Saturday, 25 August 2012

Meaning, Use and Modality: M-Facts and U-Facts

I don't have a precise definition of either "M-fact" or "U-fact", but roughly, the idea is that an M-fact is a meaning-fact, while a U-fact is a usage-fact.
Examples of M-facts might be things like:
1. "Schnee" refers-in-German to snow.
2. "sensible" is true-in-Spanish of x iff x is sensitive.
3. "Schnee ist weiss" is true-in-German iff snow is white.
4. "I" refers-in-English, relative to context $C$, to the agent of the speech act in $C$.
5. "kai" means-in-Greek logical conjunction.
In each case, the language relativity has been made explicit. I think that ignoring language relativity is a major fallacy in much writing about the foundations of linguistics and philosophy of language. Tarskian T-sentences are examples of M-facts. The bearers of the semantic (and syntactic) properties are types, not tokens. Again, I think that it's major mistake to be confused about this.

Canonical examples of U-facts might be things like:
6. Speaker X uses the string "Schnee" to refer to snow.
7. Speaker Y has a disposition to utter the string "gavagai" when there are rabbits nearby.
8. Speaker Z tends to assert the string $\sigma_1 \ast$ "kai" $\ast \sigma_2$ just when Z is prepared to assert both $\sigma_1$ and $\sigma_2$.

One might initially think that U-facts explain M-facts. Or that U-facts provide evidence for M-facts. Roughly:
U-facts: evidence/data for linguistic theories.
M-facts: theoretical content of linguistic theories.
This is, I think, roughly right, but with a very important caveat, which is that M-facts cannot be explained by U-facts. The argument is this:
(i) M-Facts are Necessities.
An M-fact, such as the fact that "Schnee" refers-in-German to snow couldn't have been otherwise. The argument for this is a counterfactual thought experiment. Suppose $L$ is an interpreted language such that "Schnee" refers-in-L to sugar. Then it seems clear to me that $L$ isn't German. If one changes the meanings of a language, the language is simply a different one. Languages are very finely individuated.
(ii) U-Facts are Contigencies
A U-fact, such as the fact that Y has a disposition to utter "gavagai" when there are rabbits nearby, is contingent. It Y needn't have had that disposition. A U-fact is connected to properties of the speaker's cognitive system.

If the previous two claims, (i) and (ii), are correct, then
(iii) U-facts cannot explain, or provide evidence for, M-facts.
This conclusion follows because contingencies cannot explain necessities.

I've given this argument is several talks since 2008 (originally in a talk "Meaning, Use and Modality" in at Universidad Complutense, Madrid). The audience frequently responds with considerable surprise!

If U-facts do not explain M-facts, then what explains M-facts? I say, "Nothing". Nothing explains why "Schnee" refers in L to sugar. It is simply an intrinsic property of the language L. There is some sense in which M-facts, along with syntactic and phonological and pragmatic facts, about a language $L$ are mathematical facts. Languages are complicated (mixed) mathematical objects. For example, suppose that
The string $\phi$ is a logical consequence in $L$ of the set $\Delta$ of $L$-strings
Then this fact, about $L$, is a necessity.

If U-facts do not explain M-facts, then what do they explain or provide evidence for? I think the answer to this is,
U-facts explain, or provide evidence for, what language the speaker/agent cognizes.
So, let me call these C-facts, and these have the form:
(C) Speaker X speaks/cognizes L
So, for example,
The (contingent) U-fact that X has a disposition to utter "gavagai" when there are rabbits nearby is evidence for the (contingent) C-fact that X speaks/cognizes a language L for which the following M-fact holds of necessity: "gavagai" denotes-in-L rabbits.


  1. Hi Jeffrey,

    This is an interesting point, and you made a similar one in response to my talk at the MCMP. I take it that the point is that we can consider a language to be an abstract object of some sort (some n-tupel, which includes a vocabulary, formation rules, and semantic interpretation rules, and whatever else you like to add). If that n-tupel is the language in question, then the M-facts about that language are necessarily true for that language. OK, so why am I unhappy with the way to put it that way? Well, at least prima facie it seems to contradict (or at least seems in tension with) what Jussi and I argue in Meta-Externalism vs Meta-Internalism in the Study of Reference (, where we argue somthing like U-facts constitute (and thus, I guess, explain) the M-facts.

