Peirce's 1885 “Algebra of Logic” • Discussion

[Jon Awbrey]

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

All,

Daniel Everett raised an interesting point on Facebook.

Re: FB | Daniel Everett
•
https://www.facebook.com/permalink.php?story_fbid=pfbid029CAsWFV17xtECsjY7dRDe4pdpwTqtQbn29wi72iqfYgaDZnaqrfQLjfXafoBYkiwl&id=100093271525294

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 ❞

I commented as follows.

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

Regards,

Jon

cc: https://www.academia.edu/community/VjQDGJ
cc: https://mathstodon.xyz/@Inquiry/112202927662807287

[Jon Awbrey]

Peirce's 1885 “Algebra of Logic” • Discussion 2
• https://inquiryintoinquiry.com/2024/04/03/peirces-1885-algebra-of-logic-discussion-2/

Re: FB | Daniel Everett
•
https://www.facebook.com/permalink.php?story_fbid=pfbid029CAsWFV17xtECsjY7dRDe4pdpwTqtQbn29wi72iqfYgaDZnaqrfQLjfXafoBYkiwl&id=100093271525294

One thing I've been trying to understand for a very long time
is the changes in Peirce's writing about math and logic from
1865 to 1885. If there's anything I've learned from reading
Peirce in the often dim light of intellectual history it is
to be wary of progressivist assumptions — but unlike many of
his other fans I apply that caution also within the body of
his own work. Long story short, from 1865 to 1885 I see
progress on several fronts but also bits of backsliding
from his more prescient early insights. So it's a puzzle …
and it will take more study to ravel out the reasons why.

Resources for reconciling Peirce's two accounts:
1. The 1870 account of logical involution
2. The 1885 account of universal quantification

Peirce's 1870 “Logic of Relatives” • Selection 12 • The Sign of Involution
• https://inquiryintoinquiry.com/2014/06/09/peirces-1870-logic-of-relatives-selection-12/
Comments —
(1) https://inquiryintoinquiry.com/2014/06/10/peirces-1870-logic-of-relatives-comment-12-1/
(2) https://inquiryintoinquiry.com/2014/06/11/peirces-1870-logic-of-relatives-comment-12-2/
(3) https://inquiryintoinquiry.com/2014/06/12/peirces-1870-logic-of-relatives-comment-12-3/
(4) https://inquiryintoinquiry.com/2014/06/14/peirces-1870-logic-of-relatives-comment-12-4/
(5) https://inquiryintoinquiry.com/2014/06/15/peirces-1870-logic-of-relatives-comment-12-5/

Peirce's 1885 “Algebra of Logic” • Selections
(1) https://inquiryintoinquiry.com/2024/03/24/peirces-1885-algebra-of-logic-selection-1/
(2) https://inquiryintoinquiry.com/2024/03/26/peirces-1885-algebra-of-logic-selection-2/
(3) https://inquiryintoinquiry.com/2024/03/30/peirces-1885-algebra-of-logic-selection-3/
(4) https://inquiryintoinquiry.com/2024/04/01/peirces-1885-algebra-of-logic-selection-4/

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

Regards,

Jon