Compositionality and Ontological Commitmenttezimmer/HP_FG-RelS/PDF/Turin.pdf · Compositionality and Ontological Commitment Thomas Ede Zimmermann, Goethe University, Frankfurt SPE

Compositionality and

Ontological Commitment

Thomas Ede Zimmermann, Goethe University, FrankfurtSPE 5, University of Turin, July 25-27, 2012

Mittwoch, 11. Juli 12

0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro


0. Intro1. Compositionality of semantic values2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro



To be is to be the value of a (bound) variable.



To be is to be the value of a (bound) variable.Quine (1961)




Ontological overkill:





Every man loves a woman.






Non-compositional analysis (formalisation)






(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]







(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]







(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]


ranging over…






(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]


ranging over…individuals






(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]


Compositional analysis (indirect interpretation)







(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]


(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))








(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]










(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]





sets of individuals



To be is to be the value of a (bound) variable.



(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]





sets of individuals





(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]





sets of individuals

To be is to be the referent of a term.




Every man seeks a woman.

(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]






sets of individuals








denoting …set of worlds (proposition)

(∀x) [M(x) →⊡x (∃y) [W(y) & L(x,y)]]


sets of individuals






(λY. λX. Y ⊆ X)(M)(λx. S(x,^(λY. λX. Y ⩙ X)(W)))


denoting …set of worlds (proposition)

(∀x) [M(x) →⊡x (∃y) [W(y) & L(x,y)]]


function from worlds to sets of sets of individuals


0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro




0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro





START



START

EXPRESSIONS


0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS

START


0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS have

semantic values〈X〉,《X》,…

START



semantic values〈X〉,《X》,…corresponding to their (communicative,…) functions: reference (potential), informational content,…

START




Some

externalcorresponding to their (communicative,…) functions: reference (potential), informational content,…

START




Some


START

GOAL




Some


START

GOAL

EXPRESSIONSsemantic values〈X〉,《X》,…

All

external (or internal)

corresponding to (the contributions they make to) the functions of expressions in which they occur

have




Some


START

GOAL


All



have


0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro

GOAL


All



have



*

* that are compositional:

GOAL


All



have



*


GOAL


All



have



*


GOAL


All



have



*


GOAL


All



have



*


GOAL


All



have



=

*


GOAL


All



have



=

*


GOAL


All



have











1st approach



1st approach Frege (1892)




START




START

EXPRESSIONS havesemantic values〈X〉,《X》,…

corresponding to their (communicative,…) functions: reference (potential), informational content,…

external




START



external




START



external

with

REFERENTIAL




START

EXPRESSIONS get their referents as

semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference

external

with

REFERENTIAL




START



external

with

REFERENTIAL




START



external

with

REFERENTIAL

=




START



external

with

REFERENTIAL

= Elvis




START



external

with

REFERENTIAL

= Elvis




START



external

with

REFERENTIAL

= Elvis

+ (somewhat mysteriously)Mittwoch, 11. Juli 12



START



external

with

REFERENTIAL




START



external

with

REFERENTIAL

= 1



2nd approach Carnap (1947)

START

corresponding to their (multiple reference: reference

external

withwith

PREDICATES get their satisfiers as

semantic values〈P〉,《X》,…

…

TERMS (= Names + Descriptions): as before




START


external

withwith



〈is dead〉

…





START


external

withwith



= {(x)| x is dead}〈is dead〉

…





START


external

withwith



= {(x)| x is dead}〈is dead〉〈is watching〉

…





START


external

withwith



= {(x)| x is dead}〈is dead〉= {(x,y)| x is watching y}〈is watching〉

…





START


external

withwith



= {(x)| x is dead}〈is dead〉= {(x,y)| x is watching y}〈is watching〉

〈is showing〉…





START


external

withwith



= {(x)| x is dead}〈is dead〉= {(x,y)| x is watching y}〈is watching〉= {(x,y,z)| x is showing y to z}〈is showing〉

