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The principle of compositionality is formulated as:

The meaning of a complex expression is a function of the meaning of its parts and of the syntactic rules by which they are combined. (Partee, ter Meulen and Wall, 1990: 318)

If I have understood proponents of this principle correctly (from mainly reading the Wikipedia article on the subject) idioms and metaphors and other notions demanding extralinguistic contexts are often excepted from this.

My wonder is, if we remove all of these entities, what is really left of language beyond simpler predicate logical expressions? Are there alternative to the principle of compositionality?

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    Not everything is compositional. By definition, idioms are not. Metaphors are not logical, but they can be compositional in context, since once the contextual metaphor theme is chosen, the metaphoric meanings of its parts and their syntactic rules become arguments of the compositional function. There are lots of sub-regularities in idioms and metaphors, too, which are worth capturing. But logic underspecifies, and context is always necessary. – jlawler Apr 18 '14 at 18:24
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As @jlawler points out, by their very definition, idioms are non-compositional. And we could think of metaphors as a sort of non-conventional idioms. Of course, there are many other types of non-literal language such as irony or in fact any speech act, that will present similar problems.

To preserve the principle of compositionality, you can shove these into the realm of pragmatics (which is where speech acts are typically kept anyway). So expressions like 'kick the bucket' or 'take X for a ride' are simply treated as having a literal meaning where the compositionality still applies.

You could also expand your definition of what constitutes a 'component' or a syntactic rule. Neither of these is very practicable when dealing with actual range of language use but they can keep the principle intact enough for the purpose of formal semantics.

But the key thing to understand is that 'the principle of compositionality' is not some sort of a universal law of language. It is really only a way to formulate certain axioms for the purposes of formal syntax and semantics. It has no counterpart in natural semantics or in cognitive semantics because there is no need for it.

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  • Thank you for your answer! Now I'm curious to what you mean by there being no need to a counterpart in natural or cognitive semantics. Do you have a good reference where I may continue my studies? – Jimmy C Apr 19 '14 at 1:06
  • What I meant by this is that because natural or cognitive semantics do not depend on a formalism, they do not need to worry about compositionality. They simply operate on the intuitive notion that components of an expression contribute to its meaning but that the understanding of the complete meaning is dependent on a variety of contexts. They would then view the distinction between semantics and pragmatics as superfluous because their framework accounts for the entirety of human meaning, not just the parts that can be modeled via formal logic. – Dominik Lukes Apr 19 '14 at 11:28
  • BTW: I like to think of this through the motto: "Words don't mean things, people mean things." – Dominik Lukes Apr 19 '14 at 11:28

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