RE: [PEIRCE-L] Intuitionistic Logic

Helmut, my book has a lot to say about relations between time and logic, but probably the most relevant to your question is here: Objecting and Realizing (TS ·12) (gnusystems.ca) . Actually there’s more of Peirce than of me in it, but I hope

RE: [PEIRCE-L] Intuitionistic Logic

Helmut, on this point you seem to disagree with Peirce about logical relations. Peirce in 1880 (W4:170) identified illation as the basic or ‘primitive’ logical relation, and in his 1906 ‘PAP’ (MS 293) he identified it with ‘the form of the relation of two instants of time, or what is the same

Re: [PEIRCE-L] Intuitionistic logic

Jon AS, List, Before getting into any speculation, I'll mention some undeniable facts: 1. R699 has the title "Assurance through reasoning", it begins with a paragraph about necessary deduction and probable deduction, and it contains a summary of the EG system from the early days up to and

Re: [PEIRCE-L] Intuitionistic logic

John, List: I rested my case last night, but now have a few rebuttals to subsequent testimony. JFS: In R669, he summarized the EG system that he had been developing since 1896. Then he developed a new system in R670 and L231 that is superior to the old system in every way. The system itself

Re: [PEIRCE-L] Intuitionistic logic

Jon AS, JAS> Remember, "nobody can claim that anything other than an exact quotation is what Peirce intended" Thank you for emphasizing my point.  The only solid evidence we have of what Peirce intended is what he wrote before and after June 1911.  But the developments during the century

Re: [PEIRCE-L] Intuitionistic logic

John, List: JFS: I admit that Peirce does not use the word scroll in r670. But he draws some scrolls, and he shows one EG as a scroll and another with shaded ovals and says that they are "equivalent". I appreciate the admission, and I already acknowledged the latter fact in an earlier post,

Re: [PEIRCE-L] Intuitionistic logic

Jon AS, I admit that Peirce does not use the word scroll in r670.   But he draws some scrolls, and he shows  one EG as a scroll and another with shaded ovals and says that they are "equivalent". If you look at the times and dates, his remark about  heaven & hell  was the first entry during the

Re: [PEIRCE-L] Intuitionistic logic

John, List: JFS: As I said, I'm writing a longer article in which I cover all the details Just a short preview of coming attractions: I sincerely look forward to reading it, but in the meantime, I respectfully suggest holding off on further posts until time and circumstances permit careful

Re: [PEIRCE-L] Intuitionistic logic

Jon AS, As I said, I'm writing a longer article in which I cover all the details  Just a short preview of  coming attractions: 1. The story about paradisaical logic is used in R669 to justify the derivation of negation from a scroll.  In L376, Peirce happens to use the same term for a logic

Re: [PEIRCE-L] Intuitionistic logic

John, List: Again, as we have been advised repeatedly, since the post to which I am replying lacks "an exact quotation by Peirce," everything in it is someone else's opinion and cannot be claimed as "what Peirce meant" or "what Peirce intended." JFS: In R670, CSP explicitly stated that the

Re: [PEIRCE-L] Intuitionistic logic

Jon AS, I'm tied up with other deadlines, and I'll post a longer article that goes into all the details in a few more days. Re rejecting R669:  In R670, CSP explicitly stated that the scroll is equivalent to a nest of two negations (12 June 1911).  On the next day, he wrote that it's so easy to

RE: [PEIRCE-L] Intuitionistic Logic

aulien Cc: s...@bestweb.net; peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Intuitionistic Logic FYI — “Every unicorn 濾 is pink” is true. Jon http://inquiryintoinquiry.com On May 19, 2021, at 5:52 PM, Helmut Raulien mailto:h.raul...@gmx.de> > wrote: List, Does anybody kno

Re: [PEIRCE-L] Intuitionistic Logic

Jon A., List: Technically, yes, at least in classical logic. Nevertheless, according to Peirce, "it can no longer be granted that every conditional proposition whose antecedent does not happen to be realized is true" (CP 4.580, 1906). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural

Re: [PEIRCE-L] Intuitionistic logic

Helmut, List: HR: I think, Jon A.S., you once gave me the following example: "Every unicorn is pink" is false, but "There is no unicorn that is not pink" is true. Here is what I actually said a few months ago. JAS (https://list.iupui.edu/sympa/arc/peirce-l/2021-01/msg00075.html): For example,

Re: [PEIRCE-L] Intuitionistic Logic

FYI — “Every unicorn 濾 is pink” is true. Jon http://inquiryintoinquiry.com > On May 19, 2021, at 5:52 PM, Helmut Raulien wrote: > > List, > > Does anybody know an example which justifies intuitionistic logic, so in > which classical logic fails? I think Jon, A.S., you once gave me the >

Re: [PEIRCE-L] Intuitionistic logic

> > > Gary f. > > > > *From:* peirce-l-requ...@list.iupui.edu *On > Behalf Of *John F. Sowa > *Sent:* 19-May-21 00:59 > *To:* peirce-l@list.iupui.edu > *Subject:* Re: [PEIRCE-L] Intuitionistic logic > > Gary R, > > I'm glad you asked.

