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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