individuate it. This, of course, contradicts the idea that an identity statement is primarily concerned with showing a thing identical to itself. I think statements of identity are primarily statements of equivalence between terms. Such statements are meaningful and useful because they make explicit the equivalencies implicit in our language.

Alan Sidelle has given the following example–in response to a similar one put out by Putnam–to show how our ability to individuate water is dependent on the language we use to describe it:

You see, according to Kripke, Sly here would be mistaken about what water IS. But how can that be if Sly actually has all the relevant scientific knowledge? The disagreement must be primarily about how to use names, and not about the metaphysical status of water.

In response to and in support of polemarchus, I would also quickly reference Korzybski’s non-aristotelian logic and the consequences of it. Check Science and Sanity. Pardon the name dropping post. I will get all hip deep in this shit in a bit.

Hi Logo,
It’s a pleasure to find such a well-considered response. Thanks so much!

I smiled when I read this, for you’ve marked my point of departure with Kripke. I reject his return to essentialism. I maintain that properties and modalities are human creations. Furthermore, I reject Platonic Forms and I deny the existence of a law outside the realm of a law-maker.

“’I wish you wouldn’t keep appearing and vanishing so suddenly…!’ ‘All right,’ said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone. ‘Well! I’ve often seen a cat without a grin,’ thought Alice; 'but a grin without a cat! It’s the most curious thing I ever saw…'” — Carroll, Alice in Wonderland

More specifically, I accept transworld identity (Kripke’s, not David Lewis’ transworld!) but I deny that transworld identity warrants a belief in essentialism.

Kripke allows that what we use to fix our reference doesn’t say everything about what we’re referring to. If anything, he sometimes appears too lax in his admission of what constitutes a valid referent:

“I think you do know who Cicero is if you just can answer that he’s a famous Roman orator.” – Kripke, N&N, p83

When I first read that I thought he was joking. Would I know who Cicero is if I could only answer: that he’s a famous dead-guy? that he wore a toga? or that he’s a man whose name begins with a “c”? This isn’t a trivial concern. If the critieria for a proper referent is too broad we’re pushed along the road towards haecceitism. An allied topic is the so-called “perfect speaker theory.” A.C.Grayling has an online paper that you might find interesting.


I think Kripke would argue that the identification of Marylin Monroe, for example, with Norma Jean Baker is known a posteriori because empirical research was required to establish the identity. But once an identity is established (once the “baptism” occurs) this identity will hold in every possible world (in every counterfactual situation).

“If you say ‘suppose Hitler had never been born’ then ‘Hitler’ refers here, still rigidly to something that would not exist in the counterfactual situation.” – Kripke, N&N, p78

Frege claimed that A=A is necessarily true, whereas A=B is not. My interpretation of Kripke is that he maintains that A=B is contingent (Hesperus is the same as Phosphorus in some possible world), but once we acquire, a posteriori, the fact of identity (Hesperus=Phosphorus) then it will be true in all possible worlds. This isn’t saying that Hesperus could not have been Phosphous in some other world; it could have been; that’s where the contingency arises. But once we declare that the two are identical then Leibniz’s Law of Identity comes in to play. To that, I’d add that Leibniz’ Law is necessary because we say it is. We’re allowed to make those sorts of declarations. Why? Because we say so (a weak argument when used by parents, but considerably more successful as a basis for metaphysical “authority”). The 17th century poet, Sir John Davies, ended his Nosce Teipsum thusly:

I know I’m one of nature’s little kings
Yet to the least and vilest things am thrawl
I know my life’s a pain and but a span
I know my sense is mocked in everything
And, to conclude, I know myself a man -
Which is proud and yet a wretched thing

Thanks for your quote by Alan Sidelle opposing Putnam’s Twin Earth scenerio. I have his Necessity, Essence and Individuation on my reading list. I remember Colin McGinn saying (The Making of a Philosopher) that Putnam’s externalism might be true for some mental case but not for all. He thinks Putnam’s externalism is an overgeneralization. McGinn supposedly makes his argument in Mental Content, another book on my reading list (So many books, so little time).

C’est possible, mon ami. I’m currently reading Colin McGinn’s Logical Properties; Identity, Existence, Predication, Necessity, Truth. Here’s how he summarizes his chapter on identity:

“I have endorsed four main theses about identity:
(i) it is unitary,
(ii) it is indefinable,
(iii) it is fundamental,
(iv) it is a genuine relation.”

(i) McGinn denies there are varieties of identity. Numerical identity is absorbed by qualitative identity.

(ii) He can’t produce a non-circular definition of identity.

(iii) “Every object (or any other entity - property, function, you name it) is self-identical…The concrete, the mental, the abstract - all instantiate the univocal concept of identity. In this respect, as in others, identity resembles existence; but it is even more universal than existence, since it holds even for non-existent objects.” (Even a square-circle is self-identical.)

(iv) “Surely it is clear that distinctness is a genuine relation between things, but then identity must also be, since it is simply the negation of distinctness. Negation cannot take us from a genuine relation to a pseudo-relation.”