…





START


external

withwith




valency

123… …





START


external

withwith




=valency

123… …





START


external

withwith




=valency

123… …

-arity

123…





START


external

withwith




=valency

123… …

-arity

123…

〈Elvis is dead〉





START


external

withwith




=valency

123… …

-arity

123…

〈Elvis is dead〉0





START


external

withwith




=valency

123… …

-arity

123…

〈Elvis is dead〉 00





START


external

withwith




=valency

123… …

-arity

123…

= {( )| Elvis is dead}〈Elvis is dead〉 00




withwith

Comparison



withwith

Comparison

NamesDescriptions

Nouns

Verbs

SentencesDeterminers…



withwith

Comparison

CarnapFrege

NamesDescriptions

Nouns

Verbs




withwith

Comparison

CarnapFrege

NamesDescriptions

Nouns

Verbs


individuals

–relations

individuals

sets

individuals

individuals

–

truth values truth values– –

– –










0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroGOAL


All



have


0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroGOAL

EXPRESSIONSextensions〈X〉

All

external or internalcorresponding to the contributions they make to the external extensions of expressions in which they occur

have




0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method


0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)



Cofinality assumptionEvery expression occurs in some sentence.

Frege (1891)




Hodges (2001)

Frege (1891)




Hodges (2001)

StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:

• + is completed by X

Frege (1891)




Hodges (2001)



Frege (1891)

cf. Zimmermann (2011; 2012) for details




Hodges (2001)



Frege (1891)

… i.e.: all values〈Xi + Yj〉and 〈 Yj〉have already been

determined (externally, by previous applications of the standard method, or otherwise).





Hodges (2001)



Frege (1891)

• + is compositional in X





Hodges (2001)



Frege (1891)


… i.e.: whenever〈Yj〉=〈 Yk〉, then:

〈Xi + Yj〉= 〈Xi + Yk〉.





Hodges (2001)



Frege (1891)

• + is compositional in X• + is representative for X





Hodges (2001)



Frege (1891)


… i.e.: whenever〈Xi + Yk〉= 〈Xj + Yk〉, for all Yk, then:

〈Z[Xi] = Z[Xi]〉, for all Z[_] already evaluated.

• + is representative for X





Hodges (2001)




Frege (1891)





Hodges (2001)




Frege (1891)


Construction of 〈Xi〉




Hodges (2001)




Frege (1891)


Construction of 〈Xi〉〈Xi〉:= λ〈Yj〉.〈Xi + Yj〉




Hodges (2001)




Frege (1891)


Construction of 〈Xi〉〈Xi〉:= λ〈Yj〉.〈Xi + Yj〉 … and ⊕ is functional application.





Example 1 (based on 1st approach to external extensions)




〈 is dead〉= λ〈NP〉.〈NP + is dead〉





(characteristic function of) set of individuals








〈 is dead〉= λ〈NP〉.〈NP + is dead〉≅ external extension according to 2nd approach





Example 2 (applicable after Ex. 1 according to 1st approach and immediately according to 2nd approach)






〈 everybody〉= λ〈VP〉.〈everybody + VP〉






〈 everybody〉= λ〈VP〉.〈everybody + VP〉

bound set variable!Mittwoch, 11. Juli 12

0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro4 problems with standard method of constructing extensions



Problem 1: Indeterminacy




Extensions (and other values) depend on choice of +.





However, the resulting value assignments (after completion) will always be isomorphic.





However, the resulting value assignments (after completion) will always be isomorphic. Hodges (2001)





However, the resulting value assignments (after completion) will always be isomorphic.

Isomorphic theories should be declared notational variants of one another – provided they agree on the external extensions (and their ‘interpretation’).

Zimmermann (forthcoming)Solution:

Hodges (2001)



Problem 2: Laziness



Problem 2: Laziness Internal extensions (and other values!) may still be in need of specification.




E.g., it is not obvious from




〈 everybody〉= λ〈VP〉.〈everybody + VP〉E.g., it is not obvious from





that〈 everybody〉characterizes the supersets of

〈 person〉.





that〈 everybody〉characterizes the supersets of

〈 person〉.Solution: Background theory for characterizations of functional values.



Problem 3: Overdetermination



Problem 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.




Example




Example

〈 V + everybody〉=




Example

〈 V + everybody〉= ???




Example Heim & Kratzer (1998)





Solution: No principled compositionality problems can arise (due to representativity of +); however standards for specifying (functional) values are needed.








〈 V + everybody〉=






〈 V + everybody〉= (λx.〈everybody〉(λy.〈V〉(y)(x))



Problem 4: No suitable + exists




Standard example




Standard example Frege (1892)




Standard example Frege (1892)

〈 V + S〉≠ 〈 V〉⊕ 〈 S〉

Attitude verbs V; e.g. no ⊕ can satisfy:

because + is not compositional in V.










