On 10/20/2017 3:26 PM, Jerry LR Chandler wrote:
My feeling is that CSP’s remarks are now out of date in the sense that many forms of mathematical reasoning are used in different structural forms - sets, groups, rings, vector spaces etc. with different modes of reasoning, even about addition and multiplication.
No. Versions of all those theories existed in Peirce's day. Category theory is new, but it formalizes the notion of analogy at the metalevel: patterns of mathematical patterns. And analogy was a method of reasoning that Peirce discussed. Turing machines and abstract automata are new. But Peirce had published an article about logical machines in 1887, he suggested the use of electricity for wiring diagrams, and his 1887 article was published in a bibliography of artificial intelligence (1963). Computer systems have pushed the technology far beyond anything Peirce could have imagined. But he was already writing about his wishes for using stereoscopic imagery and moves for representing what we now call "virtual reality". When TV programs replaced the old radio programs, people complained that the images on TV weren't as rich as the ones they imagined while listening to the radio. In just over a week, we'll be celebrating the 79th anniversary of Orson Welles's radio drama "War of the Worlds". The mental imagery of the listeners to that story caused people to panic. Do you think they would have panicked if they had seen it on TV? John
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