UofA

Spring 2004

Ling/Phil 596D: Topics in Linguistics and Philosophy

Heidi Harley and Massimo Piattelli-Palmarini

Compositionality

Wednesday March 31 & Wednesday April 14

Handout (M. Piattelli-Palmarini) on the paper:

Meaning before Truth (Draft: 15 Oct. 2003) by Paul M. Pietroski, Univ. of Maryland

Pietroski’s central theses (in a nutshell):

(a) Linguistic meanings guide and constrain without determining the truth-conditions of utterances (semantics is very similar to syntax, perhaps just a species of syntax);

(b) Fregean-Tarskian-Montagovian theories of a strict, deterministic, relation between meaning and truth-condition have value, as a fruitful first approximation,

(c) But the relation between meaning and form is tighter, while the relation between meaning and truth is looser, than those classical semantic theories suggest.

(d) We have to go beyond those first approximations, and develop a better theory.

(e) We have to determine what truth-conditional semantics explains, over and above what can be explained without supposing that theories of meaning (just) are theories of truth.

(f) As pointed out by Chomsky, a truth-conditional semantics of natural languages must be expanded to encompass some element of the Wittgensteinian-Austian-Strawsonian appeal to context and use (without accepting their holism, nor the idea that meaning is use. Meaning constrains use, just as it constrains truth).

(g) Chomsky’s indications for a theory of reference and truth have not been taken as seriously as they deserve. (The accusation of anti-realism can easily be rejected).

(h) Lexicalization is central to a semantic theory, because quite heterogeneous concepts (each having different criteria of truth-making) can be brought together only by the language system, under a word (something like a common denominator - see infra – that makes them all jointly usable by human thought).

Theories that P rejects:

(a) Disquotational-deflationist theories of truth à la Horwich;

(b) Radical-interpreters Martian-style, with self-imposed restrictions on the kind of evidence they accept to examine (Quinean externalism);

(c) Die-hard Wittgensteinian theories claiming that “meaning is use”;

(d) Strictly formalistic semantics, that treat natural language just as if it were a regimented, artificial Begriffschrift

Theories that P examines, and wants to rectify in important ways, then combine:

(a) Truthmakers of expressions of natural language are “chunks of the world” (language-independent extensional entities).

(b) Davidsonian theories, where “means that” is replaced wholesale by “is true iff”.

(c) Truthmakers are ideas (or concepts), in the sense that they are bona fide referents, but mental rather than environmental.

(d) Linguistic expressions harbor tacit indices and silent indexicals, making context variability relevantly similar to the way we commonly interpret indexicals.

(e) Putnam-Kripke’s suggestion that the speaker is causally connected to meanings and referents much in the way that perception connects us to things in the contingently surrounding world(s).

(f) Burge’s claim that truth-making is collectively (not individually) determined.

(g) Fodor’s and Schiffer’s claim that sentential utterances are standardly associated with tokens of sentences in Mentalese, plus a denotational semantics for Mentalese.

(h) Flexible meanings à la Cappellen-Lepore, with an invariant core, and suitable abstractions away from un-indexed aspects of context-sensitivity.

(i) A strict truth-meaning relation as a “regulative idea”, possibly with interesting and correct consequences for natural language.

Chomsky’s position (as we saw already, for London, book, river etc.):

The referential valences of words (the requirements on truth-makers for words) are extremely complex, filtered as they are by intensional qualifiers (points of view). There is no such thing as a univocal word-referent relation. This extends to sentences as well.

An example he used in a talk was: The distance between Boston and New York is 200 miles. This is true or false depending on the context (all approximations, all kinds of vagueness, have this property). It may be criminally false, if I am talking to someone who needs to know exactly, because he has to drive from Boston, taking a seriously ill wife to a high specialist in New York in an emergency.

There are no truth-conditions, but rather complicated “truth indicators”, to be supplemented with a host of intensional specifications. But, but, we must not, thereby, accept the Wittgensteinian-Quinean (and Austin, Strawson etc.) holistic recommendations. In Chomsky’s opinion that would only make an already hard problem totally insoluble. Semantics in not holistic. Words do have “intrinsic meaning properties” (determining entailment, just as their intrinsic sound properties determine rhyme), but also an “open texture” connecting them to points of view, tacitly understood specifications etc. His own semantic theory does not go much beyond these words of caution. As we said already, for Chomsky, the interesting and subtle semantics of natural languages is “more syntax”: The syntax of LF, not really semantics (connections between expressions and the world).

