[peirce-l] Re: on continuity and amazing mazes
Thomas:Your thoughts on the potential relation between Peirce's continuity and mathematical history were fascinating. I must confess that I am a bit of a skeptic when it comes to the possibility of a sensible relation between logic, any logic, and a philosophy of mathematics.Nonetheless, I remain puzzled by the concept of the "form" of logic, .Should logic be grounded in the logos? That is, in the sentences of the language?What is it that would trigger the jump to forms? Roughly speaking, the abstract conceptualization of mental motion from sentences to geometry?I note in passing that Waismann's concept of number as the root of mathematics avoids this particular issue as the concept of "number" already exists in the natural language and does not acquire a sense of geometry in ordinary usage, in ordinary day to day communication.CheersJerryOn Mar 15, 2006, at 1:08 AM, Peirce Discussion Forum digest wrote:Subject: Re: on continuity and amazing mazes From: "Thomas Riese" [EMAIL PROTECTED] Date: Tue, 14 Mar 2006 13:39:29 +0100 X-Message-Number: 2 On Mon, 13 Mar 2006 19:37:14 +0100, Marc Lombardo [EMAIL PROTECTED] wrote: Thomas, If you don't mind my asking, what's wrong with the "nonstandard analysis" approach to illustrating continuum, so long as that approach is VERY nonstandard? I was quite convinced by Hilary Putnam's introduction to "Reasoning and the Logic of Things." Putnam suggests that rather than understanding infinitesimals as deriving from major points, instead we understand all points as themselves infinitesimals and all infinitesimals as points, such that any infinitesimal point names another infinity of infinitesimals. It's difficult to express things in a few useful words, Marc, but I'll try. I know what Hilary Putnam writes. I believe that he extremely underestimated what a black belt master logician like Peirce can do with these seemingly simplistic, "childish" syllogistic forms. And it is very important to understand thst Peirce's logic is primarily focused on "forms". Another master in this way of thinking was the mathematician Leonhard Euler and in fact Peirce perhaps received his idea for the "cut" from Euler (in his Letters to a German Princess). John Venn later "amended" this form, but he misunderstood it completely. Euler wasn't childish. Neither was Peirce. Euler could work miracles in analysis, but he had no explicit logical theory. He simply knew what he did. Later then others came, working more or less by rule of thumb and that often landed them in the ditch. They simply did not know what they were doing. So there was a crisis in mathematics. To save mathematical logic there had to come Cauchy and Weiertrass, Dedekind and Cantor etc. Secure foundations were needed. But that also closed the door to a lot of possibilities. Peirce found the logic behind what Euler has been doing, I believe. But now we have "Bourbakism" in mathematics, i.e. set theory as a language, which is by no means "neutral". Just an example: in mathematics, if you have discovered an "isomorphism" you have made a discovery, you have "reduced" things and then you are finished with these things. They are just simply "the same thing". The equivalence relation is so to speak the primary mode of _expression_. Peirce is exactly interested in the relation between isomorphous forms. His primary relation is the general form of transitivity. The difference has far reaching, profound implications. So in nonstandard anylysis as soon as you base things on "point sets", however generally understood, you have already missed the point (no pun intended) of Peirce's continuity. Peirce can represent it in that form (and then mathematical points split etc), but I don't believe it's possible the other way round. But what I here say, can be only very loose talk indeed of course. Just to give you a vague idea what I mean. Cheers, Thomas. Jerry LR ChandlerResearch ProfessorKrasnow Institute for Advanced StudyGeorge Mason University --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: peirce-l digest: April 18, 2006
Dear Gary / Kristi:On Apr 19, 2006, at 1:05 AM, Peirce Discussion Forum digest wrote:Dear Gary, I was quite delighted in reading what you wrote: The second law, as i understand it, says that any actual use of energy degrades it, i.e. reduces its quality or usefulness. In the jargon of thermodynamics, any reduction of an energy gradient produces entropy. This means that in a given isolated system, any process of energy exchange among its subsystems results in a less orderly state of the whole system. I find this paragraph fragment to be highly controversial.Why?How does it relate to life?For example, sunlight is the source of energy for plant growth.The chemical process is called photo synthesis.During photosynthesis, photons are absorbed as the source of motion for splitting water into hydrogen ( special form of )and the metabolic chain creates carbohydrates from carbo (n dioxide) and water (hydrate.)If one considers the food web of ecologies and the role plants play in fueling the food chain (including us), one can ponder the logical consequences of such casual beliefs.In my personal opinion, such narratives are only used by individuals with a very very limited knowledge of life (and the chemical sciences) itself.CheersJerry Jerry LR ChandlerResearch ProfessorKrasnow Institute for Advanced StudyGeorge Mason University --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Peirce and Prigogine
to consciousness is ambiguous in ordinary language and needs special measures to disambiguate. One such measure is Stan Salthe's specification hierarchy, which is explained in our article at http://www.cosmosandhistory.org/index.php/journal/article/view/44 (and in many of Stan's other articles.) Stan Salthe is also a long time participant in WESS affairs. His efforts to separate hierarchy theory into two categories are notable. Your abstract pretty much sums up my interests as well. I'm reading it now. Victoria In closing, I would add a comment on symbol systems. The chemical sciences developed a symbol system, a very special symbol system, that is based on the list of atomic numbers and relations between these numbers. Chemical relations also form a particular logic that is different from physical logic. This logic can be used to calculate the number of certain structural and optical isomers - neither of which can be calculated from physical or mathematical principles. This is a very special form of logic that was used to develop molecular biology and genetics. These two sciences, both developed over the past 100 years, use chemical logic, not Newtonian calculus, to describe cause and effect relations in living systems. These two sciences also take an Aristotelian view of categories - individuals, species, and genera - for constructing decision trees. The dynamic decisions of cells in expressing DNA information are expressed in terms of relations among chemical symbols and chemical logic. I presuppose that most readers of this list will find these statements to clash with their philosophy of physics, the philosophy of genera. I can merely add that the symbol system of physics is not the sole symbol system and that the philosophy of physics is not the sole philosophy of science. The philosophy of the chemical sciences is vastly more complex than the philosophy of physics because it must posit quantitative relations among individuals, species and genera. It must provide a source of generative grammars, not merely genera. Such is Life Itself. Cheers Jerry Jerry LR Chandler Research Professor Krasnow Institute for Advanced Study George Mason University --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: Peirce and Prigogine
