The Extension Dogma Paul M. Pietroski - PowerPoint Presentation

1. The Extension DogmaPaul M. PietroskiRutgers University

2. The Extension Dogma: an initial characterizationThere are endlessly many meaningful expressions, even for a single language like spoken English. But it’s not obvious that there are meanings that these expressions have. Symbols can have extensions without having meanings (or “intensions” or “senses”) that determine the extensions. So when offering theories of meaning, we should grant that linguistic expressions have extensions, but we should not assume that these expressions have meanings in any further sense.Whatever expression meanings are—if there are any—they determine what, if anything, expressions are true of. So modulo worries about gathering what expressions are true of into sets: if an expression E has a meaning 𝛍, then E has an extension that is determined by 𝛍.Usual caveats: allow for contexts, functions, and possibilities; the extension of an expression can be a function from contexts to (functions from possibilities to) sets of entities.Corollary: psychological studies of understanding are, at best, optional additions to “core” semantics.AN OLD SUSPICION...There may be nothing else for semanticists to do apart from specifying extensionsspeakers of “the same language” may have very different (and perhaps alien) psychologiesthe “semantic commonalities” across speakers of a language may be exhausted by (i) a shared environment, and (ii) general constraints of rationality, as applied to communication

3. The Extension Dogma: Moral of The TalkThere are endlessly many meaningful expressions, even for a single language like spoken English. But it’s not obvious that there are meanings that these expressions have. Symbols can have extensions without having meanings (or “intensions” or “senses”) that determine the extensions. So when offering theories of meaning, we should grant that linguistic expressions have extensions, but we should not assume that these expressions have meanings in any further sense.Whatever expression meanings are—if there are any—they determine what, if anything, expressions are true of. So modulo worries about gathering what expressions are true of into sets: if an expression E has a meaning 𝛍, then E has an extension that is determined by 𝛍.Usual caveats: allow for contexts, functions, and possibilities; the extension of an expression can be a function from contexts to (functions from possibilities to) sets of entities.Corollary: psychological studies of understanding are, at best, optional additions to “core” semantics.REJECT THIS TROJAN HORSE!!!If we want to describe human languages and explain the natural phenomena of linguistic understanding we shouldn’t grant that human linguistic expressions have extensionswe should assume that these expressions have meanings, much as they have pronunciationswe shouldn’t assume that meanings determine extensionsand we should remember that early advocates of The Dogma were talking about “ideal” languages

4. Analogous Theses (for or another day, or Q&A) About ConceptsThere are many “contentful” concepts. But it’s not obvious that there are contents that concepts have. So when offering theories of content, we should grant that concepts have extensions. But we should not assume that concepts have contents in any further sense.Whatever conceptual contents are—if there are any—they determine what, if anything, concepts are true of. So if a concept C has a content k, then C has an extension that is determined by k.For purposes of this talk, you can assume (pretend?) that many human concepts have extensions...--But then don’t assume that the meanings I’m talking about are concepts [that’s The Dogma again]--Think of these meanings (if such there be) as properties of linguistic expressions--It’s not obvious what these properties are...ditto for phonological and syntactic properties--But the phenomenon of homophony—structural and lexical—provides a decent initial guide /ə ˈʃɛrəf dru ə gʌn nɪr ə bæŋk /a sheriff drew a gun near a bank$a sheriff drew a gun near a bank[[drew [a gun]] [near a bank]] [drew [a [gun [near a bank]]]a sheriff drew  a gun near a bank$a sheriff drew a gun near a bank What are these (eight) meanings? Does each one determine an extension?

5. The Extension Dogma for Human Linguistic MeaningsThere are endlessly many meaningful expressions, even for a single language like spoken English. But it’s not obvious that there are meanings that these expressions have. Symbols can have extensions without having meanings (or “intensions” or “senses”) that determine the extensions. So when offering theories of meaning, we should grant that linguistic expressions have extensions, but we should not assume that these expressions have meanings in any further sense.Whatever expression meanings are—if there are any—they determine what, if anything, expressions are true of. So modulo worries about gathering what expressions are true of into sets: if an expression E has a meaning 𝛍, then E has an extension that is determined by 𝛍.Usual caveats: allow for contexts, functions, and possibilities; the extension of an expression can be a function from contexts to (functions from possibilities to) sets of entities.Corollary: psychological studies of understanding are, at best, optional additions to “core” semantics.SHORT FORM: meanings—if such there be—determine extensions; theories of meaning should specify extensions for linguistic expressions; but we shouldn’t assume that there are further semantic properties to specify

