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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
Mittwoch, 11. Juli 12
0. Intro1. Compositionality of semantic values2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
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.
Mittwoch, 11. Juli 12
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.Quine (1961)
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
Non-compositional analysis (formalisation)
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
ranging over…
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
ranging over…individuals
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
Compositional analysis (indirect interpretation)
ranging over…individuals
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))
Compositional analysis (indirect interpretation)
ranging over…individuals
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))
Compositional analysis (indirect interpretation)
ranging over…individuals
Mittwoch, 11. Juli 12
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.Quine (1961)
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))
Compositional analysis (indirect interpretation)
ranging over…individuals
sets of individuals
Mittwoch, 11. Juli 12
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.
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))
Compositional analysis (indirect interpretation)
ranging over…individuals
sets of individuals
Mittwoch, 11. Juli 12
0. Intro1. Compositionality of semantic values2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
Ontological overkill:
Every man loves a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))
Compositional analysis (indirect interpretation)
ranging over…individuals
sets of individuals
To be is to be the referent of a term.
Mittwoch, 11. Juli 12
0. Intro1. Compositionality of semantic values2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
Ontological overkill:
Every man seeks a woman.
(∀x) [M(x) → (∃y) [W(y) & L(x,y)]]
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))
Compositional analysis (indirect interpretation)
ranging over…individuals
To be is to be the referent of a term.
sets of individuals
Mittwoch, 11. Juli 12
0. Intro1. Compositionality of semantic values2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
Ontological overkill:
Every man seeks a woman.
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. (λY. λX. Y ⩙ X) (W) ({y| xLy}))
Compositional analysis (indirect interpretation)
denoting …set of worlds (proposition)
(∀x) [M(x) →⊡x (∃y) [W(y) & L(x,y)]]
To be is to be the referent of a term.
sets of individuals
Mittwoch, 11. Juli 12
0. Intro1. Compositionality of semantic values2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
Ontological overkill:
Every man seeks a woman.
Non-compositional analysis (formalisation)
(λY. λX. Y ⊆ X)(M)(λx. S(x,^(λY. λX. Y ⩙ X)(W)))
Compositional analysis (indirect interpretation)
denoting …set of worlds (proposition)
(∀x) [M(x) →⊡x (∃y) [W(y) & L(x,y)]]
To be is to be the referent of a term.
function from worlds to sets of sets of individuals
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
START
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fregean compositionality5. Outro
START
EXPRESSIONS
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS
START
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS have
semantic values〈X〉,《X》,…
START
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS have
semantic values〈X〉,《X》,…corresponding to their (communicative,…) functions: reference (potential), informational content,…
START
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS have
semantic values〈X〉,《X》,…
Some
externalcorresponding to their (communicative,…) functions: reference (potential), informational content,…
START
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS have
semantic values〈X〉,《X》,…
Some
externalcorresponding to their (communicative,…) functions: reference (potential), informational content,…
START
GOAL
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS have
semantic values〈X〉,《X》,…
Some
externalcorresponding to their (communicative,…) functions: reference (potential), informational content,…
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. OutroEXPRESSIONS have
semantic values〈X〉,《X》,…
Some
externalcorresponding to their (communicative,…) functions: reference (potential), informational content,…
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
*
* that are compositional:
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
*
* that are compositional:
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
*
* that are compositional:
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
*
* that are compositional:
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
*
* that are compositional:
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
=
*
* that are compositional:
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. Given extensions3. Constructed extensions4. Intensions and Fr compositionality5. Outro
=
*
* that are compositional:
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS havesemantic values〈X〉,《X》,…
corresponding to their (communicative,…) functions: reference (potential), informational content,…
external
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS havesemantic values〈X〉,《X》,…
corresponding to their (communicative,…) functions: reference (potential), informational content,…
external
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS havesemantic values〈X〉,《X》,…
corresponding to their (communicative,…) functions: reference (potential), informational content,…
external
with
REFERENTIAL
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
=
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
= Elvis
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
= Elvis
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
= Elvis
+ (somewhat mysteriously)Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
1st approach Frege (1892)
START
EXPRESSIONS get their referents as
semantic values〈X〉,《X》,…corresponding to their (referential) functions: reference
external
with
REFERENTIAL
= 1
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
〈is dead〉