Arnold: On Apr 29, 2006, at 1:06 AM, Peirce Discussion Forum digest wrote: In Vol IV of the Collected Papers (and, I would guess, throughout the New Elements of Mathematics, a copy of Eisele's edition of which I would dearly love to get!) he goes to considerable lengths in exploring the role that the mathematics of transitive phenomena plays in grounding higher-order mathematical systems. Indeed, the importance of transitive phenomena in Peirce has recently been discussed briefly on the list. In short, we may well find that the very notion of a Symbol System involves transitivities, and that Peirce very thoroughly investigated this relation (as, of course, = a species of the Logic of Relations!!). Yes, I concur, the transitive relation is of utmost important in continuous mathematics. But not necessarily in discrete mathematics. Symbols may be used in either, often with belief in substitution of numbers into variables. The relations of a chemical bond create an ordering within a chemical word but the chemical numbers are not transitive in the sense of classical mathematics, ie, if a is greater than b, and if b is greater than c, then a is greater than c. The table of elements uses numbers in two senses, the vertical columns and the horizontal rows. This well established fact lies at the heart of chemical logic, along with electrical concepts. Indeed, one might say that chemical logic is the logic of electricity. I have read only a fraction of Peirce's works, often searching for understanding on exactly how he fit his degree in chemistry into his logic. Thus far, it appears more as an influence rather than a basis. His use of drawing have some connection with the chemical notion of functional groups or chemical radicals. At this point in time, much of medicine and biology is being rationalized, not in terms of mathematics or physics, but in terms of chemical logic, structures, and chemical symbols. Thus, the open question to the list is, How does Peirce's work relate to biology and medicine? Certainly some relation must exist, but how is it expressed in symbols? Classes? Categories? Types? Subjects? Objects? Predicates? Copula? Cheers Jerry --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Porphyry's Trees
Jim: On May 9, 2006, at 1:06 AM, Peirce Discussion Forum digest wrote: Still this account leaves untouched the matter of symbols standing for = the meaning of objects. The indexical and iconic functions of symbols = tell us what meaning is being refered to but they do not shed any light = upon how the function of standing for is accomplished. My hunch is that = on a material level (to begin with the simplest case) the act of taking = one object to stand for another is a case of mistaken identity. In = effect, the simplest case is when an icon is actually mistaken for the = object it portrays. Without getting into details it is my guess that = symbolic or imputed standing for evolved as a matter of habit from = this prototypical example. And I believe this occurred because there are = marked advantages in being able to use objects as tools for representing = or standing for other objects. Especially if the objects being used to = do the representing are much lighter and easier to manipulate than the = objects themselves, because in such cases one can then use the stand in = objects to do thought experiments and forcast the outcome of events = before actually carrying them out with the objects themselves. This is = very efficient in terms of time and energy costs, but some loss of = accuracy is inevitable because in fact the symbol is not the object it = represents and can therefore not fully duplicate the actual meaning = (conseaquences) of the object is represents. I fear I may be guilty of repeating either what is true but already well = known or suggesting things that are new but false. So I apologize for = that, but hope I've made my views sufficiently clear such that they can = be refuted. In any case this has been helpful to me and I would = appreciate any feedback. This response has been given a different title to indicate a different color of the thread, perhaps a different warp and woof. Again, I respond from the perspective of the chemical symbol system and its logic. Hence, this response may or may not be useful to you. Your paragraph above appears to my mind to be closely aligned with Porphyry's discussion of Aristotelian categories. In particular, what is your position with respect to universals and nominalism? (See: Five Texts on Mediaeval Problems of Universals, Paul V. Spade, Hackett Publishing, Cambridge, 1994.) (Also, Ernan McMullin's (Notre Dame?) book on Matter may be of interest - I do not have the title at hand.) Historically, by the mid 20th Century, empirical evidence supported the belief that all durable material objects could be listed as composed from a small number of chemical elements. Each of these chemical elements was given a symbol and the symbols can be ordered into a linear listing by number. Each object of our experience is believed to be a composition either of individual elements, a species composed from individual elements or a mixture of species, perhaps organized into networks of relations of unbounded perplexity. Uniqueness is propagated from the source(s). Identity is specific for the individual object (NOT the same as mathematical identity!) This has implications for field theories. This uniqueness, specified by a name, serves as the basis for calculations for quantum chemistry and can NOT be incorporated into thermodynamics per se. Your sentence: This is = very efficient in terms of time and energy costs, but some loss of = accuracy is inevitable because in fact the symbol is not the object it = represents and can therefore not fully duplicate the actual meaning = (conseaquences) of the object is represents. seems to confuse internal and external events and processes. Names are assigned to external objects based on properties. Assigning a systematic name does not mean that we can reify the object in our minds. But, we can point to it and we can communicate about it in an exact (and incomplete) manner. And, we can enumerate its components and their organization. And, for those skilled in the art, we can paint an exact picture of it (it being a chemical structure) in our minds. The properties of a chemical object are listed separately from the name. Two different ideas. If one contrasts these concepts with the conceptualization of physics, what does one conclude? Or with other views of categories? Your view of symbols (not signs!)? Personally, I find it utterly amazing that after nearly 20 centuries, the drawings of Porphyrean trees from Aristotelian categories often remain logically consistent today! (And, I note in passing that Topos Theory, a derivative from Category Theory, has been asserted to generate all such possible trees! This is beyond my feeble imagination.) Cheers Jerry --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: NEW ELEMENTS: So what is it all about?
