Referential opacity
I'm reading Davidson's Rational Animals, and I fell down the rabbit hole of referential opacity, which is about situations in speech that defy Leibniz' Law, which is that if x and y are the same object, then x and y have the same properties"
A typical example involves Lois Lane believing that Superman can fly, but she doesn't believe Clark Kent can. Yet Superman=Clark Kent.
Quoting IEP
From two true statements, we get an untrue conclusion.
Is it that we're misapplying Leibniz's Law? Let's look at some cases of that:
Quoting IEP
In this case, the problem is coming from the use of Tarskian quotation, which means the quoted part is a word, not a city.
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Quoting IEP
The flaw here is equivocation. The "so-called because of his size" can't skip from one name to the next.
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Quoting IEP
There a long drawn-out answer to what went wrong in this example. See next post.
A typical example involves Lois Lane believing that Superman can fly, but she doesn't believe Clark Kent can. Yet Superman=Clark Kent.
Quoting IEP
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
From two true statements, we get an untrue conclusion.
Is it that we're misapplying Leibniz's Law? Let's look at some cases of that:
Quoting IEP
a. Istanbul is Constantinople.
b. Istanbul has eight letters.
c. ? Constantinople has eight letters.
In this case, the problem is coming from the use of Tarskian quotation, which means the quoted part is a word, not a city.
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Quoting IEP
a. Giorgione is Barbarelli.
b. Giorgione is so-called because of his size.
c. ? Barbarelli is so-called because of his size.
The flaw here is equivocation. The "so-called because of his size" can't skip from one name to the next.
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Quoting IEP
a. The number of planets = 3 squared
b. It is contingent that the number of planets = 9
c. ? It is contingent that 3 squared = 9.
There a long drawn-out answer to what went wrong in this example. See next post.
Comments (172)
In each case you are dealing with mental or intentional objects, and therein lies the confusion. Things like belief or the number of letters that any given language uses for a word have to do with our thinking, not with objects in themselves. In an Aristotelian sense an accidental property is being confused with an essential property. For example, it is only an accidental property of Istanbul that its English name has eight letters. Leibniz' law was never meant to track accidental properties deriving from mental objects.
Superman is not Clark Kent.
Istanbul is not Constantinople.
The number of planets is not three squared.
It is not contingent that the number of planets equals nine, even if there were nine planets.
He's not?
He's Jor-el. Also - Lois Lane believing Clark Kent can or cannot fly is not a property of Clark Kent. It's not a property at all.
Not a property at all, or a property of Lois rather than a property of Clark?
Quoting IEP
This substitution failure results from the fact that the number of planets isn't a rigid designator. It's a singular definite description.
Sorry - Kal-el.
Referential opacity occurs between contexts. Indeed, it can be considered part of what defines a context. Getting the scope right clears up the mess.
Look at this example.
Quoting IEP
We aren't really worried about how we know what Lois believes, whether it was from observing her behavior, or she told us, or we have a mind-reading machine. We just know that she believes Superman can fly. There's a magical thing about belief: that it causes referential opacity.
But if we attribute propositional attitudes to a dog, do we still get referential opacity? We can't substitute a dog in the above =E because we aren't likely to just know specifically what the dog believes. We're just guessing from a afar, and so all our attributions will have extensional definitions, right?
"Superman is Clark Kent" is a straight forward identity - one may be substituted for the other. Superman can fly, hence Kent can fly.
"Lois believes that Superman can fly" is not directly about superman - this by way of giving a sense to "directly". It's about Lois, and something else... that we call a belief.
Whatever sort of thing that belief is, it doesn't allow the sort of substitution we are envisioning.
But we should not jump the gun. Perhaps a slower reading of the article is called for?
True. Davidson uses referential opacity to make his case that language is required for rationality. So I was just contemplating the background of propositional attitudes.
In the example of Superman, we know what Lois believes because it's a fictional story and we have a God's eye view. That Lois believes Superman can fly is not a speculation, it's one of the central columns of the story. I'm thinking we'd want to keep that in mind when using referential opacity as an element of an argument. It's going to be dragging that God's eye view in with it.
If you and I agree that Superman can fly, why should we concern ourselves with god's opinion on the topic?
Seems out of place.
How do you know Lois believes it?
You stipulated that she does. I trust you. If you now want to bring that in to doubt, go ahead, but I don't much see the point in doing so.
I don't think it's a stipulation in that context. We know what Lois believes because we know the story. It's from the narrator's point of view. That isn't available in real life.
Another angle on the same question would be: how do you ever know what other people believe? If it's charity, do you extend that charity to dogs? Why or why not?
If we are going to get somewhere we may need to focus?
I'm going to be examining an argument that says language is required for rationality. It's going to be rejecting the idea that dogs have beliefs, specifically because we have no way to be sure what they believe.
If referential opacity is drawn into the argument, which it is, then it's fair to tinker with the gears in that object.
