Bongo and I were discussing whether a behaviorist could arrive at referential opacity. We decided not, but then we examined whether we could define belief as a readiness to say a certain sentence. I don't think that will work either.

A behaviourist might say "Superman is Kent; Lois will ascent to 'Superman can fly' but not to 'Kent can fly', and so we can infer that she does not believe that Superman is Kent".

Is there a problem here?

Referential opacity shows up in the identity elimination schema;

Identity Elimination Schema

Major: t1 = t2

Minor: ϕ(t1)

Conclusion: ϕ(t2) — IEP

So we would have:

a. Superman = Clark Kent
b. Lois is ready enough to say "Superman can fly."
c. Therefore, Lois is ready enough to say "Clark Kent can fly."

T1 has to show up in the b sentence, and it's not there. There's nothing to substitute.

Isn't the move from

b. Lois is ready enough to say "Superman can fly."

to

c. Therefore, Lois is ready enough to say "Clark Kent can fly."

A supposed substitution?

What else could it be?

We decided not — frank

Haha, cheeky! No we didn't.

Notice that propositional attitudes at least internally satisfy Leibniz Law, since if Lois believes that Superman is Clarke Kent, then she believes that they have identical properties. So it might be expected that propositional attitudes and their relationship to the real world, can be depicted, albeit not explained, using traditional denotational semantics, i.e. category theory. By this proposal, we have a category L consisting of a set of names equipped with an equivalence relation (i.e a Setoid), that denotes Lois's conception of analytic equivalence, in which "Superman" is definitely not analytically equivalent to "Clarke Kent". It is reasonable to think that the relationship between L and some other category W that represents an alternative analytic conception of the world, can be described in terms of a functor F : L --> W.

Also recall that in Superman III, corrupted Superman physically expels Clarke Kent from his body, who then proceeds to strangle him to death along with the de re/de facto distinction.

Isn't the move from
b. Lois is ready enough to say "Superman can fly."
to
c. Therefore, Lois is ready enough to say "Clark Kent can fly."
A supposed substitution? — Banno

Look at this one:

a. Superman is Clark Kent
b. Toto the parrot is ready enough to say "Superman can fly"
c. Therefore Toto the parrot is ready enough to say "Clark Kent can fly"

The rigid designator, Superman, isn't in sentence b. All that's there is a sound the parrot is ready to make.

Behaviorism deflates belief to point that it's simple behavior. There is no content to speech. The rigid designator would be in the content.

So if we assert that Lois believes Sup can fly, we are talking about a propositional attitude toward content, not readiness to make certain sounds.

frank

Haha, cheeky! No we didn't. — bongo fury

Oh, I thought we did.

Also recall that in Superman III, corrupted Superman physically expels Clarke Kent from his body, who then proceeds to strangle him to death along with the de re/de facto distinction. — sime

:lol:

It is reasonable to think that the relationship between L and some other category W that represents an alternative analytic conception of the world, can be described in terms of a functor F : L --> W. — sime

Right, and I think a lot of this could be tied back to the "God's-eye view" question. If no category (L, W, etc.) is inherently privileged over any other, then it looks like the referential opacity "problem" cannot even arise.

Put differently, if we omit the presupposition that there is a "narrator" perspective which provides indisputable facts, then there is merely a disagreement between Lois ( L) and the observer (W) over whether Superman is Clark Kent. In that case each accuses the other of holding a mistaken belief which in turn influences their belief about what is permissibly substitutable.

(The reason I find this example so strange is because, depending on the time index, Lois may or may not believe that Superman is Clark Kent.)

That's a good post, frank. :up:

In Aristotelian-speak we would say that a material phoneme is not a formal word, and that the presence of a rigid designator requires certain intentions and beliefs on the part of the speaker.

T1 has to show up in the b sentence, and it's not there. There's nothing to substitute. — frank

...And so the question asks what t1 really is, given that the material markings which attend t1 are not sufficient for the presence of t1. So if we let t1 = "Superman," we haven't yet achieved what is needed for "objective" substitution-claims, given that "Superman" means different things to different people (i.e. the term is equivocal). Approaching these issues without something like 's Setoid is a dead end.

Substitutability depends on equivalence, and given that no rational or logical law/relation sidesteps the filter of belief, therefore it is false to claim that substitutability depends on equivalence irrespective of belief. If John does not believe that two terms are equivalent, then John cannot substitute them, and it is sheer confusion to think that there is some case where a substitution occurs but a "John" does not exist.