Paul Pietroski’s (PP’s) overall plan:

Whether “an utterance of S is true or false, its truth or falsity is typically a massive interaction effect due to the meaning of S and many factors not indicated by elements of S”…… “knowing what sentence S means—i.e., understanding S—is not a matter of somehow associating S with a function from contexts to truth-conditions”.

But we must not renounce a lot of good that comes from the standard truth-functional semantics of natural languages.

“Rather, the meaning of S is a compositionally determined intrinsic property of S that constrains and guides without determining how S can be used to make true or false assertions in various conversational situations”. (Emphasis in the original)

Typical problematic cases for a standard Davidsonian-Tarskian truth theory

(1) France is hexagonal, and it is a republic.

(2) This government does little for the sake of the average American,

whose children will inherit the massive deficit that is accumulating.

(3) Hamlet lived with his parents in Denmark.

In (1) there is no compositional meaning of “France” that can account for our interpretation. (A Chomskian style challenge: Nothing extensional can be a republic and be hexagonal)

In (2) there is no such person as the average American, and having children cannot be truthfully predicated of “he/she”.

(3) manifests the notoriously puzzling case of fictional entities (already pointed out by Frege, then bravely addressed by David Lewis (in his paper “Truth in Fiction”)).

PP suggests, like Chomsky, that the use of sentences may well not be scientifically tractable. The aim here is rather to re-calibrate the object and the significance of a truth-functional approach to meaning and reference.

“… if we adopt the good idea that theories of meaning are theories of understanding, we should not expect a tight connection between meaning and truth”...

“it may be best to just say that theories of meaning/understanding for natural languages are like theories of truth for formal languages in certain specifiable respects”.

Following Chomsky and Higginbotham, PP stresses the following:

(1) Learnability conditions on the interpretive system are important;

(2) Explaining how any speaker obviously understands what an expression cannot mean is of central importance, because

(3) There is no general prohibition against ambiguity in natural languages (in fact there are innumerable cases of ambiguity), but not in the interpretations of, say, “easy to please” versus “eager to please” or in The millionaire called the senator from Texas not possibly meaning that the millionaire was from Texas.

(4) This is clear to a child acquiring the language in spite of the poverty of the stimulus, also for indefinitely many expressions he/she has never encountered. This applies also to the binding principles, and much besides.

(5) Entailments à la Davidson (Brutus stabbed Caesar), and obvious cases of non-entailment, need to be explained.

All this must be prominent in our semantic theories.

PP contra Horwich and the disquotational theories of truth

A “deflationary” theory of compositionality cannot explain how syntactic composition contributes to the meaning of a sentence (we saw a similar argument last week in Pelletier 2003). If higher nodes in a syntactic derivation are meaning-assigners (à la Higginbotham), mere disquotation is unable to capture this fact.

To understand why (7) does not (and cannot) imply (7c), we must understand that “from Texas” can syntactically modify “the senator” or “called the senator”, but cannot modify “the millionaire”

(7) The millionaire called the senator from Texas.

(7c) #The millionaire called the senator, and the millionaire is from Texas.

Such structural effects find a syntactic explanation that goes beyond disquotation “plus” straightforward composition à la Horwich. An event-semantics à la Davidson, combined with the appropriate syntactic analysis, can explain why “from Texas” can be conjoined with the calling event, or with the being a senator event, but not with the being a caller event. Details are immaterial here. The important point is that lexicalization interacts in specific ways with syntactic and semantic composition. Our task is to understand how this happens. A disquotational approach has no hope of being able to do this.

PP says: “a theory with axioms like ‘easy means EASY’ or ‘x satisfies easy iff x is easy’, or theorems like ‘x satisfies called the senator iff x called the senator’, may be a poor theory of meaning. Even if such axioms/theorems are true, it is a tendentious hypothesis that they are formulated in the right way for purposes of explaining how humans understand language”. (p. 8)

Enter Martians

This is how one could argue that impossible meanings are irrelevant to a semantics of natural languages: Suppose there are intelligent creatures that correctly pair linguistic sounds and interpretations, but have no intuitions at all about impossible meanings for those expressions. There could be such creatures. Would they not be good enough, for the purposes of a semantic theory? (Quinean externalism)

