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.)


One thought on “The Fregean Conjecture

  1. Pingback: The Analytic and Synthetic in Kant and Frege | Reflecting Light

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