on paper, or in Internet searches and encyclopedia = articles, which are pretty much what's available to me. Yes. But first, the issue of Feyman diagrams. These diagram's presuppose continuous functions and physical laws. Chemistry presupposes invisible particles, indivisible particles, individual particles. In a certain sense, the atomic numbers are an index, an exact index for durable electrical particles. Physicians have elaborated vast collections of (subjective?) indices for describing diseases. Within the International System of Units, many indices are constructed, for example, the index for hardness. The geneticists have elaborated a symbolic system for representing genes and logical relations among them (cis, trans, a distance metric). Genes are also invisible particles, but usually genes do not function individually or independently but as part of the entire system of the organism. As for physical thought, it focuses on a few concepts, mass, space, time, motion, energy, and uses continuous variables to associate these variables. These are summarized by the natural international system of units (De tracy, about 1800 and subsequent elaborations) which promote substitution of one concept for another. Chemical symbols can not be substituted one for another, that is, iron can not be substituted for gold. The implications of this simple fact profoundly influence one's philosophy of science if it is accepted at face value. (Perhaps this is one point of interest to Victoria.) (I am attempting to provide short answers in a language for non- specialists. If I have failed, please let me know and I will make an effort to reformulate the grammar but not the concepts. Transdisciplinary communication is extra-ordinarily difficult.) Pick up an introductory chemistry text and ask yourself, do these sentences fit with what is written there? Now, I must run. I leave two wide open questions: Was the motivating force for Peirce's synthesis of his logical system the chemical symbol system? What argues AGAINST this possibility? Cheers Jerry On May 9, 2006, at 1:06 AM, Peirce Discussion Forum digest wrote: Subject: Re: NEW ELEMENTS: So what is it all about? From: Benjamin Udell [EMAIL PROTECTED] Date: Mon, 8 May 2006 16:54:09 -0400 X-Message-Number: 8 Jerry, Your thumbnail sketch of chemical logic seems clear to me, and my = memories from long-ago high-school chemistry fit with it. The striking thing to a gawker like me who knows very little about = chemistry is those symbols, and it's encouraging to one's intuition to = be reassured that chemists themselves find the symbols striking, a theme = worth addressing. The idea seems to be that one thinks the chemistry = through those symbols; the symbols so empower chemical thought that = chemists make a theme of it. What I wonder are two things: 1. I've seen that it's called a logic. I'd like to ask, just to be = sure, are its characteristics distinctly logical, order-theoretic, or = anything like that, as opposed to, say, abstract-algebraic, or = enumerative-combinatorial, or even graph-theoretic? 2. Is there anything that you think comparable with chemical thought's = use of chemical symbolism, using signs -- diagrams, symbols, semblances, = or indexes -- in any other major research fields physical, material, = biological, or social/human? Physicists use Feynmann diagrams, but those = don't seem to have anything like the prominence in physics which = chemical symbolism has in chemistry. On the other hand, I'm hardly one = to know. But when I think of physical thought, I think of mathematical = expressions a lot more generally, rather than just of visual diagrams. = As for some analogous sort of key vehicle of biologists' thinking, -- I = can't even think of a typical biologist, there seem such diverse = kinds, at least on paper, or in Internet searches and encyclopedia = articles, which are pretty much what's available to me. Best, Ben Udell - Original Message -=20 From: Jerry LR Chandler [EMAIL PROTECTED] To: Peirce Discussion Forum peirce-l@lyris.ttu.edu Sent: Saturday, May 06, 2006 7:39 PM Subject: [peirce-l] Re: NEW ELEMENTS: So what is it all about? Ben: My comment is from a chemical perspective. It may or may not be of = help to you. On May 6, 2006, at 1:06 AM, Peirce Discussion Forum digest wrote: But first, on a general note, let me say that among the issues driving = my current display of confusion error, is the question: if = comprehension is for quality predicate, while denotation is for = objects (resistances/reactions), then what dimension is for = representational and logical relations themselves? Words like not, = probably, if, etc. do not designate either qualities or objects, nor = do they represent objects as having this or that quality. Names of chemical substances are always a subject of a chemical = sentence. A chemical sentence
[peirce-l] Re: motivating force for Peirce's synthesis
by
Peirce himself as his destiny, from the time that he first read
Whately's _Elements of Logic_ (within a week or two of his twelfth
birthday, in 1851). Since that time, he often said late in life, it
had never been possible for him to think of anything, including even
chemistry, except as an exercise in logic. And so far as he knew,
he was
the only man since the Middle Ages who had completely devoted his life
to logic. There is nothing here to indicate that his either his logic
or his devotion to it stemmed from his studies in chemistry.
I have not read Max Fisch.
But, chemical engineering did not exist as a discipline at that time.
Engineering, such as it was, was a generic discipline. General
problem solvers.
Leibneiz was also an engineer in his early career. Applied
mathematics and machines.
If this analysis is accurate, then it's up to you to demonstrate, from
Peirce's own texts, evidence that the motivating force for Peirce's
synthesis of his logical system was the chemical symbol system.
Since
this would run very much against the grain of Peirce's general
testimony, what need is there for anyone to argue AGAINST it?
My conjecture is merely a conjecture.
Proof?
You got to be joking.
In the year 2006, I doubt that anyone can transpose themselves into
the cultural mindset of language, belief and social relations that
existed 150 years.
Let me emphasize again that i'm not trying to offer an answer to your
questions -- i'll leave that to those with more authority and
expertise
in Peirce's writings than i can claim. I'm merely asking for
clarification by trying to show why it's needed.
It certainly is not needed.
My objective is to understand chemical logic.
If Peirce has a general logic, then it should be applicable to
logical problems in modern chemistry, much as Aristotlian syllogisms.
Now, chemical logic is intimately relationed to Porphyrean trees and
a special grammar that relates nouns to nouns.
The chemical question is, is the proposal of a chemist for a
generalized logic consistent with chemical logic?
(BTW, Leibneiz's logical calculations appear to be related to his
work in chemistry.)
Now, this question may be irrelevant to the interests of philosophers
in general and to other members of this list. But, to me, it is
important.
Why is this important?
One example is given.
Prigogine claimed a chemical foundation for his views on time.
In fact, Prigogine worked strictly from classical mathematics
(differential equations).
He excluded chemical logic from his thinking. He introduces time in
terms of rate of entropy production.
When I attempted to address these issues with him, in an every so
gentle way, after a few minutes, he surmised the direction of the
conversation and shortly thereafter, terminated it.
Other examples could be given, for example, explication of the logics
of genetics or metabolism.