Well, at a minimum, there still would the problem of explaining why children are not such creatures. Unless one has good arguments to the effect that abstracting away from the differences between children and such Martians is a legitimate semantic idealization. But it’s not. Children do impose strict constraints, over and above those of mere “reasonableness”, onto the range of possible interpretations. These constraints are internal to the child, not dictated by the surrounding scene. And, if one models the Martians as “scientists”, then it’s unreasonable to impose a priori constraints on the kind of evidence they would want to access. Qua scientist, the Martian will consider all the relevant evidence (unless he is a behaviorist of some kind, but then he just is a bad scientist). Why would he consider that any heuristic used by children is dispensable? Why, then, in particular, programmatically rule out evidence about impossible meanings? Assuming that he will rule that out is quite implausible. So, those Martians are a bad idealization of any reasonable creature trying to learn to map meanings onto linguistic sounds. Rather, the case of the Martian may help us understand the gap between him and real speakers, between his semantics (whatever that may be) and the realistic semantics we are trying to construct. But nothing more.

“If all normal children in each linguistic community converge (despite varied experience) on agreement about what signals cannot mean, this suggests that such agreement is due to properties of children, not properties of their environment. Correlatively, the challenge presented by negative facts is not “merely” to explain how some learner could acquire English on the basis of evidence available to a hyperattentive child. The deeper challenge is to explain how all Englished children do acquire English, despite variability in experience and attentiveness—and likewise for every other human language”. (PP, page 10, emph. orig.)

A desperate move (à la Dummett, Burge et al.) is to conclude that individual native speakers, in fact, do not understand the language. We have a collective fuzzy super-set of idiolects, only partially understood by each individual speaker. And publicly observable facts in the surrounding world. The counter to this, basically, is that properties of the environment are the wrong kind of idealization, if constraints on interpretation are the result of the biology/psychology of the speakers (of the human species). If such constraints are internally caused, then attention to the environment and to collective use will not reveal them. What will be revealed is not “stuff referred to” by expressions, but rather external properties that are responsible for intersubjective stability in the use of linguistic expressions. But these properties presuppose meaning, they are not substitutes for meaning.

PP: “for purposes of theorizing about meaning/understanding, the best degree of abstraction will be one that (a) deemphasizes facts about what speakers actually refer to when using language and (b) highlights internalistic properties of expressions that can be used in different environments to make semantically identical but truth-evaluably distinct claims”(p. 13) (my emphasis)

Let’s consider the following:

(1a) France is hexagonal.

(1b) France is a republic.

(1c) France is a hexagonal republic.

It’s possible to find circumstances in which (1c) is not only meaningful, but true. Does this entail “There is something that is hexagonal and is a republic”? Are there mind-independent entities, out there, that are both hexagonal and a republic, and are truth-makers of (1c)? This is very doubtful. So, what’s the story?

“Perhaps the meaning of an expression is an instruction for creating a concept from available mental resources”. (page 15) (after Strawson 1950). This would be an alternative to the standard Tarskian “France” denotes France theory. It’s also an alternative to the view (ever since generative grammar) that meanings are conceptual structures (i.e. something that is a referent, a Fregean Bedeutung, but mental, instead of environmental)”.

“We can try to characterize the meaning of [a referential device ] R in terms of general directions for using R (on particular occasions) to express particular concepts and refer to, or mention, or think about, specific things”.

This saves all that is right in the alternative views, but avoids their familiar pitfalls.

“The word ‘France’ has certain features that get correlated in human minds with certain conceptual capacities, like the capacities to think about spatiotemporal coordinates, and about intentional properties of people who create institutions; these may not be capacities to think about (properties of) the same mind-independent things; and these capacities may themselves be complex and varied, in ways that tell against the claim that ‘France’ either denotes something or ambiguously denotes some things”…. “This does not establish that semantic theories should mark such distinctions. Perhaps we should diagnose such facts as reflections of what speakers know about France, and not what they know about ‘France’; see Fodor and Lepore (1992, 2002)”.

One of the key linguistic devices is lexicalization.

Lexicalization

Various mental representations that are different in kind are linked, that is, “combined to form a complex concept that is usable in human thought”. The “common denominators” are grouped into a complex mental representation, although we still have mental representations whose constituents are typologically heterogeneous. Words may often “fit together” in ways that the corresponding concepts do not. There can be (sort of) shotgun “adaptors”, connecting concepts that could otherwise not be connected. Grammatical features can do that.

Brown dog: color as a property of surfaces, combined with some object that has a surface. “Predicates as instructions for creating concepts” (page 17). Instructions to the articulatory organs, and instructions to the conceptual apparatus.

