Conjoining Meanings : sneaking up on truth

1. Conjoining Meanings: sneaking up on truth Paul PietroskiRutgers University

2. Assumption: Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. Question: What are these meanings? ___________________________________________________________________________ • The Project --offer and defend some hypotheses about natural languages of a special sort (Slangs) --not stipulating a notion of meaning and describing linguistic communication in terms of it --not trying to describe humans and conceivable aliens as special cases of “language-users” --the proposal, which owes much to Chomsky, concerns human linguistic competence • Main Negative Claims --meanings are neither concepts nor extensions --a good theory of meaning for a Slang, L, won’t be a theory of truth for L --Slang sentences don’t have truth conditions, not even relative to contexts --theorists shouldn’t describe meanings in terms of Tarskian Satisfaction or Fregean Types • Main Positive Claims --meanings are instructions for how to access and assemble concepts of a special sort --phrasal meanings are instructions for how to assemble monadic concepts --lexical meanings are instructions for how to access monadic or dyadic concepts --meanings actually compose, via relatively simple combinatorial operations

3. Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. • These languages—let’s call them Slangs—are intriguing and distinctively human (i) species specific --other smart animals don’t acquire them, even given special training --human children do acquire them, without special training (ii) interesting lexical items --numerous (10K-ish) and various…nouns, verbs, and “functional” gizmos --recursively combinable in certain ways --polysemous (‘window’, ‘book’, …) (iii) interesting kind of syntax --not Finite State (very, very, very boring recursion) --clauses clauses embed unboringly embed unboringly, and they support “transformations” (cp. Context Free Grammars) --not Context Sensitive (very very very powerful powerful powerful recursion recursion recursion) (iv) allow for homophony --lexical: ‘bear’, ‘bare’, /br/ --constructional: ‘the duck is ready to eat’ I’ll come back to this …and to this

4. Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. • These languages—let’s call them Slangs—are intriguing and distinctively human. Like most Slang words, ‘language’ (‘being’, ‘good’, ‘book’, … ) can be said/used in many ways Invented Languages Natural Languages Various Kinds of “Mentalese” Bee Dance Systems, Vervet Monkey Calls, … Arithmetic Notation, Leibniz’ Calculus, First-Order Logic, Morse Code, … English, Japanese, French, Walpiri, ASL, Latin, … Slangs ⦁ distinctive signals (pronunciations) and interpretations (meanings) ⦁ naturally acquirable by ordinary human children (but not other animals)

5. Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. • These languages—let’s call them Slangs—are intriguing and distinctively human. • ‘Slang’ is a (putative) kind-predicate, introduced via paradigmatic examples and a revisable conception of their important features; cp. ‘Quasar’ • Like most Slang words, ‘meaning’ can be used in many ways. • But theorists can use ‘meaning’ to talk about meanings of a special kind; cp. ‘water’ Various Kinds of “Mentalese” Bee Dance Systems, Vervet Monkey Calls, … Arithmetic Notation, Leibniz’ Calculus, First-Order Logic, Morse Code, … English, Japanese, French, Walpiri, ASL, Latin, … Slangs ⦁ distinctive signals (pronunciations) and interpretations (meanings) ⦁ naturally acquirable by ordinary human children (but not other animals)

6. Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. • These languages—let’s call them Slangs—are intriguing and distinctively human. • ‘Slang’ is a (putative) kind-predicate, introduced via paradigmatic examples and a revisable conception of their important features; cp. ‘Quasar’, ‘Nebula’, … • I use ‘meaning’ to talk about the meanings—whatever they are—that Slangs connect with human pronunciations, via whatever syntax Slangs employ. • The phenomena of homophony and polysemy help anchor this limited use of ‘meaning’; (cp. the meaning of life, smoke, tree rings, rings on ring fingers, E = mc2, …) --Homophony Lexical: ‘bear’, ‘bare’, /br/ Constructional: ‘visiting relatives can be unpleasant’, ‘the duck is ready to eat’, … English, Japanese, French, Walpiri, ASL, Latin, … Slangs ⦁ distinctive signals (pronunciations) and interpretations (meanings) ⦁ naturally acquirable by ordinary human children (but not other animals)

