Re: Peirce List
At: https://list.iupui.edu/sympa/arc/peirce-l/2021-03/msg00097.html
Re: Jon Alan Schmidt
At: https://list.iupui.edu/sympa/arc/peirce-l/2021-03/msg00123.html
Dear Peircers,
We had some discussion of “involution” and its kin arising from
the discussion of Robert Marty's “Podium” paper and I mentioned
the place in Peirce's 1870 “Logic Of Relatives” where he mapped
one of its standard mathematical senses into the logical realm.
Cf:
https://list.iupui.edu/sympa/arc/peirce-l/2020-04/msg00048.html
https://list.iupui.edu/sympa/arc/peirce-l/2020-04/msg00072.html
Here's a transcript of the latter post:
⁂
On 4/17/2020 12:30 PM, Jon Awbrey wrote:
Cf: Peirce's Categories • 14
At: https://inquiryintoinquiry.com/2020/04/16/peirces-categories-14/
Continuing with the discussion of Robert Marty's “Podium Diagram” ...
Re: Peirce List (
https://list.iupui.edu/sympa/arc/peirce-l/2020-04/thrd1.html#00020 )
Re: Robert Marty (
https://list.iupui.edu/sympa/arc/peirce-l/2020-04/msg00047.html )
RM: What do you think of the presuppositions between the levels? Do they make
sense to you?
At this point I have mostly questions, which would take further research to answer, not to mention unpacking many books
still in boxes from our move a year and a half ago, none of which I'm at liberty to do right now. So, just off the cuff ...
“Presupposition” is one of those words I tend to avoid, as it has too many uses at odds with each other. There are at
least the architectonic, causal, and logical meanings. It it were only a matter of logic, I would say “P presupposes Q”
means “P ⇒ Q”. But usually people have something more pragmatic or rhetorical in mind than pure logic would require,
something like enthymeme.
It's also common for people to confound the implication order “P ⇒ Q” with the causal order “P causes Q”, whereas it's
more like the reverse of that. In more complex settings we usually have the architectonic sense in mind, and that is
what I sensed in the case of the normative sciences. Viewed with regard to their bases, logic is a special case of
ethics and ethics is a special case of aesthetics, but with regard to their level of oversight, aesthetics must submit
to ethical control and ethics must submit to logical control.
Early on, Peirce used “involution” with the meaning it has in arithmetic or number theory, namely, “exponentiation”,
where x^y means taking x to the power of y. See the following passage and commentary.
* Peirce's 1870 Logic Of Relatives • The Sign of Involution
https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2#Selection_12
As far as the boolean or propositional analogue goes, x^y for x, y in {0, 1) means the same thing as x ⇐ y, as one can
tell by comparing the following two operation tables.
Exponentiation and Converse Implication
https://inquiryintoinquiry.files.wordpress.com/2020/04/exponentiation-and-converse-implication.png
I haven't looked into whether Peirce uses “involution” or “involvement” with
that sense in his later writings.
Resources
=========
* Peirce's 1870 Logic Of Relatives
https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview
* Precursors Of Category Theory
https://oeis.org/wiki/Precursors_Of_Category_Theory
Regards,
Jon
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache
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