6. Origins of The Extension Dogma: some very fast and biased historyInitially, the issues were about ideal languages designed for science (math included); see Frege.Attempts to cash out Frege’s talk of senses as empiricist “verification procedures” did not work out; see Logical Positivism. This fed suspicions that semantic notions are too “hermeneutic” for use in science. But Tarski showed that for a certain kind of invented language with a stipulated extensional interpretation, talk of truth is scientifically legit, given a semantic conception of truth. (This was a new use of ‘semantic’.)This fed Quine’s suspicion that construing scientific notation via intensions—“creatures of darkness”—would saddle theories with unwanted “analyticities”…sentences that would count as theorems because of “how things were presented” by a choice of notation, regardless of how the world is.Quine was also a behaviorist who thought there were no real facts about what natural expressions mean: on his view, linguists were—at best, regimenting—ordinary human modes of speech in convenient ways.Other philosophers in the “Harvard Extension School” followed Quine in trying to make natural language fit an extensionalist mold, thereby greasing a slide from “ideal meanings determine extensions” to “if there are meanings, or semantic properties of any kind, they determine extensions”But if we want to correctly describe the spoken/signed languages that humans regularly acquire, why insist that human linguistic meanings determine extensions?

7. before 1967, the general thesis about natural language wasn’t seriously considered; and it would have seemed obviously wrong...see (e.g.) Aristotle, Wittgenstein, Tarski, and Strawsonat MIT in the early 1960s, studies of meaning were still overtly mentalistic (cp. 1890s: Bréal, Husserl)after Davidson/Lewis/Montague/Partee/Kaplan, The Dogma became increasingly standard... but not because of any evidence for the hypothesis that ordinary expressions have extensionsthere were skeptics...see Chomsky, Harman, Foster, Fodor, Jackendoff...but many others accepted The Dogma while arguing that psychology also mattered; see Evans, Peacocke, Davies, Kamp, Heim, Higginbotham, Larson & Segal, ...lots of 21st century work has picked up this older threadsee, e.g., recent conferences including this onemost/more : Hackl (2009), Pietroski et. al. (2009), Lidz et. al. (2011), Tomaszewicz (2011), Odic et. al. (2018), Knowlton et.al. (forthcoming), ... , Wellwood (next talk) each/every/all: Vendler (1962), ... , Knowlton et.al. (forthcoming-2)21st century question: now that we’ve recognized (yet again) that representations matter, why retain The Extension Dogma, instead of jettisoning it as an odd and implausible relic?Origins of The Extension Dogma: some very fast and biased historyhttp://www.terpconnect.umd.edu/~pietro/research/Quantifiers.html

8. Davidson-style Specifications of Extensions(A1) x[TrueOf(HesperusName, x) ≡ (x = Hesperus)](A2) x[TrueOf(planetAdj, x) ≡ Planet(x)](A3) x[TrueOf([is a …Adj]VerbPhrase, x) ≡ TrueOf(…Adj, x)](A4) True([…Name …VerbPhrase]Sentence) ≡ x[TrueOf(…Name, x) & TrueOf(…VerbPhrase, x)] (T1) x[TrueOf([is a planetAdj]VerbPhrase, x) ≡ TrueOf(planetAdj, x)] ≡ Planet(x)](T2) True([HesperusName [is a planetAdj]VerbPhrase]Sentence) ≡ x[TrueOf(HesperusName , x) & TrueOf([is a planetAdj]VerbPhrase, x)] ≡ x[ x = Hesperus & Planet(x)]

9. (A1*) x[TrueOf(HesperusName, x) ≡ (x = Phosphorus)](A2*) x[TrueOf(woodchuckAdj, x) ≡ Groundhog(x)](A3*) x[TrueOf([is a …Adj]VerbPhrase, x) ≡ TrueOf(…Adj, x) & ei𝝅 + 1 = 0](A4) True([…Name …VerbPhrase]Sentence) ≡ x[TrueOf(…Name, x) & TrueOf(…VerbPhrase, x)] (T1*) x[TrueOf([is a woodchuckAdj]VerbPhrase, x) ≡ TrueOf(woodchuckAdj, x) & ei𝝅 + 1 = 0] ≡ Groundhog(x) & ei𝝅 + 1 = 0](T2*) True([HesperusName [is a woodchuckAdj]VerbPhrase]Sentence) ≡ x[TrueOf(HesperusName , x) & TrueOf([is a woodchuckAdj]VerbPhrase, x)] ≡ x[ x = Phosphorus & Groundhog(x) & ei𝝅 + 1 = 0]Unwanted (but equally true) SpecificationsREPRESENTATION MATTERS FOR MEANING...EXTENSIONAL EQUIVALENCE IS NOT SEMANTIC EQUIVALENCE