7. Elizabeth, on her side, had much to do. She wanted to ascertain the feelings of each of her visitors, she wanted to compose her own, and to make herself agreeable to all; and in the latter object, where she feared most to fail, she was most sure of success, for those to whom she endeavoured to give pleasure were prepossessed in her favour. Bingley was ready, Georgiana was eager, and Darcy was determined to be pleased. Jane Austen, Pride and Predjudice(1813) Austen didn’t, but could have, extended her description of the scene with active voice… It was equally true that Bingley was ready, Georgiana was eager, and Darcy was determined to please. Elizabeth’s guests had arrived in that desirable state of being prepared to both welcome and amplify the positive effects of their host’s attentions on all present. Bingley was ready to please. Bingley was ready to be one who pleases relevant parties. Bingley was ready to be one whom relevant parties please. Georgiana was eager to please. Georgiana was eager to be one who pleases relevant parties. Georgiana was eager to be one whom relevant parties please. Chomsky (1964)

8. Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. • These languages—let’s call them Slangs—are intriguing and distinctively human. • ‘Slang’ is a (putative) kind-predicate, introduced via paradigmatic examples a revisable conception of their important features; cp. ‘Quasar’, ‘Nebula’, … • I use ‘meaning’ to talk about the meanings—whatever they are—that Slangs connect with human pronunciations, via whatever syntax Slangs employ. • The phenomena of homophony and polysemy help anchor this limited use of ‘meaning’; (cp. the meaning of life, smoke, tree rings, rings on ring fingers, E = mc2, …) --Homophony Lexical: ‘bear’, ‘bare’, /br/ Constructional: ‘visiting relatives can be unpleasant’, ‘Bingley was ready to please’, … whatever meanings are, ‘Bingley was ready to please’ has at least two (cp. ‘eager to please’ and ‘easy to please’) _______________ | | Bingley was ready [ __ to please __ ] |_________________________| _________________ | | Georgiana was eager [ __ to please __ ] Darcy was easy [ __ to please __ ] |______________________|

9. Sidebar on Constructional HomophonySlang Sentence Meanings are not Sets of Possible Worlds(More Generally: Slang Meanings are not “syntax-neutral contents”) some odd number precedes every prime number[ambiguous] (a) some odd number x is such that for every prime number y, x precedes y [true at every world] (b) for every prime number y, some odd number x is such that x precedes y [true at every world] Bingley is eager to please[unambiguous] (a) Bingley is eager to be one who pleases others [may be true at each world where B exists] #(b) Bingley is eager to be one whom others please [may be true at each world where B exists] Bingley is eager to be pleased[unambiguous] #(a) Bingley is eager to be one who please others [may be true at each world where B exists] (b) Bingley is eager to be one whom others please [may be true at each world where B exists] ____________________________________________________________________________________ I grant that distinct expressions (e.g., ‘Al saw Bo’ and ‘Bo was seen by Al’) can have the same meaning. And you can characterize “propositional contents” that are more fine-grained than truth values. But you can’t stipulate that sentence meanings are such contents. (Not even if you’re David Lewis.) two meanings, one set of worlds (one syntax-neutral content) (a) and (b) may have the same syntax-neutral content, even if each of the Slang sentences is unambiguous in its own way If “syntactic structures” correspond to classes of equivalent derivations of strings, perhaps meanings correspond to certain equivalence classes of such structures.

10. Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. • These languages—let’s call them Slangs—are intriguing and distinctively human. • ‘Slang’ is a (putative) kind-predicate, introduced via paradigmatic examples a revisable conception of their important features; cp. ‘Quasar’, ‘Nebula’, … • I use ‘meaning’ to talk about the meanings—whatever they are—that Slangs connect with human pronunciations, via whatever syntax Slangs employ. • The phenomena of homophony and polysemy help anchor this limited use of ‘meaning’; (cp. the meaning of life, smoke, tree rings, rings on ring fingers, E = mc2, …) --Homophony Lexical: ‘bear’, ‘bare’, /br/ Constructional: ‘visiting relatives can be unpleasant’, ‘Bingley was ready to please’, … --Polysemy Distinguishing bearN1 from bearN2 is fine. But a single verb, bearV1, can be polysemous. ‘book’: spatiotemporally located things that can carry contents; abstract contents that get encoded in many ways and places (cp. ‘triangle’, ‘line’) ‘window’: opening in a wall; pane of glass that occupies such an opening; display space behind such a pane at the front of a store; envelope opening that makes an address visible; gap in a counter at a bank Even given an expansive conception of homophony, a typical word is “conceptually equivocal” in a far less arbitrary way, as if a single word can point to a family of concepts.

