Frege raised his puzzle with the statement
1A) Hesperus is Phosphorus.
So, even if that statement could be metalinguistically ambivalent, it is not so in the way your statement (3) is concerned, since "Hesperus" and "Phosphorus" are words from the same language. However, perhaps there is a way of expressing the ambivalence you believe Frege overlooked if we consider 1A) above, rather than your statement (1)? Over to you on that score.

Personally, I think Frege overlooked a different issue for his sense/reference distinction. His fundamental claim is that there can be no informative identity statements of the form
4) A is A.
But it is possible to construct a story (I'm thinking of Mark Twain's "Million Pound Bank Note") where it would make sense for someone to say something along the lines:
5) Henry Adams is Henry Adams!
and be expressing a discovery.
There are also more mundane cases where someone might be expressing something informatiive with a statement along the lines
6) Well, you know, John is John, so you shouldn't expect anything else from him.

It may be that unpacking these examples will in fact lead in the direction of your ideas, though, but we'll see.

1A) Hesperus is Phosphorus. — MetaphysicsNow

This is a mistake but I think that it does not invalidates my argument. The same analysis can be made:

(1) Hesperus is Phosporus
A) (name-name) Hesperus is (other name than, synonym with) Phosporus
B) (name-objetc) Hesperus is (the name of the planet) Phosporus

Statements such as "John is John" in your example, insofar I understand them, presuppose information without that it is not possible to make sense of it (for example, "John is stubborn", etc.), so they are only apparent identities.

I don't understand what you're saying.

(1) "Hesperus" = "Phosphorus"
(2) Hesperus = Phosphorus

(1) is just false, and (2) is the claim that "Hesperus" and "Phosphorus" designate the same object.

Other ways of switching around use and mention, such as

(3) "Hesperus" = Phosphorus

might not come out at all like you expect. We say things like this when the quotes indicate something fake about the name, like at the end of a Scooby-Doo mystery; or we end up with a start on Haddock's Eyes.

So what is it Frege is getting wrong?

(Btw, I don't think of names, unlike descriptions, as ever being translated, though they do get localized. It's an odd area.)

Statements such as "John is John" in your example, insofar I understand them, presuppose information without that it is not possible to make sense of it

Kind of my issue with Frege - the assumption is that syntax and semantics is the whole story for natural language, whereas it is not (although it might be for formal languages).

Still not clear what mistake you think Frege is making though.

Btw, I don't think of names, unlike descriptions, as ever being translated, though they do get localized. It's an odd area.

Interesting ones are place names - London and Londres for instance: Kripke makes use of that in his A Puzzle About Belief.

The issue is Hesperus is not Phosphorus. They are both Venus but that's like saying I'm a banana, Belter has eaten a banana, therefore I'm dead because I was eaten by Belter.

What are you talking about?
Bluebanana is a banana.
Belter has eaten a banana.
Therefore Belter has eaten BlueBanana

That's just an invalid argument.

Hesperus = Venus
Venus = Phosphorus
Therefore Hesperus = Phosphorus

Is a valid and sound argument based on the transitivity of identity.

Hesperus = Venus
Venus = Phosphorus
Therefore Hesperus = Phosphorus — MetaphysicsNow

It is a valid argument on the assumption that 'Venus' in the first equality has the same linguistic function than in the second one.
We can think the first as the name of a planet and the second as the name of itself, so only in "Hesperus=Venus" we can say "Hesperus is the Evening Star", but not in "Venus=Hesperus".

Still not clear what mistake you think Frege is making though. — MetaphysicsNow

My problem with Frege is his that he account natural languages equalities by reducting them to formal ones, so the problem of saying/showing emerges when we think about concrete examples.

Is a valid and sound argument based on the transitivity of identity. — MetaphysicsNow

The natural languages equalities with the name-object form are symmetrical preserving the linguistic function (saying/showing). For example, "'Venus' is Hesperus" can be transformed into "Hesperus is 'Venus'" but not into "'Hesperus' is Venus". That is, there are natural languages equalities which are identification sentences, in which a name or defined description designates an object and the other one to itself.

Hesperus = Venus
Venus = Phosphorus
Therefore Hesperus = Phosphorus — MetaphysicsNow

BlueBanana = banana
The banana Belter ate = banana
Therefore I am the banana Belter ate, and therefore I am dead.

False analogy. "Venus" is a proper noun that denotes a specific object, whereas "banana" isn't.

The analogy is a valid one. In informal language "a is b" can mean "a=b" but also "a∈b". Hesperus is Venus but Venus isn't always Hesperus, and therefore the meaning of "is" in the context is closer to the latter one.

