Friday, 3 August 2012

Is There a Philosophical Problem of Reference?

Many philosophers worry about reference, and think we need to come up with a "theory of reference". This would explain how strings get "connected" to things: the string-thing relation. So, maybe this should be analysed in terms of causation. Causation glues cats to the word "cat". And so on. Or maybe one gets worried about how, e.g., "aleph_0" and $\aleph_0$ got glued together, when causation couldn't have done that---for $\aleph_0$ is a causally inert abstractum. In fact, the string "aleph_0" is also an abstractum. Worried by the unsurprising inability to reduce reference to causation, one might go deflationary and say that there is just a reference predicate, the binary predicate "$x$ refers to $y$", governed by disquotational axioms (e.g., ""red" refers to the set of red things") and one has this in one's language (which gives the illusion of genuine reference). Or perhaps one gives up, becomes a semantic nihilist and says outright: there is no reference relation at all.

Well, maybe there is no philosophical problem of reference at all: any relation of strings to things is a legitimate reference relation. So, the theory of reference is this:
$\mathcal{I}(\sigma) = x$
where $\mathcal{I}$ is some function: any function you like. Because $\mathcal{I}$ is a parameter here, reference is really a ternary relation,
$\sigma$ refers to $x$ relative to $\mathcal{I}$.
Many authors believe, however, that reference is a binary relation that strings bear to referents. That is,
$\sigma$ refers to $x$.
With no language or interpretation relativity! It seems to me that this violates the single most basic principle of language---that anything can mean anything in some language. The language relativity is essential. And yet the view that reference is a binary relation without language relativity seems fairly standard.

Chris Gauker gave a talk on a related topic at MCMP several months back. And Chris's view is an example of the conventional view of what is required from a theory of reference:
The problem
What is reference? Offhand, it appears to be a relation, just as being heavier than is a relation. Moreover, it is a relation that holds between words and other things. It holds between "chair" and the chair I'm sitting in, between "chair" and the chair next door, and between "chair" and the chairs of the past and future. It holds between "Socrates" and Socrates, between "meson" and mesons, and between "beautiful" and beautiful things. Of course, the reason it holds between these things is not just that it holds between every word and everything. For instance, it doesn't hold between "basketball" and daffodils. The fact that the relation being heavier than holds between an atom of oxygen and an atom of hydrogen, as well as between Pavarotti and Diana Ross, but not between everything and everything, ought to make us wonder what being heavier than amounts to, if we don't already know. Likewise, the combination of diversity and specificity exhibited by the reference relation ought to make us wonder what reference is. We mustn't just call it an "unanalyzable primitive".
Accounts of reference that might satisfy us fall into two classes. On the one hand, we might seek what I'll call an analysis of reference. An analysis takes the form:
$t$ refers to $a$ if and only if $\dots$.
(Gauker 1990, "Semantics without reference", Notre Dame Journal of Formal Logic, 438.)
This seems to me to be a bit like a grammatical mistake, because it omits the crucial language parameter,
$t$ refers to $a$ in $(\mathcal{L}, \mathcal{I})$ if and only if $\dots$.
$t$ refers to $a$ in $(\mathcal{L}, \mathcal{I})$ if and only if $\mathcal{I}(t) = a$.
There are no constraints at all on what the interpretation function $\mathcal{I}$ might be. It can be any old string-thing function. On this proposal, it isn't that the famous semantic indeterminacy puzzles disappear (e.g., Quinian inscrutability of reference, Kripkenstein, Putnam's "model-theoretic argument", ec.). Rather, the puzzles turn out, on reflection, to be puzzles about what language one speaks. The question isn't how languages get referentially glued to things---they already are, in every mathematically possible way (generating uncountably many different languages). The question is how the mind gets glued to some particular language: a problem of language cognition.

1. Hi Jeff,

Thanks for the interesting post!

I want to get a bit clearer on what's been gained by the shift from reference to language cognition. Consider a really simple language L that just contains singular terms referring to objects. Two questions one might ask about L are:

(1) Why does t refer to x in L?

(2) Why do I (partially) speak L rather than L' (where t does not refer to x)?

(1) is a sharpening of the traditional metasemantic question which, as you point out, seems to have a trivial answer when L is understood as a function from terms to objects -- in particular, t refers to x in L because L(t) = x.

Of course, the traditional metasemanticist wouldn't be happy with that way of spelling out their question. Instead, I would imagine that they would claim that (2) is closer to the question they were asking, given the current framework.

Is there an easy way to see that (2) is a genuinely different question from the traditional one, and thus that this isn't just a difference in terminology?

