## Thursday, 10 July 2014

### Methodology in the Philosophy of Logic and Language

This M-Phi post is an idea Catarina and I hatched, after a post Catarina did a couple of weeks back at NewAPPS, "Searle on formal methods in philosophy of language", commenting on a recent interview of John Searle, where Searle comments that
"what has happened in the subject I started out with, the philosophy of language, is that, roughly speaking, formal modeling has replaced insight".
I commented a bit underneath Catarina's post, as this is one thing that interests me. I'm writing a more worked-out discussion. But because I tend to reject the terminology of "formal modelling" (note, British English spelling!), I have to formulate Searle's objection a bit differently. Going ahead a bit, his view is that:
the abstract study of languages as free-standing entities has replaced study of the psychology of actual speakers and hearers.
This is an interesting claim, impinging on the methodology of the philosophy of logic and language. I think the clue to seeing what the central issues are can be found in David Lewis's 1975 article, "Languages and Language" and in his earlier "General Semantics", 1970.

1. Searle

To begin, I explain problems (maybe idiosyncratic ones) I have with both of these words "formal" and "modelling".

1.a "formal"
By "formal", I normally mean simply "uninterpreted". So, for example, the uninterpreted first-order language $L_A$ of arithmetic is a formal language, and indeed a mathematical object. Mathematically speaking, it is a set $\mathcal{E}$ of expressions (finite strings from a vocabulary), with several distinguished operations (concatenation and substitution) and subsets (the set of terms, formulas, etc). But it has no interpretation at all. It is therefore formal. On the other hand, the interpreted language $(L_A, \mathbb{N})$ of arithmetic is not a "formal" language. It is an interpreted language, some of whose strings have referents and truth values! Suppose that $v$ is a valuation (a function from the variables of $L_A$ to the domain of $\mathbb{N}$), that $t$ is a term of this language and $\phi$ is a formula of this language. Then $t$ has a denotation $t^{\mathbb{N},v}$ and $\phi$ has a truth value $\mid \mid \phi \mid \mid_{\mathbb{N},v}$.

This distinction corresponds to what Catarina calls "de-semantificaiton" in her article "The Different Ways in which Logic is (said to be) Formal" (History and Philosophy of Logic, 2011). My use of "formal" is always "uninterpreted". So, $L_A$ is a formal language, while $(L_A, \mathbb{N})$ is not a "formal" language, but is rather an interpreted language, whose intended interpretation is $\mathbb{N}$. (The intended interpretation of an interpreted language is built-into the language by definition. There is no philosophical problem of what it means to talk about the intended interpretation of an interpreted language. It is no more conceptually complicated that talking about the distinguished order $<$ in a structure $(X,<)$.)

1.b "modelling"
But my main problem is with this Americanism, "modelling", which I seem to notice all over the place. It seems to me that there is no "modelling" involved here, unless it is being used to involve a translation relation. For modelling itself, in physics, one might, for example, model The Earth as an oblate spheroid $\mathcal{S}$ embedded in $\mathbb{R}^3$. That is modelling. Or one might model a Starbucks coffee cup as a truncated cone embeddied in $\mathbb{R}^3$. Etc. But, in the philosophy of logic and language, I don't think we are "modelling": languages are languages, are languages, are languages ... That is, languages are not "models" in the sense used by physicists and others -- for if they are "models", what are they models of?

A model $\mathcal{A} = (A, \dots)$ is a mathematical structure, with a domain $A$ and some bunch of defined functions and relations on the domain. One can probably make this precise for the case of an oblate spheroid or a truncated cone; this is part of modelling in science. But in the philosophy of logic and language, when describing or defining a language, we not modelling.

But: I need to add that Catarina has rightly reminded me that some authors do often talk about logic and language in terms of "modelling" (now I should say "modeling" I suppose), and think of logic as being some sort of "model" of the "practice" of, e.g., the "working mathematician". A view like this has been expressed by John Burgess, Stewart Shapiro and Roy Cook. I am sceptical. What is a "practice"? It seems to be some kind of supra-human "normative pattern", concerning how "suitably qualified experts would reason", in certain "idealized circumstances". Personally, I find these notions obscure and unhelpful; and it all seems motivated by a crypto-naturalistic desire to remain in contact with "practice"; whereas, when I look, the "practice" is all over the place. When I work on a mathematics problem, the room ends up full of paper, and most of the squiggles are, in fact, wrong.