11. Two kinds of Lexical Equivocality Homophony bæŋkbareA←br→bearV ↙ ︎ ↘︎ ↙ ︎ ↘︎ bankN$bankN▼ ︎ bearN1 bearN2 --one pronunciation, two or more lexical itemseach with its own meaning --typically arbitrary: you/ewe, die/dye, so/sew --linguistically accidental: cp. seau/sceau/saut Polysemy doorN, windowN, bankN$, triangleNbearV, ... $BANK:BLDG ⤶ ⤷ $BANK:INST --one lexical item, whose meaning supports a family of concepts/subsenses -- not arbitrary --often common across languages holdV bookN BOOK:VEHICLE ⤶ ⤷ BOOK:CONTENT my hand, the door, a title, your temper, my calls, so much weight, an opinion, a seminar, a ridge, a course (of due east) • a typical Slang meaning is conceptually equivocal (even if semanticists/logicians/aliens disapprove) •and there are many ways to be conceptually equivocal: ‘Hamlet’, ‘fish’/’tofu’, ad hoc concepts, … • Claims about what lexical meanings are need to allow for equivocality that goes beyond homophony

12. Recipes don’t Determine Outcomes which Vermouth? Byrrh, Carpano Antica Formula, Dolin, … which Gin? Tanqueray, Beefeater, Bombay Sapphire, … how much in a part? 1 ounce, 1.5 ounces, 2 ounces, … shake how vigorously for how long? serve over the ice? how many cubes of what size? serve in what kind of glass? Negroni: --one part Campari --one part red vermouth --one part gin Shake with ice and serve. Manhattan: --Bourbon or Rye --red vermouth Shake with ice, strain, and add a Maraschino cherry. (But the Vermouth of your ideal Negroni may not be the Vermouth of your ideal Manhattan.) The arrows cover a lot. (And genes are not functions from contexts to proteins.)

13. Recipes don’t Determine Outcomes Meaning[republic] = fetch@address:republic republic(_) Meaning[France] = fetch@address:France France-land France-institution Meaning[France is a republic]  Compose(Meaning[republic], Meaning[France])  republic(France-land)  republic(France-institution) the second Vermouth works better with Campari

14. Recipes don’t Determine Outcomes Meaning[hexagonal] = fetch@address:hexagonal hexagonal(_) Meaning[France] = fetch@address:France France-land France-institution Meaning[France is hexagonal]  Compose(Meaning[hexagonal], Meaning[France])  hexagonal(France-land)  hexagonal(France-institution) the first Vermouth works better with bourbon

15. Recipes don’t Determine Outcomes Music scores can encode various kinds of specificities I IV V I harmonic pattern Negroni: --one part Campari --one part red vermouth --one part gin Shake with ice and serve. Manhattan: --Bourbon or Rye --red vermouth to taste Shake with ice, strain, and add a Maraschino cherry. G C D G chord names particular notes state of a particular instrument (type) fingering diagram (shows how to put an instrument into a certain state)

16. Recipes don’t Determine Outcomes Music scores can encode various kinds of specificities G Negroni: --one part Campari --one part red vermouth --one part gin Shake over ice and serve. Manhattan: --Bourbon or Rye --red vermouth to taste Shake over ice and pour over a Maraschino cherry. But a good player need not be “automated” by a very specific instruction

17. Recipes don’t Determine Outcomes Music scores can encode various kinds of specificities G Negroni: --one part Campari --one part red vermouth --one part gin Shake over ice and serve. Manhattan: --Bourbon or Rye --red vermouth to taste Shake over ice and pour over a Maraschino cherry. Though a player need not be “automated” by a very specific instruction A good player can also “fill out” a sparescore

18. Human children regularly acquire languages, spoken or signed, that connect meanings of some kind with pronunciations of some kind. • These languages—let’s call them Slangs—are intriguing and distinctively human. • Claim: Slang meanings and pronunciations are more like recipes and scores than drinkable cocktails and audible performances. Various Kinds of “Mentalese” Bee Dance Systems, Vervet Monkey Calls, … Arithmetic Notation, Leibniz’ Calculus, First-Order Logic, Morse Code, … English, Japanese, French, Walpiri, ASL, Latin, … Slangs ⦁ distinctive signals (pronunciations) and interpretations (meanings) ⦁ naturally acquirable by ordinary human children (but not other animals)

19. Pronunciations as Scores (Utterances as Performances) If utterances are regarded as “dances” performed by…movable portions of the vocal tract, then one must also suppose that underlying each utterance (“dance”) there is a “score” in some “choreographic” notation that instructs each “dancer” what to do and when. Whatever pronunciations are, they’re not sound waves.