    Here are some thoughts, why I think it's not incompatible with our view, but rather a matter of how to identify languages:
    Now, when we are talking about the M-facts in natural languages, we identify the natural language (in unfortunately unclear ways that Chomsky always points out) as the language that is shared by a certain linguistic community. Thus, when we investigate the M-facts of English, we investigate which abstract object is the closest model for the pattern of dispositions to use expressions that we find among those people we take to be English speakers. It is a contingent fact, which of the abstract objects best models the usage we find in that linguistic community we are currently investigating. And that's I guess why I'd say that 'Schnee' refers to snow in German is constituted by the contingent fact that speakers of German have the diposition to use 'Schnee' in the way they do.

    Let's see whether I can make my point with an analogy (but I'm not so convinced by this myself). Let's relativize all factual claims to the actual world. Ignoring world-relativity seems to be a mistake like ignoring language relativity. But 'roses are red in the actual world' is certainly necessary, since if roses were green, it would surely be a different world. Thus, that roses are red in the actual world is a necessary fact that no contingent fact whatsoever could explain.

    One might point out that it's not contingent facts explaining that roses are red in the actual world, since those facts, being all world-relative themselves, are also all necessarily true. But it seems that something similar could be said in the language case: in the sense in which it is a necessary fact that 'Schnee' refers in German to snow, it gets explained by another necessary fact, namely that German speakers have the disposition to use 'Schnee' in that way, since if they wouldn't, they wouldn't be speakers of German.

  2. Hi Jeff,

    Thanks, this is cool! But I think there is a hitch:

    Your argument builds on modality, and it seems to me that this is also where the reason for people’s surprise lies.

    When we think about modality, effectively what we do is to compare what we get when we vary certain parameters. But in order to be able to make a comparison, we have to keep one parameter fixed. So for instance, we may take objects to be fixed and vary their properties (let me call this K-modality). This allows us to say, for instance, that it is a contingent fact that Aristotle was a philosopher, he might also have been a politician or a physician or what have you. We are comparing the same object but exchanging one of its properties.
    Alternatively, we can take properties as fixed and regard objects as sets of their properties (let us call this L-modality). In this case, any change to the properties gives us a different object and we could no longer regard politics as a possible occupation of Aristotle’s – someone like Aristotle in all other respects but who was a politician would simply no longer be Aristotle. We could therefore no longer say that it is a contingent fact about Aristotle that he was a philosopher. Had he not been a philosopher, he would not have been Aristotle.

    Now, when you say that “Schnee” referring-in-German to snow could not have been otherwise, this is a statement in L-modality. Conversely, when you say that Y needn’t have had the disposition to utter “gavagai” when he sees a rabbit, this is a statement in K-modality.

    I don't think I want to swallow a combination of the two in one argument - I would no longer know what it is we are comparing here. But let’s see what happens if we apply the same concept of modality to both.

    If we go by L-modality, it is no longer a contingent fact about Y that he has a disposition to say “gavagai” when he sees a rabbit, because lacking that disposition would make him someone else – he would no longer be Y. It is therefore just as necessary for him to have that disposition as it is necessary for L that ‘gavagai’ refer to rabbits. You could therefore define L as the totality of Y’s utterance dispositions; or define Y’s utterance dispositions as the totality of reference and truth conditions of L. It seems to me that in L-modality, U-facts are a very good explanation of M-facts and vice versa.

    If instead we go by K-modality, it is no longer a necessary fact about L that ‘Schnee’ refer-in-German to snow. It may well have been (and, in fact, has been) otherwise. So here again, we can explain U-facts by M-facts and vice versa.

    So applying the same concept of modality to both dissolves the puzzle (as you know I think it should) and we never need C-facts.

    I can see why one may want to apply different identity conditions to languages than to people, but that is a philosophical, not a logical issue, isn't it? Besides, usually people who apply L-modality to languages don’t tend to worry much about speakers anyway; and people who apply K-modality to speakers would not tend to regard languages as distinct enough from speakers to apply L-modality to them. If they really did, I don’t think that modality will make for a good way of linking the two.

  3. Hi Daniel,

    Many thanks! And thanks for the link to your paper with Jussi.
    You may have seen them, but I've mentioned this topic a couple of times before.

    Yes, on language individuation, I think a lot of the folk talk is a bit misleading. So, no particular individual speaks English (or German, etc.) strictly speaking. Rather, there are individual idiolects, which in a "language community" are similar enough to permit effortless interpretation usually.