So, I don't think a putative logic is somehow to be thought of as "modelling" (or perhaps to be tested by comparing it with) some kind of "practice". For example, consider the inference,
$\forall x \phi \vdash \phi^x_t$
Is this meant to "model" a "practice"? If so, it must be something like this:
The practice wherein certain humans $h_1, \dots$ tend to "consider" a string $\forall x \phi$ and then "emit" a string $\phi^x_t$
And I don't believe there is such a "practice". This may all be a reflection of my instinctive rationalism and methodological individualism. If there are such "practices", then these are surely produced by our inner cognition. Otherwise, I have no idea what the scientifically plausible  mechanism behind a "practice" is.

Noam Chomsky of course long ago distinguished performance and competence (and before him, Ferdinand de Saussure distinguished parole and langue), and has always insisted that generative grammars somehow correspond to competence. If what is meant by "practice" is competence, in something like the Chomskyan sense, then perhaps that is the way to proceed in this direction. But in the end, I suspect that brings one back to the question of what it means to "speak/cognize a language", which is discussed below.

1.c Über-language
On the other hand, when Searle mentions modelling, it is likely that he has the following notion in mind:
A defined language $L$ models (part of) English.
In other words, the idea is that English is basic and $L$ is a "tool" used to "model" English. But is English basic? I am sceptical of this, because there is a good argument whose conclusion denies the existence of English. Rather, there is an uncountable infinity of languages; many tens of millions of them, $L_1, L_2, \dots, L_{1000,000}, \dots$, are mutually similar, albeit heterogenous, idiolects, spoken by speakers, who succeed to high degree in mutual communication. Not any these $L_1, L_2, \dots, L_{1000,000}, \dots$ spoken by individual speakers is English. If one of these is English, then which one? The idiolect spoken by The Queen? Maybe the idiolect spoken by President Barack Obama? Michelle Obama? Maybe the idiolect spoken by the deceased Christopher Hitchens? Etc. The conclusion is that, strictly speaking, there is no such thing as English.

It seems the opposite is true: there is a heterogeneous speech community $C$ of speakers, whose members speak overlapping and similar idiolects, and these are to a high degree mutually interpretable. But here is no single "über-language" they all speak. By the same reasoning, one may deny altogether the existence of so-called "natural" languages. (Cf., methodological individualism in social sciences; also Chomsky's distinction between I-languages and E-languages.) There are no "natural" languages. There are languages; and there are speakers; and speakers speak a vast heterogeneous array of varying and overlapping languages, called idiolects.

