And I'll note that you've failed to answer the simple question, — Leontiskos
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
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
Davidson is happy to say that people have beliefs, and to use beliefs to explain actions, and says that such explanations are causal.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. — Banno
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
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
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
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.He himself point sout this discrepency between the phenomenological and nomological meanings when appying them to Supervenience. — I like sushi
See what I mean? — I like sushi
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."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
It seems that people are quite unwilling just to accept the restriction. It needs a rationale - apart from Frege's solution not working.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
I'm afraid that I don't see this as any kind of answer.The answer to this, From Kripke, is to drop Leibniz’s Law but keep extensional substitution - that is, to use rigid designation. — Banno
This is too simple It is certainly true that Lois does not believe that Clark Kent can fly.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
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.But then it does not seem possible to distinguish between quite different things the dog might be said to believe. — 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.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
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....this contradiction can easily be resolved. — 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.It seems that people are quite unwilling just to accept the restriction. — Ludwig V
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. Major
b. Lois believes that Superman can fly. Minor
c. ∴ Lois believes that Clark Kent can fly. a, b =E — IEP
nor with:a. Superman is Clark Kent.
b. Superman can fly.
c. ∴ Clark Kent can fly.
And indeed this last can be re-written asa. Lois believes that 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.Lois believes that:
a. 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.a. Ludwig believes that Superman is Clark Kent.
b. Lois believes that Superman can fly.
c. ∴ Lois believes that Clark Kent can fly.
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
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