10. (A1) ⟦HesperusName⟧ = Hesperus(A2) ⟦groundhogAdj⟧ = 𝛌x.<e,t>Groundhog(x)(A3) ⟦ [is a …Adj]VerbPhrase⟧ = ⟦ …Adj⟧(A4) ⟦ […Name …VerbPhrase]Sentence ⟧ = ⟦ …VerbPhrase⟧(⟦…Name⟧)  (T1) ⟦ [is a groundhogAdj]VerbPhrase⟧ = 𝛌x.<e,t>Groundhog(x)(T2) ⟦ [HesperusName [is a groundhogAdj]VerbPhrase]Sentence⟧ = ⟦ [is a groundhogAdj]VerbPhrase⟧(⟦HesperusName⟧) = 𝛌x.<e,t>Groundhog(x)(Hesperus) = <e,t>Groundhog(Hesperus)Lewis/Montague-style Specifications of Extensions

11. (A1*) ⟦HesperusName⟧ = Phosphorus(A2*) ⟦woodchuckAdj⟧ = 𝛌x.<e,t>Groundhog(x)(A3*) ⟦ [is a …Adj]VerbPhrase⟧ = 𝛌x.ei𝝅 + 1 = 0 & ⟦ …Adj⟧(x)(A4) ⟦ […Name …VerbPhrase]Sentence ⟧ = ⟦ …VerbPhrase⟧(⟦…Name⟧)  (T1*) ⟦ [is a woodchuckAdj]VerbPhrase⟧ = 𝛌x.ei𝝅 + 1 = 0 & <e,t>Groundhog(x) (T2*) ⟦ [HesperusName [is a woodchuckAdj]VerbPhrase]Sentence⟧ = ⟦ [is a woodchuckAdj]VerbPhrase⟧(⟦HesperusName⟧) = 𝛌x.ei𝝅 + 1 = 0 & <e,t>Groundhog(x)(Phosphorus) = ei𝝅 + 1 = 0 & <e,t>Groundhog(Phosphorus)Unwanted (but equally true) SpecificationsREPRESENTATION MATTERS FOR MEANING...EXTENSIONAL EQUIVALENCE IS NOT SEMANTIC EQUIVALENCE

12. He dropped the book he defaced, and he plagiarized the book you wrote. The red book was too heavy to carry, and the blue one was too hard to read. The book he stole was valuable. The book he reviewed was worthless.A thief knocked on the door and then broke a window. A thief crawled through a window and opened the door. The shuttered window was nicer than the new window that Smith installed. The window that Smith installed looked worse than one she filled. A thief took the jewelry that was in the store window. A thief approached the bank window and handed teller a note.The triangle on the board has thick lines. The proof relies on the fact that the lines have no width. The man with lines in his face was in the line to buy fishing line. Polysemy and Co-predication ⤷ BOOK:VEHICLE ⤷ BOOK:CONTENT Being is said in many ways. Ditto for book, window, line,...WINDOW:HOLEWINDOW:FILLERLINE:PERCEPTIBLELINE:ABSTRACTIONLingua (2015, special issue) --intro to work since 1972 --many interesting papers Mind & Language (2021) --paper by Quilty-Dunn ... …

13. Homophony bæŋk bareA ←br→ bearV ↙ ︎ ↘︎ ↓ bankN$ bankN▼ ︎ bearNone pronunciation, two or more expressions, each with its own meaning--typically arbitrary: you/ewe, die/dye, no/know, so/sew--linguistically accidental cp. French seau/sceau/saut Doesn’t Support Anaphora: *The banks of the river were nicer than the ones we robbed. Polysemy bareA, bearV, bankN$, triangleN, windowN, ... $BANK:INST ⤶ ⤷ $BANK:BLDG one expression, whose meaning supports a family of concepts/subsenses--not arbitrary--often common across languagesholdVSupports Anaphora in many cases: The windows that we cut in the walls were nicer than the ones we installed.my hand, the door, a title, your temper, my calls, so much weight, an opinion, a seminar, a ridge, a course (of due east) bookNBOOK:CONTENT ⤶ ⤷ BOOK:VEHICLE

