Natural Language Semantics for Musicologists

1. Lecture series Language & Music National and Kapodistrian University of Athens June 12, 2019 Natural Language Semantics for Musicologists Winfried Lechner National and Kapodistrian University of Athens

2. Overview • Language vs. Music • Modality, Form meaning mismatches • Denotation and Reference • Extension and Intensions • Concepts • Some consequences for music • Entailment • Quotation

3. Language faculty vs. Music 1MarinMersenne (1588-1648): HarmonieUniverselle. 2Lerdahl, Fred and Ray Jackendoff. 1983. A Generative Theory of Tonal Music. Cambridge MA: MIT Press.

4. Modality and Duality Modality. Language is a mind internal system that can be externalized without loss by different modalities. • Acoustic: spoken language • Visually: sign language Duality of Patterning. Primitives serve two functions. ”Duality of patterning (Hockett, 1960) is the property of human language that enables combinatorial structure on two distinct levels: meaningless sounds can be combined into meaningful morphemes and words, which themselves could be combined further.” de Boer, B., Sandler, W., & Kirby, S. (2012). New perspectives on duality of patterning: Introduction to the special issue. Language and Cognition, 4(4).

5. Form-Meaning Mismatches Ambiguity. One form, more than one meaning • Show me the bat. • Mary spotted the thief with the binoculars. • John saw her duck. • Sally invited one linguist to every party. Ellipsis. Meaning without form. • John saw her duck, and Bill did, too. Expletives. Form without meaning • a. That John won is obvious. • b. It is obvious that John won.

6. Denotation Denotation. For any expression α, the denotation of α (symbolic: α)isthe semantic value of α. Semantic competence.The ability of competent speakers of a language L to assign a denotation to every syntactically well-formed expression of L. • Heinrich Ignaz Franz Biber’s son was the supervisor of Wolfgang Amadé Mozart’s father. Three foundational questions • Q1. What is the denotation of the larges units (sentences)? • Q2. What are the meanings of its smallest parts? • Q3. How are the parts combined to form complex meanings?

7. Reference Reference. The relation which obtains between a natural language expression and an individual in the world. Examples for expressionswithreference: • Vladimir Putin • the president of the USA • this book over there The referent can be abstract! • (4) the sentence/thought you just produced Examples for expressions withoutreference: • Santa Clause, Leonard Bloom, Batman, … (if evaluated in reality) • the largest prime number • no book/every book • runVerb, tallAdjective, underPreposition, …

8. Reference ≠ Denotation I Sign.Arbitrary relation between form and meaning Charles Sanders Peirce (1839-1914) Ferdinand de Saussure (1857-1913) Arbitrary≠ random! Arbitrary relations are systematic but not grounded. Example for random mapping from form to meaning: For Mary, June 1, 9am, in Athens: tree = δέντρο For Mary, June 1, 10am, in Athens: tree = σκύλος For John, June 1, 9am, in Athens: tree = 3,1415....

9. Reference ≠ Denotation II Common misconception. Words/signs relate mind internal representations (concepts) to reality. Language links the mind and objects in the world. Denotation = Reference Problem 1. Expressions without reference. Problem 2. Even with arguable referential expressions (names), the relation between meaning and world is indirect. more complex.

10. Double Vision I < • Bill will win (the election). • Bill will not win. • Mary thinks that Bill will win. • Mary thinks that Bill will notwin. ‘Double vision’ scenario verifying (3) and (4).Mary is professionally acquainted with Bill, a promising candidate for the general elections, and is convinced that he will win. In the evening before the election, Mary joins a group of friends at a bar and they watch an interview with Bill on TV. Being drunk, Mary does not recognize Bill. Moreover, Mary does not like Bill’s performance and believes that that guy on TV will loose. (original observation due to Quine, Willard van Orman. 1956. Quantifiers and propositional attitudes. Journal of Philosophy53:177–187.) Contradiction (can’t be both true) No contradiction (can be both true)

11. Double Vision II: analysis There is a concept of Bill for Mary, such that Mary thinks that Bill will win under that concept. There is a concept of Bill for Mary, such that Mary thinks that Bill will not win under that concept. The name Bill is ambiguous and denotes one of two concepts: • Billlive = the person Mary is acquainted with in real life • BillTV = the person Mary saw on TV • Mary thinks that Billlive will win. true • Mary thinks that BillTV will not win. true Semantic competence consists in the ability to acquire, compute and combine concepts.