Finally, I have often made the mental error of thinking that I
understood something and closed the file. Nearly always, it was a
mistake to close a file.
Do open minds require open files in order to open new ideas?
I will end with another open question:
Can anyone explicate a symbol for time in terms of Firstness,
Secondness and Thirdness?
Cheers
Jerry
gary F.
}Every man is tasked to make his life, even in its details, worthy of
the contemplation of his most elevated and critical hour. [Thoreau]{
gnusystems }{ Pam Jackson Gary Fuhrman }{ Manitoulin University
}{ [EMAIL PROTECTED] }{ http://users.vianet.ca/gnox/ }{
Jerry LR Chandler
Research Professor
Krasnow Institute for Advanced Study
George Mason University
---
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[peirce-l] Re: peirce-l digest: May 11, 2006
On May 12, 2006, at 1:05 AM, Peirce Discussion Forum digest wrote: Off-list, Gary Richmond, who's quite busy, sent me this: 66~~ Chemistry expresses itself in Peirce's valency theory (the term is not his but Ken Ketner's who hasn't been given enough credit yet for his work in this area, something you hinted hadn't been developed in Pierce, etc.). In any event, see the reduction thesis at work in organic chemistry here: http://en.wikipedia.org/wiki/Organic_nomenclature Trichotomy, the reduction thesis, the development of EGs, etc. all come from Peirce's knowledge of and work in chemistry. In some writings he makes this explicit. ~~99 This is a curious paragraph. It is too terse for me to understand it. The first sentence is ambiguous to me. In particular, what is the reference for the term, reduction thesis in this context? Chemical names are assigned on the basis of a constructive thesis, as study of the indicated web address will indicate. This post apparently contradicts Gary F.'s views. Can someone untangle the intended communication? Cheers Jerry --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] If a valence of four had been known to Peirce, would he have constructed a logic of firstness, secondness, thirdness and fourthness?
Jim: Thank you very very much for these quotes! They provide a partial answer to my open query. My chemical perspective from the early 21 Century follows. Dear Ben, Gary R, Jerry-- Also in Vol 5 of the chronological edition (page 306 and 307) Peirce speaks of chemical valency: BEGIN QUOTE A straight road between two places, if not regarded itself as a place, is not a third place but only the pairedness of the two palces it connects. But a forking road involves a third place. Now no number of straight roads put end on end will ever have more than two ends after all; but forking roads put end on end with ramify into any number of ends. In like manner, in chemistry, were there no atoms but univalent ones, that is such as are capable fo pairing only, there could be no combination but binary combinations. Whereas bivalent atoms, or those capable fo uniting with two others, which are therefore thirds, might give rise to combinations of any number of atoms. But bivalent atoms may be considered as involving only secondness in respect to having only two free bonds, and consequently they can only unite two univalent atoms however they may be arranged and multiplied. While trivalent atoms because they have three free bonds will serve to unite any number of univalent atoms. END QUOTe I also find on page 393 of the same volume an entry in the Centruy Dictionary for Element in which Peirce referes to the accepted views of Mendelejeff and himself (Peirce) provides a listing of 70 elements arranged in series and eight groups. I leave it to you folks to draw whatever inferences you may -- nothing fruitful springs to my mind. Cheers, Jim Piat A chemical interpretation of the quote can be given. The first quote suggests that Peirce used a direct one to one correspondence relation with the concept of valence as the principle basis for his generalized logic. This in turn suggests a simple bijective correspondence between the concept of chemical valence values and firstness, secondness and thirdness. This is very, very surprising to me! Remarkedly simple. But how does this basis justify the generalization to a general system of logic? In particular: If a valence of four had been known to Peirce, would he have constructed a logic of firstness, secondness, thirdness and fourthness? If a valence of five had been known to Peirce, would he have constructed a logic of firstness, secondness, thirdness, fourthness and fifthness? If a valence of six had been known to Peirce, would he have constructed a logic of firstness, secondness, thirdness, fourthness, fifthness and sixthness? If a valence of seven had been known to Peirce, would he have constructed a logic of firstness, secondness, thirdness, fourthness, fifthness, sixthness and seventhness? And so forth. The metaphor of length of combinations of paths with and without branches is sort of a primitive precursor of the concept of categories of mathematical graphs. 21 st Century chemistry has developed vastly richer concepts of valence. Does this imply that 21 st Century chemistry is the potential basis for a vastly richer logic? A more general logic?:-) Is it not wonderful how a small number of facts can be abstracted into beautifully constructed narratives that expand the domain of discourse such the origins are fully and completely obscured? Thanks again for posting the quote. Cheers Jerry LR Chandler --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: algebraic logic and category theory
be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can be reformulated in the many-valued setting in terms of categorical postulations. So, it is possible, by aid of categorical machineries, to establish theories of many-valued complete lattices, many-valued completely distributive lattices, and so on. This paper presents a systematical investigation of many-valued complete distributivity, including the topics: (1) subalgebras and quotient algebras of many-valued completely distributive lattices; (2) categories of (left adjoint) functors; and (3) the relationship between many-valued complete distributivity and properties of the quantale of truth values. The results show that enriched category theory is a very useful tool in the study of many-valued versions of order-related mathematical entities. Full-text: PostScript, PDF, or Other formats References and citations for this submission: -- The abstract is available at:http://arxiv.org/abs/math/0603590 and the full article can be downloaded there in several formats including pdf(http://arxiv.org/PS_cache/math/pdf/0603/0603590.pdf) Irving H. Anellis [EMAIL PROTECTED] ; [EMAIL PROTECTED] ; [EMAIL PROTECTED] http://www.peircepublishing.com http://www.abebooks.com/home/PEIRCEPUBLISHING --=20 Jerry LR Chandler Research Professor Krasnow Institute for Advanced Study George Mason University --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: If a valence of four had been known to Peirce, would he have constructed a logic of firstness, secondness, thirdness and fourthness?