1.d Methodology
Next Searle moves on to his central methodological point:
Any account of the philosophy of language ought to stick as closely as possible to the psychology of actual human speakers and hearers. And that doesn’t happen now. What happens now is that many philosophers aim to build a formal model where they can map a puzzling element of language onto the formal model, and people think that gives you an insight. …
The point of disagreement here is again with the phrase "formal model", as the languages we study aren't formal models! The entities involved when we work in these areas are sometimes pairs of languages $L_1$ and  $L_2$ and the connection is not that $L_1$ is a "model" of $L_2$ but rather that "$L_1$ has certain translational relations with $L_2$". And translation is not "modelling". A translation is a function from the strings of $L_1$ to the strings of $L_2$ preserving certain properties. Searle illustrates his line of thinking by saying:
And this goes back to Russell’s Theory of Descriptions. … I think this was a fatal move to think that you’ve got to get these intuitive ideas mapped on to a calculus like, in this case, the predicate calculus, which has its own requirements. It is a disastrously inadequate conception of language.
But this seems to me an inadequate description of Russell's 1905 essay. Russell was studying the semantic properties of string "the" in a certain language English. (The talk of a "calculus" loads the deck in Searle's favour.) Russell does indeed translate between languages. For example, the string
(1) The king of France is bald
is translated to the string
(2) $\exists x(\text{king-of-Fr.}(x) \wedge \text{Bald}(x) \wedge \forall y(\text{king-of-Fr.}(y) \to y = x)).$
But this latter string (2) is not a "model", either of the first string (1), or of some underling "psychological mechanism".
… That’s my main objection to contemporary philosophy: they’ve lost sight of the questions. It sounds ridiculous to say this because this was the objection that all the old fogeys made to us when I was a kid in Oxford and we were investigating language. But that is why I’m really out of sympathy. And I’m going to write a book on the philosophy of language in which I will say how I think it ought to be done, and how we really should try to stay very close to the psychological reality of what it is to actually talk about things.
Having got this far, we reach a quite serious problem. There is, currently, no scientific understanding of "the psychological reality of what it is to actually talk about things". A cognitive system $C$ may speak a language $L$. How this happens, though, is anyone's guess. No one knows how it can be that
Prof. Gowers uses the string "number" to refer to the abstract object $\mathbb{N}$.
Prof. Dutilh Novaes uses the string "Aristotle" to refer to Aristotle.
SK uses the string "casa" to refer to his home.
Mr. Salmond uses the string "the referendum" to refer to the future referendum on Scottish independence.
etc.
The problem here is that there is no causal connection between Prof. Gowers and $\mathbb{N}$! Similarly, a (currently) future referendum (18 Sept 2014) cannot causally influence Mr. Salmond's present (10 July 2014) mental states. So, it is quite a serious puzzle.

2. Lewis

Methodologically, on such issues -- that is, in the philosophy of logic and language -- the outlook I adhere to is the same as Lewis's, whose view echoes that of Russell, Carnap, Tarski, Montague and Kripke. Lewis draws a crucial distinction:
(A) Languages (a language is an "abstract semantic system whereby symbols are associated with aspects of the world").
(B) Language as a social-psychological phenomenon.
With Lewis, I think it's important not to confuse these. In an M-Phi post last year (March 2013), I quoted Lewis's summary from his "General Semantics" (1970):
My proposals will also not conform to the expectations of those who, in analyzing meaning, turn immediately to the psychology and sociology of language users: to intentions, sense-experience, and mental ideas, or to social rules, conventions, and regularities. I distinguish two topics: first, the description of possible languages or grammars as abstract semantic systems whereby symbols are associated with aspects of the world; and second, the description of the psychological and sociological facts whereby a particular one of these abstract semantic systems is the one used by a person or population. Only confusion comes of mixing these two topics.
I will just call them (A) and (B). See also Lewis's "Languages and Language" (1975) for this distinction. Most work in what is called "formal semantics" is (A)-work. One defines a language $L$ and proves some results about it; or one defines two languages $L_1, L_2$ and proves results about how they're related. But this is (A)-work, not (B)-work.

3. (Syntactic-)Semantic Theory and Conservativeness

For example, suppose I decided I am interested in the following language $\mathcal{L}$: this language $\mathcal{L}$ has strings $s_1, s_2$, and a meaning function $\mu_{\mathcal{L}}$ such that,
$\mu_{\mathcal{L}}(s_1) = \text{the proposition that Oxford is north of Cambridge}$
$\mu_{\mathcal{L}}(s_2) = \text{the proposition that Oxford is north of Birmingham}$
Then this is in a deep sense logically independent of (B)-things. And one can, in fact, prove this!

First, let $L_O$ be an "empirical language", containing no terms for syntactical entities or semantic properties and relations. $L_O$ may contain terms and predicates for rocks, atoms, people, mental states, verbal behaviour, etc. But no terms for syntactical entities or semantic relations.