“And just as phonologists can try to explain relations of rhyme in terms of relations between certain instructions for creating sounds, semanticists can try to explain relations of entailment (say, between ‘Fido is a brown dog’ and ‘Fido is a dog’) in terms of relations between instructions for creating sentential concepts.” (ibid).

One can use the apparatus of model-theory to characterize such relations, but this does not warrant the hypothesis that entailment is best explained in terms of truth (or truth-in-the-model). Truth may well be pre-theoretically salient, as a first attempt, but we, then, need to re-characterize the process in a different way in a real theory.

MPP: It seems to me that PP (on the basis of previous work by Norbert Hornstein) has in mind something like a distilled case of the “bug” (Swinney) or “tire” (Tanenbaum), only vastly generalized. A lexeme “carries” with it a bunch of different concepts, often quite heterogeneous, under some minimal common denominator. The speaker can, thus, express judgments that straddle across these different, but mono-morphemically jointly lexicalized, items. A bit like, at the extreme, bugs crawling on the walls and being used by espionage agencies. France being hexagonal and a republic is a less extreme, grammatically acceptable, naturally thinkable, instance of such phenomena. Yet, obviously, PP insists that there are many things that “France” cannot mean. The process is constrained, and ambiguity is highly (and subtly) regimented. This stresses the “bottom-up” nature of semantics, and reiterates Chomsky’s emphasis on syntactically mandatory inferences (remember the cases of “persuade”, “painting the cubic sphere red”, etc. ).

PP invokes the case of Plato’s Meno, of the slave developing from the inside considerable knowledge about geometry. We know that there are subtle, yet obvious and perfectly natural, idealizations subtended by “triangle”, “square” etc. Our semantics must be coherent with such facts, and explain why ‘Triangles are imperceptible’ can be true, while ‘Imperceptible triangles differ perceptibly from imperceptible circles’ is not (MPP: I am not persuaded that they cannot both be true, in a suitable context. A Platonistic philosopher may well want to assert both.)

Possibly some of our capacities for connecting percepts with abstract concepts would be “untriggered” (quote, unquote) in the absence of a language faculty. (Data from Spelke et al. are cited as evidence). Anyway:

“We should be wary of semantic theories according to which (i) linguistic meaning cannot play this kind of role in human thought because (ii) the relation between meaning and truth is relatively simple. For this makes the study of thought and ontology even harder than it already is”. (page 19).

One hardly needs to be reminded that commonsense thought and ordinary talk cannot really be expected to match the world as it is. They rather, somehow, only roughly agree with the superficial “passing show”. Claims to the contrary have typically come from naïve empiricists, optimistic evolutionists, and via distorting simplifications such as “meaning is use”. Even when scientists try very hard to access the structure of the objective world, via painfully regimented languages, success is far from granted.

Ontology

PP wants to dispel the easy critique (raised against Chomsky by Fodor – see my previous handout - and by many in this class) that, in spite of all this, France is a real country, one we can actually visit. Real entities (referents) do enter in a sort of Davidsonian triangulation.

“The environment is surely responsible for some aspects of intersubjective stability with regard to how we use linguistic expressions to talk about things; although this kind of stability may well presuppose meaning”. (page 12)

Nuancing the very idea of “truth-makers” must not lead us to anti-realism.

Theoretical vocabularies (à la Frege, Russell, Tarski etc.) designed to describe regimented invented languages may well be unsuitable to characterize ordinary language. And ordinary language may symmetrically fail to adequately characterize things in scientifically perspicuous ways. In those languages, any syntactically not-well-formed expression is just gibberish. But, as Higginbotham has stressed over the years (see a previous handout) not-well-formed expressions of natural languages may well have a meaning, nay, a meaning that’s uniquely and immediately specifiable by any native speaker.

The force of form

Antecedence as a syntactic relation holds regardless of your theory of which meaning/referent you want to associate with France. The “it” in (1) pairs with “France” regardless:

(1) France is hexagonal and it is a republic

“With regard to (1), an obvious thought is that while a pronoun makes the full range of its antecedent’s features available for predication—modulo any restrictions, like gender or number, imposed by the pronoun—only some of these features will be semantically "activated" by any given predicate. In (1), ‘republic’ may indirectly (i.e., at the occurrence of ‘it’) activate features of ‘France’ that cannot be naturally combined with ‘hexagonal’”(page 21).