of the relation of joint identity, follows the law of=20 valency.) Thus, the predicate is blue is univalent, the predicate=20 kills is bivalent (for the direct and indirect objects are, grammar=20 aside, as much subjects as is the subject nominative); the predicate=20 gives is trivalent, since A gives B to C, etc. Just as the valency of=20 chemistry is an atomic character, so indecomposable concepts may be=20 bivalent or trivalent. Indeed, definitions being scrupulously observed,=20 it will be seen to be a truism to assert that no compound of univalent=20 and bivalent concepts alone can be trivalent, although a compound of any = concept with a trivalent concept can have at pleasure, a valency higher=20 or lower by one than that of the former concept. Less obvious, yet=20 demonstrable, is the fact that no indecomposable concept has a higher=20 valency. Among my papers are actual analyses of a number greater than I=20 care to state.+1 They are mostly more complex than would be supposed.=20 Thus, the relation between the four bonds of an unsymmetrical carbon=20 atom consists of twenty-four triadic relations. Careful analysis shows=20 that to the three grades of valency of indecomposable concepts=20 correspond three classes of characters or predicates. Firstly come=20 firstnesses, or positive internal characters of the subject in itself; = secondly come secondnesses, or brute actions of one subject or=20 substance on another, regardless of law or of any third subject; thirdly = comes thirdnesses, or the mental or quasi-mental influence of one=20 subject on another relatively to a third. Since the demonstration of=20 this proposition is too stiff for the infantile logic of our time (which = is rapidly awakening, however), I have preferred to state it=20 problematically, as a surmise to be verified by observation. The little=20 that I have contributed to pragmatism (or, for that matter, to any other = department of philosophy), has been entirely the fruit of this outgrowth = from formal logic, and is worth much more than the small sum total of=20 the rest of my work, as time will show. Benjamin Udell wrote: Jerry, Gary Richmond's view doesn't technically contradict Gary F.'s statements= , since Gary F.'s statements were qualified by the possibility of somebod= y's producing evidence, though Gary F. obviously seemed doubtful about th= e idea of the chemical connection. I felt kind of doubtful too, though = I myself have been aware of people's calling Peirce's theory about monads= , dyads, triads, a valency theory. Actually I wish I'd asked Gary Ric= hmond about it when he included the valency theory language in a presen= tation which he wrote which I produced for him in PowerPoint http://mem= bers.door.net/arisbe/menu/library/aboutcsp/pr-main.htm#richmond . At the= time, I just kind of assumed vaguely...well, I don't know what I was thi= nking. I was thinking about how I was making the presentation look kind o= f spacy and the closing theme from the old Fireball XL5 TV show was muc= h in my mind. I'm so deep sometimes. Anyway, if Gary R. says that Peirce = made the chemistry connection explicit in some passages in his writings, = then I'd assume that Peirce did so.=20 Of course, those would be some interesting passages to read! Unfortunate= ly, Gary R. has been very busy lately. But I'll ask him later because I'm= curious to read them too. I've been kind of busy myself, or I'd have res= ponded sooner. I started off writing a reply to Jim Piat and it got so lo= ng that I may never send it. The Reduction Thesis is: All relations of more than three elements are r= educible to triadic relations, but triadic relations are not reducible to= dyadic and monadic relations. Best, Ben Udell =20 [Ben] Off-list, Gary Richmond, who's quite busy, sent me this: 66~~ Chemistry expresses itself in Peirce's valency theory (the term is no= t his but Ken Ketner's who hasn't been given enough credit yet for his wo= rk in this area, something you hinted hadn't been developed in Pierce, et= c.). In any event, see the reduction thesis at work in organic chemistry = here: http://en.wikipedia.org/wiki/Organic_nomenclature=20 =20 Trichotomy, the reduction thesis, the development of EGs, etc. all come = from Peirce's knowledge of and work in chemistry. In some writings he mak= es this explicit. =20 ~~99 =20 =20 [Jerry] This is a curious paragraph. It is too terse for me to understand it. The first sentence is ambiguous to me. In particular, what is the reference for the term, reduction thesis i= n this context? Chemical names are assigned on the basis of a constructive thesis, as s= tudy of the indicated web address will indicate. This post apparently contradicts Gary F.'s views. Can someone untangle the intended communication? =20 =20 Cheers Jerry =20 Jerry LR
[peirce-l] Re: Trikonicb.ppt Slide 18
Ben / Jim: Your ppt file is very imaginative! Although I am uncertain of how much of it I understand, I enjoyed looking at it and it brings several questions to mind. In particular, I am curious about the intended meaning of slide 18. Why C2H6 - e ? Can you explain your understanding / usage of the concept of grammar? Are you seeking to invoke a concept of a directed graph with your usage of the term vector? Are you also struggling with a sign of time? (Slide 23?) Cheers Jerry --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Sinsign, Legisign, Qualisign - help!
To List: A number of recent posts have addressed the topics of: On Jun 19, 2006, at 1:05 AM, Peirce Discussion Forum digest wrote: Re: Sinsign, Legisign, Qualisign I am seeking help in understanding the importance of these terms to individual scholars. The definitions are reasonably clear, at least to me. At issue is the question of why are these terms important to understanding human communication. The appending of three unusual prefixes to the concept of a sign is clearly a creative use of language. The apparent (mechanical) objective is to form three new categories as derivatives of the parent word, sign. Could one imagine other prefixes to the word sign? Could one imagine more than three other prefixes? How is this context important in distinguishing among paths of usages? What other terms might be substituted for these terms? Do these terms impact the concept of a grammar? Is this ad hoc extension of the concept of sign desirable for mathematics? How does it contribute to the mathematical usages of signs? Is it desire to bring the concept of 'many' into the concept of 'sign' in this manner? Why? I presume that many readers of this list are teachers and have lectured on these terms. I have been struggling with these terms for some time and hope that knowledgable Peircian students can explain the importance of this seemingly disconnected usage of grammar from various perspectives. Cheers Jerry --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Sinsign, Legisign, Qualisign - help!