Hesperus is a Venus in a specific state, and these states of existence are not specific objects but classes.

The claim that "Hesperus = Venus" is as invalid as "BlueBanana = a banana".

I'm still not clear what you're saying.

Everyone agrees these assertions achieve the same purpose:

(1) Hesperus and Phosphorus are the same object.
(2) "Hesperus" and "Phosphorus" are different names for the same object.
(3) "Hesperus" is another name for Phosphorus.
(4) "Phosphorus" is another name for Hesperus.

The puzzle to be solved is that names for the same object should be substitutable salva veritate. No problem saying

(5) Phosphorus and Hesperus are the same object.

But this is weird:

(6) Phosphorus and Phosphorus are the same object.
(7) "Phosphorus" is another name for Phosphorus.

So you remember that that names are substitutable salva veritate only in extensional contexts -- it's practically the defining feature of extensional contexts -- and conclude that this is an intensional context somehow, thus akin to

(8) Pat doesn't know that Hesperus is Phosphorus.

You can't say this is equivalent to

(9) Pat doesn't know that Hesperus is Hesperus.

Everyone's clear on that much. But we don't have an obvious tip-off in sentences like (1)-(7) -- no propositional attitude verb like "know", no "that" clause.

Frege's solution, you could say, is to say there's always something a bit like an intensional component: the sense (Sinn) rather than the reference (Bedeutung).

It's not a solution everyone loves, because pure extensionality is much cleaner. [Insert a hundred years of discussion here.]

For natural language, maybe there's a solution that just treats these types of statements involving names and identity as special. The thing is, Frege was really looking at mathematics, where it seems awkward to say that equations are just a special case. ("2 + 2 = 4" is exactly the same issue.) But hey maybe they are. Mathematics as a domain is a deliberate narrowing of what we might say.

Kind of my issue with Frege - the assumption is that syntax and semantics is the whole story for natural language, whereas it is not (although it might be for formal languages). — MetaphysicsNow

I was going to pass this by because you're kinda right, but there's more to say here, coming off my last post.

Say you want to approach the natural language issue by looking at the pragmatics -- when do we have a use for statements like "Hesperus and Phosphorus are the same object"? That looks fruitful. You'd start by noting that there's "no point" in telling someone that "Hesperus is Hesperus" (which probably isn't quite true), and go from there.

But something about that isn't quite right. The reason we feel there are different uses for "Hesperus is Hesperus" and "Hesperus is Phosphorus" is precisely because we feel they don't contain the same information. So it is with "4 = 4" and "2 + 2 = 4". It's that sense that these two equations carry different information -- they "say different things" -- that drives their different uses. So the semantics drives the pragmatics here.

We could then circle back to Frege and look at the truth conditions, either in terms of possible worlds or in terms of verification, and confirm that there's a semantic difference.

But something about that isn't quite right. The reason we feel there are different uses for "Hesperus is Hesperus" and "Hesperus is Phosphorus" is precisely because we feel they don't contain the same information. So it is with "4 = 4" and "2 + 2 = 4". It's that sense that these two equations carry different information -- they "say different things" -- that drives their different uses. So the semantics drives the pragmatics here. — Srap Tasmaner

I don't think it's quite that simple.

Take your sentence (3): "Hesperus" is another name for Phosphorus.

First, look at the word "another" and it's reference. If there's "another" name, there has to be a default name that the speaker would expect the hearer to know (pragmatics). But given a context such as "What's Hesperus?" the speaker won't know which name this is until s/he arrives at "Phosphorus". That is "Phosphorus" in that sentence does pragmatic double duty: it tells you which object it is, but it also raises the topic of that planet having the name "Phosphorus". That's exactly why ["Hesperus" is another name for "Hesperus".] is weird. It has everything to do with "another", and little with Hesperus/Phosphorus. The weirdness can go away if we take care of this in context:

A: What's "Hesperus"?
B: "Hesperus" is another name for Phosphorus.
A: Hm? So what's another name?
B: Huh?
A: Other than "Hesperus".
B: *flat tone of voice* "Phosphorus" is another name for Phosphorus.
A: *embarrassed* Oh.

Note that the word "another" no longer refers forward, now. The default name ("Hesperus") has been brought up in the exchange before and is the obvious referent for "another" here. The syntax is different from the earlier sentence. And the misunderstanding in this exchange is derived from A not noticing the double duty "Phosphorus" is doing in the early sentence.

