Jon Alan, list,
Three years ago when I posted my transcription of Lowell Lecture 2 on my
website (https://gnusystems.ca/Lowell2.htm) I was quite baffled by Peirce’s
derivation of the negating signification of the cut from the signification of
the scroll with a blackened inner close or “pseudograph”. I even posted to the
Peirce list expressing my bafflement. I wish I could have read (and understood)
this post of yours back then, because it would have cleared things up for me.
But then I probably couldn’t have understood it because I was still a beginner
in the study of Existential Graphs. Your post explains succinctly much of what
I’ve learned about them since.
In logical terms, the key is that excluded middle is a principle only of
deductive reasoning, not of ampliative reasoning, which always comes first in
any inquiry; and the concept of negation is in a sense derived from the
principle of excluded middle. Consequence comes before negation. At least
that’s my understanding now, thanks to your explanation.
Gary f.
} Seeking enlightenment apart from the world is like looking for horns on a
hare. [Hui-neng] {
<https://gnusystems.ca/wp/> https://gnusystems.ca/wp/ }{ living the time
From: Jon Alan Schmidt <jonalanschm...@gmail.com>
Sent: 13-Dec-20 18:47
To: peirce-l@list.iupui.edu
Subject: [PEIRCE-L] Re: Asymmetry of Logic and Time (was multiple-valued logic)
List:
I have been thinking about existential graphs again lately and wondering how
they might be employed to represent abduction, rather than deduction. Peirce
describes the form of abductive inference as follows.
CSP: The surprising fact, C, is observed;
But if A were true, C would be a matter of course.
Hence, there is reason to suspect that A is true. (CP 5.189, EP 2:341, 1903)
He elaborates on this a few years later.
CSP: Every inquiry whatsoever takes its rise in the observation, in one or
another of the three Universes, of some surprising phenomenon, some experience
which either disappoints an expectation, or breaks in upon some habit of
expectation ... . The inquiry begins with pondering these phenomena in all
their aspects, in the search of some point of view whence the wonder shall be
resolved. At length a conjecture arises that furnishes a possible
Explanation,--by which I mean a syllogism exhibiting the surprising fact as
necessarily consequent upon the circumstances of its occurrence together with
the truth of the credible conjecture, as premisses. On account of this
Explanation, the inquirer is led to regard his conjecture, or hypothesis, with
favor. As I phrase it, he provisionally holds it to be "Plausible" ... (CP
6.469, EP 2:441, 1908)
Hence abduction is "reasoning from consequent to antecedent" (ibid) or
reasoning from conclusion to premisses--i.e., reasoning backwards, which is why
Peirce ultimately prefers to call it retroduction. Accordingly, in EGs we can
scribe any true proposition on the sheet of assertion--such as a surprising
fact (C)--and "scroll" it so that it becomes the consequent of a conditional
(in the inner close), then insert any proposition whatsoever (A) as the
hypothetical antecedent (in the outer close). Since C is true and we have
complied with the transformation rules, the resulting consequence (if A then C)
cannot be false no matter what we choose for A. But does this entail that it is
true?
On the contrary, as with intuitionistic logic, excluded middle does not hold in
such a case. Given that C is true, we only have reason to suspect that A is
true if C follows from A as a matter of course. In other words, the
plausibility of A as an explanation of C relies on there being a rational
sequence from A to C. This requirement is obscured in classical deductive
logic, "completely hidden behind the superfluous machinery which is introduced
in order to give an appearance of symmetry to logical law" (R 490:29, CP 4.581,
1906), by treating "if A then C" as equivalent to "not-(A and not-C)" or "not-A
or C"--i.e., a scroll as equivalent to nested cuts or a shaded area enclosing
an unshaded area--because the latter formulations are always true as long as C
is true.
CSP: The second failure of Selectives to be as analytical as possible lies in
their encouraging the idea that negation, or denial, is a relatively simple
concept, and that the concept of Consequence, is a special composite of two
negations, so that to say, “If in the actual state of things A is true, then B
is true,” is correctly analyzed as the assertion, “It is false to say that A is
true while B is false.” I fully acknowledge that, for most purposes and in a
preliminary explanation, the error of this analysis is altogether
insignificant. But when we come to the first analysis the inaccuracy must not
be passed over. (R 300:48-49[47-48], 1908)
Even in deductive reasoning, there is "a real movement of thought" from
antecedent to consequent, from premisses to conclusion. The continuous scroll
preserves this aspect, while discrete nested cuts or shaded/unshaded areas do
not.
CSP: All my own writings upon formal logic have been based on the belief that
the concept of Sequence, alike in reasonings and in judgments, whether the
latter be conditional or categorical, could in no wise be replaced by any
composition of ideas. For in reasoning, at least, when we first affirm, or
affirmatively judge, the conjugate of premisses, the judgment of the conclusion
has not yet been performed. There then follows a real movement of thought in
the mind, in which that judgment of the conclusion comes to pass. Now surely,
speaking of the same A and B as above, it were absurd to say that a real change
of A into a sequent B consists in a state of things that should consist in
there not being an A without a B. For in such a state of things there would be
no change at all. (R 300:49[48])
There is likewise "a real movement of thought" in abductive/retroductive
reasoning, but in the opposite direction. That is why it is ampliative rather
than merely explicative, with the tradeoff that its inferences are merely
plausible rather than certain.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt <http://www.LinkedIn.com/in/JonAlanSchmidt>
- twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt>
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu .
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu
with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of
the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and
co-managed by him and Ben Udell.
