Composition

Clearly, some 'concepts' are, at least partly, compositional.

We can't conclude from this that:

(a) we can recognise compositionality from particular structural features, or

(b) that the meaning of a composed 'concept' is exhausted by an account of its composition

This is partly because we can't sideline idiomatic uses.  'Brown suit' has a content which cannot be discovered from 'brown' and 'suit', because to wear a brown suit means something different than to wear a grey suit.  Or a pink suit.

It is possible that compositionality (ugh) is not even that important - that it sort of helps us along, but more as a kind of mnemonic than because we need it.

'But' the grammarians say 'how do you account for our indefinite capacity to construe meaning from a finite set of components?'.

The answer is in two parts:  what is the evidence that we have this indefinite capacity?  It doesn't exist, because an indefinite capacity can't be demonstrated.  It can only be a potential account - and an unlikely one, given our finite condition.

The second part is that even if we settle on requiring a rule-based account of human 'language' behaviour, this need not be a grammatical account.  A finite computational engine can produce speech-like behaviour from non-grammatical components - e.g. a list of sentences linked to a list of appropriate reponses.  Even were such an engine to do a little humanish parsing, this need not be its only method.

Dyslexic people sometimes have difficulty discriminating individual words - since they don't have the resource of a reliable capacity to decode or concoct written sentences, they are more dependent on phonetic elements.  For instance, they are more likely to think that common complex expressions - 'Just now', 'Good day', 'How are you' - are single words.

Most of us, even if not dyslexic, can remember similar errors from childhood.  I remember hearing 'Here we go round the' (... Mulberry bush) as 'Helligo rounda'.  The fact that it didn't have any clear meaning didn't especially distinguish it within my limited experience, and even adult literate reflection can't make a lot of relevant sense out of the first line of this nursery rhyme.

(Mulberries don't grow on bushes, for one thing.)

The compositionality argument has two parts:

(1) There are cases where we can deduce the meaning of an expression from grammatical rules and the 'meanings' of its parts (word meanings, in particular).

(2) We need some story about how we can decode expressions we haven't heard before.

But this is pretty ramshackle.  As above, (1) is rarely possible in a completely satisfactory way.  And (2) ignores lots of other resources we might draw on - particularly context, including any preceding linguistic exchange.

After all, that's how we start 'decoding' in the first place ...