According to informational semantics, concepts are mental particulars representing information about objects. For example, concept 'dog' is a mental particular representing information about real dogs.

Is that really what information semantics claims? To me it seems the kind of semiotic, constraints-based, approach I've described.

So meaning is use. The utterance of "dog" stands as a sign mediating a habit of relation with the world. Thus while the vocal act is particular, it only has meaning by virtue of the coordination it might bring between a mind and the world (the world including other minds that might have an interest in being likewise oriented to the world beyond themselves).

You talk about mental particulars (concepts, ideas, impressions?) representing information. But informational semantics seems to be making the same point that they don't. What signs buy as the mediating mechanism is the possibility of an externalised habit of coordination rather than an internalised state of information.

So "dog" as a concept is not the representation of a doggy essence - something closed and internally represented - but instead the anchor of a habit of coordination between self and world. Doggyness characterises all we might do, think and say in a "doggy situation". So as a "concept" it is creatively open ended - while also being still usefully or pragmatically constrained enough to function as a lexical unit, a syntactic element, of some "propositional" sentence.

Do you have no comment to make on your inconsistent statements:

1. "Many theories of concepts say that [...] concepts can be composed."

2. "If concepts can be composed, then conceptual atomism is the case."

Many theories of concepts say (1) concepts have lower level structures, and (2) concepts can be composed, "both at the same time".
The premise 2 above is different from 'many theories of concepts'. The premise 2 does not say (1) concepts have lower level structures, but says (2) concepts can be composed.

Do you see the difference???

I see the difference, but you said: "If concepts can be composed, then conceptual atomism is the case."

You have stated that there are opposing (non-atomistic) "theories of concepts" which also assert that concepts can be composed. This makes your premise 2 false.

Conceptual atomism asserts (1) concepts can be composed, and (2) concepts can be composed only if concepts are atomic. (2) can be restated as: (3) concepts *cannot* be composed if concepts have lower level structures (i.e. they are not atomic).
More precisely:
(1) If concepts are not atomic, then concepts cannot be composed.
(2) Concepts can be composed.
Therefore, (3) concepts are atomic.
Modus Tollens.

You're contradicting yourself. You said earlier: "Many [opposing] theories of concepts say that concepts have lower level structures, and that concepts can be composed."

Now you are saying: "If concepts are not atomic, then concepts cannot be composed."

One thing is a criticism on opposing theories, another is a report of which opposing theories state. There's no trouble.

Okay, justify this new claim. Why are all of the opposing theories wrong? Why can't non-atomic concepts be composed?

You said earlier that "some theories of concepts might say that 'dog' is divided into 'animal', 'quadrupedal', 'mammal', and so on." So, why isn't this an example of "dividing" the concept of 'dog' into other concepts? That is, why don't those other concepts compose the concept of 'dog'? Why can't this be done?

So, why isn't this an example of "dividing" the concept of 'dog' into other concepts? — Luke

It's because dividing concepts into lower levels causes to make compositionality of concepts fail. Infinite regress of dividing concepts into parts and parts and parts...

How does it fail?

Infinite regress of dividing concepts into parts and parts and parts... — quine

This is how.

I don't follow how the compositionality of concepts fails.

Conceptual atomism model:
'Brown' and 'dog' compose 'brown dog'. It's easy and simple.
Opposing theories model:
'Brown' is composed by 'color', and 'brighter-than-black', and so on. 'Dog' is composed by 'animal', and 'quadrupedal', and mammal', and so on. ... 'Brighter-than-black' is composed 'lighter-than-black' and 'color' and so forth. ... 'animal' is composed by 'living thing' and 'biologically constructed' and so forth. ... ... ... ... and 'quark' is composed by 'physical' and 'small particle', and so on. Is there an end?

Compare two stories.

What if there is no end? Why should that imply that the compositionality of concepts fails?

That is not a question. Explanations are sufficient. I recommend you to go back to this thread to make up what you need to get.

It certainly is a question, but if you're unable to answer it then perhaps you should reconsider your argument.

My answers are certainly answers. If you are unable to accept this fact, go to the grave.

the problem with atomism is discussed in another thread on theseus' ship.