Other examples (after Chomsky) are offered (a certain “book” being heavy and unfavorably reviewed, etc.). Predicates of natural language, like book, maybe have no “satisfiers” at all.

Examples dealing with Hamlet and fictional characters highlight these problems of reference “with a vengeance”. Unless one adopts Lewis’s unrestrained ontology (possible worlds really exists, and are as real as the real world, only different), one faces a predicament.

“I suspect that some philosophers want it both ways: a theory of meaning/truth according to which meanings themselves relate expressions to the things that speakers use expressions to talk about, so that understanding an expression is already a way of being "in contact with" the world that makes our claims true; and a theory of meaning/truth without substantive ontological commitments, so that understanding an expression does not require a theory of that which makes our claims true”.

After all, we understand without problems tales and fictional stories (a point that also Chomsky stressed in my MIT class recently – see previous handout). Our semantic theory must be able to explain how that happens. It’s unwise to consider all such cases “as a hodgepodge of marginal cases to be set aside”.

PP point is: “….to note that names like ‘Hamlet’ invite treatment in terms of the hypothesis that the meaning of a name should be specified (not by associating the name with some entity, but rather) in terms of some array of features that the name makes available for a variety of uses; where using all the features at once would be ungrammatical and incoherent”. (page 24)

A more desirable theory:

“The mental representations indicated by linguistic expressions may well have elements (not corresponding to elements of the sentences speakers utter) that track many ways in which the truth of utterances can depend on the environment”.

However, PP specifies: “My claim is not that we should abandon current semantic theories, or that standard textbooks are complete bunk. It is rather that "axioms" like ‘France’ denotes France are best read, despite appearances to the contrary, as preliminary claims about intrinsic features of linguistic expressions—and that we should bear this in mind, as we revise our current theories. But the suggestion is not that each word has a unique array of grammatical features. And I am not denying that causal-historical facts, of the sort Kripke (1971, 1980) and others have discussed, bear on what speakers refer to with names”. (page 24)

Concerning the Putnam-Burge thought-experiments, they have revealed that the relation between meaning, truth and reference is more complex than one might have hoped. However, PP says, they did not manage to refute an internalist semantics:

“The internalist view on offer is one according to which linguistic meanings guide and constrain without determining truth, reference, and other (norm governed) expression-speaker-world relations. This leaves room for the claim that such relations are interestingly externalistic. So one can hardly use the thought-experiments to argue for this claim, and then use them again to argue that meaning is like truth and reference in this respect”. (p. 26)

“We should detach the idea that speakers use names to perform acts of rigid reference from the idea that names have referents rigidly”. (p.29)

The use of counterfactuals (France once was a hexagonal monarchy; France might have been a Communist union; the boundaries of France might have been different, etc.) make it, once again, clear that the extensional notion of referent is problematic. Even more problematic is a Kripkean notion of rigid designators:

“Any such thing would be denoted rigidly by ‘France’; and so, given the truth of various counterfactual claims, it would need to have both its geometric and political properties inessentially. But what is this alleged thing, which conveniently has all the properties something needs to have to be a truth-maker for all claims of the form ‘France is, or at least might have been, F”? (ibid. F is some predicate).

Repeat: A rigid use of names is quite distinct from the idea that names have referents rigidly.

On “meanoting”

A technical term introduced to pinpoint how hard it is to expand the standard Fregean-Tarskian notion of denotation. We are familiar with axioms such as “France” denotes France.

Well, let’s introduce “meanotes” (means/denotes) “France” meanotes France as a shorthand for:

PP: “‘France’ is an expression (of a certain type) that makes certain linguistic features available for use; speakers can use these features to perform referential acts of various kinds (and thereby refer to things of different kinds); given the contingent history of how ‘France’ has been used, speakers of English can use it to refer to the various things that can count as France in various contexts, as opposed to other things (like those that can count as Germany); but these contingencies may be extraneous to theories of meaning/understanding, which may turn out to be theories of (speakers’ tacit knowledge regarding) certain essential and internalistic properties of expressions; although the contingences are relevant to questions of truth or falsity”. (pp 30-31)

“Meanotes” is a predicate of the metalanguage. What we would need now is to develop a logic of this predicate, with semantic theorems, and plausible claims about the relations between meaning, denoting and meanoting. That would be very hard indeed.

PP’s methodological punchline:

“In general, it is bad methodology to adopt a theoretical vocabulary that forces one to come up with a complete correct theory before offering any theory from which theorems can be derived. Better to let oneself write down and later revise partial theories that are false, as part of a process that might eventually lead to reasonably good idealizations that partly explain a certain range of phenomena. So we want an alternative to ‘meanotes’ that does not require a special logic”.