Second, we extend this observation language $L_O$ by adding:
• the unary predicate "$x$ is a string in $\mathcal{L}$" (here "$\mathcal{L}$" is not treated as a variable),
• the constants "$s_1$", "$s_2$",
• the unary function symbol "$\mu_{\mathcal{L}}(-)$",
• the constants "the proposition that Oxford is north of Cambridge" and "the proposition that Oxford is north of Birmingham".
Third, consider the following six axioms of semantic theory $ST$ for $\mathcal{L}$:
(i) $s_1$ is a string in $\mathcal{L}$.
(ii) $s_2$ is a string in $\mathcal{L}$.
(iii) $s_1 \neq s_2$.
(iv) the only strings in $\mathcal{L}$ are $s_1$ and $s_2$.
(v) $\mu_{\mathcal{L}}(s_2) = \text{the proposition that Oxford is north of Birmingham}$
(vi) $\mu_{\mathcal{L}}(s_1) = \text{the proposition that Oxford is north of Cambridge}$
Then, assuming $O$ is not too weak ($O$ must prove that there are at least two objects), for almost any choice of $O$ whatsoever,
$O+ST$ is a conservative extension of $O$.
To prove this, I consider any interpretation $\mathcal{I}$ for $L_O$, and I expand it to a model $\mathcal{I}^+ \models ST$. There are some minor technicalities, which I skirt over.

Consequently, the semantic theory $ST$ is neutral with respect to any observation claim: the semantic description of a language $\mathcal{L}$ is consistent with (almost) any observation claim. That is, the semantic description of a language $\mathcal{L}$ cannot be empirically tested, because it has no observable consequences.

(There are some further caveats. If the strings actually are physical objects, already referred to in $L_O$, then this result may not quite hold in the form stated. Cf., the guitar language.)

4. The Wittgensteinian View

Lewis's view can be contrasted with a Wittgensteinian view, which aims to identify $(A)$ and $(B)$ very closely. But, since this is a form of reductionism, there must be "bridge laws" connecting the (A)-things and the (B)-things. But what are they? They play a crucial methodological role. I come back to this below.

Catarina formulates the view like this:
I am largely in agreement with Searle both on what the ultimate goals of philosophy of language should be, and on the failure of much (though not all!) of the work currently done with formal methods to achieve this goal. Firstly, I agree that “any account of the philosophy of language ought to stick as closely as possible to the psychology of actual human speakers and hearers”. Language should not be seen as a freestanding entity, as a collection of structures to be investigated with no connection to the most basic fact about human languages, namely that they are used by humans, and an absolutely crucial component of human life. (I take this to be a general Wittgensteinian point, but one which can be endorsed even if one does not feel inclined to buy the whole Wittgenstein package.)
In short, I think this is a deep (but very constructive!) disagreement about ontology: what a language is.

On the Lewisian view, a language is, roughly, "a bunch of syntax and meaning functions"; and, in that sense, it is indeed a "free-standing entity".

(Analogously, the Lie group $SU(3)$ is a free-standing entity and can be studied independently of its connection to quantum particles called gluons (gluons are the "colour gauge field" of an $SU(3)$-gauge theory, which explains how quarks interact together). So, e.g., one can study Latin despite there being no speakers of the language; one can study infinitary languages, despite their having no speakers. One can study strings (e.g., proofs) of length $>2^{1000}$ despite their having no physical tokens. The contingent existence of one, or fewer, or more, speakers of a language $L$ has no bearing at all on the properties of $L$. Similarly, the contingent existence or non-existence of a set of physical objects of cardinality $2^{1000}$ has no bearing on the properties of $2^{1000}$. It makes no difference to the ontological status of numbers.)

