1. 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

2. 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.

3. 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

4. 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.

5. 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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 .

6. 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.

7. 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.

8. 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.

9. 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)

10. 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.

11. 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.

12. trivial? Compare: (i) You know ‘Ida rocks’ is true iff Ida rocks and, (ii)You know “’Ida rocks’ is true iff Ida rocks” is a truth (iii) You know “‘Y mae’r ddraig goch’ is true iff Y mae’r ddraig goch’ is a truth (iv) You know ‘Y mae’r ddraig goch’ is true iff Y mae’r ddraig goch (v) You know “’Ida’ refers to Ida” is a truth (vi) You know ‘Ida’ refers to Ida

13. 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.

14. structure This is a compositional theory of meaning. This is the key to explaining productivity and systematicity.