FYI — “Every unicorn 🦄 is pink” is true.
Jon http://inquiryintoinquiry.com > On May 19, 2021, at 5:52 PM, Helmut Raulien <h.raul...@gmx.de> 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 > following example: > > "Every unicorn is pink" is false, but "There is no unicorn that is not pink" > is true. > > "Every unicorn is pink" is false, because it means "If it is a unicorn, then > it is pink", and "If it is a unicorn" implies, that unicorns exist. So it is > equal with "Unicorns exist, and if it is a unicorn, it is pink". Because > unicorns donot exist, the proposition is false. > > "There is no unicorn that is not pink" sounds true, because there are no > unicorns at all, so there are no non-pink unicorns too. But if it would be > so, that this form of proposition too implied the existence-claim, it would > be false as well. Is that so? Is in classical logic "There is no unicorn that > is not pink" equal with "Unicorns exist, and there is no unicorn that is not > pink"? > > This might be so e.g. due to the fact alone, that the term "Unicorn" has been > mentioned. For EGs, it would mean, that every term written in any place is a > possible too in the blank sheet. Meaning, that it generally exists. Otherwise > it would not signify anything, it would e.g. be like "NOT &/(", senseless. > But this would mean, that the term "existential" in "Existential Graphs" > means, that only existing things are allowed in them. > > Another way to classically synchronize the two propositions might be to say, > that if a term signifies a nonexistent thing, it automatically signifies its > phantasy-concept instead. Then "Every unicorn is pink" is false, because in > some animated movie by Disney occurs a white unicorn. "There is no unicorn > that is not pink" then is false for the same reason. This explanation is > somewhat smoother than the first, but requires this said automatism: If A > does not physically exist, then A is the existing concept of A. > > Best > Helmut > > > 19. Mai 2021 um 06:58 Uhr > "John F. Sowa" <s...@bestweb.net> > wrote: > 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 impossible to use many widely accepted theories of mathematics > -- among them, the theory that there are hierarchies of infinities. > > Peirce was one of the mathematicians who discovered a proof of that point > independently of Georg Cantor. And it's the foundation for his theory of > continuity -- which Abraham Robinson proved was consistent in 1960. > In applications to science and engineering, especially computer science, > nobody uses intuitionistic logic. The reason why is that it "blocks the way" > of using the most convenient, efficient, and flexible methods of reasoning. > > The mainstream mathematicians don't stop intuitionists from developing their > own pet theories. They just ignore them. > > John > > > > _ _ _ _ _ _ _ _ _ _ â–º 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 . â–º To UNSUBSCRIBE, send a message NOT to PEIRCE-L > but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of > the message and nothing in the body. More at > https://list.iupui.edu/sympa/help/user-signoff.html . â–º PEIRCE-L is owned > by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and > Ben Udell. > _ _ _ _ _ _ _ _ _ _ > ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in > the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
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