List, Jon: On Jan 17, 2015, at 3:32 PM, Jon Awbrey wrote:
> But I can assure you that mathematicians as a rule, including Peirce, regard > mathematical objects as “having properties”, which makes them “real” > according to the technical Scholastic definition of “real” that Peirce always > uses and often mentions when he's being precise. I concur, the manner of usage of symbols by mathematicians is often confounding. Your assertion, however, obscures a far deeper philosophical problem. It is the sort of problem that philosophers love to ignore as it removes some from their "comfort zone" and hence jeopardizes their academic reputations. Namely, that the usage of mathematical symbols obscures the more important pragmatic differentiations between philosophical talk and mathematical talk and physical talk and chemical talk and ...many other disciplines. As I understand it, the mathematical talk of "having properties" is a critical association of logical concepts that associate mathematical concepts as structure (sets, semi-groups, groups, rings, vector spaces, topologies, matroids, categories and a large number of other mathematical forms.) For example, a group has the property of a set and a logical operation (as well as other properties.) A ring has the properties of a set and two logical operations, both addition and multiplication. Is this usage an example of philosophical realism? A similar situation occurs in the context of the chemistry. A chemical term, a concrete "real" name, as a chemical element, is considered real because it has measurable properties that are independent of time and place. A chemical element is conceived as an entity with an identity, not as a mathematical variable representing a single physical quale. The set of the table of elements is a set of concrete "real" names with the addition property of creating a set of natural relatives. Chemical talk of "having properties" refers to those measured properties from the empirical methods used in a laboratory. Pragmatically, differentiation of chemical properties lies at the heart of the practical logic of chemistry. The difference between chemical talk and mathematical talk is with respect to the conceptualization of the nature of qualia. The qualia of mathematical talk are "objective" by virtue of the meaning of mathematical symbols and mathematical traditions. At least that is how I interpret CSP's writings, such as those cited by Ben. The qualia of chemical talk are the consequences of the consistency of physical measures, independent of the time and place of measurements. By consistency, I mean the empirical reproducibility of empirical observations. But, these chemical qualia are under extremely severe constraints such that the methodology must be consistent. Here, by consistency, I mean that the coherence of the logical arithmetic on the molecular numbers, the molecular weight, the molecular formula, and the molecular icon are logically extendible. The nature of the "reality of properties" (qualia and quanta) of mathematics and chemistry rarely overlap. Indeed, Mathematical properties (qualia) are aligned with the regularity of the geometry of a line or lines such that they become merely carriers of measurements of chemical qualia. Chemical properties may be aligned with mathematical regularity (such as the graphs of methane, ethane, propane, butane, pentane...) and a corresponding set of icons (structures). Or, as is more commonly the case, chemical qualia are aligned with awesome IRREGULARITY. The combinations of valences of a set of related atoms generate a graph with millions of distinctive irregularities, as in the handedness of proteins. A central principle of molecular biology and bio-semiotics rests on the irregularities of the qualia of handedness. Is this chemical usage of the concept of realism an example of philosophical realism? Is there a distinction between mathematical realism and chemical realism? Are the three trichotomies of terms of a sign selected purposely by CSP to simply avoid the confrontation between qualia and objects (sinsigns)? Are the three trichotomies of a sign selected purposely by CSP to distinguish between mathematical realism and chemical realism? >From a century of hindsight, it is a curious game we are playing by asking >such speculative questions. Speculating about CSP's motivations is almost as >curious as speculating about current national and international political >games. As a footnote (based on my personal perceptions of my individual experiences with conceptualization of laws), it appears to me that philosophical realism is too narrowly defined to clearly and distinctly separate the pragmatic usages of the term realism in both mathematical physics and chemistry. Not to mention the far more difficult task of understanding "realism" in the sense of economics, or biology, or medicine or consciousness. Enough! I have wandered into technical terminology - a "real" no, no! Cheers Jerry > On Jan 17, 2015, at 4:05 PM, Edwina Taborsky <tabor...@primus.ca> wrote: > >> Very funny. No, that's not it. It's not Alice in Wonderland. I think it's >> objective vs subjective but I simply can't remember how Howard uses the >> terms. I just remember that at one time, it dawned on me that he uses them >> in a particular way and I then understood what he was talking about. >> >> Edwina >> ----- Original Message ----- >> From: Jon Awbrey >> To: Edwina Taborsky >> Cc: Howard Pattee ; <biosemiot...@lists.ut.ee> ; Peirce-L >> Sent: Saturday, January 17, 2015 3:54 PM >> Subject: Re: [PEIRe: Natural Propositions : Chapter 8 >> >> Edwina, >> >> For instance, “Real men don't eat quiche” and “Real mathematicians don't >> each Bourbaquiche”. >> >> Jon >> >> http://inquiryintoinquiry.com >> >> On Jan 17, 2015, at 3:32 PM, Edwina Taborsky <tabor...@primus.ca> wrote: >> >>> Howard, I think that possibly, you are using your own definition of >>> 'realism' rather than the one many of us use; we've been through this >>> difference before. The one many of us use is that 'realism' refers to >>> universals or generals or 'common rules' being objectively real. Not >>> existent as particular instances but objectively real. I've forgotten what >>> you mean by this term 'realism' but it's quite different. >>> >>> Could you remind us of your meaning? Thanks. >>> >>> Edwina >>> >>> ----- Original Message ----- >>> From: Howard Pattee >>> To: biosemiot...@lists.ut.ee ; biosemiot...@lists.ut.ee ; Peirce-L >>> Sent: Saturday, January 17, 2015 3:28 PM >>> Subject: [PEIRCE-L] Re: [biosemiotics:7934] Re: Natural Propositions: >>> >>> Thank you Ben for a clear answer. I would say, then, that in thinking about >>> formal mathematics Peirce was to some extent nominalistic, which of course >>> leaves him free to be realistic about diagrams and physics. The basis for >>> considering logic to be realistic is still mysterious to me. >>> >>> Of course there is still a great epistemic variety among today's >>> mathematicians and physicists, largely because of great mysteries. >>> Natural selection has made sure we begin life as naive realists which is >>> necessary for immediate survival. However, as physics has had to rely more >>> and more on creative imagination for models of events, which are way beyond >>> natural senses and common sense, it is only reasonable that the models >>> become more nominalistic. >>> >>> Howard >>> >>> At 12:59 PM 1/17/2015, Benjamin Udell wrote: >>> >>>> Howard, lists, >>>> >>>> My sense of it is that Peirce does not push the idea that mathematicals >>>> are real. His discussions of math and reality tend to involve a variation >>>> of sense of word 'real' into the concretely real, the actual, the >>>> existent, etc. He says that mathematicians (of whom he of course was one) >>>> don't care about the real and that their ideal forms are the truly real to >>>> them a la Plato. I do recall Peirce somewhere saying that the question of >>>> whether mathematicals are real is a question for the metaphysician, not >>>> the mathematician, and I recall him not answering the question at that >>>> point. Peirce always says that mathematical objects are purely >>>> hypothetical. >>>> >>>> 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] >>>> >>>> Peirce positively rejects the reality of generals proposed by false >>>> propositions. Such generals are figments, e.g., bat that evolved from bird. >>>> >>>> Best, Ben >>> >>> >>> >>> >>> ----------------------------- >>> 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 . >>> >>> >>> >>> > > ----------------------------- > 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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