Jon Schmidt, List,
I'd like to take up the distinction between principles and laws.
Jon S: "In other words, Peirce denies that excluded middle is an absolutely
exceptionless law (NEM 4:xiii, no date), which is presumably why he typically
prefers to call it a principle instead."
On its face, I believe this expresses some confusion about the differences
between principles and laws. I think Peirce makes the following sort of
distinction between the two. Consider the following argument, which is from the
second section of Kant's Grounding for the Metaphysics of Morals:
Everything in nature works in accordance with laws. Only a rational being has
the capacity to act in accordance with the representation of laws, that is, in
accordance with principles, or has a will. Since reason is required for the
derivation of actions from laws, the will is nothing other than practical
reason. (Ak 412)
According to a neo-Kantian view of rational laws, a law of logic governs the
relations between the facts expressed in the premisses and conclusion of an
argument. A principle, on the other hand, is our representation of such a law.
A logic utens consists of the habits of inference that embody such principles.
Those principles are subject to criticism precisely because they may not match
up with the laws of logic themselves. The purpose of a philosophical theory of
logic (i.e., a logica docens) is to build on the criticism of our common sense
principles for the sake of arriving at a more adequate theoretical
representation of the truth concerning the real laws that govern the logical
relations between such facts.
As such, we can distinguish between the principles embodied in our logica utens
and the principles embodied in a philosophical theory of logic--and either or
both of these may deviate in some respects from the real laws of logic.
This distinction is at the root of the classification of genuine triadic
relations in "The Logic of Mathematics, an attempt to develop my categories
from within". In this classificatory scheme, the laws of logic function as laws
of fact insofar as they govern those facts directly, and they are in a
genuinely triadic relation to the actual facts and those that are possible
(i.e., in the future).
The principles of logic, on the other hand, function as symbolic
representations that govern the self-controlled growth of our understanding.
The principles of logic, Peirce points out, do not govern brute facts with mere
necessity. Rather, they function as imperatives that dictate how we ought to
think. As such, the principles of logic differ from the laws of logic insofar
as they are in thoroughly genuine triadic relations to the premisses and
conclusions that are part of our inquiries. The principles that govern our
deductive inferences are capable of growth even if the laws of deductive logic
are, in some sense, necessary laws.
Yours,
Jeff
Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354
________________________________
From: Jon Alan Schmidt <jonalanschm...@gmail.com>
Sent: Tuesday, August 4, 2020 6:59 PM
To: s...@bestweb.net
Cc: peirce-l@list.iupui.edu; ahti-veikko.pietari...@ttu.ee;
francesco.belluc...@unibo.it; cdw...@iupui.edu; martin.irv...@georgetown.edu;
Gary Richmond
Subject: [PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and
final version of EGs)
John, All:
JFS: I sent a complete analysis of these issues to you and others on the CC
list.
Any analysis of these issues that treats cuts/shading as primitive in EGs,
rather than derived from the scroll, is incomplete. Peirce himself never
claims in R 670 or in RL 231 to be giving a complete analysis or explanation of
EGs.
JFS: In response to the other comments in your recent note, I'll reply with a
copy of Peirce's comments about scrolls in L231: " ", AKA silence.
An argument from silence is always logically weak, in this case especially so
since Peirce elsewhere explicitly denies that a consequence is a composite of
two negations and explicitly derives the cut from the scroll with a blackened
inner close. Again, I am not at all questioning the value of shading as a
simpler and more iconic improvement over thin lines for representing these
relations. In fact, according to what seems to be Peirce's very first
introduction of shading in EGs ("blue tint"), written five years earlier than R
670 and RL 231, it is precisely what revealed to him that "if A then B" is not
strictly equivalent to "not (A and not-B)."
CSP: But I had better tell you that practically, I content myself with
performing these cuts in my imagination, merely drawing a light line to
represent the cut. The blue tint, however, of the area within the cut is a
great aid to the understanding. How great I have only recently discovered. ...
The new discovery, which sheds such a light is simply that, as the main part of
the sheet represents existence or actuality, so the area within a cut, that is,
the verso of the sheet, represents a kind of possibility.
>From thence I immediately infer several things that I did not understand
>before, as follows: (R 490:12-15, includes CP 4.577-578, 1906)
Peirce now perceives that any oddly enclosed area "represents a kind of
possibility," rather than merely a denial of actuality. He proceeds to
describe three specific ramifications of this, the last of which is what I have
been emphasizing.
