Michael, List: MM: Hopefully a pause for breath is a kind of "outcome" that isn't final.
I agree, and am very glad to see that as a newcomer you have not already been deterred from participating further by what has transpired here lately. MM: Given I am (as yet) on the back foot in scholarly methods I treasure copious quotations. I agree, because how else can we test and support our interpretative hypotheses? MM: The value to all readers is in the exercise and the exposition by all participants, not just the initiator. I agree, and have benefited the most from discussions where there was sincere but polite disagreement, which forced me to sharpen my own thinking. MM: Time (an enthusiasm of CSP) is on our side; in it reason, prudence, perseverence and judgment can flourish: these are not zero-sum games. I agree, and have spent a considerable amount of my own time over the last few months studying Peirce's philosophy of time <https://list.iupui.edu/sympa/arc/peirce-l/2020-03/msg00001.html>, which I call *temporal synechism*. MM: I hope it's permissible for any list member to pitch in at any point and not only those whose names are at the start of the post. I agree, and consider giving a name at the beginning to be primarily just an acknowledgment of who prompted the post that follows. MM: In The nature of mathematics (1933) Max Black cites L E J Brouwer's demonstrating that excessive attempts are made to impose an excluded middle when unwarranted. I agree, and apparently so did Peirce, which is presumably why he usually called excluded middle a *principle *rather than a *law*. CSP: Logic requires us, with reference to each question we have in hand, to hope some definite answer to it may be true. That *hope* with reference to *each case* as it comes up is, by a *saltus*, stated by logicians as a *law* concerning *all cases*, namely, the law of excluded middle. This law amounts to saying that the universe has a perfect reality. (NEM 4 <https://uberty.org/wp-content/uploads/2015/12/Charles_S._Peirce_Math_4.compressed.pdf>:xiii, no date) CSP: To speak of *the *actual state of things implies a great assumption, namely that there is a perfectly definite body of propositions which, if we could only find them out, are the truth, and that everything is really either true or in positive conflict with the truth. This assumption, called the principle of excluded middle, I consider utterly unwarranted, and do not believe it. Still, I hold that there is reason for thinking it to be very nearly true. (NEM 3 <https://uberty.org/wp-content/uploads/2015/12/Charles_S._Peirce_Math_3.compressed.pdf>:758, 1893) CSP: No doubt there is an assumption involved in speaking of *the *actual state of things … namely, the assumption that reality is so determinate as to verify or falsify every possible proposition. This is called the *principle of excluded middle*. ... I do not believe it is strictly true. But that is nothing; logic does not inquire into the truth of premises. It is convenient, not only in a practical but in a philosophical sense, to commence with the study of arguments which assume such an absolutely determinate state of things, without ourselves asserting that such a state is quite realized. (NEM 3 <https://uberty.org/wp-content/uploads/2015/12/Charles_S._Peirce_Math_3.compressed.pdf>:759-760, 1893) By contrast, the principle of contradiction is indispensable. CSP: We cannot reason or think at all without making a distinction between truth and falsity; while we can perform some elementary kinds of reasoning (in point of fact, all that are considered in the traditional logic) without absolutely excluding the possibility of an intermediate state between the two, say the state of being sometimes true and sometimes false. The principle of contradiction is more elementary than that of excluded middle, so that we may begin by considering the consequences of the former while leaving the latter out of account. (NEM 3 <https://uberty.org/wp-content/uploads/2015/12/Charles_S._Peirce_Math_3.compressed.pdf>:751, 1881) CSP: The two principles of contradiction and excluded middle do not stand at all upon the same plane. All motive for the criticism of our own thoughts or those of others springs from the conviction of a distinction between truth and falsity ... . On the other hand, it has often been held, even when not professed, that concerning some matters there is no truth nor falsity. ... But putting aside, for the present, these topics of higher logic, what concerns us now is that certain rudimentary forms of reasoning, embracing all those that the traditional logic has handed down to us, depend only upon the impossibility of a fact's being both true and