    "And that's I guess why I'd say that 'Schnee' refers to snow in German is constituted by the contingent fact that speakers of German have the disposition to use 'Schnee' in the way they do."

    Yes, I think that's a plausible and fairly standard view.

    My idea is to separate out the U-facts, M-facts and C-facts, keeping the M-facts as necessities. I first define a language L such that "Schnee" refers-in-L to snow.
    (The Saussurean principle, "any string can mean/refer anything", tells us that all of these languages are already out there, as it were.)
    I then say that the contingent U-fact, that Gottlieb uses "Schnee" to refer to snow, is evidence for (or partially explains, or partially constitutes. etc.) the contingent C-fact that Gottlieb he speaks/cognizes the language L.

    Consequently, I'm able to separate semantics from the questions involving cognition and intentionality. (Semantics is then really a branch of applied mathematics, and becomes much less controversial.)

    In one of the earlier M-Phi posts ("Is There a Philosophical Problem of Reference?", in the comments with Sam), I was playing around with some accounts of "A cognizes L" along the lines of

    A cognizes L iff, for each L-string s, the concept that A assigns to s = the meaning of s in L.

    So, the basic psychological or intentional notion is the notion of an agent's *assigning* a concept (or a referent) to a string.

    The second point, adding "in the actual world, ...", is really interesting. Not sure what to say! But will think about it!

    I don't think what I'm saying is incompatible with what is usually written in this area, unless one wants to insist on the contingency of semantic facts. I think of it as an attempt to clarify what's going on in debates about semantic theory, indeterminacy of meaning/reference, empirical evidence in linguistics, etc.

    Cheers, Jeff

  4. Hi Naomi,

    Many thanks! Yes, the modal individuation of languages is the crucial point. On the view here, a language isn't a bundle of properties; rather, it's an abstract object.

    "If instead we go by K-modality, it is no longer a necessary fact about L that ‘Schnee’ refer-in-German to snow. It may well have been (and, in fact, has been) otherwise."

    The problem here is what you mean by "German". Is there a single entity that any pair of speakers in Germany and Austria speak? I think German, Spanish, etc. (what Chomsky calls E-languages) are useful approximations for certain purposes (i.e., thinking about speech communities), but can be removed from foundational discussions, where one has to focus on the idiolects that individuals speak. Chomsky calls these I-languages and he regards them as mental entities. My view (like J.J. Katz) is that they're abstract; that they're cognized somehow in the mental states of the agent: cognizing L just is a complicated mental state. (Not that I have a good account of this!)

    A separate objection to your E-language view is that there are no constraints on how an E-language can change - temporally and particularly modally. So, German could be have been indistinguishable from Thai.
    Suppose tomorrow, at 3pm, everyone who currently cognizes German comes to cognizes Thai, while you still speak German. It seems to me that, on your view, we have to conclude that everyone now speaks *German* and you are a relic of what German used to be (i.e., today). But I would say that this gets language individuation seriously wrong.

    On the view I defend, languages (including all these idiolects) are abstract entities, analogous to numbers or functions. So, a function $f : \mathbb{N} \rightarrow \mathsf{N}$ cannot "change", while keeping it "the same". Still, a physical computer might (contingently) realize $f$ today and $g$ tomorrow. This does not imply that $f$ has turned into $g$. It means the concrete system has undergone change. So, I'd argue that an agent's cognizing a language L is (somewhat) analogous to a computer's realizing a function $f$.

    Cheers, Jeff

    1. Hi Jeff,

      Thanks a lot for your reply. Can I suggest we skip the ‘What is German’-discussion, where we agree; I only brought it up because you used ‘German’ (to my surprise). I’ll also not use ‘idiolect’ now (it’ll become clear why). But your reply to Daniel suddenly gave me an “Aha-Erlebnis” (new German word for your idiolect). Am I right in thinking that, in a simplified version, the idea is something like this?:

      We have in the universe a group of interpreted languages with a certain family resemblance which vox populi calls ‘German’. Each of them consists of a countable number of words and forms of composition (I think this is best kept finite), references, truth conditions and whatever else you need for the semantics; in other words, they can be spelled out as a set of meaningful words and sentences – your M-facts. Assuming plenitude, any combination of any words and forms of composition are available, and which of them are called ‘German’ is of little concern to us now. Let’s call them G1, G2,…Gn.