I don't see why it can't be recast as a question of what follows from belief. For example, you could avoid this by rewriting b. "Suppose Lois believes that Superman can fly." It seems that the "God's eye view" comes not primarily in premise (b) but rather in premise (a), yet that too can be recast as a supposition, thus achieving the central Analytic shift from inference to consequence.
Allow me to risk being idiotic, but perhaps part of the solution lies in thinking "Lois believes that Superman can fly" is not a property of Superman. It's a fact that you can say, but it's not a property as such.
Seems more like that statement is about a property of Lois lane
Superman can fly. Lois believes that.
Yes, I misspoke. Leibniz's Law gives us the expectation that we can substitute t1 and t2 in the Identity Elimination Schema (here)
The schema itself isn't an expression of Leibniz's Law.
Wouldn't it be more a cause for wonderment if it created referential transparency?
Then the Superman of Lois' beliefs could be relied on to share all his properties with the actual fictional one?
Granted that would spoil story-telling, and perhaps also Davidson's proposed intentionality test.
It depends on how you explain belief. A behaviorist would say that what we call belief reduces to certain actions. Since Clark is Superman, we can substitute all day long, because there is no hidden object in Lois's head. There is no opaque reference. The behaviorist goes with the de re reading:
Quoting IEP
Wouldn't it also mean that the believer is omniscient, lacking no knowledge about identities?
Edit: @Leontiskos exactly :ok:
Also reference, contrasting with sense? (I wonder.)
To support that, you'd need to explain how a substitution failure cashes out in terms of behavior.
Not convinced?
Seems that folk here are solving a problem they have yet to specify. Oh, well.
Why does me saying "right" lead to you saying "not convinced?"? "That's right" is the kind of thing someone says when they are agreeing with something...
Is there then any issue here that is left hanging, once the scope is sorted?
The guts of Davidson's article is the difference between "Superman is Clark Kent" and "Lois believes that Superman is Clark Kent". The former is a relation of identity between two characters, the latter a belief on the part of a third character. The two are very different things.
Sorry, I was vague about that. The OP is from an IEP article on referential opacity. I was struggling to understand all the aspects of it. Davidson's article is called Rational Animals. I felt like I needed to understand opacity better before I digested his argument.
I read your comment (the one I replied right to) sounded like it was explicitly agreeing with me. That's all
I've looked, but have not been able to locate a good account of opacity. The IEP article is framed around Frege, and so leads in to Russell an descriptions. The SEP article on Quotation might be both clearer and of greater generality. See especially the list of five possible responses. For Davidson, the Demonstrative theory is key.
right.
The IEP article is terrible. I'll try the SEP article.
Well, as assent to contradictory sentences?
So we put two flashcards in front of Lois with contradictory sentences on them, and if she nods her head to both, we have referential opacity.
https://www.uvm.edu/~lderosse/courses/lang/Quine(1956).pdf
Yes.
How could you tell from watching Ralph's behavior that he's "ready enough to say" something? With behaviorism, we're trying to avoid a God's eye view on Ralph's psyche. In fact, for our purposes (as faithful behaviorists), Ralph has no psyche.
Let alone that the readiness is to say it "in all sincerity"!
Not sure I see an inherent problem. But I don't know if anyone (e.g. Davidson) has to be fundamentalist about the behaviourism, anyway? I think it's plausible that we describe the psychology of a linguistic animal in terms of its dispositions to assent and dissent to sentences?
You were asking if it would be more surprising if propositional attitudes did not result in substitution failure. I was saying that this would depend on how one understands belief. A behaviorist might have a hard time accepting substitution failure because beliefs reduce to behavior. Evidence for substitution failure would be scarce and unreliable.
You're identifying belief with the readiness of a subject to say S with sincerity. So it's
a. Clark Kent = Superman
b. Lois is ready enough to say S1 with sincerity, where S1 is "Superman can fly."
c. Therefore, Lois is ready enough to say S2 with sincerity, where S2 is "Clark Kent can fly."
This is a misapplication of the Identity Elimination Schema, which goes
Quoting IEP
The reason it's a misapplication is that neither t1 nor t2 show up in the b sentence. You can't substitute t1 for a mention of t1. If you do that, you'll end up with:
Quoting IEP
In other words, if we use your scheme, we'll end up applying Leibniz' Law to the speech of a parrot. Parrots can be ready enough to say S1. What does that have to do with laws of identity?
Edit. Actually, I think I'm wrong about calling that a mention, it's more just an utterance. It's just sound that Lois is making.
I dare say. More to the point, it's referential opacity. :smile:
No, you only get referential opacity if there are mental states involved... specifically of a kind a parrot wouldn't have.
Quoting IEP
In this case, the misapplication is so bad you don't even have a substitution failure. You at least have to have t1 in the b sentence.