12. Theory of Mind • (1) Mary thinks that Billwill win. • (1)  The speaker’s representation of • Mary’s belief that Bill will win. Theory of mind (ToM). The ability to reconstruct somebody else‘s mental representations. ToM is instrumental for social interaction, i.a. planning, collaborative action, detecting lies,... ToM and language. On some accounts, ToM is dependent upon the acquisition of the semantics of think/believe-predicates. Musical ToM? The ability to reconstruct somebody else‘s musical representations (harmony, rhythm, melody). Corollaries • ToM is not necessarily language dependent • Concepts can be complex, can be reconstructed and inferred. • Hence, concepts are compositional.

13. Extension and intension Each sign has two dimensions of meaning (Rudolf Carnap) • Extension: meaning at a particular context (time/place) • Intension: time/space independent meaning (≈ concept). Extension = Intension + Context

14. Concepts as definitions Concepts as definitions. Manifestations of a concept meet all the necessary and sufficient conditions for that concept. Example: Bachelor =def Unmarried + Man Problem 1. How to define ‘necessary’ and ‘sufficient’? Example: Table=deffour legs and a plane surface (Fodor 1981) but and Problem 2. Even closely related concepts have different satisfaction conditions. • Necessary conditions for healthy: ‘healthy in every respect’ • Necessary conditions for Sick: ‘not healthy in some respect’

15. Concepts as protoypes Concepts as prototypes. Manifestations of the same concept are more similar than manifestation of different concept. Problem 1. Compositionality:Pet fish is neither typical pet nor fish. Problem 2. How to quantify ‘similarity’? Observation.In general, similarity is context dependent. • (Regarding weight,) an elephant is similar to a car. • (Regarding color,) an elephant is similar to a flea. Which two individuals of A, B and C fall under the concept bird?

16. Statistical concepts Concepts as averages. Manifestations of the same concept are bound together by being above statistical average. Problem. How to define ‘average’? Scenario. 2.5 is the threshold for positive health test. Dan excels in two of categories, but fails in the third one. Sam consistently scores low, but above average in all three tests. Question. Who is healthier, Dan or Sam? • Predicted: Dan • Average health Dan: (5+5+2)/3 = 4 • Average health Sam: (3+3+3)/3 = 3 • Experimentally • confirmed intuitions: Sam • (From Sasson, Galit. 2013. A typology of multidimensional adjectives. Journal of Semantics 30: 335-380.)

17. Concepts: Innateness & universality Nativism vs. Empiricism. Are concepts innate or learned? Pro nativism • There is no good theory of concept acquisition • Some basic concepts cannot be learned (Fodor; see table) • Perception and reasoning presupposes Kantian categories • Non-human specific concepts (location, food quality,…) • Mental computations require representations Contra nativism • Human made concepts (phone, tone row, atomic weight) • There are cultural dependent concepts (Hell, democracy,…) • Some concepts are processed more effectively than others

18. Consequences for music I Language • Lexicon: list of atomic signs (form -- meaning correspondences) • Each form is assigned a syntactic category (noun, verb, adjective,…) • Rules are category sensitive. • a. S  NP VP • b. John slept = The individual Bill is a member of the sleepers. • a. *S  AP VP (not attested in any language) • b. *Tired slept = The tired individual is a member of the sleepers. • Conclusion. Rules  categories Music Claim (Katz & Pesetsky 2009). There are no form-meaning pairs (signs) in music, hence music has no lexicon. Corollary 1. Provided that categories are lexically determined, there are no categories in music. No categories  no heads

