The principle of compositionality

Frege's Principle:

The meaning of the whole is a function of the meaning of the parts.

Questions:

1.

what are the components whose meanings combine to give the meaning of the whole?

2.

how are component meanings combined?

3.

what are the minimal components of meaning?

4.

how is meaning to be represented?

Some answers:

1.

Meaningful components correspond to syntactic constituents;

2.

Given 1, we might suppose a one-to-one correspondence between syntactic rules and semantic rules:

$$\rightarrow$$ syntax: S NP VP

$$^\prime \mathcal{F} ^\prime ^\prime$$ semantics: =

The rule-to-rule hypothesis.

3.

Also given 1, the minimal units of meaning are just the lexical items (i.e., words or morphemes).