Comport yourself so that t1 shows up in the b sentence, and we can evaluate for referential opacity.
Quoting bongo fury
I haven't gotten back to Davidson. I'm still trying to figure out opacity. You're helping. :grin:
Nor have I, which is why I edited out that remark. :wink:
:up:
Quoting IEP
None of that need be about Lois believes that... It is all about clarifying the identical.
Quoting Banno
Opacity points to difference (one shielded by opacity from the other). Difference is the line drawn between contexts.
So identity is about sameness and difference. And all of the valid or erroneous permutations that follow, and that can be translated into analytic terms.
Quoting Banno
Yes they must be treated one at a time. Because the two are different things as you say.
But, though they are two different things, the process of the third person believing, only occurs once Lois forms some concrete identity in the form of what she believes; once she has a what, she can believe what she believes. So they are different things, but when discussing belief, identity must be part of the discussion. (Which is what Davidson seems to think.)
The what in this case is Superman can fly. Lois has identified the character of Superman as the particular flying man. She identifies the man Superman and believes he can fly.
So again, although identity and believing are different, belief requires there be the identity of what in particular is believed.
We analyze what she believes the way we analyze referential opacity, sameness, difference, identity; we analyze believing differently.
We analyze that she is believing X with newer/additional terms. These may refer to referential opacity, but again, that is its own issue (or can be treated as its own issue).
Quoting Banno
Now we are just getting into the nature of the permutations between sameness and difference in references to Clark and Superman, and a way error and correctness can occur when misapplying the analysis of what is identified and what is not (Clark is the same as super; Clark is different; Superman can fly; Clark cannot fly;)
Lois believes that narrows the multiple permutations among Clark and Supermans sameness and differences, down to one particular instance. So substitution found in the full story of Clark/Superman may fail without incorporating Lois particularly intentional, identity awareness, purpose in speaking (she may be lying about her belief).
Quoting Banno
And we, the readers and analysts are a fourth party, necessary to account for the coherence of a belief (Davidsons communication needed for objectivity.)
But isnt Quine saying, let it show up in a belief context and transparency will be sacrificed quite as much as if you put it in quotes?
No, you can't put it in quotes. It has to be:
t1 = t2
Lois believes t1 can fly
therefore Lois believes t2 can fly
I think what you're suggesting is a readiness to make certain sounds. That's what you're calling belief. That's fine, it's just that you won't get opacity that way.
Somehow you have to involve t1.
Not without losing transparency, no, exactly. But Quine says, do this instead:
Quoting frank
and things are no better. The " t1" in "believes t1 can fly" won't have the same reference as the one in line 1. So substitution not ok. Quantifying in (from outside) not ok. Lois' t1 not our t1.
So belief ascriptions are (if we're not careful) as chaotic in their logical consequences as quotations.
So you do get opacity that way. You don't necessarily get belief, no. You may just have lines of questionable logic about belief ascriptions, yes.
Why not?
Quoting Fire Ologist
Because if it did, we'd be able to substitute?
T1 is Superman. It's a rigid designator, which is identical to Clark Kent, also a rigid designator. The b sentence tells us that Lois believes Superman (the rigid designator) can fly.
Quoting frank
Sentence c, with a de dicto reading, isn't true.
If we do a de re reading of sentence c, we would claim that Lois really does believe that Clark can fly, she just doesn't know she believes that, or maybe she just wouldn't put it that way? So with the endless shenanigans people have played with this problem, there are some views that say it's not a substitution failure.
The normal, everyday, commonly held attitude is that Sentence C is wrong, and as as a result of an invasion of propositional attitudes, we have referential opacity.
Yes. Quine agrees. Maintain the common attitude by not quantifying in, and hence not trying to reconcile Lois' Superman with ours. Not cashing in on the (future!) "rigid" rhetoric. Not substituting. Not going de re. Not concluding sentence c.
Ok. You just can't do that if you're defining belief as a readiness to make certain sounds. If Quine contradicts me on that, I'd have to read what he says to see what it is I'm misunderstanding.
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.
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.
Is there a problem here?
Referential opacity shows up in the identity elimination schema;
Quoting 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.
to
A supposed substitution?
What else could it be?
Haha, cheeky! No we didn't.
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.
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.
Oh, I thought we did.
:lol:
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.
Quoting 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.
I cant say I understand Analytic Philosophys 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-Els 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.
Whats weird is that the person interested in this sort of thing might respond, Okay, so Superman isnt the best example of this. But what is the best example? Wouldnt 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?
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Let me sketch out my guess at what is occurring.
Consider two biconditionals:
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:
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. Its 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 equivalenteither 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.
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?
Quoting 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.
Quoting Leontiskos
Quoting 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 dont 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 . Zs belief creates a new context in which we must redefine X and Y. So we cant substitute the use of either X or Y from P1, in any sentence following P2; P2 has redefined X and Y according to Zs belief.