20. Meanings as Generable Instructions thatinterface with “Conceptual-Intentional Systems” Conjoining Meanings is an attempt to develop and motivate this idea, by providing and defending a specific version that is… --detailed enough to reconstruct a standard first course in semantics --applicable in productive ways to constructions that occupy professionals --empirically superior to truth-theoretic semantics, as standardly presented, once we take polysemy seriously The details are surely not right. But whatever meanings are, they’re not concepts or extensions. Slangs don’t connect pronunciations with language-independent things. Slangs generate expressions whose meanings are pronounceable semantic instructions. Usingthese instructions to build concepts, some of which may have extensions, involves lots of machinery that is independent of Slangs. Let’s not confuse meanings with uses of meaningful expressions.

21. Sketch of the Proposal • Each lexical item links its pronunciation to an address that can be shared by a family of concepts; where concepts are composable mental symbols with which we can think about things. • “Fetchable” concepts can be accessed by lexical items andcombined with others via the (limited) operations corresponding to phrasal syntax. All fetchable concepts are monadic or dyadic. • But fetchables can be introduced. Lexicalization need not be a simple matter of labellinga concept. GIVE(e, x, y, z) ≡ GIVING(e) & AGENT(e, x) & THEME(e, y) & RECIPIENT(e, z) TYLERIZER(x) ≡IDENTICAL(TYLERB, x) IDENTICAL(TYLERB, x) ≡A-TYLER(x) & INDEXED-WITH(x, B) • A lexical meaning is an instruction of the form “fetch@LEX”—e.g. fetch@window, fetch@give • A non-lexical meaning is an instruction for how to build a monadic concept via certain operations. • There are two basic combinatorlal operations, both of which yield complex monadic concepts two monadic concepts can be M-joined: F(_) + G(_)  F^G(_) a dyadic concept and a monadic concept can be D-joined: D(_, _) + M(_)  ∃[D(_ , _)^M(_)] |_____|____| • Other operations—including a limited form of abstraction for relative clauses—are invoked above “VP shells” (verbs+arguments+adjuncts). But these operations convert monadic concepts into other monadic concepts. So for composition, there are only two types of meanings: <M>, <D>. • A more familiar typology overgenerates wildly: <e>; <t>; <𝛂, 𝛃> if <𝛂> and <𝛃> are types. • The proposal in Conjoining Meanings is the simplest alternative I could think of that permits reconstruction of a standard first course in semantics; cp. Chomsky’s “minimalist program.”

22. Two Metaphors for Concept Composition Jigsaw Puzzles7th Grade Chemistry A THOUGHT a Monadic Concept “filled by” a Saturater yields a complete Thought Sang( ) Kermit +1KermitSang-1 saturater Unsaturated +1NaCl-1 2nd saturater a Dyadic Concept “filled by” two Saturaters yields a complete Thought Kicked( , ) -2 +1 Brutus(KickedCaesar+1)-1 -2 +1H(OH+1)-1 1st saturater Doubly Un- saturated Caesar Brutus

23. Conjoining two monadic (-1) concepts can yield a complex monadic (-1) concept Aggie Aggie Cow( ) Brown( ) +1 +1 Cow( ) -1 -1 Aggie M-joiner Brown( ) & Cow( ) Aggie Brown( ) -1

24. D-joiner Monadic ∃ Monadic Dyadic M-joiner Monadic M-joiner Monadic Monadic THREE(_)^GREEN(_)^FISH(_) ∃[UNDER(_, _)^BRIDGE(_)] |_________|_________| D-joiner Monadic ∃ M-joiner Monadic Dyadic M-joiner M-joiner Monadic THREE(_)^GREEN(_)^FISH(_)^∃[UNDER(_, _)^BRIDGE(_)] |_________|_________|

25. Instructions can be as composable as Concepts Fetch-M D-join Fetch-M ∃ M-join Fetch-M M-join Fetch-D Fetch-M M-join[ , M-join(fetch@three, M-join(fetch@green, fetch@fish)) Fetch-M ] D-join Fetch-M ∃ M-join M-join Fetch-M Fetch-D M-join Fetch-M D-join(fetch@under, fetch@bridge)

