but the issue is similar, — Count Timothy von Icarus

No, it isn't. An individual is not a kind.

Israel is Palestine
Israel is a Jewish state
Therefore, Palestine is a Jewish state. — 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.

:ok:

To be sure, anomalous Monism remains an area of great interest and ongoing development. Just look at the list of supplements to the SEP article on that topic.

Referential opacity is to do with individuals, not natural kinds. — Banno

I would have thought so, too. But what do we make of Kripke?

In Naming and Necessity, Kripke argues that proper names and certain natural kind terms—including biological taxa and types of natural substances (most famously, "water" and "H2O") designate rigidly. — Wikipedia - Rigid designator

I realize encyclopedias get things wrong, but this coincides with my memory.

Steam is H2O
Ice is H2O
Therefore, steam is ice
This is obviously incorrect. — Count Timothy von Icarus

That's true. But you don't diagnose the problem.

It's the same as "All cats are mammals, all dogs are mammals, therefore all cats are dogs". — Banno

Banno is right. Undistributed middle.

Ice is water.
Ice makes for a good bridge.
Therefore water makes for a good bridge. — 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.

The problem here is an equivocation on "water" as chemical identity versus as a particular phase of that substance. — Count Timothy von Icarus

Yes. Mostly, this does not bother us, but in this kind of discussion, it matters.

it seems clear that my cup of water is the same water when it has frozen, ... — 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.

Referential opacity is not about ambiguity. — 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.

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. — 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.

Banno is right. Undistributed middle.

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.

You repay the money you borrowed, but not the same individual money - the very idea is meaningless

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.

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 — Count Timothy von Icarus

There's no equivocation. Steam is water in the same way the statue is clay.

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." — Count Timothy von Icarus

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.

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. — 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.

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. — Count Timothy von Icarus

Yes. That was my point.

But what do we make of Kripke? — Ludwig V

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...

• Alice believes that water is refreshing.
• Alice does not believe that H₂O is refreshing.

The response is the same. A contradiction only occurs if Alice believes that water = H₂O. Not if water = H₂O.

Ice is water.
Ice makes for a good bridge.
Therefore water makes for a good bridge. — 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.

It is not wrong. — Ludwig V

Yeah, it is.

Presumably, the implication goes the other way, so that if we can replace a with b in a formula, then we have a=b. — 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 = H₂O, we are asserting the latter, since we are also by symmetry asserting that H₂O = 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)

"Water" can mean the liquid only, or it can mean any of liquid, solid, and gas. If we assert that water = H₂O, we are asserting the latter, since we are also by symmetry asserting that H₂O = water. I don't see an issue, provided we are clear here. Tim's post seems tangential.

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, H₂O≠ liquid water. Palestine ≠ Israel. Stop equivocating.

Stop equivocating

That's the whole point of the example though?

"Water" can mean the liquid only, or it can mean any of liquid, solid, and gas. If we assert that water = H₂O, we are asserting the latter, since we are also by symmetry asserting that H₂O = water.

Dude, H₂O≠ liquid water.

Referential opacity is a different issue to referential equivocation.

You mash them.

"Water" can mean the liquid only, or it can mean any of liquid, solid, and gas. If we assert that water = H₂O, we are asserting the latter, since we are also by symmetry asserting that H₂O = water. I don't see an issue, provided we are clear here. Tim's post seems tangential. — Banno

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?

Referential opacity is a different issue to referential equivocation. — 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.

substitution of "water" for "ice" suggests that the narrow sense applies. — Ludwig V

Yep.

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:

Water is H₂O, and water is always a liquid.

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:

Water is H₂O, and Alice believes that water is always a liquid.

Same ambiguity, two states.

I think that's right. What do you think?

The ice bridge argument is just invalid. It's another undistributed middle.

(i = w) ∧ Bridge(I) ⊢ Bridge(w)

Is not an undistributed middle.

Is not an undistributed middle. — Count Timothy von Icarus

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 Leibniz’s 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.

Anyhow, for another topic of conversation related to my confusing example: we might question whether we can really avoid a solution more like Ockham's so easily. Can opacity vis-á-vis belief wholly semantic and logical?


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?

I just brought that one up because it is an example that seems like obvious equivocation that is not actually equivocation — Count Timothy von Icarus

This?

(i = w) ∧ Bridge(I) ⊢ Bridge(w) — 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.

...it's also the case that if "ice is water (any phase)" is meant as identity — 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.

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. — 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 speaker’s (or text’s) 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 can’t capture the interpretive force of a whole body of text. That’s where holism starts to look more natural.

Thanks for the thought.

Leibniz's Law at the Post Office

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)

ϵF = ϵG → ∀x(Fx ≡ Gx)

Here, the difference is that ϵF and ϵG 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.

Can opacity vis-á-vis belief wholly semantic and logical? — 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.

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? — 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.

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. — 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?

So the book example illustrates why opaque contexts may not be exhausted by local quotation rules — a single quote can’t capture the interpretive force of a whole body of text. That’s where holism starts to look more natural. — 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.