false, and remain equally sound arguments, if we suppose that some things are neither true nor false. (NEM 3 <https://uberty.org/wp-content/uploads/2015/12/Charles_S._Peirce_Math_3.compressed.pdf>:753, 1881) Peirce even anticipated the development of a three-valued logic, more than a decade before anyone else. CSP: Triadic Logic is that logic which, though not rejecting entirely the Principle of Excluded Middle, nevertheless recognizes that every proposition, S is P, is either true, or false, or else S has a lower mode of being such that it can neither be determinately P, nor determinately not-P, but is at the limit between P and not P. ... Thus the Triadic Logic does not *conflict *with Dyadic Logic; only, it recognizes, what the latter does not ... Triadic Logic is universally true. But Dyadic Logic is not absolutely false ... (R 339:515[344r] <https://rs.cms.hu-berlin.de/peircearchive/pages/preview.php?ref=13412>, 1909) The concrete thing denoted by S has "a lower mode of being" with respect to possessing the abstract quality denoted by P whenever an *event *is realized involving both. Rather than "S is P" or "S is not-P" being true, either "S is *becoming *P" or "S is *becoming *not-P" is true. MM: What we should be doing IMO is not so much "agreeing to differ" as leaving our ideas on the table for continued evaluation (at everybody's leisure). I agree, and the List archive <https://list.iupui.edu/sympa/arc/peirce-l> is always available to anyone who prefers not to retain posts in their own e-mail folders. MM: Additionally, I heartily recommend visual and spatial thinking to all. I agree, and apparently so did Peirce, since he believed strongly in the superiority of his existential graphs for studying logic. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, May 16, 2020 at 1:10 AM <michael...@waitrose.com> wrote: > List, > Hopefully a pause for breath is a kind of "outcome" that isn't final. > It always struck me a constellation of overlapping / intermeshing formal > languages would perform the very function Joe describes. > Taking "methodology" to mean "method" I'm sure instances of lack of method > (rather than just method) need to be critiqued on their own terms on a case > by case basis. Sharing insights in to "the universe and everything" isn't > suited to be turned into a blame game. > Given I am (as yet) on the back foot in scholarly methods I treasure > copious quotations. We must of course pick up where we see a conclusion as > not following well enough. The value to all readers is in the exercise and > the exposition by all participants, not just the initiator. > Time (an enthusiasm of CSP) is on our side; in it reason, prudence, > perseverence and judgment can flourish: these are not zero-sum games. > When I attend a seminar room (informal ones) I always hear questions like > "when you said such & such would the Big Bang theory / Punctuated > Equilibrium theory be an example of that?" I've often seen eminent > featured speakers carry off "being stumped" with honest aplomb. It doesn't > matter who brought the universe in with them - I always find it there. > I hope it's permissible for any list member to pitch in at any point and > not only those whose names are at the start of the post. In 1st century > Aramaic speaking society the quality of questions was considered a great > enhancement and not a detraction. > Newman's degrees of inference require that we each see what weight we > provisionally wish to give across a range of hypothetical ideas / concepts > / notions. This is not dried or (often) even cut. Tentative is another > vital quality. > To impute tentativeness when it apparently wasn't projected can be tactful. > Given that logic is huge and our idea of infinity has to be (as I see it) > an approximation to an approximation, can a notation be developed for > paradox? > In The nature of mathematics (1933) Max Black cites L E J Brouwer's > demonstrating that excessive attempts are made to impose an excluded middle > when unwarranted. > What we should be doing IMO is not so much "agreeing to differ" as leaving > our ideas on the table for continued evaluation (at everybody's leisure). > If we don't want to agree do we have to say more than "I shall think about > it" or even just stay momentarily silent? > The logic of time is that now is not forever. I haven't responded, yet. > Here's to all our yets! > Additionally, I heartily recommend visual and spatial thinking to all. > P.S I'd love it if participants can translate the above into your > favourite notations / technical terminology. > Michael Mitchell > former translator, UK >
----------------------------- 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 .