word, sign. Could one imagine other prefixes to the word sign? Peirce imagined quite a few other prefixes to the word sign. But = presumably you mean such as to make a semantic distinction, not merely a = morphological improvement. Could one imagine more than three other prefixes? Your question would be helpfully clarified if you stated it directly = instead of morphologically. Obviously one can imagine, so to speak, many = more classes of signs, and Peirce certainly did. Can one imagine a = classification into a 4-chotomy of signs? Of course one can, but, for = better or worse, it would be unPeircean. Triadism is built deeply into = Peirce's semiotic. How is this context important in distinguishing among paths of usages? It's a way of distinguishing between specific occurrences of signs, the = appearances of signs, and the general meaning or habitual = 'conventional' interpretation of a sign. (The symbol's interpretant, in = being an inferential outcome, usually goes beyond such conventional = significations.) For many practical and theoretical purposes, English = horse and Spanish _caballo_ are the same legisign. Horse and = _caballo_ won't be regarded as the same qualisign (except by those for = whom all human words are indistinguishably the same qualisign). Horse = and _caballo_ won't be regarded as ever being the same sinsign (except = by those for whom pretty much all human occurrences are one single = undecomposable occurrence). What other terms might be substituted for these terms? Peirce himself offered, at various times, at least three sets of words = for the same trichotomy of logical terms: Tone, token, type. Qualisign, sinsign, legisign. Potisign, actisign, famisign. One might call them: a quality-as-a-sign, a singular-as-a-sign, and a general-as-a-sign. He at least mentioned other words as candidates as well. Do these terms impact the concept of a grammar? It depends on the grammar. If this were some other forum, your = conception of grammar might be implicitly understood and accepted. = Here, in a philosophical forum which happens to be a crossroads of many = specialties and traditions, you need to define it and state the context = and tradition from which you are drawing your sense of the word, in = order to make yourself widely understood. Is this ad hoc extension of the concept of sign desirable for = mathematics? How does it contribute to the mathematical usages of signs? You specified neither the hoc nor the basal concept of which you = characterize Peirce's terms as an extension. I guess everybody likes to = think of his or her concept as the genus and of the other forms of the = concept as the specializations. But you haven't said what your concept = is, so there's no way to judge the plausibility of your characterization = of it as an ad hoc extension. Peirce would probably argue that semiotic is desirable for philosophy = about mathematics. His classification of semiotic (aka logic aka sign = studies) as part of philosophy is his statement that semiotic = presupposes mathematics and that mathematics does not presuppose = semiotic. Nobody actively participating on peirce-l has self-identified as a = mathematician, but perhaps some peirce-lister could say whether any = mathematician has commented on the possibilities of the = qualisign/sinsign/legisign conception's contributing to mathematical = usages of signs. Maybe somebody could say whether Peirce himself said = anything on the subject. Is it desire to bring the concept of 'many' into the concept of 'sign' = in this manner? Why? I'm not sure what you mean by to bring the concept of 'many' into the = concept of 'sign' in this matter. However, in a general way, the = Peircean answer is that logic is semiotic and is more basic than = metaphysics. Peirce defined and pursued semiotic as a philosophical = field, not as a field in linguistics, which is concerned with language = as a concrete historical phenomenon involved especially with _homo = sapiens_ and as may turn out to be involved with intelligent life = elsewhere than Earth, and as may become involved with such intelligent = life as _homo sapiens_ or its heirs eventually breed or engineer. Best, Ben Udell I presume that many readers of this list are teachers and have = lectured on these terms. I have been struggling with these terms for = some time and hope that knowledgable Peircian students can explain the = importance of this seemingly disconnected usage of grammar from various = perspectives. Cheers Jerry Jerry LR Chandler Research Professor Krasnow Institute for Advanced Study George Mason University --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: Sinsign, Legisign, Qualisign - help!
Patrick, Jean-Marc. On Jun 28, 2006, at 7:27 AM, Jean-Marc Orliaguet wrote: Patrick Coppock wrote: At 0:11 -0400 25-06-2006, Jerry LR Chandler wrote: I will be at the Whitehead Conference in Salzburg next week so I do not anticipate much time for replies. ... However, for us to believe that Firsts, Seconds and Thirds actually exist, beyond their being mere transitory events in an ongoing semiosic process, would be fallibilistic in Peirce's terms, or a Fallacy of Misplaced Concreteness in Whitehead's terms. Not at all. Peirce was a three-category realist, acknowledging the reality fo Firsts, Seconds and Thirds early on. What you call Fallacy of Misplaced Concreteness is just another word for nominalism in that context. Peirce was not a nominalist. Peirce acknowledge the reality of actuality or of secondness (around 1890). Look for outward clash, or Scotus in the CPs and his criticism of Hegel's idealism. He acknowledged the reality of firsts (the universe of possibility), and of course the reality of thirdness (the universe of thought or signs) I don't have the exact references, but that's not too difficult to find if you go through the Collected Papers, look for nominalism, realism, idealism ... However he wrote that some thirds and seconds are degenerate, meaning that they have no real existence. Regards /JM Thanks for your stimulating comments. My take on the distinctions between Peirce and Whitehead is rather different. In early Peirce (1868), the analogy with distance functions and branching was the given basis for distinguishing paths of logic, relation to chemical valence and the more general concept of extension. The later writings of Peirce describing division of a sign in natural language is not a crisp way of looking at the concept of extension. (One might substitute for the term division such terms as partition, trichotomy, lattice, subtraction, incomplete parts, lack of additivity, and so forth; but I do not see how that would create a coherent concept of relational extension.) In late Whitehead, Process and Reality, he gets into bed with set theory and never re-emerges from this highly restrictive view of extension. In modern chemistry, a multitude of possibilities for extension exist . (The flow of passions in a bed are great, but they should not be conflated with the light of reason. :-) One might say that modern chemistry has in richer view of extension - valence is richer than -1,2,3- and it is richer than set theory by using irregularity as a basis of calculation. Also, the propensity of process philosophers to neglect the concept of inheritance of properties in time restricts the potential correspondence between process philosophy and scientific philosophy. A modern philosophy of chemistry must cope with numbers of relations grater than three and also recognize that islands of stability exist within the torrential seas of change. (I repeat my earlier disclaimer - I am neither a philosopher nor mathematician, my background is in biochemistry and genetics - so everyone ought to take my conjectures in these fields that are remote my personal area of concentration with a huge grain of salt.) BTW, the Whitehead conference includes sessions on Mathematics, Physics, Chemistry and Biology. Several abstracts were quite novel and may be of interest to readers of this listserve. see: http://www2.sbg.ac.at/whiteheadconference/index2.html Cheers Jerry LR Chandler (PS: Patrick, if you know David Lane, please convey my personal greetings to him.) --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: Sinsign, Legisign, Qualisign - help!
