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I think the outline provided by Robert Marty is very important - and
one that this List has been overlooking.
That is - there is a difference between chronological and logical
order in the interactions that an organism has with its environment.
We cannot insist that these interactions are either one OR the other.
They are both - and we have to acknowledge that both types of
interaction exist.
Peirce himself was clear that we don't 'begin' with complete doubt
[yes, yes, I'll find the exact quotation later] but must begin our
interactions with the knowledge base of 'what we already have'. That
is, our phenomenological interactions, which are chronological
between X and Y, are also logical interactions.
This means, in my view, that all our interactions with our
environment are triadic; they operate as O-R-I; that is, they are
mediated interpretations by our organism of that environment. There
is no such thing as a direct knowledge of objective reality. This
does not mean that our triadic interpretations always include our
human Minds; they might just include the 'Minds' embedded in our
physiological nature...As an example, where a brute force of a stick
on my arm will result in a bruise on my skin - which is the skin
cell's Mind-reaction to external force.
My view of 'what we already have' is not simply our learned
knowledge base but our physico-chemical and biological knowledge
base. Even a cell has its infrastructure of 'How Do I Interact With
the World' already built in to its format as that cell. There are
certain interactions it can do and many that it cannot do. These, I
would say, are its LOGICAL base. Therefore, given this existent
logical base - it can then, chronologically, interact with its
environment.
Within the human species, where Mind has become heavily located
within a separate brain, much of the Logical base is learned, and
works with the Chronological experiences to evaluate and interpret
individual experiences with the environment. That is, the two, Mind
and Body are correlated.
I don't see how even the chronological and phenomenological
observation of the categories can be accomplished without a logical
framework.
Edwina
On Wed 25/08/21 4:23 PM , robert marty robert.mart...@gmail.com
sent:
List,
Following ...
B1 – To state the logical order (of the discovery), we must
follow Peirce "I am partially inverting the historical order, in
order to state the process in its logical order"(CP 5.589, EP
2:54-55, 1898), as quoted by Jon Alan Schmidt.
I recall the chronological order observed in part A
(https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00177.html ) :
1- observation of phanerons by "phaneroscopists" who identify
"candidate" forms. Peirce himself has found forms that come from his
knowledge of theoretical chemistry: the "valences" of the elements.
2- for each "candidate" form found, search in the mathematical
repository or creation of isomorphic mathematical forms.
3-choosing, by the scientific community involved in the discovery,
of the "best form."
4-generate, by pure mathematical activity, new mathematical forms to
be submitted to a new validation process.
What is then the order advocated by Peirce? It is the dependencies
stated in his classifications of sciences with respect to
mathematics, which generates the process of the Sciences of Discovery
described below:
1- Mathematics (the "good" forms found in 3 above)
2- Cenoscopy - Philosophia prima- positive science (which rests
upon familiar, general experience): continuation of the
"phaneroscopic" activity which may give rise to the emergence of new
competing candidates.
3- Phenomenology - Phaneroscopy (1904-) - study of Universal
Categories (all present in any phenomenon): Firstness, Secondness,
Thirdness. Work of the phaneroscopists driven by the mathematics of
the 1.
" Phaneroscopy... is the science of the different elementary
constituents of all ideas. Its material is, of course, universal
experience, -- experience I mean of the fanciful and the abstract, as
well as of the concrete and real. Yet to suppose that in such
experience the elements were to be found already separate would be to
suppose the unimaginable and self-contradictory. They must be
separated by a process of thought that cannot be summoned up
Hegel-wise on demand. They must be picked out of the fragments that
necessary reasonings scatter, and therefore it is that phaneroscopic
research requires a previous study of mathematics. (R602, after 1903
but before 1908")
4 - unchanged
The chronological order 1,2,3,4 is changed to logical order: 3, 2,
1, 4.
"Phaneroscopists" cannot constitute a category in themselves and
that, since they do not study mathematics, they would be better
advised to collaborate with mathematicians who have "forms in mind".
