I'll leave you to your own resources, then. Enjoy.

And I'll note that you've failed to answer the simple question, "What does <Superman = Clark Kent> mean?," three times now.

More of the same from Banno.

And I'll note that you've failed to answer the simple question, — Leontiskos

Dude,

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” have 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 - if 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. — Banno

Dude, — Banno

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. — Leontiskos

You're just kicking the can and avoiding the concrete question. What you mean by "=" is something like, "equivalent with respect to the properties that we take to be relevant," and you haven't the slightest idea of what should count as a relevant or irrelevant property. Else, on your "all properties" account, there are no two things that are equal. Therefore, as I said, your "=" is just a matter of different names for the same thing. Again:

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. — Leontiskos

SA is a linguistic impossibility. Leibniz' whole point was that if you have two things with all the same properties, then you don't have two things. You were mistaken and there is only one thing after all. Thus the "=" on your definition is by definition not a two-place relation. Instead it is a reflexive relation where the object is identical to itself, and where we have mistaken a single object for two different objects. It is epistemology trying to disguise itself and pass for a static proposition. It is a conflation of reference and referent.

"Superman = Clark Kent" is logically presupposing both that there are two things being related, and that there are not two things but only one thing. It's that inherent contradiction that is the problem, and which is so bound up in your own thought.

All you have shown here is the inability of a merely syllogistic logic to represent relations, including equivalence.

Your SA is muddled. It conflates logical identity with linguistic identity. "Hesperus" and "Phosphorus" both refer to Venus, but one in the evening and the other in the morning. Utterances, especially those in a natural language, occur in context.

Merely syllogistic logic cannot deal with modal or other intensional contexts. It treats identity as just another predication. That's one of the reasons it's not much used anymore.

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. — frank

Davidson is happy to say that people have beliefs, and to use beliefs to explain actions, and says that such explanations are causal.

So not behaviourist.

Anscombe - and by association, Wittgenstein - also accepts that actions are explained by beliefs. Neither is behaviourist.

Davidson is happy to say that people have beliefs, and to use beliefs to explain actions, and says that such explanations are causal.

So not behaviourist.

Anscombe - and by association, Wittgenstein - also accepts that actions are explained by beliefs. Neither is behaviourist. — Banno

No stones were being thrown. Just exploring.

Sure.

Merely syllogistic logic cannot deal with modal or other intensional contexts. It treats identity as just another predication. That's one of the reasons it's not much used anymore. — Banno

You're floundering in your continual ignorance of history and philosophy, and you still haven't answered the question at hand. Ironically, the problem with your own view is that it treats identity as just another predication, failing to think through the equivocation between self-identity and other-identity.

Leibniz' whole point was that if you have two things with all the same properties, then you don't have two things. You were mistaken and there is only one thing after all. Thus the "=" on your definition is by definition not a two-place relation. Instead it is a reflexive relation where the object is identical to itself, and where we have mistaken a single object for two different objects. — Leontiskos

If you understand logic, you should be able to address the explanation of "=" given twice, above, as well as in another thread.

But you choose not to.

What are we to conclude?

This is exactly where Davidson's regard for mental causation breaks down. He even admits himself that there is a discrepency between the phenomenal-description-of and the nomological-description-of.

I've no idea what you said here. Sorry.

The exact same point can be argued for Venus as Evening and Morning star. The Planet remains the same physically, other than relative daytime positioning, but the appreciation and importance of this difference gives them distinct identities that transcend the mere nomological description.

Maybe this is a very particular connection that is tangental to the discussion. I think it is an important considered though.

I can't see how that links to what I understand about Davidson.

A striking feature of attempts at definitional reduction is how little seems to hinge on the question of synonymy between de niens and de niendum. Of course, by imagining counterexamples we do discredit claims of synonymy. But the pattern of failure prompts a stronger conclusion: if we were to find an open sentence couched in behavioural terms and exactly coextensive with some mental predicate, nothing could reasonably persuade us that we had found it. We know too much about thought and behaviour to trust exact and universal statements linking them. Beliefs and desires issue in behaviour only as modified and mediated by further beliefs and desires, attitudes and attendings, without limit. Clearly this holism of the mental realm is a clue both to the autonomy and to the anomalous character of the mental.

