Relatives Of Second Intention

[Jon Awbrey]

Cf: Relatives Of Second Intention • Comment 1
http://inquiryintoinquiry.com/2021/04/08/relatives-of-second-intention-comment-1/

Re: C.S. Peirce • Relatives of Second Intention
https://inquiryintoinquiry.com/2012/04/07/c-s-peirce-relatives-of-second-intention/

Re: Paradisaical Logic and the After Math
https://inquiryintoinquiry.com/2012/04/09/paradisaical-logic-and-the-after-math/
https://inquiryintoinquiry.com/2021/04/04/paradisaical-logic-and-the-after-math-comment-1/
https://inquiryintoinquiry.com/2021/04/07/paradisaical-logic-and-the-after-math-comment-2/

All,

I am getting a feeling I occasionally get when discussing Peirce’s work
in a group setting — as though we had a grand feast set before us while
the dining philosophers wrangle over the amuse-bouche. With that in mind
I’d like to return to the inciting text, the one so exciting me all those
years ago, and see what’s truly substantial and tantalizing in it.

Selections from C.S. Peirce, “The Logic of Relatives”, CP 3.456–552
===================================================================

488. The general method of graphical representation of propositions has now been given in all its essential elements,
except, of course, that we have not, as yet, studied any truths concerning special relatives; for to do so would seem,
at first, to be “extralogical”.

Logic in this stage of its development may be called paradisaical logic, because it represents the state of Man's
cognition before the Fall. For although, with this apparatus, it is easy to write propositions necessarily true, it is
absolutely impossible to write any which is necessarily false, or, in any way which that stage of logic affords, to find
out that anything is false. The mind has not as yet eaten of the fruit of the Tree of Knowledge of Truth and Falsity.

Probably it will not be doubted that every child in its mental development necessarily passes through a stage in which
he has some ideas, but yet has never recognised that an idea may be erroneous; and a stage that every child necessarily
passes through must have been formerly passed through by the race in its adult development. It may be doubted whether
many of the lower animals have any clear and steady conception of falsehood; for their instincts work so unerringly
that there is little to force it upon their attention. Yet plainly without a knowledge of falsehood no development of
discursive reason can take place.

489. This paradisaical logic appears in the study of non-relative formal logic. But there no possible avenue appears
by which the knowledge of falsehood could be brought into this Garden of Eden except by the arbitrary and inexplicable
introduction of the Serpent in the guise of a proposition necessarily false. The logic of relatives affords such an
avenue, and that, the very avenue by which in actual development, this stage of logic supervenes. It is the avenue of
experience and logical reflexion.

490. By logical reflexion, I mean the observation of thoughts in their expressions. Aquinas remarked that this sort
of reflexion is requisite to furnish us with those ideas which, from lack of contrast, ordinary external experience
fails to bring into prominence. He called such ideas second intentions. Is is by means of relatives of second
intention that the general method of logical representation is to find completion.

Reference
=========

* Charles S. Peirce, “The Logic of Relatives”, The Monist, vol. 7, 161–217, (1897). Reprinted, CP 3.456–552.

Regards,

Jon

[Jon Awbrey]

Cf: Relatives Of Second Intention • Comment 2
https://inquiryintoinquiry.com/2021/04/08/relatives-of-second-intention-comment-2/

Re: Relatives Of Second Intention • Comment 1
https://inquiryintoinquiry.com/2021/04/08/relatives-of-second-intention-comment-1/
Re: FB | Medieval Logic
https://www.facebook.com/groups/medievallogic/permalink/1717213205147844
::: Kollbjorn Oldtheyn
https://www.facebook.com/groups/medievallogic/permalink/1717213205147844/?comment_id=1717314148471083

Dear Kollbjorn,

The way I understand Peirce's parable, he is asking, “How do we first arrive
at a condition far enough removed from our immersion in a current experience
to question it, to reflect on it, and thereby conceive the possibility of
something other?” Until we do that we do not have a concept of “not”.

Regards,

Jon

[Jon Awbrey]

Cf: Relatives Of Second Intention • Comment 3
http://inquiryintoinquiry.com/2021/04/08/relatives-of-second-intention-comment-3/

Re: C.S. Peirce • Relatives of Second Intention
https://inquiryintoinquiry.com/2012/04/07/c-s-peirce-relatives-of-second-intention/

Re: FB | Medieval Logic
https://www.facebook.com/groups/medievallogic/permalink/1717213205147844
::: Kollbjorn Oldtheyn

https://www.facebook.com/groups/medievallogic/permalink/1717213205147844/?comment_id=1717352898467208&reply_comment_id=1717411868461311
)

Dear Kollbjorn,

I used to think I knew what Peirce was talking about in this passage —
but it may be time to make a new examination of that.

• Guess 1. Strictly speaking he's talking about his earlier system
of “entitative graphs” which are logically dual to existential graphs
as far as propositional calculus goes. That may not affect his point,
except he did not extend the entitative graphs to cover the logic of
relative terms, so he may be talking about the limitations of absolute
versus relative terms.