Davidsonian semantics followed the latter method, with excellent results. The core semantic notions are extensional, and apparent counterexamples were treated as special cases. We can go quite a long way with that, without committing ourselves “to the hypothesis that a correct theory of meaning for English will associate ‘France’ with an entity that satisfies any predicate F, such that utterances of a sentence formed by combining ‘France’ with F are true”. (Page 31)

Rather, we offer idealizations like the following:

“For purposes of explaining the limited range of facts this theory purports to explain,

we’re ignoring a lot of what makes ‘France’ the expression it is—an expression that

can (given contingent facts) be used to refer to the various things that can count as

France; likewise, many typological differences between predicates (including those

that distinguish ‘hexagonal’ from ‘republic’) will be ignored; indeed, all that really

matters for these purposes is that ‘France’ is (i) a potential grammatical argument of a

predicate, (ii) a word that can be used to refer to something, and (iii) semantically

distinct from other words of this type, unless some other axiom says otherwise”.

This leads to a crucial consideration, for the whole of PP’s project:

“Blaming the language-independent world for the apparent gap between meaning and truth is even less plausible than blaming logic. And if axioms like ‘France’ denotes France reflect idealizations that abstract away from all the reasons for thinking that there are no theories of truth for natural language, then the use of such axioms does not even suggest that there are such theories”.

This, basically, preserves all we want/need to preserve of truth-conditional semantics, and, at the same time, leave adequate space for the internalist components emphasized by Chomsky.

Flexibility

Several considerations follow about variable “standards” (of hexagonality), vagueness and supervaluation, various hypotheses on “satisfaction” (commonsensical versus theoretical), invariant core components and limited context-sensitivity, tacit indexicals etc.

None, in PP’s opinion, saves the idea that theories of meaning are theories of truth.

“Flexible axioms” are contrasted with rigid “deflationary” theories, with fixed axioms such as “x satisfies ‘easy’, iff x is easy”.

His inclination is toward “A Chomsky-style view, combined with a preference for encoding semantic theories in terms of constraints on truth imposed by expressions, as opposed to features of expressions that impose constraints on truth”. (page 34)

PP concludes:

“I am not saying that causal-historical facts are irrelevant with regard to what a given predicate is intuitively true of. Nor am I saying “axioms” like x satisfies ‘hexagonal’ iff x is hexagonal are bunk. This is one way of encoding a perfectly fine idea: ‘hexagonal’ is a monadic predicate; and given some things to talk about, such a predicate is apt for use (on a given occasion) as a device for sorting the things in a certain way, just as ‘France’ is apt for use as a device for referring (on a given occasion) to one of the things. But given some things, there are many overlapping ways of sorting them such that for each of those ways, a speaker of English can use the word ‘hexagonal’ to sort the things in that way. The question is whether we theorists should describe this fact about language use by characterizing the meaning of ‘hexagonal’ in terms of a mapping from things to ways of sorting them—and not in terms of intrinsic features of the word that make it possible to use ‘hexagonal’ as a device for sorting things in certain ways across various conversational situations. The theoretical task, as always in this domain, is to figure out how meaning is related to use. It is not enough to just say that each aspect of use reflects meaning; but encoding each aspect of use in claims about meaning is just a special case of ensuring descriptive adequacy at the cost of explaining nothing”.

“Meaning constrains both use and truth, in subtle and interesting ways. An account that does justice to natural language will have to accommodate facts which suggest both that (i) use are {sic, perhaps should be “and”} truth are very complicated, perhaps in many intractable ways, and (ii) meaning is systematic and in many ways theoretically tractable, even for creatures with our limited cognitive powers”.