**

A second (but to me less interesting) complication is that the planet Venus has the respective names in specific contexts only: even if you see the same object, you can't see the Evening Star in the morning - if you activate all its denotations and connotations (which you don't have to, but which you activate is a matter of pragmatics). Even though "Hesperus" and "Phosphoros" refer to the same planet, they're not complete synonyms, though they may be functional synonyms in many context (in most of which, we'd use "Venus" these days with overwhelming likelihood).

Agree completely that the use of "another" implies some stuff I was ignoring, much of which you described nicely.

There are so many ways to do this. Some run into the issue you and @BlueBanana raise that these terms are only (supposed to be) used in certain situations.

(1) You can call me "Pat".
(2) You can call the Morning Star "the Evening Star".

(1) might turn out only to apply in a range of situations, not all, or not, but it's tempting to say (2) is just, well, if not wrong, then really weird.

Whether the use of a particular name (or nickname or description) is appropriate may not change the truth conditions of sentences it's used in, appropriately or not. I think if my son pointed at Venus of an evening and said, "Look, the Morning Star has risen," that would be true if a bit arch.

More weirdness with definite descriptions. A run in baseball is only "the go-ahead run" if the game is tied before the run scores. If the game's not tied, that description just doesn't seem to have a reference.

With Venus, we cross into territory where the object is persistent and the description can be capitalized into a Name. Maybe others feel the description still bleeds through, but I wish I had a clearer example.

ADDED: Sometimes it refers to a possible run because you can do the math. Announcers talk this way: if your team's down by one with a runner on base, they might describe the player coming up to bat as "the go-ahead run". You still can't score the go-ahead run if you're already ahead.

Whether the use of a particular name (or nickname or description) is appropriate may not change the truth conditions of sentences it's used in, appropriately or not. I think if my son pointed at Venus of an evening and said, "Look, the Morning Star has risen," that would be true if a bit arch. — Srap Tasmaner

Well, true. But focussing on the sentence's truth condition may itself be missing the point. I don't know your son (or even if you have one), so I'm not trying to get personal here. But your son might say the sentence in full knowledge of this thread and intend it as a rib, because you care about things he does not, in which case the word choice "Morning Star" indicates irony, but you won't find the irony if you focus on the referential object and truth condition. That could cause a hiccup in the conversation, which could have been expected (or even intended) - a sort of private in-joke thematising differences in outlook.

It's not that easy to do something like this in a formal system like maths.

That's all dead on. Sometimes when he and I sit on the front porch, I teach him a little philosophy.

With "the go ahead run" I was imagining the case of someone learning about baseball and misusing that phrase as meaning "run".

"Did we score another go-ahead run, Daddy?"
"No, sweetie, this one was tacked on -- only the first one this inning was the go ahead run."

So there's your hiccup.

(The example I really wanted to use was, "Did we score another equalizer, Daddy?" but I don't even know if football announcers still say, "It's the equalizer!" like Toby Charles did.)

Heh. I don't know much about sports and very little about baseball, so I was staring at your post and didn't really understand it, until the edit. So basically, if you're already ahead you can make a go-further-ahead run, except that nobody says that. (My confusion stemmed from an instinctive association of "go ahead" with "give the go-ahead", so I was sort of expecting some sort of rule bound complication...)

The thing about language is that it's complex, but easy to use. Easy to use, hard to analyse - to the extent that sometimes analysing it can make you less effective at using it because you start seeing problems that should be there but aren't. Describing language as a formal system is still useful (especially in second language learning), but, IMO, it's important to realise that language isn't actually a formal system: it's a type of social behaviour that uses cues from outside to resolve formal ambiguities (famous example: "We saw her duck.") and in this way uses these ambiguities for versatility. On writing boards, they tell you that "you must know the rules to break them." But I think that's the wrong way round: "you must know the rules to follow them" - if you're literate you can write. When it comes to language, right/wrong is often open to negotiation, and the things that are not open to negotiation are usually not talked about (if you're ever bored look up the difference between nominative-accusative languages and ergative-absolutive languages and see how often that comes up).

@BlueBanana

BlueBanana = banana
The banana Belter ate = banana
Therefore I am the banana Belter ate, and therefore I am dead.

Nope,
BlueBanana = a banana
The banana Belter ate = a banana
Therefore I am the banana Belter ate, and therefore I am dead.

Invalid argument. "BlueBanana = banana" is not a statement - ever heard anyone say something like "John is identical to cabbage, therefore John is identical to the cabbage" and thought they were on to something?

