Peirce's 1885 “Algebra of Logic” • Discussion 1
• https://inquiryintoinquiry.com/2024/04/02/peirces-1885-algebra-of-logic-discussion-1/

Re: FB | Daniel Everett

DE:
❝One of the most important papers in the history of logic. “On the Algebra of Logic” was the first to introduce the term “quantifier”.

❝Peirce, C.S. (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7, 180–202.
• https://www.jstor.org/stable/2369451 ❞

As far as quantification by any other word goes, Peirce had already introduced a more advanced and “functional” concept of quantification in his 1870 “Logic of Relatives”. The subsequent passage to Fregean styles of first order logic would turn out to be a retrograde movement toward syntacticism (a species of nominalism), as seen in the general run of what fol‑lowed in the fol‑lowing years.

See ☞ Peirce's 1870 “Logic of Relatives”
• https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/

Especially ☞ “The Sign of Involution”
• https://inquiryintoinquiry.com/2014/06/09/peirces-1870-logic-of-relatives-selection-12/

The connection between logical involution and universal quantification which Peirce put to use in his 1870 Logic of Relatives will turn up again a century later with the application of category theory to computer science and both of those in turn to logic. Just one more time Peirce was that far ahead of it.

See ☞ Lambek and Scott (1986), Introduction to Higher Order Categorical Logic, Cambridge University Press.
• https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#Lambek

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#Semiotics #PredicateCalculus #Quantification #LogicalInvolution #ComputerScience