Re: [PEIRCE-L] Intuitionistic logic

John, List: JFS: But in R670. Peirce definitively rejected the idea of defining negation in terms of implication and falsity. Also JFS (https://list.iupui.edu/sympa/arc/peirce-l/2021-05/msg00045.html): In discussions about Peirce and his writings, anything other than an exact quotation by Peirce

RE: [PEIRCE-L] Intuitionistic logic

Gary R and list, Being a non-mathematician myself, I’ve been drafting an introduction to Peirce’s EGs for the likes of us. I have the current draft online now here: EG introduction (gnusystems.ca) It includes many links both to Peirce’s own

RE: [PEIRCE-L] Intuitionistic logic

o as many as possible. Our system is intended to facilitate the study of reasoning but not to facilitate reasoning itself. Its character is quite contrary to that purpose.]] Gary f. From: peirce-l-requ...@list.iupui.edu On Behalf Of John F. Sowa Sent: 19-May-21 00:59 To: peirce-l@list.iupui.

Re: [PEIRCE-L] Intuitionistic logic

Gary R, I'm glad you asked.GR> Please explain how this "blocks the way of inquiry" for folk like me who are apparently radically deficient in mathematics and logic so simply can't see it as such.  Intuitionistic logic is a restriction on the permissible rules of inference. That makes it

Re: [PEIRCE-L] Intuitionistic logic

John, Jon, List, JAS: Peirce anticipates aspects of the formal system that is now known as intuitionistic logic--e.g., defining negation as the implication of falsity... JFS: Nobody knows what Peirce would have said about the less dogmatic treatment of intuitionistic logic by Heyting and

Re: [PEIRCE-L] Intuitionistic logic

Jon AS, I'm writing an article about Peirce's writings on logic in 1911, which I'll post to P-list soon.  And I'm glad that we can agree on that point. JFS> However, Peirce and Brouwer were on opposite sides of fundamental issues about the nature of mathematics.  ...  In general, Brouwer's

Re: [PEIRCE-L] Intuitionistic logic

John, List: I was hoping that the archive would be back in operation by the time I posted this, but I guess not. JFS: There have been some discussions about intuitionistic logic and the claim that Peirce anticipated aspects of Brouwer's version of intuitionistic logic The actual (and

Re: Re: Re: Re: [PEIRCE-L] Intuitionistic logic

List: This is just a quick note to correct a couple of errors that I discovered in the last paragraph of a post from a while back, which is quoted below. Here is what I should have said. On the other hand, in intuitionistic logic the three expressions are *not *equivalent. Specifically, "not-(X

Re: [PEIRCE-L] Intuitionistic logic

Ben, List: No worries and no rush. I realized today that Stjernfelt ( http://frederikstjernfelt.dk/Peirce/Optimal%20and%20operational%20iconicity.%202011%3A2014.pdf, p. 22) quotes Peirce as spelling out "the strange rule" in "Prolegomena to an Apology for Pragmaticism." CSP: The logical

Re: [PEIRCE-L] Intuitionistic logic

Jon A.S., list, I picked a heck of a time to (attempt my) return to serious discussion at peirce-l.  I may be unable to reply on these things for a week or so, because of practical matters. Sorry about that! Best, Ben On 12/28/2020 8:35 PM, Jon Alan Schmidt wrote: Ben, List: I seem to

Re: [PEIRCE-L] Intuitionistic logic

Ben, I agree with your analysis, and I'd like to add a comment about modal logic.  Consider the sentence "It might rain tomorrow, and it might not."  That sentence cannot be falsified because neither side makes a firm promise. But if you replace 'might' with 'will', the following statement is

Re: Re: Re: Re: [PEIRCE-L] Intuitionistic logic

Helmut, List: Indeed, that passage by Peirce in R 490 is challenging to untangle. I had to read and reread it several times myself when I first studied it a few months ago, and then again yesterday while drafting my previous post. Both graphs are existential, not entitative. The only difference