…
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(x)| x is dead}〈is dead〉
…
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(x)| x is dead}〈is dead〉〈is watching〉
…
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(x)| x is dead}〈is dead〉= {(x,y)| x is watching y}〈is watching〉
…
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(x)| x is dead}〈is dead〉= {(x,y)| x is watching y}〈is watching〉
〈is showing〉…
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
…
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
valency
123… …
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
=valency
123… …
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
=valency
123… …
-arity
123…
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
=valency
123… …
-arity
123…
〈Elvis is dead〉
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
=valency
123… …
-arity
123…
〈Elvis is dead〉0
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
=valency
123… …
-arity
123…
〈Elvis is dead〉 00
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
2nd approach Carnap (1947)
START
corresponding to their (multiple reference: reference
external
withwith
PREDICATES get their satisfiers as
semantic values〈P〉,《X》,…
= {(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〉
=valency
123… …
-arity
123…
= {( )| Elvis is dead}〈Elvis is dead〉 00
TERMS (= Names + Descriptions): as before
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
withwith
Comparison
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
withwith
Comparison
NamesDescriptions
Nouns
Verbs
SentencesDeterminers…
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
withwith
Comparison
CarnapFrege
NamesDescriptions
Nouns
Verbs
SentencesDeterminers…
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
withwith
Comparison
CarnapFrege
NamesDescriptions
Nouns
Verbs
SentencesDeterminers…
individuals
–relations
individuals
sets
individuals
individuals
–
truth values truth values– –
– –
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroGOAL
EXPRESSIONSsemantic values〈X〉,《X》,…
All
external (or internal)
corresponding to (the contributions they make to) the functions of expressions in which they occur
have
Mittwoch, 11. Juli 12
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
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Frege (1891)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
Frege (1891)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
Frege (1891)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
Frege (1891)
cf. Zimmermann (2011; 2012) for details
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
Frege (1891)
… i.e.: all values〈Xi + Yj〉and 〈 Yj〉have already been
determined (externally, by previous applications of the standard method, or otherwise).
cf. Zimmermann (2011; 2012) for details
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
Frege (1891)
• + is compositional in X
cf. Zimmermann (2011; 2012) for details
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
Frege (1891)
• + is compositional in X
… i.e.: whenever〈Yj〉=〈 Yk〉, then:
〈Xi + Yj〉= 〈Xi + Yk〉.
cf. Zimmermann (2011; 2012) for details
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
Frege (1891)
• + is compositional in X• + is representative for X
cf. Zimmermann (2011; 2012) for details
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
Frege (1891)
• + is compositional in X
… i.e.: whenever〈Xi + Yk〉= 〈Xj + Yk〉, for all Yk, then:
〈Z[Xi] = Z[Xi]〉, for all Z[_] already evaluated.
• + is representative for X
cf. Zimmermann (2011; 2012) for details
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
cf. Zimmermann (2011; 2012) for details
Frege (1891)
• + is compositional in X• + is representative for X
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
cf. Zimmermann (2011; 2012) for details
Frege (1891)
• + is compositional in X• + is representative for X
Construction of 〈Xi〉
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
cf. Zimmermann (2011; 2012) for details
Frege (1891)
• + is compositional in X• + is representative for X
Construction of 〈Xi〉〈Xi〉:= λ〈Yj〉.〈Xi + Yj〉
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method
Cofinality assumptionEvery expression occurs in some sentence.
Hodges (2001)
StrategyTo extend the evaluation to a class X of (valueless) expressions, choose a suitable construction +:
• + is completed by X
cf. Zimmermann (2011; 2012) for details
Frege (1891)
• + is compositional in X• + is representative for X
Construction of 〈Xi〉〈Xi〉:= λ〈Yj〉.〈Xi + Yj〉 … and ⊕ is functional application.
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
〈 is dead〉= λ〈NP〉.〈NP + is dead〉
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
〈 is dead〉= λ〈NP〉.〈NP + is dead〉
(characteristic function of) set of individuals
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
〈 is dead〉= λ〈NP〉.〈NP + is dead〉
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
〈 is dead〉= λ〈NP〉.〈NP + is dead〉≅ external extension according to 2nd approach
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
〈 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)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
〈 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〉
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal extensions4. Intensions and Fregean compositionality5. OutroConstruction of internal extensions:standard method Frege (1891)
Example 1 (based on 1st approach to external extensions)
〈 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〉
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
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
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 +.
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.
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. Hodges (2001)
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.
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)
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 2: Laziness
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 2: Laziness Internal extensions (and other values!) may still be in need of specification.
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 2: Laziness Internal extensions (and other values!) may still be in need of specification.
