# The Fregean Conjecture

“Semantic composition is functional application” – the Conjecture.

In an extensional theory of linguistic meaning, there are only three kinds of things: individuals, functions, and truth-values.  The meaning of a sentence is determined by the individual meanings of each of its words as well as its syntactic structure.  A simple example:

Jack drinks

There is “Jack”, an individual, and there is “drinks”, a function.  Drinks is a function which takes a single argument (in this case, “Jack”), and maps it to a truth-value.  The meaning, then, is a truth-condition: “Jack drinks” is true iff Jack drinks = T.  Suppose Jack does in fact drink.  Then we plug in “Jack” into the function “(x) drinks”, and the output will be the truth-value, T.  Suppose instead that Jack’s been sober almost two months.  The function “(x) drinks” will map “Jack” onto the truth-value, F.  (Probably.)  More formally:

[Jack](Let F be that function f  such that For All x in domain, f(x) = T  if and only if x drinks, otherwise f(x)=F.) = T

As sentences grow in complexity, it can be difficult to keep track the syntactic structure – that is, exactly which component of the sentence is an argument for whatever other function in the sentence.  It can be useful to see an example of a sentence broken up into its constituents.

The cowboy on the cliff rides hard into the west.

([The [cowboy]] [[on] [the [cliff]]) ([[rides] [hard]] [[into] [the [west.]]])

Note that the only individuals in this sentence are “cowboy”, “cliff”, and “west”.  This means that rest of the words are functions.

(Will update.)