Catarina continues by noting the usual way that workers in the (A)-field generally keep (A)-issues separate from (B)-issues:
I also agree that much of what is done under the banner of ‘formal semantics’ does not satisfy the requirement of sticking as closely as possible to the psychology of actual human speakers and hearers. In my four years working at the Institute for Logic, Language and Computation (ILLC) in Amsterdam, I’ve attended (and even chaired!) countless talks where speakers presented a sophisticated formal machinery to account for a particular feature of a given language, but the machinery was not intended in any way to be a description of the psychological phenomena underlying the relevant linguistic phenomena.
I agree - this is because when such a language $L$ is described, it is being considered as a free-standing entity, and so is not intended to be a "description". Catarina continues then:
It became one of my standard questions at such talks: “Do you intend your formal model to correspond to actual cognitive processes in language users?” More often than not, the answer was simply “No”, often accompanied by a puzzled look that basically meant “Why would I even want that?”. My general response to this kind of research is very much along the lines of what Searle says.
I think that the person working in the (A)-field sees that (A)-work and (B)-work are separate, and may not have any good idea about how they might even be related. Finally, Catarina turns to a positive note:
However, there is much work currently being done, broadly within the formal semantics tradition, that does not display this lack of connection with the ‘psychological reality’ of language users. Some of the people I could mention here are (full disclosure: these are all colleagues or former colleagues!) Petra Hendriks, Jakub Szymanik, Katrin Schulz, and surely many others. (Further pointers in comments are welcome.) In particular, many of these researchers combine formal methods with empirical methods, for example conducting experiments of different kinds to test the predictions of their theories.
In this body of research, formalisms are used to formulate theories in a precise way, leading to the design of new experiments and the interpretation of results. Formal models are thus producing new insights into the nature of language use (pace Searle), which are then put to test empirically.
The methodological issue comes alive precisely at this point.
How are (A)-issues related to (B)-issues?
The logical point I argued for above was that a semantic theory $ST$ for a fixed well-defined language $L$ makes no empirical predictions, since the theory $ST$ is consistent with any empirical statement $\phi$. I.e., if $\phi$ is consistent, then $ST + \phi$ is consistent.

5. Cognizing a Language

On the other hand, there is a different empirical claim:
(C) a speaker $S$ speaks/cognizes $L$.
This is not a claim about $L$ per se. It is cognizing claim about how the speaker $S$ and $L$ are related. This is something I gave some talks about before, and also wrote about a few times before here (e.g., "Cognizing a Language"), and also wrote about in a paper, "There's Glory for You!" (actually a dialogue, based on a different Lewis - Lewis Carroll) that appeared earlier this year. A cognizing claim like (C) might yield a prediction. Such a claim uses the predicate "$x$ speaks/cognizes $y$", which links together the agent and the language. But without this, there are no predictions.

The methodological point is then this: any such prediction from (C) can only be obtained by bridge laws, invoking this predicate linking the agent and language. But these bridge laws have not been stated at all. Such a bridge law might take the generic form:
Psycho-Semantic Bridge Law
If $S$ speaks $L$ and $L$ has property P, then $S$ will display (verbal) behaviour B.
Typically, such psycho-semantic laws are left implicit. But, in the end, to understand how the (A)-issues are connected to the (B)-issues, such putative laws need to be made explicit. Methodologically, then, I say that all of the interest lies in the bridge laws.

6. Summary

So, that's it. I summarize the three main points:
1. Against Searle and with Lewis: languages are free-standing entities, with their own properties, and these properties aren't dependent on whether there are, or aren't, speakers of the language.
2. The semantic description of a language $L$ is empirically neutral (indeed, the properties of a language are in some sense modally intrinsic).
3. To connect together the properties of a language $L$ and the psychological states or verbal behaviour of an agent $S$ who "speaks/cognizes" $L$, one must introduce bridge laws. Usually they are assumed implicitly, but from the point of view of methodology, they need to be stated clearly.

I hadn't totally forgotten -- I sort of semi-forgot. But Catarina wrote about these topics before in several M-Phi posts, so I should include them too:
Logic and the External Target Phenomena (2 May 2011)
van Benthem and System Imprisonment (5 Sept 2011)
Book draft: Formal Languages in Logic (19 Sept 2011)
(Probably some more, that I actually did forget...) And these raise many questions related to the methodological one here.

1. Your "Wittgensteinian view" isn't a representation of Wittgenstein's view. Wittgenstein distinguished between language as a free-standing "abstract" system, which is a system of rules that can at best be recited accurately, and as a sociological and psychological historical phenomenon, which is described by means of propositions.