In his writings, Peirce presents his research relative to the
categories either in chronological order by reporting his
observations (CP 1.284, 1.286), or in a logical order by reporting
the result of his observations in formal terms, in particular by
reasoning by analogy with the notion of valence in chemistry (CP
1.292 ) and more formally with the monad, dyad, and triad.
"I invite you to consider, not everything in the phaneron, but only
its indecomposable elements, that is, those that are logically
indecomposable, or indecomposable to direct inspection.[ … ]
Fortunately, however, all taxonomists of every department have found
classifications according to structure to be the most important." (CP
1.288)
Depending on the context, the "phaneroscopists" will find by
"pressicive" observation and/or by "abstractive hypostatization",
either pure forms (expressible in mathematical diagrams) or informal
"bricolage" to which mathematicians may or may not give form. One
finds in particular in Categories (Peirce) - Wikipedia the following
compiled table:
Name:
Typical characterization
As universe of experience:
As quantity
Technical definition:
Valence, "adicity":
Firstness
Quality of feeling
Ideas, chance, possibility.
Vagueness, "some."
Reference to a ground (a ground is a pure abstraction of a quality
Essentially monadic (the quale, in the sense of the such,[11]
which has the quality).
Secondness
Reaction, resistance, (dyadic) relation.
Brute facts, actuality.
Singularity, discreteness, “this
Reference to a correlate (by its relate).
Essentially dyadic (the relate and the correlate).
Thirdness
Representation, mediation.
Habits, laws, necessity.
Generality, continuity, "all".
Reference to an interpretant*.
Essentially triadic (sign, object, interpretant*).
We see that the only terms that can be linked to mathematics are
"monadic," "dyadic," and "triadic." No other mathematical object is
mentioned.
I conclude this part B1 by quoting an article
(https://www.jstor.org/stable/40321072 [1], 2005) widely by Cornelis
de Wall, who says much better than I do the impossibility of
relegating mathematics and mathematicians to a corner where they
would devote day and night in endless deductions, while
self-proclaimed "phaneroscopists" would propose specific informal
bricolage without "skeleton-sets" to support them:
"By defining science in terms of the activities of its promoters,
Peirce's division of the sciences largely comes down to a division of
labor. This attitude toward science enables Peirce to argue that it is
the mathematician who is best equipped to translate the more loosely
constructed theories about groups of positive facts generated by
empirical research into tight mathematical models:
'The results of experience have to be simplified, generalized, and
severed from fact so as to be perfect ideas before they arc suited to
mathematical use. They have, in short, to be adapted to the powers of
mathematics and of the mathematician. It is only the mathematician
who knows what these powers are; and consequently the framing of the
mathematical hypotheses must be performed by the mathematician.' (R
17:06!)
Now what constitutes a well-equipped mathematician? The three mental
qualities that in Peirce's view, come into play are imagination,
concentration, and generalization. The first is, as Peirce put it,
"the power of distinctly picturing to ourselves intricate
configurations"; the second is "the ability to cake up a problem,
bring it to a convenient shape for study, make out the gist of it,
and ascertain without mistake just what it does and does not
involve"; the third is what allows us "to see that what seems at
first a snarl of intricate circumstances is but a fragment of a
harmonious and comprehensible whole" (R 252:20).6 In particular the
power of generalization, which Peirce believes "chiefly constitutes a
mathematician" (R 278a:9 l ), is a difficult skill to attain. Peirce's
emphasis on imagination, concentration, and generalization draws the
attention away from the notion that it is the premier business of
mathematics to provide proofs."
In section B2, I will study how some of the most prominent Peircean
have confronted this dependence of phaneroscopy on mathematics and
the responses they have provided.
Best regards,
Robert Marty
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty [2]
https://martyrobert.academia.edu/ [3]
Links:
------
[1] https://www.jstor.org/stable/40321072
[2] https://fr.wikipedia.org/wiki/Robert_Marty
[3] https://martyrobert.academia.edu/
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