MPP: General comments

I am wholeheartedly sympathetic to Pietroski’s project. I share his opinion that Chomsky’s critique of denotational semantics is important and correct. (Contra my friends Fodor and Higginbotham, and some of you here, who think it’s just extravagant). There is no theory that Pietroski argues against that I would rather defend. But I do not think he is offering a real semantic theory. All these are interesting meta-theoretical considerations, general guidelines for constructing one (see also a manuscript by Wolfram Hinzen with germane considerations). Let’s briefly examine the few of his suggestions that are specific enough:

Lexicalization: Fine, but it gives a name to a mystery. We understand what it would be for brown to be “true of” all and only brown objects. We also understand what it would be for it to be (à la Putnam old style) something like colored + specific + ostensive exemplar of typical brown here and now. Or, à la Fodor, to mean the property of being brown (a sort of LOT, atomistic, Tarskian formula). But I do not understand what it is to be, à la Pietroski, some recipe for building up concepts. And, if there is (as he suggests) a “common denominator” uniting heterogeneous concepts under the lexeme “France” (or “hexagonal”), would that be their lexical meaning? What are these “common denominators”? Do we get them by subtraction, without falling prey to the subtraction fallacy (as Fodor rightly warns us not to do)? Does this bring us any further than Chomsky’s puzzled considerations, and his notion of “points of view”? I do not see that it does.

Constraining use and truth: Maybe, as he says, these processes are intractable (as Chomsky also suggests). But we also have compositionality, context-independence and syntactic constraints, and some parcel of truth in the Tarskian-Davidsonian picture. The puzzle is how to combine these intrinsic meaning components with context dependence (in this whole course we had this problem as its focus). Pietroski’s suggestions do not bring a solution.

Mental resources: Something different from conceptual structures. Not Fregean mental denotata (à la Fodor). But, then. what? This remains, in my opinion, totally unspecified. We only know that learnability considerations, under the poverty of stimulus, apply, and that they are form-driven (syntax and lexicalization) in important ways. Considerations on “sorting things across various conversational situations” do not enlighten us here. As Fodor rightly says in Hume Variations (see my previous handout), sorting presupposes a theory of meaning and a theory of ontology, but does not explain either.

Some of PP’s interesting suggestions (but I am not sure I fully understand them):

The kind of semantics we want is “like” (sic) theories of truth for formal languages in certain specifiable ways: But these ways are not really “specified”. We gather that these theories are partial, a starting point, a first approximation to the semantics of portions of natural language. His own example of “meanotation” shows how hard it is to generalize and rectify them. His hint at a relevant similarity remains a promissory note.

“Semantically identical but truth-evaluably distinct claims¨: Many suggestions have been made in the literature (a lot of which is cited by PP) to this effect. Not clear to me what is the solution actually suggested here.

Platonist analogies: Higginbotham also stresses (in Elucidations of meaning) the importance of such tacit, and not directly accessible by introspection, deep components of our knowledge of meaning. Many natural, complex idealizations, hinted at, but not resolved. Some of our mental capacities for connecting percepts with abstract concepts are, PP says, only triggered by the language faculty. Interesting, but left unresolved.

The environment contributes intersubjective “stability” (sic) to our use of linguistic expressions: That presupposes, but does not explain, meaning. Sure, but how?

Names used rigidly without, thereby, having their referents rigidly: How can that happen? By tacit convention? Kripke-Putnam had a story to tell: direct causality traceably transmitted across communities. What’s the story now? Causal-historical facts are acknowledged as relevant, but the semantics still is internalistic. Puzzling, as stated.

A truth-functional semantics as a regulative notion: My understanding is that this can well be a regulative notion (an idealization conceived as such) for the speaker (not just for the theorist). Great, but this is only briefly mentioned and not developed at all.

All in all, an interesting promissory note.

(1) Coda: Paul Pietroski’s comments on this handout:

I can't add anything in response to your queries at the end, apart from the still vague thought that we should perhaps think of 'France' as a predicate that (like 'rained down' or 'formed a circle') CAN be used as a plural predicate, satisfied by some things that TOGETHER constitute France (or perhaps a France) - allowing that in some contexts, we talk about a bunch of people somehow constituting France, and in other contexts, we talk about a bunch of dirt (or something like that) constituting France.

Clarification (for our class, by MPP)

All this is explained fully in a dense and difficult, and very interesting, paper by Pietroski (on his website) “Quantification and Second-Order Monadicity” (Philosophical Perspectives 17: 259-298, 2003)

Take Boolos’s example:

(40) The rocks rained down on the mountain huts

No single rock is such that it can “rain down”. But no set of rocks can, qua set, “rain down” either. The same applies to the property of “forming a circle”.

Cases à la Barry Schein are of the following kind:

(41) The elms are clustered in the middle of the forest

No single elm is “clustered”, nor does the set of the elms, qua set, “cluster” in the middle of the forest.