Quoting Banno
Exactly. Lois isnt talking about the Superman or the Clark Kent from the first premise.
Like B.F. Skinner?
Quoting SEP
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?
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.
:D
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:
Quoting Donald Davidson, Rational Animals
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.
Quoting 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.
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.
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.
"=" is very well defined in both maths and logic, but cannot be adequately defined in merely syllogistic logic, which cannot deal with relations.
Then give your account of what
I only grant that it is well-defined in mathematics.
Quoting 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 Im telling you is, dont 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)), Leibnizs 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 Leibnizs 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 Leibnizs 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 Leibnizs Law but keep extensional substitution - that is, to use rigid designation.
This is not a complete account, but it'll do.
So again, what does
(I of course responded to your confusions yesterday.)
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.
And I'll note that you've failed to answer the simple question, "What does
More of the same from Banno.
Dude,
Quoting Banno
Quoting 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:
Quoting 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.
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.
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.
No stones were being thrown. Just exploring.
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.
Quoting Leontiskos
But you choose not to.
What are we to conclude?
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.
EDITTED
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.
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 doesnt actually formulate in those terms.
Might let it go until there is an agreed background?
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.
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.
Quoting Banno
It seems that people are quite unwilling just to accept the restriction. It needs a rationale - apart from Frege's solution not working.
Quoting Banno
I'm afraid that I don't see this as any kind of answer.
Quoting 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.
Quoting 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.
Quoting 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.
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.
Quoting 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:
Quoting 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:
nor with:
And indeed this last can be re-written as
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.
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".
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?
I think I'll just write a paper on it and send to a Journal. Looks like no one else has written about it yet.
"Physiological" is an odd term to use here. Did you mean something more like "Psychological"? But I take the point. But it seems to have turned out that the logic used to state the problem can't resolve it.
Quoting Banno
I believe that "Lois believes that Superman is Clark Kent and Superman can fly, so Clark Kent can fly" represents things better. Whether, post Davidson, "Superman is Clark Kent and Superman can fly, so Clark Kent can fly. Lois believes that." is better, I wouldn't care to say. What I'm after is that it's not enough that she believe three separate sentences. She has to put them together, and that's what it is hard to represent in language. Perhaps what I'm trying to say is that there something like a Gestalt at work here, which it is hard to represent with atomic sentences/propositions. I'm thinking of something like Quine's web of belief.
Quoting Banno
There are many things that I ought to know and do not know. I did not know that Quine has an actual diagnosis and a solution.
Like all good philosophy, it is obvious when you see it. So thanks for that.
I was not asking in the spirit that some philosophers ask questions to which they believe they know the answer in order to lodge an objection - though I have to admit that I have been known to do that.
However, there are many cases when a form of language is misleading, such as reification. But there are others where it is not, such as a categorial distinction. I'm not sure which kind the intensional/extensional distinction is.
When Macbeth sees Macduff's sword when Macduff comes to kill him, we are all clear the Macbeth sees Macduff's sword. There is a real sword, so it's an extensional context. When Macbeth sees a dagger before him, does Macbeth see an intensional dagger - i.e. a hallucination? What kind of object is that? I want to say that he does not see a dagger and that a hallucination is not an object. You can, I assume, see the implications.
Steam is H2O
Ice is H2O
Therefore, steam is ice
This is obviously incorrect. So too:
Ice is H20
Fog is H20
Ice can be walked upon and makes for a good bridge.
Therefore, fog can be walked upon and makes for a good bridge.
Or another false argument can be based on the fact that ice becomes water when heated, yet steam does not.
And yet:
This water is water.
This water has become steam.
Therefore this steam is that water.
Seems fine. These are pretty easy to explain in terms of water. The interesting thing is rather the general form. With the last one, while it seems clear that my cup of water is the same water when it has frozen, consider:
These frogs are frogs.
These frogs have been digested and become a turtle.
Those frogs are this turtle.
...does not seem to work, although we might agree that in some sense the composition of the turtle bears a similar relation to the frogs as the ice to the water.
You aren't using the identity elimination schema there.
That's a nice and thought-provoking collection of examples.
Quoting frank
I'm afraid I don't know or can't recall exactly what the identity elimination schema. Do you mind just outlining what it is?
I'm afraid I'm not competent to express an opinion about what you are trying to say. I don't understand it.
Sure, but you could easily make one that fits the form you were using. The difficulty there is that, in a simple three premise form, you end up with the questionable premise that "ice is steam." Well, that's true in a sense, but the whole point is that it is false in another. But you could do it in terms of a = c and b = c, which implies that a = b E.g.,
Ice and steam are H2O
Ice makes for a good bridge.
Therefore, steam makes for a good bridge.
You could also do it with the less questionable "ice is water."
Ice is water.
Ice makes for a good bridge.
Therefore water makes for a good bridge.
