The Quotation is not the Referent

[-]Nick_Tarleton18y122

Studying programming seems like it should be an even better way; mixing up 'int' and 'int*' will get you problems fast. On the other hand, I gather from your example that a lot of programmers made this mistake.

[-]John_O18y101

I like these posts, but let me add a couple of comments. In philosophical circles the "type distinction", as you call it, is known as the use/mention distinction, i.e. the distinction between using a phrase like "evening star" (to talk about the thing itself) and merely talking about the phrase (usually signaled by quotation marks).

But that's not the first problem you mentioned, which is known in philosophical circles as the failure of substitution in intensional (i.e., roughly, mental) contexts. I'm not so sure the use/mention distinction is useful in explaining this failure. For example, the sentence "Lois is looking for Superman" cannot be substituted for "Lois is looking for Clark Kent", because she may not know that that Superman and Clark Kent are identical. Obviously we never make that mistake, but if someone were to make it, the reason is surely to do with failing to realise that Lois may have false beliefs. But that's not a category mistake.

[-]TheOtherDave15y11-1

But that's not a category mistake.

Really?

What is Lois actually looking for? When we say she's looking for Superman, we mean she's got a search target in her mind, a conceptual representation of Superman, and she's looking for something that matches that target closely enough to satisfy her. (Or, well, we ought to mean that. What we actually mean, I'm less sure of.)

If I introduce the typographical convention to designate a conceptual representation of an object X and the convention m(x) to designate an object that matches a concept x, then Lois is looking for m().

Superman is Clark Kent, but is decidedly not . To expect that because Superman is Clark Kent that Lois is looking for m() sure sounds like a category mistake to me.

One nice thing about this is that if you know the secret, then in your mind starts to resemble very closely... they aren't identical, but any m() is almost undoubtedly also a m() and vice versa. Which is exactly what we would expect -- the more I believe Clark Kent and Superman are one and the same, the more likely it is that if I'm looking for one I'll terminate the search upon finding the other.

[+]wedrifid15y-90

[-]Richard418y92

Yes, like John O, I think this post misdiagnoses the problem.

John and Mary have beliefs about the evening star, not 'the evening star'. Their beliefs are about the world, not about the words. Neither of them believes that 'the evening star' is the god Venus. Who ever thought that the god Venus was a string of three words!?

Further -- though more contentiously -- we might even deny that Mary has any beliefs about the evening star (that very thing, i.e. the planet). She takes the world to be a certain way, such that a god Venus appears in the evening sky, etc. But given that our term 'the evening star' actually denotes a planet, perhaps we misdescribe Mary's belief by employing this term. She might attempt to use the term herself in describing her belief, but this is because she doesn't really know what it means, so she doesn't realize that linguistic error is causing her to misdescribe her belief contents.

For further explanation, see: Belief Content and Linguistic Error.

[-]bigjeff515y30

But given that our term 'the evening star' actually denotes a planet, perhaps we misdescribe Mary's belief by employing this term.

I believe that is exactly what Eliezer is saying.

"The evening star" refers to two entirely different things to Marry and John. John believes 2+2 = 4, while Marry believes 2+2 = red and 4 = blue. Attempting to substitute 4 for red does not work, because John's 4 is not even the same type of thing as Mary's.

John learns that Mary believes 2+2 = red. When John sees Marry write ((2+2) + 4) = purple, John incorrectly thinks Mary believes (red + red) = purple.

The problem, of course, is that Mary does not believe 2+2=4, to her that would be ridiculous, so John makes an incorrect inference about what Mary does believe because his beliefs are entirely different.

[-]Frank_Hirsch18y100

I know a really bad one which nearly turned my stomach: Some newspaper wrote "Survey uncovers that X's have the property Y!" (I forget the details). I read the article and it turned out that, according to some survey, most people believe that X's have the property Y. Argh!

[-]Tom_Breton18y70

In classical logic, the operational definition of identity is that whenever 'A=B' is a theorem, you can substitute 'A' for 'B' [but it doesn't follow that] I believe 2 + 2 = 4 => I believe TRUE => I believe Fermat's Last Theorem.

The problem is that identity has been treated as if it were absolute, as if when two things are identical in one system, they are identical for all purposes.

The way I see it, identity is relative to a given system. I'd define it thus: A=B in system S just if for every equivalence relation R that can be constructed in S, R(A,B) is true. "Equivalence relation" is defined in the usual way: reflexive, symmetrical, transitive.

My formulation quantifies over equivalence relations, so it's not properly a relation in the system itself. It "lives" in any meta-logic about S that supports the definition's modest components: Ability to distinguish equivalence relations from other types, quantification over equivalence relations in S, ability to apply a variable that's known to be an equivalence relation, and ability to conjoin an arbitrary number of conjuncts. The fact that it's not in the system also avoids the potentially paradoxical situation of including '=' among its own conjuncts.

Given my formulation, it's easily seen that identity needs to be relative to some system. If we were to quantify over all equivalence relations everywhere, we would have to include relations like "Begins with the same letter", "Has the same ASCII representation", or "Is printed at the same location on the page". These relations would fail on A=B and on other equivalences that we certainly should allow at least sometimes. In fact, the =' test would fail on every two arguments, since the relation "is passed to the NNNNth call to=' as the same argument index" must fail for those arguments. It could only succeed in a purely Platonic sense. So identity needs to be relative to some system.

How can systems differ in what equivalence relations they allow, in ways that are relevant here? For instance, suppose you write a theorem prover in Lisp. In the Lisp code, you definitely want to distinguish symbols that have different names. Their names might even have decomposable meaning, eg in a field accessor like my-struct-my-field'. So implicitly there is an equivalence relationhas-same-name' about the Lisp. In the theorem prover itself, there is no such relation as has-same-Lisp-name or even has-same-symbol-in-theorem-prover. (You can of course feed the prover axioms which model this situation. That's different, and doesn't give you real access to these distinctions)

Your text editor in which you write the Lisp code has yet another different catalog of equivalence relations. It includes many distinctions that are sensitive to spelling or location. They don't trip us up here, they are just the sort of things that a text editor should distinguish and a theorem prover shouldn't.

The code in which your text editor is written makes yet other distinctions.

So what about the cases at hand? They are both about logic of belief (doxastic logic). Doxastic logic can contain equivalence relations that fail even on de re equivalent objects. For instance, doxastic logic should be able to say "Alice believes A but not B" even when A and B are both true. Given that sort of expressive capability, one can construct the relation "Alice believes either both A and B or neither", which is reflexive, symmetrical, transitive; it's an equivalence relation and it treats A and B differently.

So A and B are not identical here even though de re they are the same.

[-]aspera13y00

I think that in physics we would deal with this as a mapping problem. Jonh's and Mary's beliefs about the planet live in different spaces, and we need to pick a basis on which to project them in order to compare them. We use language as the basis. But then when we try to map between concepts, we find that the problem is ill posed: it doesn't have a unique solution because the maps are not all 1:1.