Hello all - sorry to come late onto this thread. I'm very interested to hear about Peirce's late shift in view as to the meaning of his cut - from simple univocal falsity, to varieties of possibility (which may divide into further kinds). I am reminded to Wittgenstein's Tractatus where logical space must 'contain' false states of affairs as well as true ones, otherwise we could not understand the meaning of false statements.
I'm confused though about Peirce's big announcement about now being able to give a meaning to graphs which cross a cut. This crossing cannot just mean lines of identity, right? As those have always crossed cuts. He must mean something else, but what? Can someone show me an example? I once tried to prove Peirce's famous two statements about the suiciding wife and the man who fails in business equivalent in regular FOL, but couldn't do it. Are people sure they're equivalent in FOL, as in the beta graphs? The case of ∃(A or B) ≡ ∃A or ∃B is one of the Barcan rules if I'm not mistaken. These are controversial in modal logic, and metaphysics. Cheers, Cathy Cheers, Cathy On 2/11/15, Kirsti Määttänen <[email protected]> wrote: > Negations are very, very troublesome in logic. I think it would serve a > purpose to return to the meanings of the terms. - Contradictories apply to > statements only. To what is claimed. Contraries apply to empereia, too. > > Kirsti > > Kirsti Määttänen [[email protected]] kirjoitti: >> Leading principle(s) may not be fixed. The principle of triadicity >> contains Mediation, thus change. Anything organic stays changeable, still >> with some continuity. This is something empirical and valid in all cases. >> - Is it not? >> >> Kirsti >> >> Jerry LR Chandler [[email protected]] kirjoitti: >> > Ben, John, List: >> > >> > Thank you for the stimulating perspectives. As you both know, I am >> > interested in the logic of chemistry as it relates to biology and >> > mathematics. >> > >> > The discussion under this thread illustrates the differences between the >> > foundations of chemical logic and classical logic in an extraordinarily >> > subtile manner. >> > >> > The motivation for the unfolding of a portion of the discussion was >> > Ben's phrase, "looking for the diametrical contrary of 'indubitability' >> > in Peirce's sense". >> > >> > Ben's phrase suggested to me that the reference for the term >> > "diametrical contrary" was the logical square of opposition. >> > Furthermore, this suggests that the more abstract reference was that of >> > a connotation of something akin to diagrammatic logic / geometric >> > logic. >> > >> > Further posts led to further mis-understandings about the nature of >> > meanings of sentences and the possible meanings of contrary and >> > contradictory. >> > >> > Ben concludes: >> > >> > > As to contradictories, contraries, etc., that stuff is quite >> > > elementary. I mean, suppose I kept pestering you about how many >> > > protons are in a hydrogen atom? Look it up yourself, man. I'll let you >> > > have the last word on this, because this whole line of discussion is >> > > so...you know.... >> > >> > >> > apparently frustrated with the exchanges. >> > >> > At the root, Ben, the question you may wish to ask yourself, is, as you >> > say "quite elementary". >> > >> > Is your understanding of logic sufficiently complete such that your >> > usage of the traditional terms of logic are also valid for chemical >> > logic? biological logic? social logic? >> > >> > The fact is that the logic of chemistry/biology/medicine is based on a >> > separate and distinct syntax and semantics such that the combinatorial >> > operations on nouns generate new semantic terms that are physical and >> > metaphysical entities. For example: H, O, N, C,and P combine to >> > generate DNA. DNA is neither a contrary of H,O,C,N,P nor is it a >> > contradiction of those elements. >> > >> > Yet, at one and the same time, empirically valid logical relations exist >> > between physical representamen and chemical representatamen (as is well >> > known,) but by no means simple. >> > >> > Ben, your saltation to the sweeping generalization: >> > > As to contradictories, contraries, etc., that stuff is quite >> > > elementary. >> > >> > suggests to me that you have reached a closure on the nature of >> > elementary logic. >> > >> > I have NOT. Elementary logic remains open to inquiry. >> > Indeed, from my perspective, one of CSP's major contributions to logic >> > was to abandon the several forms of syllogisms, which restricted >> > possible relations among syllogisms (barbara, etc) by introducing the >> > concept of "leading principles" (CP 2.588 and hence opening the >> > terminology/methodology/syntax/semantics of logic to the highly >> > irregular natural forms of human rhetoric, including the highly >> > irregular forms of chemical structures. >> > >> > Within this context, CSP notes 2.589 that: >> > >> > Quote: >> > Only that man's reasoning would be good whose leading principle was true >> > in all possible cases. >> > End quote. >> > >> > Many Peircians may accept this assertion about leading principles. >> > Frankly, I think it is empirically impossible. >> > The chemical sciences (chemistry, biology, medicine, ecology,...) >> > require several leading principles in addition to correspondence >> > relations with physical principles. Roughly speaking, the difference is >> > rather simple. Physical principles are grounded in the first order logic >> > of terms. Chemical principles are grounded in generativity of chemical >> > terms (emergence, growth, extension, evolution, and so forth.) >> > >> > Cheers >> > >> > Jerry >> > >> > >> > >> > >> > >> > >> > >> > > On 1/20/2015 12:07 AM, Benjamin Udell wrote: >> > >> Jerry, >> > >> >> > >> I was posting about a hexagon and a hexadecagon (not really, two of >> > >> its corners were internal) of opposition many years ago at peirce-l >> > >> before I learned that they had all been found as obvious many years >> > >> before. The hexadecagon (which looks like a shadow of a tesseract) >> > >> were covered by some fellow in _Studies in the Logic of Charles S. >> > >> Peirce_. >> > >> >> > >> I just don't feel like digging through boxes to find the logic text >> > >> book where I first learned about contraries, contradictories, etc. >> > >> But I believe that it's covered well enough in Quine's _Methods of >> > >> Logic_. >> > >> >> > >> Best, Ben >> > >> >> > >> On 1/19/2015 11:51 PM, Jerry LR Chandler wrote: >> > >>> List, Ben: >> > >>> >> > >>> Let's look at the history of your posts on this topic: >> > >>> >> > >>> Jan. 17: I think that Gary F. is looking for the diametrical >> > >>> contrary of 'indubitability' in Peirce's sense. >> > >>> >> > >>> Jan. 17: I guess I should have said 'diametrical opposite' instead >> > >>> of 'diametrical contrary' which is an atypical phrase. >> > >>> 'The dogs are four' and 'the dogs are five' are contraries: >> > >>> >> > >>> Jan. 17: A pair of contraries consists of two propositions such as >> > >>> 'John is blue' and 'John is quiet and not blue', >> > >>> >> > >>> Jan. 17. I won't provide references, look at 20th-Century logic text >> > >>> books. >> > >>> >> > >>> Ex cathedra. >> > >>> >> > >>> BTW, I find the 21st Century extensions of the "Square of >> > >>> Oppositions" to the Hexagon of oppositions and higher order >> > >>> geometric representations of logical geometry. See works on >> > >>> para-consistent logics and by Jean-Yves Béziau. >> > >>> >> > >>> Cheers >> > >>> >> > >>> Jerry >> > >>> >> > > >> > > ----------------------------- >> > > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >> > > PEIRCE-L to this message. PEIRCE-L posts should go to >> > > [email protected] . To UNSUBSCRIBE, send a message not to >> > > PEIRCE-L but to [email protected] 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 >> > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L >> > but to [email protected] 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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