These remarks apropos definitional behaviourism provide at best hints of why we should not expect nomological connections between the mental and the physical. The central case invites further consideration

- Davidson, 2003, p. 217, 'Essays on Actions and Events'. — Donald Davidson

EDITTED

Yeah, OK. Phenomenological difference is a difference in conceptual role, not a difference in referent, so not following this at all. Have you a phenomenological account of referential opacity?

EDITTED

He himself point sout this discrepency between the phenomenological and nomological meanings when appying them to Supervenience. — I like sushi

I don't see that. I don't see what it is you are driving at. I don't think he is doing what you claim; but then, I'm not sure what it is you are claiming.

Indeed, on a search, the word 'phenomenological' does not appear to occur at all in Actions and Events. "Phenomenalism" does, also on p. 217, in "the catalogue of philosophy's defeats".

I hope it is clear that Davidson is rejecting nomological connections between the mental and the physical. That's the very point of the anomalism of the metal.

He does not use that term. EDITTED

I'm still not following you. He certainly thinks there are physical causes - laws, if you like. You'd have to explain how what he calls a mental even is always a phenomenological event, if that is what you are claiming - it's not what I understand. He does deny the identity of mental and physical events. He rather infamously accepts extensional first order logic, so he does use substitution.

The position he takes is quite developed, a life's work, so difficult to do justice to it in a few sentences. You seem to be importing a phenomenological gap that Davidson doesn’t actually formulate in those terms.

Might let it go until there is an agreed background?

I think the issue here is nothing other than a mismatch in terminology.

See what I mean? — I like sushi

Not really. You have three distinct issues, phenomenology, referential opacity and Anomalous Monism. Bringing them together is no short order.

Cheers.

I used the term Phenomenological as it is the standard terminology in Philosophy of Mind.

"Superman = Clark Kent" is logically presupposing both that there are two things being related, and that there are not two things but only one thing. It's that inherent contradiction that is the problem, and which is so bound up in your own thought. — Leontiskos

I'm sympathetic to most of what you have been saying. But this contradiction can easily be resolved. "Superman" and "Clark Kent" are both names for the same person - but each name is assigned to a different persona. This is not particularly strange - pen names, professional names, character names (Barry Humphries, for example), regal names, baptismal names, adoptive names, married names, aliases of all sorts.

Quine showed that Frege's solution didn't work, and told us not to try to substitute in such circumstances. Not really an answer so much as a statement of the problem. — Banno

It seems that people are quite unwilling just to accept the restriction. It needs a rationale - apart from Frege's solution not working.

The answer to this, From Kripke, is to drop Leibniz’s Law but keep extensional substitution - that is, to use rigid designation. — Banno

I'm afraid that I don't see this as any kind of answer.

a. Superman is Clark Kent. Major
b. Lois believes that Superman can fly. Minor
c. ∴ Lois believes that Clark Kent can fly. a, b =E
— IEP
From two true statements, we get an untrue conclusion. — frank

This is too simple It is certainly true that Lois does not believe that Clark Kent can fly.
I don't suppose anyone thinks that we can be expected to automatically believe all the logical consequences of what we believe. We have to work them out for ourselves. But we need to believe some of them if our beliefs are to have any meaning. Yet there seems no way of drawing a line between logical consequences that we can be expected to believe and the rest.
At least, I would be reluctant to generalize this example, as the standard account of extension and intention does. There needs to be some room for paying attention to each case. They may not all fit the same mould.


I can't resist commenting on your quotation from Davidson.