I’d elbow my way to the head of the complaint line if I thought that were actually the case. But again, I deny that a relation exists outside of a relation-former. My metaphysics is stridently anti-anthropomorphic. You see, I’m one of nature’s little kings. :wink:


Polemarchus and Logo,

Excellent posts.

Always a pleasure to read you both.

WOW GREAT STUFF ALL AROUND! looks like i’ve got some new reading material to tackle. i can’t follow up on any of that at the moment… you two (polemarchus and logo) sure are thorough. :sunglasses:

logo, where are you going to school? i too studied on the “east coast”. private message me as not to disturb this gem of a thread.

I stumbled across this in an old Word document. I posted it a few months ago, but I lost it when the site was hacked. Luckily, I’ve been conditioned by countless “invalid session” messages to save my material!

Polemarchus, your posts never fail to remind me of all I haven’t read…

It seems we’ve established one point at least: that identities are strange, spooky things. At one moment in N&N Kripke says he himself doesn’t quite know what to make of identity statements (and I would certainly agree with him on that). I think that in saying identities are concerned with expressing equivalence between terms, we get pretty close to pinpointing what they DO for us–the function they serve in our language. The mystery seems to lie in what they are about.

It sounds like we’re on the same page with what they are NOT about: they do not refer to mind-independent essences. As Sidelle puts it, “natural kinds are creatures of the understanding” (83). And, “[essence-stating truths are] explained in terms of us, in terms of our carving up of the world, and not in terms of an independently existing modal structure of reality” (23). I think that’s the right way to look at it.

However, it also seems to me that if the world were different then my way of individuating (for example) this chair might also be different. Kripke’s concern seems to center on the fact that when we designate (or, when we decide on what is and is not worthy of designation), we refer to that which is outside ourselves—that how we “carve up the world” depends on the way the world is to begin with. And this reasoning clearly points in a direction very different from the classic conventionalist thesis that identities “simply record our determination to use words in a certain fashion” (A.J. Ayer, Language, Truth and Logic 84).

It does seem that in a very real, intuitive sense, we give names to that which we take to be outside of ourselves. Identities are about things that exist in the world. But that doesn’t mean those things are individuated apart from us. As Sidelle’s twin Earth scenario illustrates, individuation is an entirely human affair.

I think he’s aiming at the idea that you can designate Cicero as that man, that physical person, without knowing anything about what he did. What Cicero did is contingent for Kripke; he essentially WAS that man. He could’ve been an obscure Italian farmer and no one today would’ve heard his name. But he would still have been that man. He could not, however, have been a cat–even if evolution had taken a different path and cats were intelligent enough to be famous Roman orators. When Cicero was “baptized”, his name was used in reference to a human being–so anything he did after he was baptized was contingent; the qualities he possessed at baptism were not.

I think the original baptism idea has some problems to begin with (like, could Cicero have had a cleft lip?). But I mainly take issue with the assumption that what is named in a baptism is a naturally individuated object.

A few months ago, we had a big discussion in my philosophy of language seminar on Kripke’s claim, “it might have been the case that Aristotle was not a philosopher” (13). I disputed that claim—or at least, I thought that what the name “Aristotle” applied to depended on the constraints of the conversation. If we’re trying to write a biography of that man, it may well be contingent that he was a philosopher. Perhaps he might have become the greatest general of antiquity instead of the greatest philosopher; perhaps he might have fought, rather than taught, Alexander the Great.

However, if we’re in philosophy class, and we’re discussing, say, the Metaphysics, does it really matter if the author of that work was that man—with the physical properties Kripke ascribes to Aristotle? I happen to think that even if we discovered that the author of the Metaphysics was an alien, we’d still call him Aristotle; because in that kind of situation, Aristotle’s only significant quality is that he authored the work under discussion. Kripke actually addresses this in one of his footnotes:

I disagree with this—or at least, I don’t think this is what we always do with names. Perhaps I’m wrong about Aristotle: maybe we would change the author’s name on every copy of the Metaphysics if we discovered it’d been written by an alien. But that’s certainly not what we’ve done with the Iliad. It seems the author of that work will remain Homer, regardless of which “that man” (or woman) actually wrote it.

-Note: Kripke might say that “Homer” here functions like a title (on the level of “Jack the Ripper”); I simply contend that there is no clear distinction between a name and a title. Who’s to say that “Aristotle” is not a title also?

It seems to me that pragmatism governs the way we designate more than anything else. We see this with Sidelle’s twin earth scenario: if it is less useful to us that we designate a thing based on its chemical qualities than on its physical manifestations, it’s not a mistake for us to refer to twin earth water as “water.” We are not naming something based on its deep metaphysical essence (for starters there’s no way for us to know what that essence is); we are naming it based on its pragmatically relevant qualities. So designation is based on the mind-independent world in this sense: if the world were constructed differently, we would have different needs, and therefore different descriptive priorities. And we would individuate things differently.

So what, then, are identity statements about? One answer may be, “whatever we, as members of a linguistic community, need them to be about.” And then, once we have established our need to identify a thing, it becomes useful for us to pretend it is absolutely individuated in a mind-independent reality. Hence Kripke’s “intuitive” account of rigid designation.

Your thoughts?

…and where the hell have you been?