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From: John Jones on 6 Nov 2009 21:02
In logic, is there a conflict between the Context Principle and the
Principle of Compositionality? It looks as though there might be:

PREAMBLE
The "Context Principle" was first proposed by Frege:
"Never ask for the meaning of a word in isolation, but only in the
context of a proposition." This is self-explanatory I hope (for
"proposition" also read "sentence"). Words are, then, for Frege signs
whose meaning is incomplete. Similarly, for Wittgenstein, a sign (cf.
"word") only has meaning in the application (proposition or sentence) in
which it occurs.

Next, the "Principle of Compositionality" was also developed by Frege
and Wittgenstein: "a proposition [or sentence] must communicate a new
sense with old words" (Tract. 4.03). We understand a sentence because
its parts or words are put together in familiar ways.

DISCUSSION
First, the "Context Principle":
It looks as if there is something not quite right about the Context
principle on its own, and I am not referring to the standard objection
that single words CAN have meanings (this objection is dealt with by
considering single words as ellipses for sentences, e.g. the word "yes"
is a short form of a sentence). But is it coherent to talk of "the
meaning of a word" if that "meaning" is given only through the sentence
in which the word occurs?

For, if a word has its own meaning AND also has a meaning which is given
to it through the sentence in which it occurs, THEN
1) the meaning of a word would be the meaning of the sentence in which
the word occurs, and the word would be an ellipsis for that sentence, or
2) a sentence would have its own meaning, PLUS the meanings of each of
its words.
The existence of these mutually exclusive options points to a confusion
within the Context Principle over the source of meaning - word, sentence
or both?

Second, the "Principle of Compositionality":
The Principle of Compositionality describes how words that are put
together in a certain way make a meaningful proposition or sentence. But
again, where exactly does meaning originate - in the words, sentence, or
both? The Principle of Compositionality doesn't square with 1), above,
nor with 2).

CONCLUSION
The Context Principle and the Principle of Compositionality may appear
to be mildly at odds with each other, but only appear so because a
failure in clarity compounds a conflict.

Such clarity is achieved, and conflict dispelled, if we re-write the
Principles. First, if we consider the option, not given, that words
cannot be considered in isolation from their sentences, and that what
passes for "the meaning of a word" is, in fact, an ellipsis or
abbreviation for a sentence.

Second- and here I draw attention to two fundamental distinctions
(totality/whole) hitherto confused in the two Principles discussed
above; a sentence is a symbol, not a sign. The meaning of a symbol is
not given through a syntactic summation of its parts, elements, signs or
words. The meaning of a symbol is invoked, and its invoked form is
called a whole. The whole is a sufficient condition of its syntax or
parts, signs or words. Further, a whole is independent of its syntax,
elements, etc. even though they are its necessary conditions. For
example, a set of flowers is a necessary condition of a bouquet, while a
bouquet is a sufficient condition for a set of flowers, yet is
independent of them. Similarly, we can consider the relationship of
sentences to words.
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