@bongo fury

I can’t say I understand Analytic Philosophy’s interest in this sort of substitutability and “referential opacity.” It seems endlessly confused.

For example, suppose “Superman” = “Clark Kent.” This looks like an absurd supposition from the start. The only reason Clark Kent exists at all is because “Superman” != “Clark Kent.” If Superman and Clark Kent were equivalent and therefore substitutable, then this would only mean that Kal-El’s disguise or pseudo-identity had failed.

More generally, if we have two names for the exact same thing (identical both notionally and mind-independently), then one of the names is superfluous and pointless. This hangup with referential opacity seems to be a matter where one posits that superfluous and pointless case and then supposes that it is a centrally important case. How the heck is this case deemed so important?

Probably what is happening is that the “objective” identity is focused on so strongly that one forgets that what is (supposedly) “objectively” identical need not be notionally identical. It seems controversial to claim that the “objective” referent of “Superman” and the “objective” referent of “Clark Kent” are identical, but I would say that it is clearly false to claim that the two signs have notional equivalence. Even to the narrator, “Superman” means something like, “Kal-El in his superhero identity,” whereas, “Clark Kent,” means something like, “Kal-El in his secondary identity, disguised as a human.” That they are not simply equivalent means that they cannot be substituted in every context.

More simply, “Superman” and “Clark Kent” are not different names for the same thing. The whole point of a disguise is to create a “name” that does not reference the true referent. Thus it is much truer to say that “Clark Kent” means “Not-Superman” than to say that “Clark Kent” and “Superman” name the same thing.

What’s weird is that the person interested in this sort of thing might respond, “Okay, so Superman isn’t the best example of this.” But what is the best example? Wouldn’t the best example be something that is completely absurd rather than only partially absurd (like Superman)? It seems like the best example would be two words which refer to the exact same thing, such that there is no notional difference, no difference of semantic range, no connotative difference, etc. The best example looks to be a sheer linguistic impossibility.

Am I missing something important here?

---

Let me sketch out my guess at what is occurring.

Consider two biconditionals:

• SC: The two terms can be substituted salva veritate within this context ↔ The two terms are equivalent within this context
• SA: The two terms can be substituted salva veritate in every context ↔ The two terms are equivalent in every context (i.e. the two terms are absolutely identical)

Both of these biconditionals are true, but this is the argumentation that leverages SA:

i. [Claim that two terms can be substituted in every context]
ii. [Identify a context in which the two terms cannot be substituted]
iii. Draw a reductio of some kind

For example:

1. "Superman" = "Clark Kent."
2. Lois believes that Superman can fly.
3. ∴ Lois believes that Clark Kent can fly.

As I pointed out above, (1) is false, but it is false in a very deep sense. This is because SA is a linguistic impossibility, and therefore to stipulate that some pair of terms satisfies SA is to stipulate a linguistic impossibility. It’s therefore no surprise that one can always find a context in which the two terms cannot be substituted once one moves out into the real world.

I think the issue has to do with epistemic direction, and this error plagues much of Analytic Philosophy. SC and SA are only epistemically coherent (and generally useful) when one moves from the first half to the second half. “These two terms are substitutable, therefore they are equivalent—either in this context or in every context.” That is how one reasons. A judgment of equivalence is inherently a conclusion rather than a premise. Equivalence is never intuited or stipulated.

Now we did get a kind of argument for equivalence in this thread. In this thread (1) was supported by the argument, “Term1 and term2 both rigidly designate the same thing.” Yet note that this does not fulfill SA, namely because it does not address the “context” where such a thing is not believed by Lois. Validity would require, “Term1 and term2 both rigidly designate the same thing, and every rational agent knows this.”

Note that this sort of thing happens all the time among TPF Analytics. For example, in the thread from which this thread was spawned, was just assuming by fiat that the Christian theological terms “Jesus” and “God” are unconditionally substitutable. It is the same sort of move from, “Superman is Clark Kent,” to, “Superman = Clark Kent” (in the sense of SA), albeit with a different context-valence.

The rigid designator, Superman, isn't in sentence b. All that's there is a sound the parrot is ready to make. — frank

Yes, and arguably neither is Superman in 'Lois is ready enough to say "Superman can fly"', that that sentence is not about Superman, but about something Lous says. I gather your behaviourist is not inferring any intentionality to Lous or to the parrot. Do you know of any one who proposes such an approach?

