Dear Howard, lists, Den 28/04/2015 kl. 14.47 skrev Howard Pattee <[email protected]<mailto:[email protected]>> :
At 07:04 AM 4/28/2015, Frederik Stjernfelt wrote: [Howard's] questions about your view: (1) What "parts of nature" do you include in "naturalization of semiotics"? I am not sure I understand the question. I do not think the results of mathematics are a human invention. I think mathematics is part of nature in the sense that it contains structures which are as they are without human agency - no matter whether they have physical realizations or not. They may be seen as hypothetical or modal in order to avoid naive Platonism. (2) Do you think of mathematics and logic as a part of (subset) of semiotics? No. I rather think semiotics is a subset of logic in Peirce's broad epistemological conception of logic. (3) When in the history of the universe do you say the first proposition occurs? By the first semiosis Good. I think we agree except for your placing logic and math as more general than semiosis. Are you thinking of logic and math as cases of natural laws? In some sense yes, but they are not empirical laws like physical laws. Or are they conditions for describing laws? Indeed they are, but more than that. Parts of mathematics which are not (yet?) applied in any science are unproblematically developed. So I would not subscribe to Quine's idea that it is utility in physics which is the only validity test for math How do you test their validity? We will have to ask mathematicians. Internal consistency, fit with other parts of mathematics, things like that. Attempts to reduce math to applicability, mental construction, symbol use, etc. appeare to me to transgress ontological parsimony and rather become ontological stinginess. In a certain sense, the ontology of mathematics remains an open question. I like Peirce's idea saying that all of math consists of hypotheses only so it contains no positive or empirical knowledge - a sort of hypothetical Platonism. But that is probably not the last word on that issue. In that sense, I can understand why it may be seen as a too easy gesture on my part to categorize math as part of nature. I just think that whatever ontology math proves to have, it will have to be part of nature in a broad sense. Best F
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