While I couldn’t find the Peirce quote I was searching for I did find this from 
Joe Ransdell:

Qualities are not what philosophers sometimes call "the given" to which 
"interpretation" is somehow to be added to form cognitive units; for qualities 
are not objects of predication but rather that which is (monadically) 
predicated of objects, though not considered AS predicated since that would 
involve conceptual recourse to the other categories. [Note: this is treacherous 
territory: I am inclined at present to say, though, that quality is, first of 
all, predicable content not regarded as predicated though regardable in that 
way as well, and, second, when so regarded (via hypostatic abstraction) they 
are regarded as properties, in which case certain further things can be said of 
them considered as such. I do not think this means that he simply uses the term 
"quality" sloppily or even ambiguously.  I think he regards it as legitimate to 
speak of quality sometimes as a matter of firstness and sometimes as a matter 
of thirdness depending on which way of regarding it is intended, as should be 
clear enough from the context if one is aware of the two different kinds of 
regard for it.)

While he’s more talking about the myth of the given I think he is getting at 
the idea by Peirce that all thought is mediated. Working the details of this 
out relative to something like “the given” (and its myths) can be tricky. I’m 
not entirely sure of it myself.

My guess is that for any sign there is an experience of the sign before us. But 
in terms of the raw feeling of that sign there is this new example of 
firstness. That in turn, to think upon, ends up being thought in terms of 
thirdness. However where the confusion pops up is that it’s very easy to then 
think that thinking is just a series of representations before the mind. I’m 
not sure Peirce makes that move although it remains the dominant paradigm in 
psychology and probably cognitive science. (I confess I can never quite make 
sense of that distinction although most people I encounter who self-identify as 
cognitive scientists seem much more open to non-representational views)

Having said that though here there may be more disagreement over how to read 
Peirce. I know some do read Peirce as entailing a kind of representationalism. 
So perhaps somewhat against my earlier comment that this is all semantics there 
may be a deeper disagreement between the sides. I suspect the question can be 
productively be formed as whether the experience of a quality is a thought or 
whether it is just the experience of the mediation of a quality that is a 
thought.

Part of the issue appears to be that firstness proper is in a sense ineffable. 
To make it effable is to represent it in a sign but then it’s no longer 
firstness. Is it only thought when in the sign? That’s fundamentally the issue. 
While yesterday this seemed primarily a semantic issue now I’m just not quite 
so sure. The main argument I think is that Peirce distinguishes thought from 
mind in a few places. I think for thought he’s talking of proposition-like 
entities.

The mode of being of the composition of thought, which is always of the nature 
of the attribution of a predicate to a subject, is the living intelligence 
which is the creator of all intelligible reality, as well as of the knowledge 
of such reality. It is the ENTELECHY, or perfection of being. (CP 
6.339-341;1908)




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