More simply, “Superman” and “Clark Kent” are not different names for the same thing. The whole point of a disguise is to create a “name” that does not reference the true referent. — Leontiskos

A judgment of equivalence is inherently a conclusion rather than a premise. Equivalence is never intuited or stipulated. — Leontiskos

I think that says a lot.

There are conclusions prior to the three parts of the Lois/Clark syllogism based on prior contexts that necessitate non-equivalence for “Clark” or “Superman” to then make sense enough to consider whether they are also equivalent or not. What led anyone to conclude P1? That conclusion (not premise) could only be made by someone who knew both the differences and sameness between what is a “Clark” and what is a “Superman”.

How the heck is this case deemed so important? — Leontiskos

What’s weird is that the person interested in this sort of thing might respond, “Okay, so Superman isn’t the best example of this.” But what is the best example? — Leontiskos

P1: X = Y
P2: Z is ready enough to say "X can fly."
P3: Therefore, Z is ready enough to say "Y can fly."

I don’t think this apparent controversy is about an apparent flaw in the notion “X = Y”, but from the insertion of the “Z is ready to say that…”. Z’s belief creates a new context in which we must redefine X and Y. So we can’t substitute the use of either X or Y from P1, in any sentence following P2; P2 has redefined X and Y according to Z’s belief.

Lois is ready enough to say "Superman can fly"', that that sentence is not about Superman, but about something Lous says. — Banno

Exactly. Lois isn’t talking about the Superman or the Clark Kent from the first premise.

Yes, and arguably neither is Superman in 'Lois is ready enough to say "Superman can fly"', that that sentence is not about Superman, but about something Lous says. I gather your behaviourist is not inferring any intentionality to Lous or to the parrot. Do you know of any one who proposes such an approach? — Banno

Like B.F. Skinner?

Behaviorism, the doctrine, is committed in its fullest and most complete sense to the truth of the following three sets of claims.

Psychology is the science of behavior. Psychology is not the science of the inner mind – as something other or different from behavior.

Behavior can be described and explained without making ultimate reference to mental events or to internal psychological processes. The sources of behavior are external (in the environment), not internal (in the mind, in the head).

In the course of theory development in psychology, if, somehow, mental terms or concepts are deployed in describing or explaining behavior, then either (a) these terms or concepts should be eliminated and replaced by behavioral terms or (b) they can and should be translated or paraphrased into behavioral concepts. — SEP

Sure. But not Davidson, nor any one else under consideration here. Arn't we here considering only those who do attribute belief?

Sure. But not Davidson, nor any one else under consideration here. Arn't we here considering only those who do attribute belief? — Banno

We were just talking about referential opacity. I told Bongo that we can't get that with behaviorism. He disagreed. Anyway, it just establishes that if we're using the term "opacity" we're in line with folk psychology that affirms full bodied propositional attitudes. We can't be talking about a deflated or reductive version of belief, because you don't get opacity with that.

I'm also curious about the implications of identifying with confidence what someone else believes. That's why I was asking how we know Lois believes x. Like, am I saying I'm a mind-reader? Am I employing charity? Is there any way to discover what she believes other than to be told by her?

Nice.

Prima Facie Davidson might reject this, since it implies a separation between schema L and world W.

We talk about beliefs becasue we sometimes find that what we have taken to be the case is mistaken - that there is a difference between how we think things are and what is true. It's tempting to think of W as the One True Description of the World, something to which Davidson might have objected.

Perhaps we can drop W from the schema, and instead consider how we might go about understanding Lois' beliefs L in terms of our own beliefs, say L'. We charitably match the structure of L to L', maximising agreement. In doing so we find the "best" match is made when we include "Superman is not Kent" in L, despite including it in L'.

And again we do not need the god's eye view.

You can't surmise belief from action? Why not?