The problem here is an equivocation on "water" as chemical identity versus as a particular phase of that substance.
Now the error in the first is obvious in that H2O is sometimes treated as a sort of identity, chemical identity, (or a rigid designator) and yet the properties of its phases are distinct, and "ice" and "steam/fog" refer to particular phases. But I imagine a clever person could come up with less obvious examples.
Quoting Ludwig V
This is from the IEP article. (Beware, I've found incorrect info in the IEP before).
Quoting IEP
So after explaining the Superman substitution failure, the IEP sort of asks if this might be a misapplication of the schema. It goes through some misapplications, which I looked at
Quoting frank
We end up concluding that this isn't a case of misapplication, but we still have a substitution failure. Are you familiar with de re vs de dicto?
Yes, but don't see how it applies in the planets case.
Sure, if you have something to add. I was just thinking of similar cases that don't involve belief. Another equivocation with proper names would be the provocative:
Israel is Palestine
Israel is a Jewish state
Therefore, Palestine is a Jewish state.
Which seems false, whereas:
Israel is Palestine.
Israel is considered to be the Holy Land.
Therefore, Palestine is considered to be the Holy Land.
Seems fine. I was thinking this is just old-fashioned equivocation between Israel and Palestine as names for geographic regions versus as names of political entities (you could do it with Tibet or East Turkestan "being Chinese" as well). You could disambiguate with "the state of Israel/Palestine." Wouldn't "Constantinople" / Istanbul just be a sort of special case of equivocation?
Edit: with Superman we could also avoid belief and still get an apparent error with "Clark Kent appears on the Daily Planet payroll." This might be considered the same sort of equivocation as "Constantinople"/Constantinople. It's not as immediately obvious though. One could say it is true in one sense and not in another that Superman appears on the payroll.
The planet case is a misapplication because the number of planets isn't a proper noun. Both t1 and t2 have to be rigid designators.
Do you mean something like a blank space to be filled in with a number - hopefully the correct number?
Or perhaps more like a question "How many planets are there?" I get that. Thanks.
BTW. What is "9" the rigid designator of?
I think the number of planets is a singular definite description. It's not the same in all possible worlds.
9 is an abstract object.
Let's just share the blame.
I get the point about "the number of planets".
Sorry, but I don't really get the relevance of being an abstract object to rigid designation.
9 is the same abstract object in all possible worlds, so it's a rigid designator.
Oh, I see. I would have expressed that by saying that the number is the same in all possible worlds, so the numeral "9" designates the same number in all possible worlds. I should have worked that out. Sorry.
Also objective, contrasting with subjective, according to Davidson.
Also semantics, contrasting with syntax, according to Searle in his Chinese Room.
Also rigid, contrasting with flaccid.
Also real, contrasting with pretend, according to any five year old.
Or real, contrasting with suppose, from about 10 years.
Let's take care not to confuse the two, as @Banno says. Sure. But let's maybe see the possibility or likelihood of confusion (and the struggles to avert it) as a condition of "rationality", as Davidson says?
@frank's objection is to making it a sufficient as opposed to merely necessary condition of rationality? A machine doesn't achieve beliefs just by getting in a logical tangle over sentences?
Just trying to over-simplify. Carry on.
Too much caffeine will do that.
Well, if the personas have different properties then you have solved the "puzzle."
Right, or:
Quoting Leontiskos
I don't know I would go that far. That "if" tells me that you have reservations. I suspect there will still be issues to discuss, but it might be a change from going through that argument over and over again.
Oh, Tim.
Referential opacity is to do with individuals, not natural kinds.
In first-order logic a,b,c... are variables picking out individuals. Identity elimination is the rule that if a=b than for any formula that contains a we can write another formula replacing every instance of a with b and this formula will have the exact same truth value. That's pretty much the definition of "=".
That's why we use the individuals Superman and Kent.
Your examples use kinds, not individuals.
Quoting Count Timothy von Icarus
would be parsed as
U(x)(x is steam ? x is H?O)
U(x)(x is ice ? x is H?O)
Therefore
U(x)(x is steam ?x is ice)
It's the same as "All cats are mammals, all dogs are mammals, therefore all cats are dogs".
Quoting Ludwig V
I don't agree.
Fair enough.
Yep.
The schema says that if we have a true formula containing an individual variable a, and if we have a=b, then we can replace a in with b, and the formula will remain true.
Do you recall this?
Quoting Count Timothy von Icarus
No. The problem is that you have moved from individuals to natural kinds.
Sure, but the issue is similar, as evidenced by the Israel/Palestine geographic area versus state equivocation.
I am not sure how the move to natural kinds explains the issue. If x is y natural kind and z is y natural kind, then in theory they have the same essential properties. If "water" is taken to be equivalent to H2O, i.e., chemical identity, then what is true of H2O is true for water. But water refers to both a chemical identity and a specific phase, which is what allows for equivocation, just as Israel can refer to a certain section of the Levant or the modern state of Israel, or the ancient Northern Kingdom.
