Interesting discussion, but one that bothers me a bit due to my reading of Boscovic as an undergrad and my familiarity with the Scottish “Common Sense” philosophers.
My understanding of Boscovician atoms is that they are centres od force fields that very in sign and intensity, being effective over varying distances. The overall effect is a sinusoidal liker wave centred on the atom. In this sense Boscovician atoms are not points, but have an extended scope, which varies with distance. The point aspect stems from this filed being zero at the centre, all the effects stemming from more distant fields centred on the atom. The Scottish Common Sense Philosophers, Like Thomas Young (usually classed as an empiricist) took the view that we should treat a phenomena as it appears, irrespective of its real nature, until we know more. In the Boscovician case this would mean treating atoms as very small, but with the Boscovician field properties, without reference to their smaller nature or their real structure. Young, the wave theorist, was a follower of this school, and so was, to some extent Maxwell. So I think it is historically misleading to compare Boscovician atomism with continuous views – I see no contradiction – much as the problem might be interest in itself. I am more than a little reluctant to set up metaphysical problems that aren’t supported by the science itself, and I think it requires careful and unbiased historical study to ensure this is enforced. John Collier Emeritus Professor and Senior Research Associate Philosophy, University of KwaZulu-Natal http://web.ncf.ca/collier From: Jerry LR Chandler [mailto:jerry_lr_chand...@icloud.com] Sent: Wednesday, 08 March 2017 6:51 PM To: Peirce List <peirce-l@list.iupui.edu> Cc: Benjamin Udell <baud...@gmail.com>; Frederik Stjernfelt <stj...@hum.ku.dk>; Jeffrey Brian Downard <jeffrey.down...@nau.edu>; Jeffrey Goldstein <goldst...@adelphi.edu>; Jon Alan Schmidt <jonalanschm...@gmail.com>; Ahti-Veikko Pietarinen <ahti-veikko.pietari...@helsinki.fi>; John F Sowa <s...@bestweb.net> Subject: Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and Boscovich points. List, John: I’m rather pressed for time so only brief responses to your highly provocative post. Clearly, your philosophy of mathematics is pretty main stream relative to mine. But this is neither the time nor the place to develop these critical differences. My post was aimed directly at the problem of the logical composition of Boscovich points. This is inferred from CSP’s graphs and writings. I would ask that you describe your views on how to compose Boscovich points into the chemical table of elements. Please keep in mind that each chemical element represents logically a set of functors in the Carnapian sense. see: p. 14, The Logical Syntax of Language. > On Mar 7, 2017, at 8:56 AM, John F Sowa > <s...@bestweb.net<mailto:s...@bestweb.net>> wrote: > > Jerry, > > We already have a universal foundation for logic. It's called > "Peirce's semiotic”. Semiotics is not, in my view, a foundation for logic which is grounded on antecedent and consequences. Neither antecedents nor conclusions are intrinsic to the experience of signs yet both are necessary for logic. Logic is grounded in artificial symbols. Applications of logic to the natural world requires symbolic competencies appropriate to the application(s). > > JLRC >> the mathematics of the continuous can not be the same as the >> mathematics of the discrete. Nor can the mathematics of the >> discrete become the mathematics of the continuous. > > They are all subsets of what mathematicians say in natural languages. I reject this view of ‘subsets’ because of the mathematical physics of electricity. Many mathematics reject set theory as a foundations for mathematics, including such notables as S. Mac Lane (I discussed this personally with him some decades ago.) My belief is that numbers are the linguistic foundations of mathematics and the physics of atomic numbers are the logical origin of (macroscopic) matter and of the natural sciences. (Philosophical cosmology is a different discourse.) > > For that matter, chess, go, and bridge are just as mathematical as > any other branch of mathematics. They have different language games, > but nobody worries about unifying them with algebra or topology. > Board games are super-duper simple relative to the mathematics of either chemistry and even more so wrt life itself. > I believe that Richard Montague was half right: > > RM, Universal Grammar (1970). >> There is in my opinion no important theoretical difference between >> natural languages and the artificial languages of logicians; indeed, >> I consider it possible to