0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroSolution strategy (for Problem 4): Local repair



Frege (1892)



Frege (1892)

If + is not compositional in X, find alternative values《Y》and put:



Frege (1892)

〈Xi〉:= λ《 Yj》.〈Xi + Yj〉




Frege (1892)

〈Xi〉:= λ《 Yj》.〈Xi + Yj〉


Attitude reports:

〈believe〉:= λ《 Sj》.〈believe + Sj〉

… where (e.g.) 《S》is the intension of S




0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroExternal intensions


0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro Carnap (1947), inspired by Wittgenstein (1922)External intensions



Identify informational content with sets of possible worlds (‘regions in Logical Space’), thereby obtaining intensions of (declarative sentences).




Observation




Observation(!)《S》≅ λw. 〈S〉w




Observation(!)《S》≅ λw. 〈S〉w

Internal intensions Carnap (1947)

where 〈S〉w is the extension of S according to w.

Generalize (!) from S to arbitrary expressions.




0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroIntensional compositionality



It is generally assumed that:《 X + Y》=《 X》⊕《 Y》for any construction +




e.g. Kaplan (1989), pace Montague (1970)





Fregean compositionality implies, but is not implied by, intensional compositionality.

Remark






Remark Sternefeld & Zimmermann (forthcoming)



Fregean Laziness







Fregean Laziness

Laziness is particularly popular when it comes to applying Fregean compositionality.







Fregean Laziness

Laziness is particularly popular when it comes to applying Fregean compositionality.





Zimmermann (1999), Larson (2002),…







Fregean Laziness

Laziness is particularly popular when it comes to applying Fregean compositionality. Zimmermann (1999), Larson (2002),…


0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroFregean Laziness

Laziness is particularly popular when it comes to applying Fregean compositionality. Zimmermann (1999), Larson (2002),…

HoweverRelational analyses of referentially opaque transitive verbs are not the result of Fregean Laziness.The compositional analysis


(∀x) [M(x) →⊡x (∃y) [W(y) & L(x,y)]]

ofcan be obtained from the non-compositional modal paraphrase:

by the standard method of constructing extensions.

(λY. λX. Y ⊆ X)(M)(λx. S(x,^(λY. λX. Y ⩙ X)(W)))











Thank you for your attention!


ReferencesCarnap, Rudolf: Meaning and Necessity. Chicago/London 1947.

Frege, Gottlob: Function und Begriff. Jena 1891.

Frege, Gottlob: ‘Über Sinn und Bedeutung’. Zeitschrift für Philosophie und philosophische Kritik NF 100 (1892), 25–50.

Heim, Irene; Kratzer, Angelika: Semantics in Generative Grammar. Oxford 1998.

Hodges, Wilfrid: ‘Formal Features of Compositionality’. Journal of Logic, Language and Information 10 (2001), 7–28.

Kaplan, David: ‘Demonstratives. An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and Other Indexicals’. In: J. Almog et al. (eds.), Themes from Kaplan. Oxford 1989. 481–563.

Larson, Richard: ‘The Grammar of Intensionality’. In: G. Preyer & G. Peter (eds.), Logical Form and Language Oxford 2002.

Montague, Richard: ‘Universal Grammar’. Theoria 36 (1970), 373-398.

Quine, Willard Van Orman: ‘Quantifiers and Propositional Attitudes’. Journal of Philosophy 53 (1956), 177–187.

–: ‘On what there is’. In: W. V. O. Quine, From a Logical Point of View. New York 1961. 1–19.

Sternefeld, Wolfgang; Zimmermann, Thomas Ede: Semantics. A Gentle Introducion to Compositional Meaning. Berlin, forthcoming.

Wittgenstein, Ludwig: Tractatus logico-philosophicus. Logisch-philosophische Abhandlung. London 1933.

Zimmermann, Thomas Ede: ‘Meaning Postulates and the Model-Theoretic Approach to Natural Language Semantics’. Linguistics and Philosophy 22 (1999), 529–561.

–: ‘Model-theoretic semantics’. In: C. Maienborn et al. (eds.), Semantics. An International Handbook of Natural Language Meaning. Berlin 2011. 762-801.

–: ‘Equivalence of Semantic Theories’. In: R. Schantz (ed.), Prospects for Meaning. Berlin, forthcoming.


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Compositionality and Ontological Commitmenttezimmer/HP_FG-RelS/PDF/Turin.pdf · Compositionality and Ontological Commitment Thomas Ede Zimmermann, Goethe University, Frankfurt SPE