CSP: Thirdly, my previous account of Existential Graphs was marred by a
certain rule which, from the point of view from which I thought the system
ought to be regarded, seemed quite out of place and unacceptable, and yet which
I found myself unable to dispute. I will just illustrate this matter by an
example. (R 490:19-20, CP 4.580)
As Ahti-Veikko Pietarinen points out in the introduction to his own
transcription of the manuscript
(https://www.researchgate.net/publication/271419583_Two_Papers_on_Existential_Graphs_by_Charles_Peirce),
its presentation in CP is "seriously incomplete," and the EGs that serve as
Peirce's illustrative example "are all erroneous." Among the unfortunate
omissions is the text at the ellipsis in CP 4.580, which is his statement of
the widely accepted rule that he now deems to be "quite out of place and
unacceptable."
CSP: A conditional proposition is false only if the condition of it is
satisfied, while the consequent is falsified. For the proposition asserts
nothing at all in case the condition is not satisfied. So then it is only if
the condition is satisfied, while the consequent is falsified, that the
conditional proposition is false. But a proposition that is not false is true.
(R 490:23-24)
There is an assumption underlying this approach that Peirce had only come to
recognize (and abandon) in conjunction with his renewed interest in pragmatism.
CSP: This reasoning is irrefragable as long as a mere possibility is treated
as an absolute nullity. Some years ago, however, when in consequence of an
invitation to deliver a course of lectures in Harvard University upon
Pragmatism, I was led to revise that doctrine, in which I had already found
difficulties, I soon discovered, upon a critical analysis, that it was
absolutely necessary to insist upon and bring to the front, the truth that a
mere possibility may be quite real. That admitted, it can no longer be granted
that every conditional proposition whose antecedent does not happen to be
realized is true, and the whole reasoning just given breaks down. (R 490:25-26,
CP 4.580)
When A is realized, both "if A then B" and "not (A and not-B)" are true when B
is realized and false when B is not realized. However, when A is not realized,
"if A then B" is not necessarily true, even though "not (A and not-B)" is
always true. Yet "if A then B" is still not false in such cases, either. The
usually innocuous but ultimately faulty supposition here is that "a proposition
that is not false is true," which is the principle of excluded
middle--precisely the aspect of classical logic that intuitionistic logic
rejects. Peirce even acknowledges (many years earlier) that it is not strictly
true.
CSP: The two principles of contradiction and excluded middle do not stand at
all upon the same plane. ... [C]ertain rudimentary forms of reasoning,
embracing all those that the traditional logic has handed down to us, depend
only upon the impossibility of a fact's being both true and false, and remain
equally sound arguments, if we suppose that some things are neither true nor
false. (NEM 3:753, 1881; cf. NEM 3:751-752, 1881)
CSP: A consequence ut nunc is one in which the range of possibility is limited
to the actual state of things. To speak of the actual state of things implies a
great assumption, namely that there is a perfectly definite body of
propositions which, if we could only find them out, are the truth, and that
everything is really either true or in positive conflict with the truth. This
assumption, called the principle of excluded middle, I consider utterly
unwarranted, and do not believe it. Still, I hold that there is reason for
thinking it to be very nearly true. (NEM 3:758, 1893; cf. NEM 3:758-760, 1893)
In other words, Peirce denies that excluded middle is an absolutely
exceptionless law (NEM 4:xiii, no date), which is presumably why he typically
prefers to call it a principle instead. Nevertheless, it is only after
accepting "the truth that a mere possibility may be quite real" that he
"discovers" how a scroll in EGs can represent a consequence whose range of
possibility is not limited to the actual state of things, such that excluded
middle does not hold for it. Peirce has more to say about this, but that seems
like enough for now.
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>
On Tue, Aug 4, 2020 at 9:46 AM John F. Sowa
<s...@bestweb.net<mailto:s...@bestweb.net>> wrote:
Jon AS,
I sent a complete analysis of these issues to you and others on the CC list.
For a copy, see the attached eg1911.txt. For the unsolved research problem
from 1988 and an outline of the solution, see the attached ppe65.png. For more
detail, see the slides "Peirce, Polya, and Euclid" -- URL in the eg1911.txt.
For even more detail, see the 76-page article from the Journal of Applied
Logics (URL in a footnote on p. 2 of ppe.pdf).
Re the word 'scroll': In terms of the semantics (endoporeutic) and permissions
(rules of inference) of eg1911, a scroll is *indistinguishable* from a shaded
area with a nested unshaded area. Anything that Peirce wrote about scrolls
prior to 22 June 1911 is useful only for understanding the development of his
thought. After that date. the word 'scroll' could only create confusion --
some readers might be misled by Peirce's earlier writings to think that there
is some "deeper" meaning that is not expressed by a nest of two ovals.
In response to the other comments in your recent note, I'll reply with a copy
of Peirce's comments about scrolls in L231: " ", AKA silence.
John
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