Wednesday, December 17, 2014

Burgess on Tarski on truth

One of Jerry Fodor’s great lines is that you know you’re getting older when cyclic theories of history start making perfect sense. This Ecclesiastical (viz. there is nothing new under the sun) sensibility can be quite attractive to the mindset of the older academic (e.g. moi) for it provides an excellent excuse (e.g. it’s just rehashed X) to stop reading the current literature, which, truth be told, is an exhausting thing to do. However, every now and then a nice thing happens. Something is thrust in your way that you should have known about but didn’t. My non-academic self “discovered” Trollope and Dvorak and Callas in this way (and more recently I’ve gotten similarly hooked on Tana French novels). What makes this invigorating is that all of a sudden you get access to a whole lot of new good stuff that is exciting and amusing due to its freshness and that you had no idea even existed. And every now and then it even happens in the academic part of your life. In fact, this happened to me a couple of weeks ago. “Pray tell”, you say. “How? Spill!”

A month or so ago John Burgess (JB) came to campus to give a talk. Though I may have heard of this guy (and I’m not even sure of that) I am pretty sure that I had never read anything he wrote. But to get ready for the talk (I was also invited out to supper with him) I asked Alexander Williams (a dept colleague who studied with Burgess) what I should read of his to get acquainted with his work.  Alexander pointed me to this and I am forever in his debt for doing so (though don’t think you will ever collect Mr. Williams, I am notoriously bad at repayment). The essays are delicious: funny, informative, wry, insightful and just plain charming to read. Burgess in person is equally so, but I suspect that it’s easier to meet him in print than in person. At any rate, the essays were great fun to read and one in particular got me thinking about the sorts of theoretical issues that linguistic semanticists prefer to tackle mainly by avoidance. One particular question stood out: what’s the role of truth in a theory of meaning?  More particularly, what role does truth play in Tarski’s semantic theory? Burgess has a nice historical discussion of this entitled “Tarski’s Tort.”

Note that it’s ‘tort’ (as in between a felony and a misdemeanor), not ‘torte’ as in cakish pie.  At any rate, the essay discusses the kinds of confusions Tarski’s “semantic conception of truth” has wrought. In JB’s opinion, Tarski’s use of the term ‘semantic’ has caused nothing but trouble, and some of it serious.  Why? Well as JB puts it (156):

…there can hardly be any question that what “semantics” conveyed and conveys to the mind of the general theory is a theory of meaning, which Tarski’s theory most emphatically was not.

JB reviews some of the problems this terminological misstep has had for philosophical logic as well as for linguistic semantics via Davidsonianism. A little précis of the history he reviews can give you a taste of what he has in mind.

According to JB, Tarski could care less about truth. Indeed, he thought the naïve notion hopelessly confused and unredeemable. Why? Because it was beset by paradox. In other words, he thought that the standard notion was unfixably inconsistent. What he wanted was a substitute for that notion that could be serviceable for mathematical ends. As JB puts it, what Tarski sought was (167):

A restricted replacement for it [i.e. Truth, NH]: a serviceable substitute applicable not to all languages, but only to languages of a certain comparatively simple sort.

In fact, as JB outlines, Tarski used the notion of meaning to provide a local substitute for the hopelessly confused notion of truth. Or, he presupposed that we knew the meanings of certain terms to allow an extensionally adequate and precise limited definition of truth. How so?

JB again (154):

…in Tarski’s original set-up, the ‘object language” for which truth is being defined is contained in the metalanguage on which the proof is being given…In order to understand the definitions, one must understand the metalanguage, and that includes understanding the object language which is part of it, and therewith each of the words or symbols of the object language.

For example, Tarski did not (and could not) intend the various clauses of his theory to provide meanings for the words and symbols. Thus a clause that says “(A and B) is true iff A is true and B is true” cannot define what ‘and’ means as such a definition would be circular given the use of ‘and’ on the right hand side of the bi-conditional. Similarly in “(A/\B) is true iff A is true and B is true” we understand ‘/\’ in terms of understanding the meaning of ‘and.’ None of this improves when we start using model theory “talk” to set-up the relevant notions (see 163ff for discussion).

JB identifies two “syllogisms” (one ontotlogical, one semantic) that he argues are simply illegitimate, though commonly employed. These are outlined in the inferences from (1)-(3) and (4)-(6):

(1)  It’s there in the model
(2)  So it’s there in the semantics
(3)  So it’s there in the meaning

(4) These sentences have models
(5) These sentences have a semantics
(6) These sentences have a meaning

As JB puts it: “…it is one thing to have a theory of models and another thing to have a theory of meaning” (160). By themselves, giving a model theoretic semantics “does nothing towards establishing the coherence and intelligibility of any underlying motivating ideas or intended intuitive interpretation” (161).