comprehend the syntax and semantics of >> both kinds of languages within a single natural and mathematically >> precise theory. The logic of chemistry necessarily requires illations within sentences that logically connect both copula and predicates associated with electricity. This logical necessity is remote from the logic of the putative “universal grammars.” (I presume that a balanced chemical equation is analogous to the concept of the term “sentence” in either normal language or mathematics.) > > But Peirce would say that NL semantics is a more general version > of semiotic. Every version of formal logic is a disciplined subset > of NL (ie, one of Wittgenstein's language games). > JLRC >> For a review of recent advances in logic, see >> http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf, >> 13 QUESTIONS ABOUT UNIVERSAL LOGIC. > > Thanks for the reference. On page 134, Béziau makes the following > point, and Peirce would agree: >> Universal logic is not a logic but a general theory of different >> logics. Analyze this quote. Is he saying anything more beyond a contradiction of terms? >> This general theory is no more a logic itself than is >> meteorology a cloud. What the hell is this supposed to mean? Merely an ill-chosen metaphor? > > JYB, p. 137 >> we argue against any reduction of logic to algebra, since logical >> structures are differing from algebraic ones and cannot be reduced >> to them. Universal logic is not universal algebra. > > Peirce would agree. > > JYB, 138 >> Universal logic takes the notion of structure as a starting >> point; but what is a structure? > > Peirce's answer: a diagram. Mathematics is necessary reasoning, > and all necessary reasoning involves (1) constructing a diagram > (the creative part) and (2) examining the diagram (observation > supplemented with some routine computation). > > What is a diagram? Answer: an icon that has some structural > similarity (homomorphism) to the subject matter. Chemical isomers are not mathematical homomorphisms because of the intrinsic nature of chemical identities. Thus, this reasoning is not relevant to the composition of Boscovichian points. The reasoning behind chemical equations is not “necessary” in this sense of generality, but is always contingent on both the (iconic?) perplex numbers and the functors. See, for example, Roberts, p. 22, 3.421. > JYB, 145 >> Some wanted to go further and out of the formal framework, namely >> those working in informal logic or the theory of argumentation. >> The trouble is that one runs the risk of being tied up again in >> natural language. > > Universal logic (diagrammatic reasoning) is *independent of* any > language or notation. The differences between the many variants > are the result of drawing different kinds of diagrams for sets, > continua, quantum mechanics, etc. (Note Feynman diagrams.) If this is the case, then find a mode of explanation that is relevant to Boscovichian points and compositions of matter. To me, these sentences are a very slippery use of language. Logic remains tied to its ancient roots, antecedents and consequences. Diagrammatic reasoning is just a picture. See the excellent book by Greaves on the Philosophy of Diagrams. > > I develop these points further in the following lecture on Peirce's > natural logic: http://www.jfsowa.com/talks/natlogP.pdf > > See also "Five questions on epistemic logic" and the references > cited there: http://www.jfsowa.com/pubs/5qelogic.pdf I read these very nice papers. But, I do not find your arguments very useful for either chemistry or biology which demand that the concept of identity is antecedent to all consequences for the logic of the grammar and the “algebra” of the sentences. My general view is that if such broad assertions were valid pragmatically, then we would have a mathematics of life itself. So, how do you relate your work (and your logical assertions) to the dynamic of life grounded in the genetics and contextual relations to health and disease? These are the issues of interest to me. I believe that both the logic of Tarski (meta-languages) and mereology (part-whole illations over chemical identities) are necessary and have published papers to that effect. Thus, by and large, we are talking past one another. It is my view that 21 st Century scientific logic is dependent on symbolic competencies. Cheers Jerry > > John > > ----------------------------- > 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<mailto:peirce-L@list.iupui.edu> . To UNSUBSCRIBE, > send a message not to PEIRCE-L but to > l...@list.iupui.edu<mailto: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. 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