E.g., it is not obvious from
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 2: Laziness Internal extensions (and other values!) may still be in need of specification.
〈 everybody〉= λ〈VP〉.〈everybody + VP〉E.g., it is not obvious from
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 2: Laziness Internal extensions (and other values!) may still be in need of specification.
〈 everybody〉= λ〈VP〉.〈everybody + VP〉E.g., it is not obvious from
that〈 everybody〉characterizes the supersets of
〈 person〉.
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 2: Laziness Internal extensions (and other values!) may still be in need of specification.
〈 everybody〉= λ〈VP〉.〈everybody + VP〉E.g., it is not obvious from
that〈 everybody〉characterizes the supersets of
〈 person〉.Solution: Background theory for characterizations of functional values.
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 3: Overdetermination
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
Example
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
Example
〈 V + everybody〉=
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
Example
〈 V + everybody〉= ???
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
Example Heim & Kratzer (1998)
〈 V + everybody〉= ???
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
Solution: No principled compositionality problems can arise (due to representativity of +); however standards for specifying (functional) values are needed.
Example Heim & Kratzer (1998)
〈 V + everybody〉= ???
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
Solution: No principled compositionality problems can arise (due to representativity of +); however standards for specifying (functional) values are needed.
Example Heim & Kratzer (1998)
〈 V + everybody〉=
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 3: Overdetermination After internal extensions (…) have been constructed they may still appear in other constructions.
Solution: No principled compositionality problems can arise (due to representativity of +); however standards for specifying (functional) values are needed.
Example Heim & Kratzer (1998)
〈 V + everybody〉= (λx.〈everybody〉(λy.〈V〉(y)(x))
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 4: No suitable + exists
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 4: No suitable + exists
Standard example
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 4: No suitable + exists
Standard example Frege (1892)
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 4: No suitable + exists
Standard example Frege (1892)
〈 V + S〉≠ 〈 V〉⊕ 〈 S〉
Attitude verbs V; e.g. no ⊕ can satisfy:
because + is not compositional in V.
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroSolution strategy (for Problem 4): Local repair
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroSolution strategy (for Problem 4): Local repair
Frege (1892)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroSolution strategy (for Problem 4): Local repair
Frege (1892)
If + is not compositional in X, find alternative values《Y》and put:
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroSolution strategy (for Problem 4): Local repair
Frege (1892)
〈Xi〉:= λ《 Yj》.〈Xi + Yj〉
If + is not compositional in X, find alternative values《Y》and put:
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroSolution strategy (for Problem 4): Local repair
Frege (1892)
〈Xi〉:= λ《 Yj》.〈Xi + Yj〉
If + is not compositional in X, find alternative values《Y》and put:
Attitude reports:
〈believe〉:= λ《 Sj》.〈believe + Sj〉
… where (e.g.) 《S》is the intension of S
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroExternal intensions
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro Carnap (1947), inspired by Wittgenstein (1922)External intensions
Mittwoch, 11. Juli 12
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).
Mittwoch, 11. Juli 12
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
Mittwoch, 11. Juli 12
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(!)《S》≅ λw. 〈S〉w
Mittwoch, 11. Juli 12
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(!)《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.
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroIntensional compositionality
Mittwoch, 11. Juli 12
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 +
Mittwoch, 11. Juli 12
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)
Mittwoch, 11. Juli 12
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
Mittwoch, 11. Juli 12
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 Sternefeld & Zimmermann (forthcoming)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroIntensional compositionality
Fregean Laziness
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 Sternefeld & Zimmermann (forthcoming)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroIntensional compositionality
Fregean Laziness
Laziness is particularly popular when it comes to applying Fregean 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 Sternefeld & Zimmermann (forthcoming)
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. OutroIntensional compositionality
Fregean Laziness
Laziness is particularly popular when it comes to applying Fregean 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 Sternefeld & Zimmermann (forthcoming)
Zimmermann (1999), Larson (2002),…
Mittwoch, 11. Juli 12
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 Sternefeld & Zimmermann (forthcoming)
Fregean Laziness
Laziness is particularly popular when it comes to applying Fregean compositionality. Zimmermann (1999), Larson (2002),…
Mittwoch, 11. Juli 12
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
Every man seeks a woman.
(∀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)))
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Mittwoch, 11. Juli 12
0. Intro1. The compositional enterprise2. External extensions3. Internal Extensions4. Intensions and Fregean compositionality5. Outro
Thank you for your attention!
Mittwoch, 11. Juli 12
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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