But I'd argue that with the person/persona distinction similar sorts of equivocation can occur. Spiderman is the main character of a Marvel franchise. Peter Parker? Well, in the newer versions there is only Miles Morales from what I understand.
No, it isn't. An individual is not a kind.
Quoting Count Timothy von Icarus
All this shows is ~(Israel = Palestine). They are not identical, and so substitution fails.
That there is some difference as to the identity of Spiderman suggests that we sort out the identity before we start substitution.
Referential opacity is not about ambiguity.
Quoting Banno
I would have thought so, too. But what do we make of Kripke?
I realize encyclopedias get things wrong, but this coincides with my memory.
Quoting Count Timothy von Icarus
That's true. But you don't diagnose the problem.
Quoting Banno
Banno is right. Undistributed middle.
Quoting Count Timothy von Icarus
I have doubts about this. It is not wrong. But it doesn't mean that any old chunk of ice will make a good bridge. Ice only makes for a good bridge if it is handled properly. One could argue that the conclusion is true, provided we specify that it needs to be handled properly (i.e. turned into ice). There's a complication here because the same could be said of water.
Quoting Count Timothy von Icarus
Yes. Mostly, this does not bother us, but in this kind of discussion, it matters.
Quoting Count Timothy von Icarus
I think that this is where the example is clearly in a different category from our referential examples. "Water" is a mass term - it doesn't do individuals. The only ways you can identify "the same water" is indirectly, via, for example, a cup. When you borrow a cup of sugar from your neighbour, you will, of course, return it. But you don't have to return the same grains of sugar, do you? The same goes for borrowing money. You repay the money you borrowed, but not the same individual money - the very idea is meaningless.
Quoting Banno
Well, we agreed, I think, that the problems occur between contexts, which may be one kind of ambiguity. But it is true that there are ambiguities that are not about reference. Nonetheless, I'm beginning to think that there are issues about the "description under which" we think about things that I have not seen discussed.
Quoting Banno
There is something I don't understand here. Presumably, the implication goes the other way, so that if we can replace a with b in a formula, then we have a=b. So we need an independent way of establishing one or the other.
[Quote]
Banno is right. Undistributed middle.
[/quote]
I think that's right, but the question of why it is more plausible seems to lie in the ability to equivocate on the way in which water, ice, and steam "are" H2O. It is, in some contexts, perfectly correct to say that ice and steam are water. A science teacher teaching the water cycle or phases of matter would say just this sort of thing. There isn't a correct context for "cats are dogs."
This is more obvious in a context where the relationship is more genuinely informative, such as "dry ice is carbon dioxide." It is true, in one sense, to point to dry ice and say "this is what you exhale," and obviously false in another sense.
I don't think it's meaningless. Sometimes people hold money for other people, and they expect them not to mess around with it. Money is fungible though, so exchanging it isn't generally meaningful. It would be though if you had different sorts of bills, e.g. old precious metal backed bills.
You can refer to specific volumes of water. In a steam engine, we might talk exclusively about the water in a given system, and also its passage between different phases of matter. The difficulty in picking out individual instances of water (or air, etc.) would seem to have to do with their extremely weak principle of unity. It is very easy to divide volumes of water. Volumes of gas naturally expand. A water molecule is different. It has a stronger principle of unity. Solid water does as well, but you can easily break a block of ice apart and then you just have multiple blocks of ice. Compare this with something with a strong principle of unity like a tree. Break a tree in half and you have a dead tree, you have timber, not a tree at all arguably. Break it up more and you have lumber that is clearly not a tree.
There's no equivocation. Steam is water in the same way the statue is clay.
I don't understand you. All I'm saying is that "water" is ambiguous and this makes it easy to fall into error. To be sure, we usually manage the ambiguity. BTW. "Cat" is ambiguous between the species and the genus. So there is a similar ambiguity there. I'm sure there are others.
Quoting Count Timothy von Icarus
I'm not sure I know what "fungible" means, but I think I get the point. Exchanging money for money would indeed be pointless. Borrowing and lending money is not a straightforward exchange so it is different.
Quoting Count Timothy von Icarus
Yes. That was my point.
Natural kinds - ice, water, and so on - are not individuals. Referential opacity is a problem for individuals.
Both natural kinds and individuals can be named using rigid designators. We can construct similar case...
The response is the same. A contradiction only occurs if Alice believes that water = H?O. Not if water = H?O.
Quoting Count Timothy von Icarus
U(x)(x is ice ? x is water)
Ux(x is ice ? x makes a good bridge)
Ux (x is water ? x makes a good bridge.)
That's invalid. Sorry, Tim.
Quoting Ludwig V
Yeah, it is.
