Transcript Striking fact

What makes communication by
language possible?
Striking fact (a) If someone utters a sentence and you
know which proposition her utterance expresses,
then it’s likely that you will also understand which
propositions other utterances of the same
sentences express. Conversely, if you don’t
understand one utterance of a sentence, it is likely
that you won’t understand other utterances of it
either.
The natural approach to explaining this fact is
encoded in what I called Hypotheses 1:

sentences have meanings

language users know the meanings of sentences

knowing the meanings of sentences enables
language users to know which propositions
utterances of those sentences express
Striking fact (b) Linguistic abilities are systematic—
someone who understands an utterance of “Leo
ate John” can probably also understand an
utterance of “John ate Leo”

Systematicity “there are definite and predictable
patterns among the sentences we understand. For
example, anyone who understands ‘The rug is
under the chair’ can understand ‘The chair is under
the rug’” {Szabó, 2004 #800}.
Striking fact (c) Linguistic abilities are productive—
we can understand utterances of an indefinitely
large range of sentences we have never heard
before. Example: “John ate Leo who ate Ayesha
who ate …”

Productivity we can understand utterances of an
indefinitely large range of sentences we have
never heard before.
Hypothesis 2:

words have meanings

speakers know the meanings of words


the meanings of words, together with rules of
composition, determine the meanings of sentences
speakers are thus able to know the meanings of
sentences by virtue of knowing the meanings of
words and rules of composition
Recall that we can extract purely functional
characterisations of meanings from the
hypothetical explanation of productivity and
systematicity.


meaning of a sentence: whatever it is
knowledge of which enables language users to
understand utterances of that sentence (that is,
to know which proposition the utterer
expresses)
meaning of a word: 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.
FOL
Your abilities to use FOL are systematic and
productive.
Systematic. If you understand:
AB
then you can probably also understand:
BA
Productive. If you understand:
A
then you can probably also understand:
A
and also:
A
and so on …
sentence connective -- an operator that joints zero or
more sentences to produce a new sentence; in
FOL sentential connectives include ,  and .
In trying to say what meanings are, what we are
looking for is things knowledge of which enable us
to understand sentences of FOL.
Suppose you can translate a sentence of FOL into
English. Since you understand English, the
translation enables you to understand the FOL
sentence too.
For instance, if you know that:
(T) ‘A  B’ can be translated as ‘Ayesha is tall and
Mo is rich’
Then you understand the FOL sentence A  B.
meaning of a word: 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.
To know the meaning of a sentence of FOL it
would be sufficient to know a statement
translating it into English. So to find out what the
meanings of the symbols of FOL are we should
ask: What do you need to know about a symbol of
FOL in order to be able to translate sentences
containing that symbol into English?
For the sentential connectives ,  and so on, the
answer is that you need to know their truth tables.
Knowing the truth table for  enables you to
translate sentences containing this symbol into
English. Therefore the truth table gives the
meaning of the symbol.
In summary:
1. 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.
2. Knowing the truth table for a sentence of FOL is
sufficient, together with knowledge of what the
sentence letters mean, for translating the sentence
of FOL into English.
3. Being able to translate a sentence of FOL into
English is sufficient, together with knowledge of
English, for knowing what that sentence of FOL
means.
Consider this sentence of FOL:
F(a)
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
Given this interpretation, you could translate the
sentence F(a) into English. It ‘F(a)’ means Ayesha
is tall. And given the above statements, you could
translate any sentences of FOL involving ‘F’ and ‘a’
into English, e.g.
F(a)F(a)
Consider this sentence of English:
‘Ida rocks’
In the case of FOL, we suggested that a translation
into English gives the meaning of FOL sentences.
We said the meaning of ‘AB’ is given by this
statement:
(T) ‘A  B’ can be translated as ‘Ayesha is tall and
Mo is rich’
In the case of English, the comparable statement
would be:
(T) ‘Ida rocks’ can be translated as ‘Ida rocks’
The problem is that we have English sentences on
both sides of the statement.
Davidson’s suggestion, consider (W):
(W) ‘Ida rocks’ is true if and only if Ida rocks.
Knowledge of the statement would be sufficient for
understanding utterances of this sentence. And
that is what our functional characterisation says
meanings are.
Now that we know what the meanings of sentences
are, we can evaluate the proposal about the
meanings of words. Recall the functional
characterisation:
meaning of a word: 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.
Now consider the statements about the words in ‘Ida
rocks’:
The referent of ‘Ida’ is Ida
The extension of ‘rocks’ is the set of things which
rock.
In English, a name plus a predicate constitutes a
sentence. Any such a sentence is true if and only
if the referent of the name is in the extension of
the predicate. In the case of this particular
sentence, ‘Ida rocks’, it is true if and only if Ida is
in the set of things which rock. That is:
(W) ‘Ida rocks’ is true if and only if Ida rocks.
Deriving the meanings of sentences
Statements giving the meanings of sentences can be
derived from statements giving the meanings of
words. How?
Consider
‘Ida rocks or Louie rocks’
From the meaning of ‘or’ 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.
structure
This is a compositional theory of
meaning.
This is the key to explaining
productivity and systematicity.