All the best,
Sam

2. Hi Sam,
Thanks - yes, as you say, for the first question (1), that is just what L does, on this Lewisian picture: t refers to x in L because L(t) = x. So, the question is a bit like "why is the value of sine on 30° equal to 0.5?", and the answer is "Because sin(30°) = 0.5". So, (1) gets a trivial answer: nothing explains why L(t) = x. It's a necessity.

I do think the view, even if it's only a reformulation, has benefits. It removes objections to the causal theory of reference; it is a competitor to deflationary and nihilist views about reference. It respects the Saussurean principle that anything can mean anything.

Then the second question, (2), I call the "cognizing problem", is a separate one; I think it is:
(a) very hard - the hard problem of representation.
(b) the problem meta-semanticists have normally been interested in.

But I don't think it's merely a difference of terminology, because, e.g., on this view, reference (and semantic notions generally) is language relative and reference facts are necessities (so, there's no hope of, or even need for, a causal reduction of "x refers to y").

But why do I speak L rather than L*? (I have a bit on this in the "There's Glory or You" post a couple of months ago.)
Here's my rough attempt at an explication of the contingent relation, "A speaks L":

(*) A cognizes/speaks L iff, for any concept C, string s: A assigns C to string s iff L(s) = C.

This assumes an intentional primitive, "A assigns C to s" (call this A's noetic function). So: A speaks L when A's noetic function matches the meaning function for L.

So what seems like referential or semantic indeterminacy arises when the speaker's noetic function is indeterminate. E.g., for the Kripkenstein case, It might be indeterminate whether the mind of Tim Gowers assigns + to "plus" or +* to "plus" (where +* is some odd function, whose restriction coincides with +).

In this sort of case, I don't think it is indeterminate, actually, but I think that is where the problem is: it concerns language cognition. Of course, I don't know how to work out the answer to that ... perhaps the mind selects certain concepts because the concept is simpler. So, some of the approaches advocated by (realist) meta-semanticists may well be similar on both ways of looking at these problems.

Cheers, Jeff

3. Hi Jeff,

I'm glad we agree where the real meta-semantic action is on your framework -- namely with (2). Just to be clear, I do think the framework is neat; but I suppose I'm still not entirely clear what it says about existing debates about reference. For instance, take the causal theory of reference. In your framework, such a theory looks misplaced (as you say "there's no hope of, or even need for, a casual reduction"). But I don't think that the casual theorist will be happy equating "reference" in their sense with "reference in L" in your sense. Rather, I would imagine they would want their talk of "reference" to be interpreted in your framework by talk of "assigns".

Or is there some simple reason why that interpretation of the old reference language into your assigns language fail?

All the best,
Sam

4. Hi Sam,

Thanks! With current debates I want to say there's a conflation of a semantic notion (the meaning relation for L, mapping strings to meanings) and a cognitive notion (the cognizing relation, between agent and language L). And the ternary nature of meaning/reference (language relativity) is important, as it yields that meaning facts like,
(i) "Schnee" denotes in German snow
(ii) "Schnee ist weiss" expressed in German that snow is white
etc.
are necessities. (This is a problem for naturalistic theories of reference, and tends to push people towards deflationism. It's not a problem for me because all the contingency resides in the "A speaks L" relation.)

But then to look at your question, suppose the meaning naturalist agrees, and then says, "Ok, fair enough. Let's grant you your "anything-can-mean-anything" account of reference/meaning, and conclude that there isn't a problem there, and discuss instead the intentional assigning relation - the agent assigns meaning m to string. Isn't that a causal relation?".

Then, I'd say that it's while it's temporally and modally contingent what concepts an agent is assigning to strings, I don't think it can be a causal relation, as the relata aren't always (or even sometimes) causally related: e.g., assigning say the concept of membership to the string "is a member of".
So, one has to buy into the idea that the mind can grasp concepts or rules or referents, understood as abstracta. (E.g., suppose the mind just can realize the addition function, somehow. It can concanenate mental strings, maybe. Then it's not so implausible that the mind can assign the genuine, abstract, addition function + to the string "plus")

I say all this because I don't want to do anything sneaky. I'm trying to be clear up front that the intentional primitive, "A assigns C to string s" is a rather metaphysically weighty notion. It's a bit like Fregean grasping or Putnam's noetic rays (he mocks it a bit, so I copied the word).

A slightly different approach, more in line with assertibility semantics, might be to take "A believes p" and "s is assertible for A" as primitive, and then define,

A speaks/cognizes L iff for any string s, and proposition p (if s means-in-L p then s is assertible for A iff A believes p).

But I'm unhappy with this approach. It's not fine-grained enough.

Cheers, Jeff

5. Hi Jeff,

One last thing: for singular terms t, do speakers and languages in your sense assign objects to t, or concepts? For instance, does my idiolect of English map "Sam Roberts" to me, or to some concept?

