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PH130 Meaning & Communication
Lecture 02: open can, find widget
Then you understand the FOL sentence A 
B.
Terminology. sentence connective -- an
operator that joints zero or more sentences
to produce a new sentence; in FOL
sentential connectives include ,  and .
But we have functionally characterised the
meaning of a sentence as whatever it is
knowledge of which enables language users
to understand utterances of that sentence
(that is, to know which proposition the utterer
expresses).
What are meanings? Case study: FOL
So possibly (T) gives the meaning of ‘AB’ in
FOL.
Our abilities to use and understand
sentences of FOL are systematic and
productive.
What are the meanings of words (i.e.
symbols)?
Systematic. If you understand:
AB
then you can probably also understand:
BA
We have functionally characterised the
meaning of a word as whatever it is
knowledge of which, together with
knowledge of rules for composition, enables
language users to know the meanings of
sentences containing the word.
Productive. If you understand:
A
then you can probably also understand:
A
and also:
A
and so on …
What are the meanings of sentences? If you
know that:
(T) ‘A  B’ can be translated as ‘Ayesha
is tall and Mo is rich’
So the question, What does ‘’ mean? is the
question, What do you know about ‘’ that
enables you to understand the meanings of
sentences containing ‘’? Answer: the truth
table for ‘’. Why? Because knowing the
truth table for a sentential connective is
sufficient, together with knowledge of the
syntax of FOL, to work out the truth table of
any complex sentence containing that
connective.
Names and predicates. Consider:
What could you know that would enable you
to translate this into English? Consider an
interpretation which assigns an extension to
the predicate and an object to the name:
F : the set of tall things
a : Ayesha
We can write these more fully thus:
The extension of ‘F’ is the set of tall
things
The referent of ‘a’ is Ayesha
These statements could give the meanings
of ‘F’ and ‘a’. Why? Because knowledge of
these statements would enable you to
translate the sentence ‘F(a)’ into English and
to translate any sentences of FOL involving
‘F’ and ‘a’ into English.
From FOL to natural language
Davidson’s (1967 [1984]; 1973 [1984])
insight: knowledge of statement (W) is be
sufficient for understanding utterances of
‘Ida rocks’:
(W) ‘Ida rocks’ is true if and only if Ida
rocks.
If knowledge of this statement would be
sufficient for knowing the meanings of
utterances of ‘Ida rocks’, we can say that
(W) gives the meaning of this sentence.
F(a)
What are the meanings of words? Consider:
1
The referent of ‘Ida’ is Ida
The extension of ‘rocks’ is the set of
things which rock.
These statements could give the meanings
of ‘Ida’ and ‘rocks’. Why? Because
knowledge of these statements, together
with knowledge that an English sentence
consisting of a name followed by a predicate
is true if and only if the referent of the name
is in the extension of the predicate, is
sufficient for knowing (W).
Similarly, the meanings of the connectives
‘and’ and ‘or’ may be given by these
statements:
‘A and B’ is true if and only if A is true
and B is true
‘A or B’ is true if and only if A is true or B
is true
Deriving the meanings of sentences
Consider:
‘Ida rocks or Louie rocks’
From the meaning of ‘and’ we have:
(1) ‘Ida rocks or Louie rocks’ is true if
and only if ‘Ida rocks’ is true or ‘Louie
rocks’ is true.
From the rules of composition for English we
have:
(2) ‘Ida rocks’ is true if and only if the
referent of ‘Ida’ is in the extension of
‘rocks’
From the meanings of ‘Ida’ and ‘rocks’ we
have:
(3) ‘Ida rocks’ is true if and only if Ida
rocks
And similarly:
(4) ‘Louie rocks’ is true if and only if
Louie rocks
Putting (3) and (4) into (1) we get:
(5) ‘Ida rocks or Louie rocks’ is true if
and only if Ida rocks or Louie rocks.
Overview
1. functional characterisation: the meaning
of a sentence is whatever it is knowledge of
which enables language users to understand
utterances of that sentence.
2. Davidson’s insight: Knowing the
conditions under which a sentence is true is
sufficient for understanding utterances
containing that sentence.
Therefore:
3. The meaning of a sentence is given by a
statement identifying the conditions under
which it would be true.
4. functional characterisation: the meaning
of a word is whatever it is knowledge of
which, together with knowledge of rules for
composition, enables language users to
know the meanings of sentences containing
the word.
of names, about the extensions of
predicates, and about the truth conditions of
statements containing connectives it is
possible, together with rules of composition
for English, to derive statements about the
conditions under which any sentence
containing those words is true.
Therefore:
6. The meanings of words are given by
statements about the referents of names,
extensions of extensions of predicates, and
so on.
This theory of meaning, together with
Hypotheses 1 & 2 from Lecture 1, explains
productivity and systematicity.
References (not recommended reading)
Davidson, Donald (1967 [1984]), "Truth and Meaning",
in Inquiries into Truth and Interpretation. Oxford:
Oxford University Press.
--- (1973 [1984]), "Radical Interpretation", in Inquiries
into Truth and Interpretation. Oxford: Oxford
University Press.
Tarski, Alfred (1935 [1956]), "The Concept of Truth in
Formalized Languages", in J. H. Woodger (ed.)
Logic, semantics, metamathematics : papers from
1923 to 1938. Oxford: Clarendon Press.
--- (1936 [1956]), "The Establishment of Scientific
Semantics", in J. H. Woodger (ed.) Logic,
semantics, metamathematics : papers from 1923 to
1938. Oxford: Clarendon Press.
5. Tarski’s (1935 [1956]; 1936 [1956])
insight: From statements about the referents
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