The intuition, here, is that we need plurals of individuals or “essential plurals” (repeated instances of the property of being “one of them” where “they” = the rocks, the elms), not single individuals, nor sets. Schein has developed for plurals an event-semantics à la Davidson, with quantification over events. In that theory bottles is true of several events of being a bottle, and we also have something like in(e, x), and with(e, y) and stab (e, x, y). Complex predication comes out strictly conjunctive, as an immediate consequence of this model. Events are individuals, and quantification is strictly over individuals. Plurals à la Schein are not sets.

Second-order quantification à la Boolos is developed in the same spirit:

$X is a distinctively plural quantification over the very same things that ‘x’ ranges

over, with ‘Xx’ meaning that x is one of the Xs (and not that x Î X). Is one of is not the same as “is a member of” (details in the paper, and in Boolos’s papers and book).

Boolos said: “It is not as though there were two sorts of things in the world, individuals and

collections of them, which our first- and second-order variables, respectively, denote.

There are, rather, two (at least) different ways of referring to the same things, among

which there may well be many, many collections”. (Boolos 1998, p.72).

Notice the affinity with Chomsky’s “points of view”. This is why, I think, Pietroski capitalizes on Boolos’s approach to quantification.

Pietroski’s own rendition of this idea is: “The proposal is that we should invoke distinctively plural quantification over singular entities, not singular quantification over distinctively plural entities”.

We have a second-order quantification, but still over individuals, not over sets, or sets of sets.

FROM THE PAPER: “Every bottle is red” is true iff there are some value-entity pairs that satisfy three conditions: every one of them associates its entity with t (the value TRUE); they associate (all and only) the bottles with values; and each of them associates its entity with t iff its entity is red. But without independent motivation, this might seem ad hoc. And by itself, it says nothing about how to embed second-order quantification over value-entity pairs in an otherwise plausible theory that accommodates plural constructions. But luckily, the needed work has already been done (by various theorists) in the context of accounting for some facts that present difficulties for the Frege-Montague conception of propositional structure and compositional semantics”.

Pietroski’s paper justifies and specifies this style of second-order monadic quantification.

Pietroski’s e-mail to me then continues:

But issues of rigidity, and relations between things constituted and constituting things, have me as baffled as ever - whether I try to think in semantic terms or metaphysical terms. (Somehow we need to get straight, as Gareth Evans suggested, about how much of Kripke's phenomena reflect constraints on spoken languages and how much reflect constraints on thought. And I'm not clear about this at all.)

For better or worse, though, my plan is to see if we can get anywhere by thinking about linguistic meaning involving a very general second-order (Boolos-Schein style) existential quantification over "real-world" entities, but then have all the compositional work done at the level of "constituted" semantic Values whose relation to the former is left almost completely

unspecified. My gut tells me that even this is too much a concession to the standard picture, and not sufficiently Kantian. But I'm hoping that a rewrite of standard theories in these terms might be suggestive for how to pursue the more radical idea. We'll see. I really have no idea how this is going to turn out.

MPP: I have also read your paper developing Boolos' ideas on plurals. A smart, subtle idea, but frankly I do not quite see the overall thrust. Can you tell me briefly why you think it's SO important for semantics as a whole?

PIETROSKI: It's the only real alternative I can see to the idea that (i) concatenating a predicate with an argument signifies function-application, and (ii) plural noun-phrases are devices for quantifying over plural entities. Since the combination of (i) and (ii) seems pretty bad to me, for lots of reasons, I follow Boolos and Schein. The next question, then, is whether the needed apparatus is peculiar to plurality or more general. There's a book manuscript arguing for the latter. [The intro chapter is on my website.]

Turns out, I think, that there's a lot to be said for the following idea: in natural language, concatenation typically signifies predicate-conjunction; but the required metalanguage for a semantic theory is basically the one George Boolos described., i.e. second-order monadic predicate logic, with second-order quantification understood his way. You can think of it as a revision of Davidson's proposal to do it in first-order pred calc, with (effectively) syncategorematic treatments of determiners (and very little to say about plurality). It's closer to Higginbotham's view, which is couched in a second-order framework, but which appeals to two kinds of grammatical combination (theta-linking and theta-binding) and then (effectively) syncategorematic treatments of determiners. I try to do it all in terms of saying that all the main grammatical combinations (predicate-adjunct, predicate-argument, determiner-predicate) all signify predicate conjunction. If that's right, then UG just has to say: merge means CONJOIN. I think this has both conceptual and empirical payoffs. It's certainly more constrained than the more standard Montague-inspired proposals, even Heim and Kratzer's account, which has many virtues.