14. Homophony bæŋk bareA ←br→ bearV ↙ ︎ ↘︎ ↓bankN$ bankN▼ ︎ bearNone pronunciation, two or more lexical items, each with its own meaning Polysemy bareA, bearV, bankN$, doorN, triangleN ... $BANK:INST ⤶ ⤷ $BANK:BLDG one lexical item, whose meaning supports a family of concepts/subsenses bookNBOOK:CONTENT ⤶ ⤷ BOOK:VEHICLEThink about lexical acquisition. Luckily, kids are pretty good at (i) guessing which concepts speakers are expresssing and (ii) confirming/revising their initial guesses; see Gleitman and Trueswell.But if kids adopted a “One Word, One Concept” policy, it would be nightmarishly hard to decide when a new utterance of a word is an utterance of old word. And then homophony would presumably be way more rampant than it is.Polysemy looks like a result of kids treating homophony as a “last resort” strategy, with paradigm cases of polysemy involving concepts that “dovetail.”If kids let lexical items become polysemous, then over time, conceptually equivocal will become the norm.REPRESENTATION MATTERS... but EXTENSIONS?

15. Proper Nouns are also Conceptually EquivocalTextbooks (and classes) in semantics often start by assuming that Proper Nouns (e.g., ‘Aristotle’ and ‘Napoleon’) are atomic terms that designate individuals.But initial assumptions can be false. Theorists don’t get to stipulate that certain nouns are “singular denoters.” Claims about nouns have to be justified. And prima facie, Proper Nouns are a lot like Common Nouns.Napoleon lost at Waterloo. (But cp. Greek, which disallows bare PN subjects.)There were three Napoleons at the party. Two of them were wearing hats. The third one sang.The Napoleon who sang is a good cook. Our Napoleon would never do such a thing. But the Napoleon on the soccer team would.The little Napoleon on the committee must be stopped. DP / \ D Nthe / \ N RCNapoleon who sang DP / \ D Nour Napoleonthatthe ∅No need to posit homophony instead of polysemy.

16. Alleged “Kind Terms” do not have Kinds as ExtensionsIt is often suggested that words like ‘rabbit’ and ‘dog’ and ‘water’ are somehow “drawn to” natural properties—e.g., being a member of certain biological kind, or being a sample of H2O modulo trace impurities—and that these properties determine extensions for the words.One can have various “kind-concepts” --a concept of the Leporids--a concept of the Lagomorphs--a concept of the European Rabbits--a concept of the Cottontail Rabbits--a concept of the local sub-genus of Cottontail Rabbits↑↑A child can have a concept of the sort psychologists (e.g., Keil and Gelman) describe when talking about innate tendencies to “essentialize”Theorists can have other concepts of rabbits—e.g., the Lagomorphs minus the pikas, jackrabbits, and any hares.This suggestion is in tension with the idea, mentioned at the outset,that speakers of English can have very different psychologies.

17. Alleged “Kind Terms” do not have Kinds as ExtensionsIt is often suggested that words like ‘rabbit’ and ‘dog’ and ‘water’ are somehow “drawn to” natural properties—e.g., being a member of certain biological kind, or being a sample of H2O modulo trace impurities—and that these properties determine extensions for the words.But given the biological facts, why think the nouns in ‘a dog chased a rabbit’ have extensions? extensions? Taxonomical distinctions need not correspond to clean genetic distinctions. CANIS ... latrans coyotes lupus familiaris grey domestic wolves dogs↑↑

18. Alleged “Kind Terms” do not have Kinds as ExtensionsIt is often suggested that words like ‘rabbit’ and ‘dog’ and ‘water’ are somehow “drawn to” natural properties—e.g., being a member of certain biological kind, or being a sample of H2O modulo trace impurities—and that these properties determine extensions for the words.But given the biological facts, why think the nouns in ‘a dog chased a rabbit’ have extensions? And ‘water’ is an even worse example. Percentage of H2OClub Soda: 99.9 Coffee: 99.39 Diet soda, not cola: 99.8 Espresso: 97.8Tea: 99.7 Ocean Water: 96.5 Diet Cola: 99.54 Bud Light: 95.0 stuff from my well < 99.4 Distilled vinegar: 94.78 in New Mexico many examples of --very high H2O content--but not watermany examples of --lower H2O content--and yet waterSo why insist that Putnam’s imagined substance, XYZ, couldn’t be described as water?