Why is this worth noting? Well because of the role that truth plays in contemporary theories of meaning. JB observes that Davidsonians (and most other contemporary semanticists so far as I can tell)[1] in pursuing truth conditional theories of meaning (TCTM) have stood Tarski “on his head” (162). As JB puts it on (166):

…[Davidsonians, NH] make what for Tarski were clauses in a definition of truth in terms of already understood notions like negation and conjunction, into definitions of a kind of those operators in terms of a notion of truth taken as primitive.

So, whereas Tarski defined a mathematically serviceable theory of truth by taking for granted an understanding of meaning, TCTM theory takes truth as basic and intends to define meaning with it, a move that Tarski, being skeptical of the viability of a general notion of truth would have been very very skeptical of. And why? Because Tarski held that the notion of truth was inconsistent (due to the problems raised by the paradoxes) and “the inconsistency theory of truth is incompatible with the truth conditional theory of meaning” (167).

Paul Pietroski has discussed the consequences of some of this for current semantic theory (see here and here). The upshot is that the paradoxes constitute a serious theoretical problem for TCTMs.  This does not mean that all work done assuming TCTM must be cast to the flames. But it does mean that there exists an important theoretical task of either defending the TCTM against the problems the paradoxes raise or seeing how the results obtained using a TCTM can be reinterpreted in less conceptually fraught terms.  Having read JB, I am pretty sure that were Tarski asked, he would have endorsed the second kind of re-analytic project, given his jaundiced views concerning the viability of a coherent general conception of truth.[2]

Linguistic semanticists have been, by and large, uninterested in foundational issues. From where I sit, this is because semanticists have mainly been interested in describing (or “capturing”) the semantic facts.  The aim has been to put into formal terms “semantic” facts. There is nothing wrong with this. Indeed, there is a lot that is right on. It is analogous to what syntactitians spent most of their time doing in the 60s (i.e. establishing a body of analyses that hopefully would provide fuel for more serious theoretical speculation). However, even more than in syntax, it is tempting to confuse formal work with theoretical work, especially given the awesome mathematical “look” of the proposals.  But, to reiterate a point JB makes repeatedly, the two are very different.

For whatever reasons, linguists have shied away from investigating the theoretical core. Maybe, having been reassured by philosophers that recursive truth theories were conceptually ok and given a kind of Davidsonian (and also Lewis, and Montague, etc.) seal of approval, we have assumed that there is nothing foundationally suspect with truth as a basic interpretive notion. But, this assumption is, and always was, very very controversial, and qua theorists (even if not as descriptivists) we ought to worry about these foundational notions.[3]

To end: Burgess writes great papers. The one on Tarski and TCTMs is one of many in his book of essays. Aside from being entertained (and I mean lol kinds of moments), the points raised are also edifying and present plenty for the theoretically minded linguist interested in meaning to chew over.  

[1] With the conspicuous exception of Paul Pietroski (see here), I believe.
[2] JB noting some work by Kripke on the topic suggests that things are pretty much where Tarski left matters wrt getting a more coherent general conception. See p. 167.
[3] Before ending, let me point to one other paper worth looking at, Hartry Field’s old paper on Tarski’s theory of truth (here). Field outlines a project for a conceptually respectable theory of truth that focuses on scientifically understanding (i.e. conceptually and theoretically grounding) another semantic notion, primitive denotation.

1 comment:

  1. I think one reason for the popularity of 'truth conditional technology' might be that it is a very smooth way to produce theories of entailment, which is an intuitively accessible relationship between sentences that the methods of linguistics clearly apply to (cf Katz in his 1972 book). Smooth in part because it's a Marr level 1 theory, which is not bogged down in the details of how entailment might be enumerated or detected (also, back in the day, proof theory was much less well developed and accessible; but now, Greg Restall has apparently gotten some $$ to develop proof theoretical semantics for NLs). This suggests an 'agnostic' view towards truth itself, which is explicitly adopted by Keenan and Faltz in their Boolean Semantics book.

    I have occasionally pointed out to formal semanticists that fs textbooks tend to begin with some programmatic discussions of truth, Cresswell's picture of a door, etc, and then devote the body of the text to producing a nonconstructive theory of entailment, with direct investigation of truth almost entirely absent.

    But you can't deny that truth is important, it would seem to be the critical notion behind entailment; X entails Y iff "you can't think like this: [X is true. Y is not true]". But to study it directly, you need to work with psychologists, it seems to me, as Pietroski does