John, I appreciate the clarification in your post: when you wrote that intuitionist logic "blocks the way of inquiry", what you really meant was that it "blocks the way" of using the most convenient, efficient, and flexible methods of reasoning. Peirce's idea of inquiry, and specifically of the inquiry he was developing by means of Existential Graphs, was very different from that, especially in his one presentation of EGs to a mixed audience (meaning an audience not composed entirely of mathematicians). He made this clear at the very beginning of his second Lowell lecture <https://gnusystems.ca/Lowell2.htm> of 1903:
[[ Before beginning, let us distinctly recognize the purpose which this system of expression is designed to fulfil. It is intended to enable us to separate reasoning into its smallest steps so that each one may be examined by itself. Observe, then, that it is not the purpose of this system of expression to facilitate reasoning and to enable one to reach his conclusions in the speediest manner. Were that our object, we should seek a system of expression which should reduce many steps to one; while our object is to subdivide one step into 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 <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. 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
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