Dear Patrick:A few quick notes from Salzburg as I found your comments of interest and perhaps I can clarify some issues.My goals are more concerned with a coherent philosophy of science, especially a coherent relation between chemical philosophy and biological philosophy and medical philosophy. Peirce, as a 19 th Century chemist should be relevant to my interests. Whitehead asserts a philosophy of organism, which also should be relevant.While the course of development of an individual's thought and patterns of digestion and indigestion are always relevant to understanding the individual, they are not always relevant to my restricted interests. In particular, at the turn of the 21 Century, we see highly specialized logics in Quantum mechanics, chemistry (valence) and molecular biology (genetic code). The challenge I face is to place the modern logics in context of earlier logics. The QM advocates have a highly developed narrative. Chemistry and biology do not. Thus, I seek connections that allow development of coherent narratives for these sciences. It is in this context that I appreciate the narratives you construct.Now for a few comments:On Jul 2, 2006, at 1:08 AM, Peirce Discussion Forum digest wrote: In any case, I can see I'll have my work cut out=20 to be brief in replying to your notes, since=20 brief though they may be, they are also fairly=20 "dense" in "content". terms, at least if I try to=20 read between the lines.. I would prefer the terms "concise" and "crisp", but, if you insist on the term "dense" I accept your judgment. :-) You wrote: My take on the distinctions between Peirce and Whitehead is rather differen= t. In early Peirce (1868), the analogy with=20 distance functions and branching was the given=20 basis for distinguishing paths of logic,=20 relation to chemical valence and the more=20 general concept of extension. The later=20 writings of Peirce describing "division" of a=20 sign in natural language is not a crisp way of=20 looking at the concept of extension. (One might=20 substitute for the term "division" such terms as=20 partition, trichotomy, lattice, subtraction,=20 incomplete parts, lack of additivity, and so=20 forth; but I do not see how that would create a=20 coherent concept of relational extension.) Well, first off, I personally think it is very=20 important that "early" and "late" Peirce's are=20 seen as part and parcel of one and the same=20 philosophical project, that developed (emerged)=20 over a considerable time period, but always with=20 the key notion of synechism ("the tendency to=20 regard everything as continuous") at its base.=20 Kelley Parker's work on Peirce's continuity is a=20 useful point of reference here.This comment identifies a critical issue. It is not clear to me how relate Peirce's later views to continuity. I do not know the writings of Parker. Clearly, the concept of continuity as well as chemistry was in the early writings. However, in later works, the "flow of semiosis" displaces the relevance to chemical logic; it remains consistent with various aspects of "signal processing" and "Memory Evolutive Systems." When you write that "The later writings of Peirce=20 describing "division" of a sign in natural=20 language is not a crisp way of looking at the=20 concept of extension", I think I'll have to ask=20 you for a bit more detailed explanation of what=20 you mean by that... Very simple. Extension as growth; as increase; as sequence of relations, the later extending the former.My conjecture is that extension is easy in number/arithmetic, difficult in chemistry, and very difficult in natural language.In the example, sign is extended to qualisign, sinsign and legisign. This extension appears to me to include a fair amount of arbitrariness. Fine for a philosophy of belief, not adequate for chemical or biological purposes. It would be helpful if someone could suggest a path that associates these terms with chemical, biological or medical practice. In late Whitehead, Process and Reality, he gets=20 into bed with set theory and never re-emerges=20 from this highly restrictive view of extension.=20 In modern chemistry, a multitude of=20 possibilities for extension exist . (The flow=20 of passions in a bed are great, but they should=20 not be conflated with the light of reason. :-) Regarding "early" and "late" with regard to=20 Whitehead, the same considerations as above=20 regarding the recursive, stepwise development of=20 Peirce's architectonic, I think also holds for=""> Whitehead. From the beginning he was a=20 mathematician (and education theorist) more than=20 a philosopher (and in fact, like Peirce, he never=20 "formally" studied philosophy apart from his own=20 personal readings of other philosophers' work),=20 but process and reality is built round ideas=20 developed in his many other philosophical=20 writings, such as "Adventures of Ideas", "Science=20 and the Modern World" -- in my opinion a good=20 starting
[peirce-l] Re: Sinsign, Legisign, Qualisign - help!
