Here's a thread surveying some 'classic' work on #compositionality. Lots of people seem to be discussing this right now, but with partial references to the whole story. My aim is to highlight some of the philosophical and psychological issues in the history of the concept. 1/
Small recap first... There are two principles usually associated with #compositionality, both (possibly incorrectly) attributed to Frege. See Pelletier's "Did Frege believe in Frege's principle?" (2001). 2/
1) Bottom-up, the 'compositionality principle': "... an important general principle which we shall discuss later under the name Frege's Principle, that the meaning of the whole sentence is a function of the meanings of its parts.'" Cresswell (1973) 3/
2) Top-down, the 'context principle': "[I]t's a famous Fregean view that words have meaning only as constituents of (hence, presumably, only in virtue of their use in) sentences." (Fodor and LePore, 1992) 4/
The two principles are at odds. So what *is* compositionality? Partee's answer (1984): "Given the extreme theory-dependence of the compositionality principle and the diversity of existing (pieces of) theories, it would be hopeless to try to enumerate all its possible versions."/5
So it may be impossible to clearly define #compositionality, but Partee suggest to at least pinpoint the latent features of the phenomenon. I'll focus here on a) its relation to syntax; b) relation to cognition; c) the nature of meaning itself; d) the nature of 'context'. /6
The first use of the term #compositionality, as far as I know, is in Katz and Fodor (1963): "As a rule, the meaning of a word is a compositional function of the meanings of its parts, and we would like to be able to capture this compositionality." /7
In that paper, K&F try to adapt Chomsky's notion of competence to the area of semantics. They're concerned with the bottom-up principle, which they call 'the Projection Problem'. They propose that semantics follows grammar rule-by-rule, according to an 'amalgamation' process. /8
K&F's 'amalgamation' is "the joining of elements from different sets of paths under a given grammatical marker if these elements satisfy the appropriate selection restrictions". Appropriate rules are encoded in the lexicon, and mastery of the lexicon is part of competence. /9
For K&F, semantics -- like syntax -- does not use "information about setting" and is "independent of individual differences between speakers". However they also readily accept a weak version of context as discourse dependence in the spirit of Harris and the distributionalists /10
The problem with the Chomskian account (and by extent K&F's) is that it gets into trouble with quantifiers. "Every candidate voted for every candidate" is not equivalent to "Every candidate voted for him/herself." But that's what transformational grammar would predict. /11
Enters Montague. Like K&F, Montague believes in a homomorphism between syntax and semantics, but the actual implementation of that homomorphism is to be done via model theory. Suddenly, sentences have truth values and parts of sentences have extensions. /12
An important side note on truth from Partee (2011): "semantics itself is in the first instance concerned with truth-conditions (not actual truth, as is sometimes mistakenly asserted) and entailment relations, not with internal representations." /13
That is, the Montagovian account is not a cognitive account. Also, truth does not have anything to do with the real world. If you want ideas sleeping (furiously or not), you intersect the set of ideas and the set of sleeping things. Done. /14 
Montague posits an infinity of possible worlds, with sentences being true in a set of worlds and constituents having intensions that map worlds to extensions. The account seems essentially bottom-up. And still, the notion of context does appear in his work... /15
In a 1970 essay on pragmatics, Montague introduces contexts of use: who utters the sentence, where and when; the state of the world; the surrounding discourse, etc. Context is formalised as a finite tuple of indexicals. Intensions become functions from indices to extensions. /16
One problem with the Montagovian account is its anti-psychologism. Partee (1979, 2014) highlights the difficulties of reconciling truth theory with the notion of competence, in particular when it comes to propositional attitudes. /17
I also note that logicians take possible worlds for granted and never explain where exactly they come from. Here's where Fillmore comes in. /18
Initially, Fillmore is involved in syntactic work in the spirit of transformational grammar (1982). He develops 'case grammar' to encode selectional restrictions and Katz and Fodor’s projection rules. This is to become frame semantics. /19
For Fillmore, a frame is a conceptual representation of a scene: "I thought of each case frame as characterizing a small abstract 'scene' [...] so that to understand the semantic structure of the verb it was necessary to understand the properties of such schematized scenes." /20
Fillmore is interested in explaining why a speaker chose the specific words they uttered. He formalises this idea in the notion of 'U-semantics' (1985). His semantics is perhaps the first to try and explicitly encode the paradox of the two principles of compositionality: ... /21
"The U-semantics account is compositional in that its operation depends on knowledge of the meanings of individual lexical items [...], but it is also 'non-compositional' in that the construction process is not guided by purely symbolic operations from bottom to top." /22
As in Katz & Fodor, Fillmore's account is cognitive, but it does not cleanly distinguish syntax from semantics from pragmatics.
As in Montague, truth is no metaphysical truth, it is the way speakers *perceive* the real world. But it does not provide a notion of extension. /23
As in Montague, truth is no metaphysical truth, it is the way speakers *perceive* the real world. But it does not provide a notion of extension. /23
Frame semantics does not have a proper account of things, worlds, and quantification over things/worlds.To find a cognitive account of the way truth values can be computed over possible worlds, we must jump to generative probabilistic models (e.g. Goodman and Lassiter, 2015). /24
Where do generative models stand? Against Fillmore, they draw a clear boundary between the world creation process and semantics. Against Montague, they anchor their possible worlds in probabilities learned from the real world. But there is more to language than the real world /25
Talking of concept combination, Hampton (1991) shows people will try to make sense of anything (contra Chomsky). What is a fish that is a vehicle? "Some put a saddle on the back of the fish [...] while others surgically implanted a pressurized compartment within the fish." /26
So when making sense of unattested combinations, people are able to generate the possible world that would make the sentence true / the extension non-empty. If required, that world can be very far from reality. /27
To summarise, let's just note that theories overlap and disagree on the topics of cognition, the autonomy of semantics wrt syntax and pragmatics, the idea of acceptability, the focus on (lexical) types vs (world) objects /28
The message: #compositionality remains a mystery because it is difficult to isolate the phenomenon. It interacts with our notions of syntax and pragmatics, our working definitions of meaning/worlds, and epistemological questions about linguistics (do we care about the mind?) /29
So there may not be an ultimate definition of #compositionality in sight. Still, we can develop working definitions that are useful to subfields. A great example is @emilymbender et al (2015) wrt parsing, which explicitly addresses the compositionality vs context paradox. /30
Let's just make sure we are *aware* of all aspects of the question. It is a rather large one. /31
PS: For those interested, I have put a list of references for the thread above on my website: aurelieherbelot.net/linguistics/su…. Happy Reading!