19. rabbits √rabbit +CT +PL Maybe we can specify the content of a certain “mass concept” of rabbit in terms of a primitive “count concept” that applies to countable rabbits, andsomething like a Lewisian “universal grinder” (cp. Russell, Cartwright, Pelletier, Link, Chierchia, … )But presumably, the “uncount nouns” √rabbit and √tofu have meanings of the same kind.Moreover, these meanings allow for errors: a child might encounter rabbit (fish, chicken, ...) on a plate and think it grows out of the ground; or someone might think that tofu comes from free-range tofus.So even if we temporarily waive concerns about whether “count nouns” have extensions, what’s the general story for nouns without the +CT feature?And maybe we can specify the content of a certain “count concept” of tofus in terms of a primitive “mass concept” that applies to samples of tofusome kind of “unitizer” that lets us think about countable units of tofu tofus√tofu +CT +PL“Root Nouns” can also be conceptually equivocal

20. anxiety nature business oppression color philosophydemocracy religionenergy sciencefate sinceritygusto skyhistory spaceintelligence timejudgment utilitylanguage vigorlife visionmoney weathermorality wisdommusic witThe Extension Dogma:meanings determine extensionsconcept, conceptionmeaning, meaningslanguage, languages

21. Accommodating Conceptual Equivocality isn’t HardInstead of assuming that expressions have extensions, think of expressions as instructions (or recipes) for how to access and assemble conceptsInstead of assuming that a theory of meaning specifies extensions for complex expressions in terms of extensions for constituent expressions, allow for theories that specify how complex expressions can be used to build concepts from polysemous constituents saw a linguist open a windowsaw a linguist v open a window 21don’t insist that the larger phrase is true of processes that(i) were done by something in the extension of ‘linguist’, and (ii) ended with events in the extension of ‘open a window’don’t insist that ‘open a window’ is true of events of opening in which the thing opened is in the extension of ‘window’Why think that ‘window’, ‘open’ , and ‘linguist’ have extensions?

22. Accommodating Conceptual Equivocality isn’t HardInstead of assuming that expressions have extensions, think of expressions as instructions (or recipes) for how to access and assemble conceptsInstead of assuming that a theory of meaning specifies extensions for complex expressions in terms of extensions for constituent expressions, allow for theories that specify how complex expressions can be used to build concepts from polysemous constituents saw a linguist open a windowsaw a linguist v open a window build a concept of the form: ∃[OPENING-OF(_ , _)^WINDOW(_)]select a concept from the ‘window’-familyselect a concept from the ‘open’-familyselect from the ‘linguist’-familybuild a concept of the form: ∃[AGENT(_, _)^LINGUIST(_)]^∃[ENDED-WITH(_, _)^OPEN-WINDOW(_)]|________________|____________||__________|___________||________________|_________________|The Extension Dogma is notthe only game in town.

23. The Extension Dogma (for Human Linguistic Meanings)There are endlessly many meaningful expressions, even for a single language like spoken English. But it’s not obvious that there are meanings that these expressions have. Symbols can have extensions without having meanings (or “intensions” or “senses”) that determine the extensions. So when offering theories of meaning, we should grant that linguistic expressions have extensions, but not assume that these expressions have meanings in any further sense.BEWARE THIS TROJAN HORSEIf we want to describe human languages and explain the natural phenomena of linguistic understanding we shouldn’t grant that the relevant expressions have extensionswe should assume that these expressions have meanings, much as they have pronunciationswe shouldn’t assume that meanings determine extensionsand we should remember that early advocates of The Dogma were talking about “ideal” languages For those who prefer Monty Python to Homer… jettison The Trojan Rabbit

24. The Extension Dogma (for Human Linguistic Meanings)There are endlessly many meaningful expressions, even for a single language like spoken English. But it’s not obvious that there are meanings that these expressions have. Symbols can have extensions without having meanings (or “intensions” or “senses”) that determine the extensions. So when offering theories of meaning, we should grant that linguistic expressions have extensions, but not assume that these expressions have meanings in any further sense.BEWARE THIS TROJAN HORSEIf we want to describe human languages and explain the natural phenomena of linguistic understanding we shouldn’t grant that the relevant expressions have extensionswe should assume that these expressions have meanings, much as they have pronunciationswe shouldn’t assume that meanings determine extensionsand we should remember that early advocates of The Dogma were talking about “ideal” languageswe can and should deny that human linguistic expressions have extensionsThanks, and thanks to the organizers!