Quoting Ludwig V
Not quite. Not just a formula, but all formula. If in all formula we can substitute a for b, without altering any truth value, then a=b. That's Leibniz's law.
"Water" can mean the liquid only, or it can mean any of liquid, solid, and gas. If we assert that water = H?O, we are asserting the latter, since we are also by symmetry asserting that H?O = water. I don't see an issue, provided we are clear here. Tim's post seems tangential.
That's because of how you are translating it. If the relation is identity then it is:
(i = w) ? Bridge(I) ? Bridge(w)
That was exactly my point. And on the view that ice is water, water can indeed be made into a good bridge/ice road given the right conditions.
The reason I thought of it is because you can construct a parallel with proper nouns that share a name in some contexts and not others, which results in similar looking "errors."So for instance, "Palaestina" was a Roman renaming of the same exact provinence following their explosion of the Jews, and the general geographic area is referred to as either "Israel" or "Palestine," whereas the modern political entities are clearly different.
If you allow for a distinction between personae and persons, you get something quite similar. For instance, Stone Cold Steve Austin loves beer. That's part of the character. In theory, the actor might not.
Dude, H?O? liquid water. Palestine ? Israel. Stop equivocating.
That's the whole point of the example though?
You mash them.
That's right. The problem with the ice/bridge argument, IMO, is although one could argue that the first premiss tells us that the wider sense applies, the conclusion is misleading, because the substitution of "water" for "ice" suggests that the narrow sense applies. Does that work?
Quoting Banno
Yes. I'm a bit slow sometimes. I finally realize that referential opacity is the result of cross-contextual confusion, but old-fashioned equivocation, which is what @Count Timothy von Icarus is talking about takes place within a single context. Is that right?
I said they were different. My point is that those sorts of equivocations look similar in natural language, and involve only nomological contexts, but still involve shifting between contexts.
As and were discussing, we also might make a distinction between personae and persons. This happens whenever actors are referred to by their real names to describe events in movies they act in for example. This seems context dependent too.
The ice bridge argument is just invalid. It's another undistributed middle.
Equivocation can take place in the same context, but it is not necessary; it can occur over different contexts. Consider:
There's an ambiguity between the two uses of "water", the first refering to any state, solid, liquid, gas, the second to the liquid only. But we might have:
Same ambiguity, two states.
I think that's right. What do you think?
(i = w) ? Bridge(I) ? Bridge(w)
Is not an undistributed middle.
Yeah, maybe not. It's a bit of a muddle, really. I'm not at all sure what you are claiming here. So what looks like a violation of Leibnizs Law is really just equivocation about the reference of "w". Not sure what your point is in relation to the topic. Yes, some problems are to do with ambiguity, but some problems are also to do with referential opacity, and they are not the same.
What are you trying to argue?
I just brought that one up because it is an example that seems like obvious equivocation that is not actually equivocation (or false) depending on how the first premise is meant (the first premise can also be true or false depending on how it is meant). And my thoughts were that the same might be true for a person / persona distinction.
But, it's also the case that if "ice is water (any phase)" is meant as identity, but then "water (makes for a good bridge," is meant as "liquid water makes for a good bridge" then we have a fallacy of four terms, having introduced "liquid water" for the very first time in the conclusion.
So, there is a valid and true version, an undistributed middle, or four terms. The way you switch between them despite an identical natural language rendering could be described under supposition theory. Supposition theory was also used for referential opacity in the past. That's how Ockham covers belief, in belief statements the term for the object supposes for the knower's mental conception of the known (an unfortunate move that contributed to representationalism). There are similar moves around modality with the idea that terms suppose differently (are ampilated by the modal context).
I thought of it because Ockham's solution is similar to Quine's in some ways, but works using a theory that explains some types of "equivocation." So, there is a sort of similarity.
Consider a book, rather than a believer. A book says something like: "Superman can fly" or "Mark Twain is a best seller." Does the book also say that Clark Kent can fly and that Samuel Clemens is a best seller? Does identity substitution work here? Now, on one view, we could ask what the writer intended. If the writer intended to express their beliefs and has no idea that Mark Twain = Samuel Clemens, and the text is taken as an expression of belief, then it seems that we cannot substitute? Whereas, on a "death of the author view" it would seem to be the reader who determines in substitution holds in ambiguous situations.
But, if we want to keep to a view where opacity is purely a function of language/contexts itself, what of ambiguous statements in the context of something like an anonymous text, a p-zombie, random text generator, or AI?
This?
Quoting Count Timothy von Icarus
I=W" can only be true if we restrict the referent of 'water to its solid form. But doing so would be an error. The referent of "water" is not just ice.
Quoting Count Timothy von Icarus
If that's how you mean it, then it's wrong, since ice is water in it's solid form; ice is never liquid water.
I'll leave you to the complexities of Occam. It's been surpassed.