Also recall that in Superman III, corrupted Superman physically expels Clarke Kent from his body, who then proceeds to strangle him to death along with the de re/de facto distinction. — sime

:D

You can't surmise belief from action? Why not? — Banno

Maybe you could. I'll have to think on it. Anyway, if you're interested, this part of Davidson's argument that we can't tell what dog's believe from Rational Animals:

Norman Malcolm tells this story, which is intended to show that dogs think:

"Suppose our dog is chasing the neighbor’s cat. The latter runs full tilt toward the oak tree, but suddenly swerves at the last moment and disappears up a nearby maple. The dog doesn’t see this maneuver and on arriving at the oak tree he rears up on his hind feet, paws at the trunk as if trying to scale it, and barks excitedly into the branches above. We who observe this whole episode from a window say, ‘He thinks that the cat went up that oak tree’2. (Malcolm added, we would say the dog was barking up the wrong tree.)

Malcolm claims that under the circumstances someone who attributed that belief to the dog might well - almost surely would -be right; he would have exactly the sort of evidence needed to justify such an attribution. Let me give a preliminary argument designed to put Malcolm’s claim in doubt. It’s clear that the evidence for the dog’s ‘belief‘ depends on taking belief as a determinant of action and emotional response. We are asked to infer from what we see that the dog wants to catch the cat, that he runs where he does because of this desire and a belief about where the cat has gone, and that he is venting his frustration at not being able to follow the cat up the tree by barking, pawing the ground, and so forth.

The details do not need to be right, of course. The point is so far obvious: if we are justified in inferring beliefs, we are also justified in inferring intentions and desires (and perhaps much more). But how about the dog’s supposed belief that the cat went up that oak tree? That oak tree, as it happens, is the oldest tree in sight. Does the dog think that the cat went up the oldest tree in sight? Or that the cat went up the same tree it went up the last time the dog chased it? It is hard to make sense of the questions. But then it does not seem possible to distinguish between quite different things the dog might be said to believe.

One way of telling that we are attributing a propositional attitude is by noting that the sentences we use to do the attributing may change from true to false if, in the words that pick out the object of the attitude, we substitute for some referring expression another expression that refers to the same thing. The belief that the cat went up that oak tree is not the same belief as the belief that the cat went up the oldest tree in sight. If we use words like ‘believe’, ‘think’, ‘intend’ while dropping the feature of semantic opacity, we are not using those words to attribute propositional attitudes. For it has long been recognized that semantic opacity distinguishes talk about propositional attitudes from talk of other things.

Someone may suggest that the position occupied by the expression ‘that oak tree’ in the sentence ‘The dog thinks the cat went up that oak tree’ is, in Quine’s terminology, transparent. The right way to put the dog’s belief (the suggestion continues) is ‘The dog thinks, with respect to that oak tree, that the cat went up it’ or ‘That oak tree is the one the dog thinks the cat went up’. But such constructions, while they may relieve the attributer of the need to produce a description of the object that the believer would accept, nevertheless imply that there is some such description; the de re description picks out an object the believer could somehow pick out. In a popular if misleading idiom, the dog must believe, under some description of the tree, that the cat went up that tree. But what kind of description would suit the dog? For example, can the dog believe of an object that it is a tree? This would seem impossible unless we suppose the dog has many general beliefs about trees: that they are growing things, that they need soil and water, that they have leaves or needles, that they burn. There is no fixed list of things someone with the concept of a tree must believe, but without many general beliefs, there would be no reason to identify a belief as a belief about a tree, much less an oak tree. Similar considerations apply to the dog’s supposed thinking about the cat. — Donald Davidson, Rational Animals

That conclusion (not premise) could only be made by someone who knew both the differences and sameness between what is a “Clark” and what is a “Superman”. — Fire Ologist

Right. In order for (1) to avoid tautology there must be rational movement, and this requires some difference between the two relata.

And of course I don't mean that we can't use (1) as a premise, but rather that we must be prepared to give an argument for such premises. Such premises are not self-evident.

P1: X = Y
P2: Z is ready enough to say "X can fly."
P3: Therefore, Z is ready enough to say "Y can fly."

I don’t think this apparent controversy is about an apparent flaw in the notion “X = Y”, but from the insertion of the “Z is ready to say that…”. Z’s belief creates a new context in which we must redefine X and Y. So we can’t substitute the use of either X or Y from P1, in any sentence following P2; P2 has redefined X and Y according to Z’s belief. — Fire Ologist

Yeah, I think you're right about this. P3 requires a premise about whether X = Y for Z.

But drumming my point, we could also scrutinize P1. What does P1 mean? In the Superman case it is supposed to mean that one and the same thing goes by two different names. Is that what it means in a mathematical context? I'd say the fact that we don't really know what we are saying with (1) is significant. Given that there are so many multivalent meanings to P1, it is itself a kind of analogical claim. Presumably disambiguating P1 would shed light on P3.