Dear Jim, Rob and List:Before turning to Jim's post, a couple of comments about the Salzburg conferences.The Whitehead conference attracted about three hundred (300!!) participants. The Chinese are keenly interested in Whitehead. It was rumored that they intend to establish 25 research institutes to explore philosophical and political relations. The sessions on mathematics, physics, chemistry and biology attracted about 25 participants to each! very impressive relative to other philosophical conferences.Peirce was frequently mentioned in sessions. A special session included discussions about the Whitehead - deChardin linkages. Roland Faber's paper suggested to me an orthogonality between these two views of philosophy. By orthogonality in this context I mean the approach to extensions.The abstracts are on the web and papers will also be posted on the website for the conference.The Biosemiotics gathering was attended by about 50 participants from perhaps a dozen different countries. Peirce played a role in many many papers. The abstracts are on the web and the papers will be posted. Lots of discussions of coding and bio-logic.Is it not absolutely wonderful that we can access current research reports from our desktops in a timely and efficient manner? Now, on to the issue of Peirce and chemical isomers that are distinguished by a specific property of rotating light that has passed through a crystal, generating what is called "polarized light." Jim wrote:From: "Jim Piat" [EMAIL PROTECTED] Date: Mon, 3 Jul 2006 18:17:21 -0400 X-Message-Number: 7 Jerry Chandler wrote: "But, my point is that if four different groups are necessary to = construct an optical isomer of carbon such that it distinguishes between = the logic of polarized light, then it is mathematically impossible to = achieve this logical distinction with any notion of 'threeness". = Optical isomers are not a question of trichotomies and triadicies. They = are questions of tetrachotomies and tetraadicies. I would welcome = arguments to the otherwise". Dear Jerry, =20 Actually, handedness and materials that polarize light are among the = very examples Peirce gives of his notion of Thirdness. Do you have a direct source of this passage? The notions of = left verses right (which distinguished between mirror image optical = stereo-isomers) Peirce pointa out require the consideration of the = triadic relation of three directions (up-down, front back, left right). = It may well be that different carbon groups are involved naturally = occuring steroisomers but in fact only three conjoined points are = required to achieved the distniction beween left and right.This is an interesting point. Of course, it refers to the cartesian plane, not space itself.In general, chemistry operates in space and optical isomers rotate light is space. Triadic examples of handedness Left Right A---B B--A l l l l C C Verses "redundant" tetradic examples of handedness Left Right A--B--D DB-A l l I I C C I don't mean to be present the above as authoritative -- this is merely = my understanding of the issue.=20Modern theory (simplified) considers light rotation to be a spatial operation emerging from the difference between four DIFFERENT material attachments to a central carbon atom.In order to deduce the relation with "left" or "right", one starts with the concept of a tetrahedron.Hold the tetrahedron in space and imagine looking down one of the apexes through the middle point (the central carbon atom) and out the plane opposite the apex and middle point.The "back plane" will contain the other three points of the tetrahedron. These three points can be in two possible orders: A - B - C or A - C - B.Pastuer noticed that two crystal forms of tartaric acid existed and was able to separate them "by eye".One rotated light left, the other right. Many years later it was found that two crystalline forms of tartaric acid with identical molecular formula and structure, represented the order A_B_C or the order A_C_B, differed by the organization in space. This is a slightly simplified version of the narrative but captures the essential features.From a philosophy of science perspective, the existence of optical isomers clears shows the irreducibility of chemistry knowledge to independent physical concepts. As nearly all biochemical molecules are optical isomers, often having hundreds or thousands of optical centers, it is widely believed that a theory of biology depends on explaining the origins of optical isomerism in living systems.I certainly would appreciate any insights individuals may have on how this related to
[peirce-l] Whitehead Conference, Biosemiotics Gathering web addresses
To the list: In response to the query, the Whitehead Conference index is at www.sbg.ac.at/whiteheadconference/index2.html It should be noted that I tried to access the site before composing this post with out success. I presume that it is a temporary problem. The Biosemiotics site is: www.biosemiotics2006.org Cheers Jerry --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Open Questions, MS 325 (c.1907),
To the List:The following quote, the fourth and part of the fifth paragraphs, is from Ms. 325, "Pragmatism Made Easy" (We are thankful to Juan Pablo Serra for posting this Ms.)"The particular point that had been made by Bain and that had most struck Green, and through him, the rest of us, was the insistence that what a man really believes is what he would be ready to act upon, and to risk much upon. The writer endeavoured to weave that truth in with others wich he had made out for himself, so as to make a consistent doctrine of cognition. It appeared to him to be requisite to connect Bain’s doctrine, on the one hand, with physiological phenomena, and on another hand, with logical distinctions. It had long been said that the phenomena of consciousness were of three kinds, Feeling, Volition and Cognition. The writer proposed to amend that enumeration in one particular, so as to make it correspond with a logical division. Logical predicates are of three kinds; these of wich each is connected with a single subject, these of wich each is connected with two subjects, one grammatically called the subject nominative and the other the object, and these whose connections with subjects exceed two and wich are analyzable into predicated at once of subjects nominative, of direct objects, and of indirect objects.Now feelings always arise as predicates of single objects; and it is only by subsequent reflexion, wich is not Feeling, that they may become connected with two or more subjects." I note the following:In the earlier (1869?) essay, the example of the logic of three objects was a spatial example of three paths. More directly, if two paths, then the paths could only be added, if three paths, then branching was possible. The distinction was based on the possible arrangements of two ro three "objects" in the plane or in space. This reasoning was very consistent with the chemical symbolism of Dalton in terms of relational logic among chemical radicals.In MS 325, the logic is explicitly expressed in terms of grammar. More precisely, in terms of predicate logic. The phrase:Logical predicates are of three kinds; is a particular belief about English grammar. I am skeptical that it is true for all grammars.Does anyone know of languages that have more than three kinds of predicates?Or, less than three kinds of predicates?Given the extraordinary richness of human communications, it seems highly probable that such examples exist; I would like to quote a specific example.Continuing on with the sentence:...these of wich each is connected with a single subject,This phrase, in this context, could mean that Peirce was expressing the potential of a copula to connect the subject with a particular property of the subject. For example, "The apple is red."Does this example of the logic of predicates of English grammar start the notion of "Firstness"?If so, how does one categorize the notion of a simpler logical sentence, "Apples exist"? Continuing to decompose the sentence, these of wich each is connected with two subjects, one grammatically called the subject nominative and the other the object,This phrase appears to continue the metaphor between English grammar and logic. Does this example of the logic of predicates of English grammar start the notion of "Secondness"?I note that one could also construct a sentence of the form: Apples and oranges exist.The final part of the sentence reads: and these whose connections with subjects exceed two and wich are analyzable into predicated at once of subjects nominative, of direct objects, and of indirect objects.At this point, Peirce appears to abandon examples of Aristotelian species and goes directly to the genus, namely, with the word pair, "exceed two".Does this example of the logic of predicates of English grammar start the notion of "Thirdness"?Does this example have any explicatory value with respect to the nature of thirdness?I note that one could also construct a sentence of the form: Apples and oranges and peaches and pears exist.I also note that I have chosen examples of existential sentences with the names (categories?) of fruit. I feel that these examples would be equally germane if I had chosen the names of chemical elements or or Daltonian signs. Am I mistaken in this belief?The introductory phrase of the next paragraph:Now feelings always arise as predicates of single objects; and it is only by subsequent reflexion, wich is not Feeling, that they may become connected with two or more subjects."is simply beyond my comprehension. I have not a method to relate to the proposed illation.My belief is that my feelings are internal impulses and are independent of English grammar but are manifestations of relations intrinsic to my internal existence. If I wish to think about my feelings or to communicate a feeling to another, then I may chose to invoke grammar. For example, my dog often responds to my feelings even before the feeling is manifest in my mind. So, what