@BlueBanana

My problem with Frege is his that he account natural languages equalities by reducting them to formal ones, so the problem of saying/showing emerges when we think about concrete examples.

With this, however, I agree.

I'm still not clear what you're saying. — Srap Tasmaner

The method of substitution salva veritae is valid, for example, in mathematical equations (x-5= y+2; y=3-x; => x=3-x +2+5 => x=5). In natural languages identities, the principle of substitution is not valid when names are designating to themself. In "Hesperus is Phosphorus", a priori, we can not know which member plays the role of showing. In mathematics, both terms, a priori, designates the same reference ("x" and "y" designate numerical values).
If neither "a" nor "b" are showing in natural language indentities, but saying, then "a=b" => "a=a". But we do not use natural language identities to say non-informative tautologies but to make identifications between words (synonymy relation) and a word and an object (reference relation).

But we do not use natural language identities to say non-informative tautologies but to make identifications between words (synonymy relation) and a word and an object (reference relation). — Belter

Okay, I think I understand what you're saying now.

Frege analyzes "Hesperus is Phosphorus" as asserting the identity of the objects picked out by the names "Hesperus" and "Phosphorus" -- they refer to the same thing.

On your analysis, "Hesperus is Phosphorus" is one of these:

(1a) "Hesperus" refers to Phosphorus.
(1b) "Phosphorus" refers to Hesperus.
(2) "Hesperus" and "Phosphorus" are synonyms.

At least one of the names is implicitly being mentioned rather than used, and that blocks substitution. But it blocks substitution only within the quotation marks, so you still need a way to block

(1a') "Hesperus" refers to Hesperus.
(1b') "Phosphorus" refers to Phosphorus.

and this you get by arguing that we don't (cannot?) know which of (1a) or (1b) is intended. (Is "intended" right? Or is it that there is no "fact of the matter" as to which analysis is right?)

If we're unable to use (1a) or (1b), we must take "Hesperus is Phosphorus" as (2).

(2) asserts the synonymy of the names used; Frege asserts the identity of the things named.

But what is the meaning of a name?

If the meaning of a name is its reference, then asserting two names have the same meaning is asserting they have the same reference, refer to the same object. Isn't that exactly where Frege starts?

Sorry, still a little confused.

If we're unable to use (1a) or (1b), we must take "Hesperus is Phosphorus" as (2). — Srap Tasmaner

Thank you for your exposition of my argument. However, I think that (1a') and (1b') have not equivalent to the a=a identities of Frege. They are with the form: 'a'=a and 'b'=b, so the properties of the equality relation are not the same.

I wouldn't have even thought of "... refers to ..." as being an identity relation. It's clearly not. A symbol is not the thing it symbolizes. I don't think Frege anywhere suggests that reference is an identity relation.

How about this one?

(1a'') "Hesperus" refers to Venus.

Frege's approach here is to say that this has the same truth value as (1a) and (1a'), but that there are real semantic differences between these sentences. The referring expressions in each refer to the same object, the planet Venus, and that's what determines truth value; but each expression specifies or determines the reference in a different way -- i.e., they have different senses but the same reference. Anyway, that's where Frege lands, as I understand it.

Thank for your analysis. My claim is just that. The "Hesperus is Phosphorus" sentences are only apparent "identities", but actually they are identification assertions (fixation of a reference, extensional interpretation) and synonymy ones (fixation of sense, intentional interpretation).

Frege's view is that "Hesperus" and "Phosphorus" have different senses but refer to the same object. Since he splits meaning into two "components", it's not clear if you and he agree on what "synonymy" means here.

Still not sure where you stand, sorry.

Frege's view is that "Hesperus" and "Phosphorus" have different senses but refer to the same object. — Srap Tasmaner

Yes. But he also said that it is an identity sentence, and "synthetic a posteriori". My view is that "Hesperus is Phosphorus" is not a true "identity", and it has two "analytic" senses (commented above; in kantian sense) neglected by Frege. Thus, Frege wrote the following (On sense and reference):

The reasons that seem to favour it are the following: a = a and a = b are obviously sentences of
different cognitive value: a = a holds a priori, and, following Kant, should be called
analytic, while sentences of the form a = b often contain valuable extensions of our
knowledge and cannot always be justified a priori.

He thought that "Hesperus is Phosphorus" is not "analytic" but "synthetic a posteriori". I arrive to the same conclusion than Frege (we must distinguish sense and reference, for concepts and sentences as a hole) but by other way (supposing that a=b is "analytic" so it is a "linguistic" or "conventional" equality sentence).