I have the article.

Given the confusions here, I'm not keen on moving on to it quite yet - it presumes quite a bit about the way we might view belief, and won't be understood without those presumptions.

Given the confusions here, I'm not keen on moving on to it quite yet - it presumes quite a bit about the way we might view belief, and won't be understood without those presumptions. — Banno

I agree. But that snippet gives a hint as to why you can't get opacity with behaviorism. You'll end up with a de re reading of everything.

I'd say the fact that we don't really know what we are saying with (1) is significant. — Leontiskos

"=" is very well defined in both maths and logic, but cannot be adequately defined in merely syllogistic logic, which cannot deal with relations.

"=" is very well defined in both maths and logic — Banno

Then give your account of what <Superman = Clark Kent> means.

I only grant that it is well-defined in mathematics.

Analytics like Banno seldom have any idea what they are doing when they say, "x = y," as they assume that anything can be placed into that form. They don't recognize the mathematical context and the single genus of the relata that their formulation takes for granted. — Leontiskos

I set out a bit of an explanation fo "=" yesterday. Here it is again.

A part of analytic method is to use formal logic to model natural language. The bits and pieces of a formal logic are much more rigorous than those of a natural language. We can borrow this rigour in order to show clearly some differences in use in natural languages.

This is brought out nicely in predicate logic. Three differing uses of "is" are:
1. The "is" of predication - "The ball is red" - f(a)
2. the "is of equivalence - "Two plus two is four" - a=b
3. The "is" of quantification - "There is a ball" - ∃(x)f(x)

We can see similar uses in a natural language such as English. A clear English sentence containing "is" might be parsed as one of these, but it may be that there are English sentences that include "is" but do not parse into one of these three; or at least that are somewhat ambiguous or difficult. Consider auxiliary uses, "What I’m telling you is, don’t touch that switch." So the list is not intended to be exhaustive.

It's also worth noting that (2) is a special case of (1). The "=" is a binary predicate over a and b.

In syllogistic logic, all relations are reduced to single-places predications. “Socrates is taller than Plato” has to be paraphrased into one-place predicates like “Socrates is-a-thing-taller-than-Plato” before entering a syllogism. Something like "Tully is Cicero" has to be treated not as a relation, but as a single-placed predicate. It has to be treated the same way as, say, "Tully is a writer". Tully is a member of the group of writers, and Tully is a member of the group of things which are Cicero.

An adherence to merely syllogistic logic might explain some of the difficulties had hereabouts.

"=" is reflexive, symmetrical and transitive; A=A; if A=B then B=A, and if A=B and B=C then A=C. Other relations can have all three - your birth month is your birth month, and if it is the same as mine, then mine is the same as yours, and if mine is the same as yours and yours is the same as hers, then mine is the same as hers. Taken together these three give us equivalence but not identity.

Classically we can add x=y⇔∀P (P(x)↔P(y)), Leibniz’s Law. This is the standard definition of "=" for first-order logics. Two things are identical if they have exactly the same properties.

It's extensional. What that means is that if A=B, then for any theorem that contains "A", we can instead stick "B", without changing the truth value. The truth of the theorem is not dependent on the term used, but on the thing - the extension - of that term. So since "A" and "B" refer to the very same thing, we can swap 'em, and what we say stays true.

But Leibniz’s Law falls over in modal contexts. The Opera House is in Sydney, but might have been instead built in Melbourne (God forbid! Picture it on the banks of that dank cloaca, the Yarra, in the rain...). But if we keep Leibniz’s Law then it would not be the Opera House, that very building, that was built in Melbourne, and so on... The answer to this, From Kripke, is to drop Leibniz’s Law but keep extensional substitution - that is, to use rigid designation.

This is not a complete account, but it'll do.

This is not a complete account, but it'll do. — Banno

So again, what does <Superman = Clark Kent> mean? And is the "binary predicate" true or false in this case?

(I of course responded to your confusions yesterday.)

It might be best if you did the homework for yourself...

Why not just admit what I've said from the start: that you don't know what you mean when you say things like, "Superman = Clark Kent"?

On your reasoning, we can disprove the thesis simply by noting that Superman wears a cape whereas Kent does not. Therefore they are not equal or identical.