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26. 26WORLDTHOUGHTLANGUAGEWORLDTHOUGHTLANGUAGEidealnatural ???Traditional PictureMuch of 20th Century Analytic Philosophy

27. Terminological Nightmare intention, intentional, intentionality intension, intensional, intensionality mental aims/targets contrast with extension(al(ity)) “aboutness” of thought failures of substitutivity…“opacity”Brentano, Meinong, Frege, Husserl,Russell, Evans, Sainsbury, Rey, …Fodor, Dretske, Millikan, …concerned with concepts—“composable ideas” we use to “think about things” in various ways—often with special attention to: concepts like ghost, unicorn, Pegasus, … that apply to nothingconcept pairs like Hesperus/Phosphorus and woodchuck/groundhog…used to think about the same things in different waysintensions as ways of “presenting” extensionsintensions as functions-in-extensionthat map each possible state, s, of the universe to a (perhaps empty) set of things that “exist at s”Frege, Church, Carnap, Quine/Goodman (as critics), Marcus, Kripke, Hintikka, Lewis, Montague, Tichy… --Frege’s Sinnen--Husserl’s Noema (?)--Church’s procedures or functions-in-intension𝛌x.|x−1| ≠ 𝛌x. nat√(x2−2x +1)--differ in kind from functions-in-extension𝛌x.|x−1| = 𝛌x. nat√(x2−2x +1)--Lewis’ word values--sets that have special elements

28. intensions as ways of “presenting” extensionsintensions as functions-in-extensionthat map each possible state, s, of the universe to a (perhaps empty) set of things that “exist at s”--Frege’s Sinnen--Husserl’s Noema (?)--Church’s procedures or functions-in-intension𝛌x.|x−1| ≠ 𝛌x. nat√(x2−2x +1)--differ in kind from functions-in-extension𝛌x.|x−1| = 𝛌x. nat√(x2−2x +1)--Lewis’ word values--sets that have special elementsTerminological NightmareThe Extension Dogma (for Human Linguistic Meanings)highlights the question of whether or notlinguistic expressions have meanings in the traditional sense of having semantic properties that “present” the things we talk about in certain ways;where “talk about” is understood in anintenTional sense that allows for talk about ghosts and unicorns, and for talkIng about ghosts on Hesperus without thereby talking about unicorns on Phosphorus.

29. intensions as ways of “presenting” extensionsintensions as functions-in-extensionthat map each possible state, s, of the universe to a (perhaps empty) set of things that “exist at s”--Frege’s Sinnen--Husserl’s Noema (?)--Church’s procedures or functions-in-intension𝛌x.|x−1| ≠ 𝛌x. nat√(x2−2x +1)--differ in kind from functions-in-extension𝛌x.|x−1| = 𝛌x. nat√(x2−2x +1)--Lewis’ word values--sets that have special elementsTerminological NightmareThe Extension Dogma (for Human Linguistic Meanings)highlights the question of whether or notlinguistic expressions have meanings in the traditional sense of having semantic properties that “present” the things we talk about in certain ways.But it highlights this question by presupposing that meaningful expressions have extensions…and inviting us to askwhether we should also assume thatthese extensions are determined by furthersemantic properties (e.g., Sinnen).The Dogma is, however, compatible with many views about the alleged extensions. In particular, it is compatible with saying that the “semantic value” of a word (e.g., ‘rabbit’) is a Lewis-style function (in extension) that maps each possible world, w, to a set of things that “exist at w”.

30. intensions as ways of “presenting” extensionsintensions as functions-in-extensionthat map each possible state, s, of the universe to a (perhaps empty) set of things that “exist at s”--Frege’s Sinnen--Husserl’s Noema (?)--Church’s procedures or functions-in-intension𝛌x.|x−1| ≠ 𝛌x. nat√(x2−2x +1)--differ in kind from functions-in-extension𝛌x.|x−1| = 𝛌x. nat√(x2−2x +1)--Lewis’ word values--sets that have special elementsTerminological NightmareThe Extension Dogma (for Human Linguistic Meanings)highlights the question of whether or notlinguistic expressions have meanings in the traditional sense of having semantic properties that “present” the things we talk about in certain ways.But it highlights this question by presupposing that meaningful expressions have extensions…and inviting us to askwhether we should also assume thatthese extensions are determined by furthersemantic properties (e.g., Fregean senses).I agree that a lexical item L does not “present” the things we talk about (with L) in any particular way, except in a very boring sense: uses of L will be associated with concepts we can express with L; and concepts have contents that we can describe as “senses.”But we need to abandon the myth of “One Word, One Concept.”