1. And, of course, the rules in the former case were understood as rules governing human actions as well. That doesn't obviate the distinction between rule(-statements) and proposition. Only the latter has truth value.

2. In the post above, the "representation" you're referring to is Catarina's: "Language should not be seen as a freestanding entity, as a collection of structures to be investigated with no connection to the most basic fact about human languages, namely that they are used by humans, and an absolutely crucial component of human life. (I take this to be a general Wittgensteinian point, but one which can be endorsed even if one does not feel inclined to buy the whole Wittgenstein package.)"

This seems to me a perfectly ok "representation" of "a general Wittgensteinian point": namely, that languages should be seen as somehow embodied, not to be divorced from "the most basic fact about human languages, namely that they are used by humans, and an absolutely crucial component of human life".

Lewis says the opposite, and distinguishes language as a social-psychological phenomenon, and languages - which are, roughly, complicated structured sets of expressions, along with meaning functions, and then adds, "only confusion comes of mixing these two topics". This is what the methodological debate concerns.

Jeff

2. I find your distinctions very useful. In particular, the difference between (A) language and (B) language that you take from Lewis is illuminating. However, I think you would agree that very often, (A) languages are build to explain/model (B) languages. This is exactly the goal of David Lewis in Counterfactuals (1973) : explain and describe our use of counterfactual sentences in English. Considering this approach, I understand Searle's comment in the following way. A) languages have important limitations when they are used to understand better (B) languages. They are perhaps not the best tool.

Mathieu

3. Thanks, Mathieu - once the distinction (A)/(B) is made, the philosophical problem is what this "(A) languages are built to explain/model (B) languages" involves. I.e., which properties of the languages (i.e., (A) languages, in Lewis's sense) are meant to "correspond to" or "model" which properties of verbal behaviour, cognition and so on for a given speaker or agent? E.g., to use your examples, if there are three different abstract languages L1 (Lewis), L2 (Stalnaker), L3 (Adams), each involving different properties of a conditional, then what makes it the case that a speaker S speaks L1, rather than L2 or L3?

Jeff

4. The scepticism here that logic can model natural language apparently involves denying, for instance, that the truth function conjunction provides a good translation of "and" in English, or at least a better translation than any other truth function.

Arguments for some account of the natural language "if" obeying some conditional logic other than the material conditional are not in principle ultimately different than arguing that "if" does not mean conjunction.

Discussion of the particular differences between certain theories of conditionals can be found, for instance, in SEP entries by Dorothy Edgington and Horacio Arlo Costa.

David

5. There is scepticism that there even exist such collective entities as "natural languages", rather than particular idiolects, or even micro-idiolects, associated with an agent at some particular time.

The methodological point is: what is the assumed relation (bridge law) between (A)-things (languages) and (B)-things (social-psychological phenomena), and how is this connecting bridge law stated explicitly?

Jeff

6. My use of "natural language" above didn't assume that it refers to anything with more world historical being than the competence of a Robinson Crusoe at time t.

Much work in semantics is independent of the meta-semantic views of the philosopher or linguist in question.

David

7. Is your scepticism just about semantics of language? You'd make a good "mysterian": there is no explicit bridge law linking psychology to physics, therefore physicalism about the mental is false, or at best we have no idea what it would be for it to be true.

David

8. The absence of psychophysical bridge laws was more or less Davidson's argument for "anomalous monism", yes. So, your point is right there.

But, in the logic & language case, it's not the absence I'm referring to. It's the secrecy about them. They're hidden assumptions, and I think they should be made explicit.

9. E.g., we define three languages L1, L2, L3, otherwise the same, but with three different semantics for the syntactical construction "if ...". There is also an agent S on whom we may perform experiments, about their speech behaviour, psychological states, responses, etc. We wonder whether S speaks L1, L2 or L3 (or perhaps none, or maybe whether one is a "better model" than the others, etc.).

How do we empirically distinguish them?

Jeff

10. The conditional logics are a side show here, you can run your line entirely in standard propositional logic: how do authors of logic textbooks justify their claim that truth functions (any of them) translate, interpret or model any word in any natural language?