Best,
Sam

6. Hi Sam,

I have quite a long story to tell on this topic, but on the standard view in phil language, minds assign referents directly to words. So we have Davidsonian referential semantics, and I think that's a widely held account. (In parts of formal semantics the situation is different.) But I think that a reference-first view faces some independent problems. E.g., how does the mind assign the class S of spacetime points to "spacetime point" or assign the sets to "set". If p is a single spacetime point, then why does my word "spacetime point" refer to S, and not S / {p}? So, I think it must be intensional (or concepts a la Frege) rather than extensional, and reference is indirect.

And, in this case, it's your individual concept that I assign to "Sam Roberts". The referent is determined indirectly, since Sam is (by necessity) the unique satisfier of this intension. For the theory of meaning & reference for a language, this seems ok: what string refer to are the extensions of their intensions.

But for making sense of cognizing, maybe this is not ok. To pin down "A speaks L" (which is really what I want to do), one has to assume certain intentional primitives, though which ones, I'm not sure. E.g., "A uses string s to refer to x", "A assigns referent x to string s", "A assigns concept C to string s", etc.,

Even making sense of cognizing syntax is rather hard.
Basically, the idea of a physical system computing or realizing a program/function. Still, it's easier to make sense of cognizing a program for computing recursive function than it is to make sense of cognizing the referent of "spacetime point". (Which is why deflationism is so attractive.)

Cheers, Jeff

7. Hi Jeff,

So there are two options; either we assign objects to singular terms or we assign their haecceities. The former option you think faces problems -- namely, on this option one needs to give an account of how agents can assign objects to a singular terms. And the latter is supposed to get around this problem.

It looks to me like a casual theory would be apposite in both cases. For instance, I can assign x to t because of some causal connection I have to x; and similarly I can assign H(x) to t because of some causal connection I have to x -- since having a relevant causal connection to x seems sufficient for having the relevant (perhaps non-casual) connection with H(x).

In general, I don't yet see why it is easier for an agent to assign a haecceity to t rather than an object. What is it about concepts that makes this easier?

Thanks for all the help so far!

Sam

8. Hi Sam,

There are two orthogonal bits here. First, resolving the philosophical demand for a theory of reference; in particular, a causal/naturalistic theory of reference, like "x refers to y iff Ryx", with R some causal relation. I want to resolve that by just saying reference isn't causal to begin with. It's a three-place relation of a string s, a language L and a referent x, and facts of that kind are necessities. I'm quite confident on that. Reference is ok; semantics, more generally, is ok. (Including all sorts of non-classical semantics as well.)

But then ... there's the cognizing problem(s). The usual debates become reformulated as questions about what language one speaks/cognizes, and these resolve into how the mind assigns meanings to strings. I think they become clearer problems in the way I set things up. But I am way less confident about how to make progress on any of these particular problems!

I have some preference for an internalist view: the mind grasps intensions/concepts more easily than it might grasp individual objects or sets. I nothing knock-down here. Maybe because there are logical operations on concepts. If I can grasp $C$ and negation, I can grasp $\neg C$. That's the sort of consideration.

For singular terms, and names in particular, maybe you're right. If x is a causally active concretum, then the choice between assigning x, and assigning H(x), to a string t might be about the same. But then what if x is a future event? Or x is an abstractum?

I tend to think the only way to solve these kinds of problems is to accept some form of grasping of abstract concepts, because trying to build things up from, e.g., causal contact with local concreta (or sense data) is not workable.

My not-so-hidden agenda here is an epistemology for logic, mathematics and modality!

Cheers, Jeff

9. Hi Jeff,

Thanks!

Yes, I agree the problems become clearer in this framework! I also think that the problems you raise for causal accounts are right (if we're on board with abstract objects). But I think they are just as forcefully raised on the old framework for the reference relation. I wanted to see if your framework threw some more light on the casual theory, once we interpret it to be about the assigns relation.

All the best,
Sam

10. Hi Sam,

Thanks so much - all helps me think out this stuff more carefully.

If I take the intentional relation "A assigns C to string s" as primitive, then I can define "A speaks L", and can shed light on the usual kinds of Quine-Kripke-Putnam style problem - so long as it's determinate. (Spoken languages are idiolects, and can fluctuate and change rapidly. They are very finely individuated - sameness of phonology, syntax, semantics and pragmatics.) But, on my set-up, a metasemantical sceptic (e.g., defending Quine on "gavagai") will just say "A assigns C to string s" is indeterminate, or even that it is just a mystical, unscientific grasping notion.

I can't yet say anything interesting about it. On the other hand, it's rather like the subsentential correlate of believing a proposition, so if that's an ok intentional primitive, then assigning should be too. I guess that causation, sense input, internal or innate properties of the mind, all certainly should play a role in making it determinate what concept/referent/extension etc. an agent assigns to a string.

Cheers, Jeff

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