Clark and Claudio,

Clark
I think my point about modal realism is more that connection
between universals and particulars. Does he make that connection
with mathematics early on? Again I don’t know. It’s one thing to
speak about the nature of mathematics as possibilities and quite
an other to speak about the relationship of mathematics to
particulars. The old “why is the universe so mathematical.”

I would relate two of Peirce's points:  Mathematics is necessary
reasoning.  And all necessary reasoning consists of drawing (or
imagining) a diagram and making observations about the diagram.

Therefore, everything we can understand is limited to the kinds
of diagrams we are able to invent and apply.  Every universal is
a specification for some kind of diagram, and every particular
is something we classify by relating it to some diagram.

I'm using the word 'diagram' in a very broad sense that includes
all kinds of images or icons in any sensory modality.  Then the
distinction between nominalism & realism depends on the way you
interpret the specification:  Is it just a verbal agreement, or
is it a law of nature that is independent of anything we may say?

Therefore, the knowable universe is limited to everything we can
imagine, and mathematics can analyze anything we can imagine.
(This point is independent of the nominalist-realist debate.)

Claudio
Signs can only construct other signs (images, texts, speeches,etc.),
perhaps, sometimes, "a more developed sign" (CP 2.228).

Yes.  And every kind of sign begins with an image (icon),
and every sign constructed from other signs is a diagram.
Therefore, all reasoning begins with perception of external
images and continues with internal images (diagrams).  Higher
cognition consists of constructing and examining diagrams.

The simpler constructions are called "common sense", and the
more disciplined constructions are called logic or mathematics
or the many kinds of -ologies.

Claudio
I think that a very good aspect of Peirce's proposal is that
there is no 'THE TRUTH' anymore.

But it's misleading to say that -- because all the "fake news"
people will take that as justification for their outright lies.

Peirce's version is more general and nuanced:
It is easy to speak with precision upon a general theme.
Only, one must commonly surrender all ambition to be certain.
It is equally easy to be certain. One has only to be sufficiently
vague.  It is not so difficult to be pretty precise and fairly
certain at once about a very narrow subject.  (CP 4.237)

This is the answer to both extremes:  those who seek absolute
certainty and those who claim that truth is irrelevant.

John
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