David

11. Precisely! What is the principle assumed?

Jeff

12. (Presumably the first guess is that the bridge principle will be something like this:

If $S$ speaks $L$ and $A \vDash_L B$, then if $S$ accepts $A$, then $S$ accepts $B$.

But this has counterexamples.)

13. You are right. The first idea for a bridge principle is that if the language L validates some inference, then a (vast majority of) speaker must accept the inference.

For instance, classical propositional logic validates the strenghtening of the antecedent: "If A, C" entails "If A and B, C" and not the other (Stal, Lewis, Adams). Stalnaker validates "If A, C or If A, not C". Adams does not accept embedding of conditionals. Lewis offers several systems. So, the inferences are the first criteria used to distinguish the correct modeling.

Mathieu

14. Yes, so rewriting a bit, the bridge rule is: "Suppose $L$ validates inference $I$. Then if $S$ speaks $L$, S "accepts" $I$".

So suppose $L$ validates $I$, but S doesn't accept $I$!! Then the bridge principle tells us that S does not speak $L$. But this could easily be the wrong conclusion. For it might be that $S$ does speak $L$, and simply doesn't "get" the inference, or makes an error, etc. Maybe $S$ speaks $L$ but is irrational.

That is, the bridge principle assumes a perfect match between what the logic/language $L$ specifies and the observable cognitive performance of the speaker of $L$. One might fix this by

"Suppose $L$ validates inference $I$. Then if $S$ speaks $L$, and circumstances are ideal, $S$ is disposed to accept $I$".

An experiment showing $S$ does not accept $I$ might now be accounted for by the speaker's being irrational, or confused, or the circumstances being non-ideal, etc.

Jeff

15. I've asked my philosophy of science friends to solve the problem of induction for us. Once they've devised a general theory-neutral rule for fitting curves to data points then I'll get back to you with how it rationalizes methodology in semantics-pragmatics. In the meantime I'll proceed with my ad-hoc armchair ruminations.

In Inquiry (Ch 7), Stalnaker concedes there may not be any deep dispute between certain rival theories of the conditional; in "A Counterexample to Modus Ponens", McGee worries that the conditional may not have a logic. I am not aware of similar views in print about "and".

David

16. Then it seems Stalnaker is not getting the conceptual/methodological problem, as there is no such thing as a "theory of the conditional". There are certain mathematical definitions of certain languages, $L_1, L_2, \dots$, and these aren't theories, in the empirical sense. They have nothing to do with empirical fact. For semantics is conservative over any bunch of empirical facts, as proved above. Similarly "$2+2=4$", "$\forall x (s(x) \neq 0)$", etc., are conservative; no one suggests that "$2+2=4$" is an empirical claim. Similarly, "$A \vDash_L B$" is not an empirically testable claim. It is not empirical science at all.

Jeff

17. All of the conditional logics mentioned above are non-empirical abstractions, but the question of which if any best fits natural language usage is an empirical matter (perhaps a woefully undertermined or overdetermined one).

David

18. How the properties of a given $L$ "match up" with or "fit" an agent's verbal behaviour, psychological states, etc., is, more or less, Quine's "gavagai" problem dressed up in Lewisian terms. Lewis also has this idea that perhaps vagueness should be understood consists not as a single language $L$ which has vague semantics, but in an agent "cognizing" a multiplicity (maybe indeterminately) of languages, all varying a bit from each other. This idea, of a single agent, speaking at the same time, a huge multiplicity of languages or micro-idiolects has a kind of Borgesian appeal.

Jeff

19. Yup. Lewis also says that his cluster of languages view amounts to supervaluationism (a sentence is supertrue if it is true in all the micro-idiolects), with the latter being favored by Keefe in her Theories of Vagueness.

If this were applied to conditionals, one would wind up with a rather weak conditional logic as "valid", depending on what range of examples one takes as (at least) borderline phenomena rather than cognitive error/noise. More difficult to integrate into the supervaluationist framework than the dispute between say Stalnaker, Lewis and Pollock over which formulas are valid would be Adams' probabilistic semantics.

David