Aw: Re: Re: Re: [PEIRCE-L] Intuitionistic logic

Jon, List,   Thank you! I need examples. This one is tricky, I have to read it some more times, as now I don´t see the asymmetry. And I don´t understand   "Nevertheless, these are different propositions that signify different states of things, which is reflected by their different existential

Re: Re: Re: [PEIRCE-L] Intuitionistic logic

Helmut, List: HR: I have tried the reversion including possibility with an example: Those examples are not appropriate since they include "possibly" within the statements themselves, which makes them *modal *propositions. Moreover, what Peirce finally recognized in accordance with his

Aw: Re: Re: [PEIRCE-L] Intuitionistic logic

      Supplement: The attachment has arrived, with Johns post, sorry. I am afraid, that in my example a weak negation is blended in, so the example doesn´t count. You cannot say "NOT possibly female", but have to say instead "possibly not female". The adverb, I think, indicates the weak

Aw: Re: Re: [PEIRCE-L] Intuitionistic logic

Jon, List,   The attachment has not arrived. I have tried the reversion including possibility with an example:   Let a dodo be a animal close to extinction, of which we only know about its extinction status, that maybe all still living dodos are male, maybe females still exist too. We have a

Re: Re: [PEIRCE-L] Intuitionistic logic

John, Helmut, List: I agree with John's additional remarks about intuitionistic logic. Addressing Helmut's worry, it does not "blur" the concept of truth; on the contrary, there is a sense in which it establishes a *higher *standard than classical logic because it *requires *constructive proofs

Aw: Re: Re: Re: Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Edwina, so, if we want both democracy and capitalism, we should support individual private enterprises, I agree. And for companies bigger than an individual co-operatives. Otherwise the business-owners cannot become majority. I don´t think, that all knowledge is incomplete. Due to Goedel, as far

Re: Aw: Re: Re: Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Helmut - No, I don't think that Godel's incompleteness theory has anything to do with democracy. After all, if we take as a given, that all knowledge is incomplete [and Peirce would be the first to say this!], then, we'd have to question other historical forms of governance - such as a

Aw: Re: [PEIRCE-L] Intuitionistic logic

  John, Jon,   Thank you! My first idea is, that to negate each step and reverse the order only is valid with the excluded middle, so exclusion of the  middle should be necessary for both ways of proof too. But I will read your links, thank you for your patience! I think, the concept of truth

Re: Re: Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Helmut, List: I am still having trouble following you here. Intuitionistic logic does not have anything to do with belief or truth, except as a formal system for drawing valid deductive inferences such that the conclusion is true as long as the premisses are true. Its main difference from

Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Steven, List: SS: Notice the large amount of leeway given in this notion of “justified true” belief: There is indeed considerable leeway for "justified" since it can range from merely plausible for abduction/retroduction to probable for induction to certain for deduction. Even in the last case,

Aw: Re: Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Jon, List,   the fallacy of intuitionistic logic in my hypothesis is, that it first includes belief into the concept of truth, then sees, that belief is not two-valued, and then denies the law of the excluded middle for both. But the NOT-operator can only be applied for truth-problems, and so

Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Jon Schmidt, We appear to state the same things. Notice the large amount of leeway given in this notion of “justified true” belief: justified true belief justified if it is the conclusion of a valid argument (note: valid argument includes mere plausibility) a belief is true if the

Re: Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Helmut, Steven, List: HR: For me it is not clear, what exactly is claimed to justify intuitionistic logic. What would it mean to *justify* intuitionistic logic? What kind of reasoning would one use to do so? From my standpoint, it is "justified" by not imposing excluded middle as if it were an

Aw: Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

      Correction: I guess I meant "operator" instead of "quantor". I am not a certified logician. Steven,   yes, I nearly totally agree. Interesting, that Goedel said that. An observer cannot know the onologic state of a system the observer is part of. Then calling it knowledge is false, it

Aw: Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Steven,   yes, I nearly totally agree. Interesting, that Goedel said that. An observer cannot know the onologic state of a system the observer is part of. Then calling it knowledge is false, it is belief. Truth can only justifiedly be assumed about a system the observer is not part of, like a

Re: [PEIRCE-L] Intuitionistic logic, WAS: Asymmetry of Logic and Time

Helmut, I think I follow. You guys are clearly expert logicians, but it is easy to get so far into the weeds the way out is lost forever. Now the problem with knowledge is, to call it a classification, there cannot be knowers besides knowers-that-not about one topic. Yes. Logic can kill you.