26. Meanings really Compose • On the view urged in CM, phrasal meanings are as composite as phrases and their pronunciations. • Once upon a time, this would have seemed obvious. Indeed, one might have thought that Slang expressions are pronunciation-meaning pairs, and that phrasal meanings are (like phrasal pronunciations) composite in ways that closely reflect syntactic structure. • But the currently standard view is that complex expressions have “semantic values” (e.g., truth values) that are recursively specifiable in terms of lexical “semantic values” given relevant syntax. Calling this “compositionality” is very misleading, since the idea is that complex expressions don’t have meanings that compose; cp. expressions of a Tarskian language. • Imagine a language in which the pronunciation of ‘snow is white’--𝛑(‘Snow is white’) is specifiable in terms of 𝛑(‘Snow’) and 𝛑(‘is white’), which is specifiable in terms of 𝛑(‘is’) and 𝛑(‘white’); but there’s no sense in which the sentence has the lexical pronunciations as parts. (The words are pronounced as in English, but the sentence sounds like ‘Dogs bark’ sounds in English.) I think it would be odd to say that such a language has a compositional phonology. • If a theory of truth for a Slang can “do duty” as a theory of meaning for the Slang, then as Davidson stressed, one can (for certain purposes) avoid positing meanings that actually compose. But one might wonder if it’s good to eschew meanings that actually compose. • If Slang meanings are instructions for how to build concepts, then for some purposes, it may be OK to pretend there’s only way to execute an instruction. (1 bottle of vermouth, 1 bottle of gin, …) And for some purposes, it may be OK to pretend that every buildable concept has an extension. • But adopting the pretenses wouldn’t make them true. And it wouldn’t show that Slang expressions don’t have meanings that are as composite as the expressions.

27. Negative Theses A Theory of Truth (for a Slang) won’t ”do duty” as a Theory of Meaning • Foster’s Problem runs deep • It’s fatal given sentences like my favorite one, ‘My favorite sentence is not true’ A Good Theory of Meaning (for a Slang) won’t be a Good Theory of Truth • The sky is blue • France is hexagonal, and it’s a republic, but there are no hexagonal republics. • Al chased Theo happily while Theo chased Al unhappily

28. Sneaking up on Truth (from more than one side) Two Valuable Activities • A Logician’s Project --Invent languages that are like Slangs in various respects, including having a predicate that is like ‘true’ in interesting respects. --Think about what you’re doing. In particular, think about respects in which truth is (and isn’t) like the invented notions of truth-in-a-model. • A Cognitive Scientist’s Project --Don’t assume that we already know how meaning is related to truth; assume that Slangs connect meanings with pronunciations. --Try to find out what these meanings are, and how they are related to truth. --Instead of shoehorning truth conditions onto Slang sentences, try to develop theories of meaning that accommodate polysemy. --If we use meanings and other cognitive resources to build thoughts, then let’s not pretend that philosophy of language—as practiced by philosophers or linguists—will evade the need for philosophy of mind and cognitive science.

29. Pronunciations ↓↑ Growth + and  Experience Language Faculty Language Faculty Initial Mature ↓↑ Meanings Pronunciations ↓↑ Concepts Language Faculty Rest of Mind Growth + and  Experience Language Faculty other concepts ↓↑ Meanings Rest of Mind F-concepts Initial Mature “F” for “fetchable”

30. Vocal Tract Changes Pronunciations ↓↑ PHONO-Executor Pronunciations  ↓↑ Language Faculty Rest of Mind other concepts Language Faculty ↓↑ Meanings ↓↑ Meanings  SEM-Executor F-concepts F-concepts Primal Thawts other concepts CarBacNati Enhancer 2.5-D Thawts 2-D Thawts Science, including Logic & Math Rest of Mind Better Thoughts Thoughts

31. Vocal Tract Changes Fregeinvented a Begriffsschrift that Tarski and Church cleaned up. Humans don’t spontaneously acquire languages that have a truth-theoretic semantics. Humans are animals. Minds and mind-world relations are complex. Characterizing meaning in terms of truth demeans both. PHONO-Executor Pronunciations  ↓↑ Language Faculty ↓↑ Meanings  SEM-Executor F-concepts Primal Thawts Don’t pack Logic in here (or elsewhere) without evidence other concepts CarBacNati Enhancer 2.5-D Thawts 2-D Thawts Science, including Logic & Math Rest of Mind Better Thoughts Thoughts

32. Thanks especially to Dunja and those who have already spent a lot of time with