      Then we have a countable number of speakers of ‘German’. Let’s pick out one, Y. Y has dispositions to say certain things in certain situations. The totality of Y’s such dispositions at any time is one of our Gs above (that’s why I suggested to keep them finite). Now, with language being essentially subject to perpetual change, we need to time-slice Y. Thus at t1 Y’s dispositions are, say G75, at t2 they are G79, etc. Which Gs Y ‘cognises’ (as you say) in the course of his life is a contingent fact, as is which situations he is in and hence which words and sentences he actually utters.

      If this is correct, it seems to me that all taken together, U-facts are at least triply (in fact much more) contingent. So I am not quite sure why the first and the third of these get names – ‘C-facts’ and ‘U-facts’ – but not the second? C-facts link a G to Y’s dispositions but not yet to his utterances, don't they.

      Also, we will need an account of how the G Y cognises at any tn relates to the G he cognises at tn-1, because there must of course be a very large overlap between them. (This is also in reply to your Thai example.)

      And, by the bye, if this *is* what you have in mind, would you define ‘idiolect’ as any one G, or as the series of Gs Y cognises in the course of his life? (Nothing hinges on this, it is just for the sake of clarity in future.)


    2. Hi Naomi,

      Great, yes, that's right; but with a caveat:

      "The totality of Y’s such dispositions at any time is one of our Gs above"

      But I don't think it can't be "is", here. The totality of dispositions is not the same as a language. For example, suppose agent Y (at t) has:
      (i) a disposition to say "Eine Katze" when there's a cat nearby.
      (ii) a disposition to say "Gavagai" when there's a rabbit nearby.
      (iii) etc.

      But this isn't a language. It's a list of dispositions (and characterizes speech-behaviour).

      On the other hand, a language $L$ involves an alphabet $A$, the set of strings for $A$, a syntax for $L$ (certain special subsets of $L$-strings), and semantic and pragmatic functions for $L$ (mapping the strings to intensions, referents, mental states and whatnot).

      This isn't a totality of dispositions. And the main problem is that there isn't a logical relationship between the U-fact,

      (U) Agent A has the disposition to utter "Gavagai" when there are rabbits nearby.

      and the M-fact,

      (M) "Gavagai" means-in-L RABBIT.

      This is, in a sense, precisely what the whole discussion is about.
      Note that (M) doesn't even involve a *speaker* and note that (U) doesn't involve a language L.
      Although, (U) is contingent, I'm arguing that (M) (if it's the case), is necessary. A contingent bridge principle is required, connecting the agent A and the language L for which (M) holds. I.e.,

      (C) Agent A speaks/cognizes an L such that (M) holds.

      Then, I can say that (C) *explains* (U). And I can say that (U) is evidence to support (C).
      Whereas (M) itself is a background necessity concerning the intrinsic properties of L.

      I think I'd define "the idiolect of A at t" as: "the language L cognized by A at time t". As you can see, I think this can be fluctuating and changing quite a lot. For example, a Kripkean baptism is a small idiolectic extension, rather analogous to skolemization, the introduction of a new constant in model theory.

      Cheers, Jeff

  5. Hi Jeff,
    Thank you for the response. Let me try again. You want to argue that although your account is just a rediscription of the usual story, there is nevertheless an interesting lesson, viz. that semantic facts are necessary facts, and thus need no explaining. The explaining should be somewhere else, namely when we explain how we manage to cognize one language rather than another, and the semanticist should go on happily with his job not worrying too much about that contingent question, but do semantics, basically a part of mathematics.
    First of all, it is right that one might study the abstract systems we call semantics in their own right. But that would be just mathematics. In what sense and why could one claim that one is studying "semantics" rather than just the relation or interplay between two or more abstract set-theoretic structures? It seems to me that the reason that this study is considered "semantics", is precisely because we believe these abstract structures correspond to systems and their relations that we call natural languages.
    Let me make my analogy-argument in a slightly different form (perhaps that makes it easier to point out where I misunderstood you): let's take some system of objects and relations between them, call it S, and let's stipulate that the S-facts are contingent facts. Let's suppose further that there is a set-theoretic (or in any case mathematical) model of S, call it M. In set theory we can design very many models like M, that all are somewhat different from M in how they specify the relations over its domain, for example. Let's assume that, however, only one of the models corresponds to S. Just as we can model various possible mappings of expressions on referents, only one of which corresponds to the mapping of English expressions onto objects in the world that we find in English.
    M can be studied mathematically, and the M-facts are, relative to M, necessary facts. But although we can identify M-facts with S-facts, if M corresponds with S, this doesn't turn all (or any) S-facts into necessities.
    Thus, when we study semantics (the relation between actual expressions and their actual meanings), we use abstract models to do that, and they have their properties necessarily (on my account because we stipulated all of them), but that doesn't make the facts of semantics necessary.
    We can, of course, revise our normal way of speaking, and call a certain branch of pure mathematics "semantics", but I don't see what we would win that way.
    Cheers, Daniel

  6. Hi Daniel,

    Yes, thanks for that - that's very close to what I have in mind!
    But there's an important difference I'd stress, between "pure" mathematics and "mixed" mathematics (terminology from the theory of applicability of mathematics).