But then it does not seem possible to distinguish between quite different things the dog might be said to believe. — Donald Davidson, Rational Animals

Of course not - not in a thumbnail sketch. But if we live with the dog, we can work out a fuller picture. There's nothing special here. All beliefs are surrounded by a penumbra of ancillary beliefs - many of them logical consequences, many others mere associations. Deciding which of them a believer has and which they do not have needs a wider view than two lines.

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? — Donald Davidson, Rational Animals

In one sense, there cannot be a description of the tree that suits the dog. The dog doesn't describe things. On the other hand, there seems no bar to our deciding what description suits the dog and applying it to the dog. We do that to other human beings as well and when we do that, we take their behaviour into account as well as what they say. What people say about their beliefs is important evidence, but it is not especially authoritative; sometimes behaviour over-rules it.

Great post! I'll be back soon.

...this contradiction can easily be resolved. — Ludwig V

What contradiction? Leon seems to think that no relation can be between a thing and itself. But seven is less than or equal to seven, and your phone is the same size as your phone, and you are the same age as yourself. There's no logical problem in something standing in relation to itself.

It seems that people are quite unwilling just to accept the restriction. — Ludwig V

Yep. Quine's contribution was to put the problem in terms of substitution, and hence in terms of extensionality, and so presenting it as a puzzle of logical form as opposed to a physiological issue. It's a change in emphasis, one that greatly clarifies the apparent problem. To talk in terms of believing, knowing, questioning and so on is to set different logical contexts. Mixing those contexts is what leads to our considering the opacity of reference.

So let's look at the example:

a. Superman is Clark Kent. Major
b. Lois believes that Superman can fly. Minor
c. ∴ Lois believes that Clark Kent can fly. a, b =E — IEP

The logical problem is that there are two contexts in this deduction. The first line is in a different context to the other two. There's no problem with:

a. Superman is Clark Kent.
b. Superman can fly.
c. ∴ Clark Kent can fly.

nor with:

a. Lois believes that Superman is Clark Kent.
b. Lois believes that Superman can fly.
c. ∴ Lois believes that Clark Kent can fly.

And indeed this last can be re-written as

Lois believes that:
a. Superman is Clark Kent.
b. Lois believes that Superman can fly.
c. ∴ Lois believes that Clark Kent can fly.

In this last we can see the whole in a single context. The problem - so far as there is one - only arrises when the contexts are muddled together. That's what Quine pointed out.

The context here is not mysterious - it's simply the result of our being able to talk about sentences. The "god's eye view" answer is another muddle, supposing some transcendent truth.

In a forum in which even the logically straight forward puzzle posed by incites page after page of disagreement, such a response will not satisfy everyone. Here's another example that might help make the contexts clear.

a. Ludwig believes that Superman is Clark Kent.
b. Lois believes that Superman can fly.
c. ∴ Lois believes that Clark Kent can fly.

Hopefully folk can see why this is a non sequitur. Ludwig's beliefs are a different context to Lois' beliefs, so the deduction fails.

Notice that the reasons that Ludwig and Lois have different beliefs are irrelevant to the analysis here. Nor do we need to attach a sense to the proper names involved, in the way Frege suggested. Quine's answer is elegant and brief.

I suspect that you, @Ludwig V, are familiar with all this.

You might notice that the "Lois believes..." appears to predicate over sentences. The Problem Davidson set himself was to parse as much as he could of English (and any natural language) into first order logic. Hence, very roughly, his solution of treating the content of beliefs as themselves an individual. "Superman can fly. Lois believes that" where "that" refers to the first sentence.

We might still wish to explain the psychology - why Lois and Ludwig have such different beliefs. But that's a seperate question.

Anyway, that might make clearer what I meant by "sorting out the scope".

He is inconsistent with his views at this juncture -- if he is dismissing the view that Clark Kent cannot Fly so readily. — I like sushi

If Superman and Clark Kent are the same entity, and Superman can fly, then so can Clark Kent. Do you think that Superman needs his suit in order to be able to fly?

@Ludwig V Do you understand what I am getting at above? No one seems to :(

It is a subtle point.