19. Consequences for music II Claim (Katz & Pesetsky 2009). No lexicon in music. Corollary 2. No categories  no heads  no endocentric structure Conclusion. No categories & no structure  no rules in music • But: Categories might not emerge from signs/semantic properties. Semantic grounding of categories?Are there semantic invariants for syntactic categories (noun, verb, adjective,…)? •  Nouns denote things/objects (prime number, Batman) •  Verbs denote actions (to know, to exist) • Adjectives denote properties (also true of verbs and nouns). Consequence 1.There is no reason to deny music a lexicon – it’s just not made up of Saussurian signs, but of notes and chords. Consequence 2. Music might be better amenable to Categorial Grammar, a system where syntactic and semantic rules operate in tandem (see e.g. Granroth-Wilding & Stedman 2017).

20. Categorial grammar Categorial Grammar (Richard Montague, Mark Steedman, Anna Szabolcsi, i.a.) • Syntactic & semantic rules are in the lexicon • All dependencies are local • Lexicon, not independent rules, drives the derivation • Lexion • (1) ‘sleep’ is of category NPS • (sign that combines with an NP and creates sentence) • (2) ‘John’ is of category NP Music.Harmonicchordprogressioncanbemodeled in categorialframwork(s.a. Granroth-Wilding & Steedman 2017). • (3) IV – V – I • (4) ‘IV‘ is of category VI • (chord that combines with dominant and results in tonic)

21. Entailments I Inferences. Language triggers different types of inferences. Logical entailment. A entails B if B cannot be false if A is true. (1) Sally likes animals.  Sally likes fish. Presupposition. Information that is taken for granted by speaker. (2) Mary forgot that it is John’s birthday today.  It is John’s birthday today. Implicature. Information that follows from an utterance without being logically entailed; can be cancelled. (3) John has three children.  John has not mor he e than three children. (4) If John has three children, is eligible for tax reduction. not:  John has not more than three children.

22. Entailments II Cancellability. Implicatures can be cancelled, entailments can’t. Logical entailment. A entails B if B cannot be false if A is true. (1) Sally likes animals (2) Sally does not like fish. (Contradiction) Implicature Context. Citizens with three children are eligible for tax reduction. (4) John has three children. So he can apply for tax reduction. (5) Actually, John has even four children. (No contradiction) Music.Are inferences e.g. about chord or rhythmic progression entailments, implicatures or presuppositions? Do they reflect properties of the system (entailment) and/or properties of “information exchange” (communication)?

23. Quotation Direct quotation • ‘Aristotle’ refersto Aristotle. • Quinesaid, ‘Quotations are interesting’. • (1)  The string ‘Aristotle’ refers to Aristotle. Mixed quotation • (3) Alice said that life "is difficult to understand.” • (3)  Alice said that life is difficult to understand and • she used the words "is difficult to understand.” • Quasi quotation. Read corner quotes ⌜n+1⌝ as „concatenate value of n with ‘+‘ and with value of 1“ • (4) If n is a natural number, then ⌜n+1⌝ is a natural number. • (5) If 2 is a natural number, then 2+1 is a natural number. • If 3 is a natural number, then 3+1 is a natural number. • Music. Citation of motives is almost never direct or mixed quotation.

24. Conclusions Natural language meaning is not based on reference. Semantic competence consists in the ability to acquire and compute intensions/concepts. Intensions/concepts are probably the basis of the Theory of Mind. There is no good theory of concepts. Formal semantics provides a precise characterization of concepts. [not discussed here] Linguistics also affords insights into core properties of phenomena relevant for the study of concepts such as vagueness, indeterminacy, gradability, and genericity. The absence of signs does not entail that music lacks a lexicon. Linguistic inferences fall into different classes. Why are there so many musicians, but so few poets or writers, who are interested in scientific (mathematical, logical, acoustic, neurological) properties of their subject matter?