• Guess 2. He may be alluding to the complex way he treated negation
in his 1870 Logic of Relatives, which is very tricky but worth revisiting.

• Guess 3. He may be talking about the threshold between first intentional
and second intentional relatives, which may or may not be the same thing as
first order versus second order logic.

At any rate, I'll be looking further into it …

Regards,

Jon

[Jon Awbrey]

Cf: Relatives Of Second Intention • Comment 4
http://inquiryintoinquiry.com/2021/04/10/relatives-of-second-intention-comment-4/

Re: C.S. Peirce • Relatives of Second Intention
https://inquiryintoinquiry.com/2012/04/07/c-s-peirce-relatives-of-second-intention/

Re: Laws Of Form
https://groups.io/g/lawsofform/topic/relatives_of_second_intention/81938598
::: Lyle Anderson
https://groups.io/g/lawsofform/message/220

<QUOTE LA:>

Here Peirce is confusing Truth and Falsity with Good and Evil.
The Creator of the Universe (CotU) created Truth and Falsity
when He drew the First Distinction. The Universe started
with Bet (2) not Aleph (1). What was the First Commandment?
Do NOT eat of the Tree of the Knowledge of Good and Evil.
Good and Evil are many levels of abstraction away from
True and False.

</QUOTE>

Dear Lyle,

Thanks for making that observation. I had seen what Peirce did there, too,
and it's one reason I saw him as making an allegorical or parabolic use of
“felix culpa” at that point, since I know he knows his Scripture too well to
imagine it anything but intentional. Read in that spirit Peirce is inviting
us to contemplate a particular form of distinction — a threshold between an
immersive state of being and a reflective stage of critical thought.

Regards,

Jon

[Jon Awbrey]

Cf: Relatives Of Second Intention • Comment 5
http://inquiryintoinquiry.com/2021/04/11/relatives-of-second-intention-comment-5/

Re: C.S. Peirce • Relatives of Second Intention
https://inquiryintoinquiry.com/2012/04/07/c-s-peirce-relatives-of-second-intention/

Re: Peirce List • John Sowa
::: https://list.iupui.edu/sympa/arc/peirce-l/2021-03/msg00205.html
::: https://list.iupui.edu/sympa/arc/peirce-l/2021-04/msg00001.html
Re: Peirce List • Jon Alan Schmidt
::: https://list.iupui.edu/sympa/arc/peirce-l/2021-04/msg00043.html

<QUOTE JAS:>

Thanks for providing a longer excerpt of that passage than I did, including Peirce's statement about “the lower
animals.” I see now that I was wrong when I said on Tuesday, “Peirce makes no claim in the relevant texts about
non-human animals at all.” What I should have said is that he makes no claim in the relevant texts about whether
non-human animals can “learn to recognize negations.” He merely expresses doubt that they “have any clear and steady
conception of falsehood,” and adds that “without a knowledge of falsehood no development of discursive reason can take
place.”

In other words, it is not reasoning per se that distinguishes humans from other animals, since no notion of falsity is
required for that — only a capacity for drawing inferences, which in “non-relative formal logic” corresponds to the
relation of implication such that one proposition necessarily (i.e., deductively) follows from another. Instead, what
distinguishes humans from other animals is discursive reasoning, which does require “a knowledge of falsehood” and the
more sophisticated “logic of relatives.”

In accordance with Peirce's own words, it is important to keep in mind that these points all have to do with logic, not
psychology or linguistics. His thesis is that we acquire the notion of falsity and associate it with the formal
relation of negation through “the avenue of experience and logical reflexion,” when reality confronts us with surprising
observations that call for explanation, thus compelling us to initiate the process of inquiry by which we eventually
revise our previous beliefs that grounded our incorrect expectations.

</QUOTE>

Dear Jon Alan,

Thanks for your comments, which I look forward to studying further.
Earlier I mentioned CP 3.488–490 as one of “the very doors I first
walked through into the wonderland of logic à la Peirce”. That is
because, just the other side of that door, at CP 3.491, Peirce
introduces a triadic relative term signifying of three elements
A, B, C in the universe of discourse that A is neither B nor C.

Now, a relation among three elements of an arbitrary universe of
discourse is more general than a relation among three logical values
but they are kin enough to connect the passage with Peirce's marking
of the amphecks ( https://oeis.org/wiki/Ampheck ) Nand and Nnor and
their sole sufficiency ( https://oeis.org/wiki/Sole_sufficient_operator )
among boolean operations.

What flashed me back this time, though, was John Sowa raising
the topic of reflection on visual diagrams, those being forms
of expression and calling to mind what Peirce wrote about
“logical reflexion” being “the observation of thoughts
in their expressions”.

I'm now going to hold off further commentary on this passage and
stand back to take in a broader view of its context, Peirce's 1897
Logic of Relatives, as I'm seeing many issues I did not appreciate,
much less understand in times past. This looks like it will take me
no little time …

Regards,

Jon