Quoting Count Timothy von Icarus
The writer's intention is irrelevant. The book says "Superman can fly" not "Clark Kent can fly", and any one who says otherwise would be misquoting. Substitution of co-referents is not licensed inside quotation or belief reports.
Hmm.
Added: the book idea is actually quite neat- see the SEP article on quotation, the quotes there are pretty much considered independently, but in a book or other body of literature we might need a more holistic account. So for example, Quine and Davidson use ideas of holism that might be comparable to a book rather then discreet quotes.
Quine: No statement is assessed in isolation; its truth-value depends on the whole theory. Likewise, perhaps no quote in a book can be fully interpreted in isolation.
Davidson: Meaning emerges through interpretation of the speakers (or texts) whole pattern of use, not individual utterances.
So the book example illustrates why opaque contexts may not be exhausted by local quotation rules a single quote cant capture the interpretive force of a whole body of text. Thats where holism starts to look more natural.
Thanks for the thought.
The postal system relies upon referential transparency, namely of knowing an immutable address that is associated with an intended recipient, as opposed to knowing the mutable personal details of the sender and the recipient which are kept hidden from the postal service ("information opacity").
So here, the information space (that is hidden from the postal service) is comprised of vectors of information, where a vector is a possible list of attributes corresponding to a possible user. This information space is dual to the address space, namely the set of possible postal addresses for possible users.
The information space is a vector field; the vector field indices are the address space.
Address information can also be an attribute of information space, but this shouldn't be confused with the address space: the address information that you put on your resume isn't the address used by the postal system. Address information is mutable information that is considered to be an attribute of senders and recipients, whereas a postal address is part of the immutable structure of the postal system.
What if user moves house?
if a user moves house, this is represented by an arrow linking 'before' and 'after' vectors in information space (assuming the info is available there). But from the perspective of the postal service, users don't move house, rather houses change their occupants - because the postal system uses postal addresses to designate rigidly.
Leibniz's Law
Assuming that Leibniz's Law holds with respect to a given postal service, then it holds internally in the sense of characterising the postal operations of that given postal system, but it does not hold externally in the sense of surviving a change to the postal service itself.
The indiscernibility of identicals is a definitional criterion for the meaning of a pair of addresses:
?x ?y[ x = y ? ?F(Fx ? Fy)] (i.e. identical addresses imply identical occupants).
Compare that to Frege's disasterous Basic Law V(b)
?F = ?G ? ?x(Fx ? Gx)
Here, the difference is that ?F and ?G are extensions, namely vectors in information space rather than addresses. If these vectors are finite then they can be fully observed , meaning that if they are observed to be identical then they must be same vector, meaning that V(b) is applicable. But in the infinite case, the two lists cannot be exhaustively observed, in which case we have at most equality between two incomplete lists, which obviously cannot imply that they denote the same vector due to the problem of induction.
(Frege and many logicians after him, conflated the notion of addresses, which can always designate rigidly by virtue of merely being indexicals devoid of information content, with observation vectors that cannot rigidly designate the set of concepts that they all under).
The identity of indiscernibles is postally invalid if multiple home ownership is allowed:
?x?y[?F(Fx ? Fy) ? x = y ] (which is true of a vector space, but generally false of a vector field).
That's a splendid example.
Quoting Count Timothy von Icarus
Formal logic depends on treating language as a structure - unless someone has begin devising a logic that includes speakers - who would be an abstraction anyway.
Quoting Count Timothy von Icarus
I think we would treat such texts as if there were a speaker. The text itself posits an author. The author of the text is not necessarily the same as any specific person. It's a trope in literary studies.
BTW I don't believe in p-zombies.
Quoting Banno
I have a feeling that what you meant to say was that the writer's intention is irrelevant for the purposes of logic. That's true. But if you know that Dostoevsky was a devout Christian, you will be licensed to interpret his texts in the light of that knowledge. Surely?
Quoting Banno
That's why we can't take "believes that.." as something like a quotation.
Davidson's account of "said that" starts from a quotation and analyzes it on that model. But quotation and reporting are not the same language games (contexts). The rules and criteria are different. Neither is the same as a recording, but a quotation is expected to be more like a recording than a report. The exact same words are key in a quotation, though pronunciation and tone are not relevant. This attracts philosophers, because it is (reasonably) clear and emphasizes accuracy But reports are more complex. On the other hand, "X reported the fire in the kitchen" is a rotten quotation but a perfectly acceptable report. In some contexts, we are not much bothered about the difference between "The President", "Trump". In others, we are.
In particular, we are not allowed to replace referring expressions inside a quotation. If someone said "Rickard Starkey was a drummer", we have to stick to "Richard Starkey" if we are quoting. But if we are reporting, depending on the audience, we may well substitute "Ringo Starr was a drummer", because that is more relevant in the context of the report or because it is more effective if the audience for the report cannot be expected to know that Richard Starkey was Ringo Starr.