List, Ben: On Jan 17, 2015, at 11:59 AM, Benjamin Udell wrote: > My sense of it is that Peirce does not push the idea that mathematicals are > real. > Thanks, Ben. This is a critical thought, at least to me. It is of substantial importance for interpreting the relations between CSP's notion of a sign and many modern notions of mathematical signs.
If one seeks to analysis the trichotomistic components of a sign, (QS - SS - LS, Icon - index - symbol, R - D - A), one notes that the selected trichotomies do NOT use mathematic terminology. But, the concept of an index necessitates the separation of the whole (sinsign) into parts and the concept of the medad (in his iconic graphs of logical sentences) infers the counting of the terms composing the sinsign. (As noted previously, an index is necessary for enumerating the parts of the whole, such as CSP usage of the common notions of molecular weight and molecular formula.) These in term are necessary to specify CSP's specification of a component of a sign which he names "Rheme". Thus, these CSP's trichotomies refer to the index/medad/count properties of the components of a sign but NOT to calculations of arithmetic or calculus of the real numbers. One conjectures that CSP constructed these trichotomistic views of signs in such a manner as to clearly separate and distinguish his notion of logic from his notion of mathematics. I suppose that mathematical terms were excluded from these trichotomies purposefully, potentially as an expression of his understanding of the external nature of signs (QS-SS) and the trichotomy of objects, signs and interpretations. > Here's an example, from _Writings_ 6:255: > The reasonings and conclusions of the mathematician do not in the least > depend upon there being in the real world any such objects as those which he > supposes. The devoted mathematician cares little for the real world. He lives > in a world of ideas; and his heart vibrates to the saying of his brother > Plato that actuality is the roof of a dark and sordid cave which shuts out > from our direct view the splendors and beauties of the vast and more truly > real world,—the world of forms beyond. A great mathematician of our day said > with gustful emphasis: "A great satisfaction in the study of the theory of > numbers is that it never has been, and never can be, prostituted to any > practical application whatever." > [End quote] Many modern physicists and computer scientists often presuppose the CONTRARY to the last sentence of this quote and presuppose that the meaning of signs can be encoded into numbers. Indeed, the success of computer science and Shannon information theory is directly dependent on encoding signs into numbers and hence numbers into electrical signals and hence into transmissible forms that can then be decoded from numbers into signs, signs into symbols and symbols into icons. This is a powerful and useful set of concepts, but it has severe limitations. Cheers Jerry > Peirce positively rejects the reality of generals proposed by false > propositions. Such generals are figments, e.g., bat that evolved from bird. > Best, Ben > On 1/17/2015 12:24 PM, Howard Pattee wrote: > >> At 12:44 AM 1/17/2015, Gary Richmond wrote: >>> Howard wrote: I agree with SEP Realism: >>> >>> Those who have looked at this article may or may not, have noticed that >>> Peirce's understanding of realism isn't even mentioned in it. >> >> HP: Which is why I keep asking for specific cases that Peirce did not >> consider real. If you say that a peer refereed and recently updated >> review of realism doesn't include Peirce's concept of realism, then I think >> that is a reasonable question. >> >> For example, it is not clear to me if Peirce considered as real his >> intuitive concept of infinity as a "supermultitudinous" collection of sets >> of infinitesimals. In any case he concluded that this concept was too >> unwieldy to be useful in scientific models. What about complex numbers? What >> about n-dimensional spaces, etc. that are necessary for scientific models? >> >> Howard >> > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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