    Languages aren't (usually) the objects of pure mathematics (like, say, $\pi$ or $e^{i \pi}$ or $\aleph_0$); rather, they are (usually) *mixed* mathematical entities. E.g., they involve sets of linguistic types, utterances, phonemes, functions to sets of chairs, tables, or to intensions, etc. I definitely think that ordinary natural languages are mixed mathematical entities. ("Natural" languages are a tiny subclass of the infinitely large class of languages; they are "natural" only in that human minds happen to cognize/speak them.)

    Actually, I think this is the standard way of studying semantics!
    It's hard to imagine eliminating types, strings, functions, extensions and intensions from semantics. To eliminate this, one would have to nominalize semantics, as Hartry Field has tried with physics, but it would be very hard to carry out. One would have to introduce "possible tokens" and strange modal relations.

    "M can be studied mathematically, and the M-facts are, relative to M, necessary facts. But although we can identify M-facts with S-facts, if M corresponds with S, this doesn't turn all (or any) S-facts into necessities."

    But if a language L is a *mixed* mathematical entity, then it is the S-facts themselves (they are mixed facts) about L that we're studying here. For example, for example, a modal version of mixed comprehension says,

    (C) For all worlds w, there is a set Chair(w) such that for all y, y is in X(w) iff, at w, y is a chair

    This itself is a necessary mixed mathematical assumption. Although it asserts the existence of various sets of chairs, it implies nothing about these sets (e.g., their cardinality). Then, we might consider a language L with the function $\lambda_{w}Chair(w)$ as the intension of some string, say, "silla". Then the semantic fact about L,

    (S) The intension of "silla" in L is $\lambda_{w}Chair(w)$

    is necessary. (That's the gist of the idea.)

    (This L is similar to Spanish in this respect.)

    It isn't that there's some other, pure, representation M of this. One can do that if one wishes (e.g., replace phonemes by numbers, strings by sequences of numbers, a la Gödel, worlds by numbers, and functions from worlds to chairs by functions from numbers to sets of numbers, say). But that would then be the semantics of a language whose domain was purely abstract; while, normally, the domain and predicate extensions for a natural language contain concreta.

    Cheers, Jeff

  7. Oops, (C) should be

    (C) For all worlds w, there is a set $Chair(w)$ such that for all y, y is in $Chair(w)$ iff, at w, y is a chair.

  8. Does your argument extend to social practices outside language which have constitutive rules? It is necessary truth e.g. that football is played with a ball and 11 players on each team, since a game that didn't have these rules wouldn't be football, but another game. Does that mean we can't explain how football came into being in terms of e.g. our practices or dispositions to uphold these rules, indeed can't explain it at all?

  9. Mons,

    "Does your argument extend to social practices outside language which have constitutive rules?"

    I think so, yes. On an analogous view for games, football doesn't "come into being". Footballers do; their brains undergo neurophysiological change, and these footballers exhibit certain patterns of collective activity. (Cf., speaking/cognizing a particular language.)

    "It is necessary truth e.g. that football is played with a ball and 11 players on each team, since a game that didn't have these rules wouldn't be football, but another game."

    I'd say yes. If one tries to define "football" exactly - as a single unique entity - the entity one defines does have this modal property. There, however, no such unique entity as "football". There is a somewhat heterogeneous variety of games, played with slightly different rules.

    "Does that mean we can't explain how football came into being in terms of e.g. our practices or dispositions to uphold these rules, indeed can't explain it at all?"

    We can try to explain psychological facts, yes. E.g., how an activity came into being "in terms of e.g. our practices or dispositions to uphold these rules". But if one considers a particular game $G$, then we cannot explain how $G$ "came into being", much as we cannot explain how 6 came into being. After all, $G$ didn't "come into being"! Footballers did.