I know what book you are talking about; today it can be downloaded for
free...
I looked at your diagram... it rejuvenated me... indeed, I was always the
terror of my students because, whenever they presented me with a diagram I
demanded that every single point, every single line be documented... so I
look at your diagram and I see first of all ovals,5 , with words inside...
I wonder if they delimit sets of points of the plane which would represent
each one an object of the extension of each of the labels inscribed in the
oval... the answer is obvious, it's not. So the ovals are just decorative
elements that direct attention to the 5 terms of the language they surround.
I come to the lines ... the graphic conventions in use (signs of law)
strongly suggest to me that they are relationships between concepts ...
perhaps of dependence given the context of communication ... the same
conventions and context suggest that they should be considered top-down
relationships ... I can't go beyond that as I have no information about
these lines and the modes of correspondence they cover ... in advance of
the upcoming debate, I say that if all the lines represent top-down
dependency relationships then this diagram comes into open conflict with
Peirce's classification ... conflict involving debate in the Sciences of
Discovery ...I am ready...
On Thu. Jul 29, 2021 at 2:30 PM, Jon Awbrey <jawb...@att.net> wrote:
Dear Robert, John, Edwina, ...
This discussion reminds me a lot of the time I spent the big bucks
buying a book on "Diagrammatology" which ran to over 500 pages with
many sections in very small print and had just over 50 diagrams in
the whole thing.
So I think the real "versus" here is more like the difference
between people who "think in words about thinking in diagrams"
and people who "think in words about thinking in words".
Those of us, the very few, who have actually been
working on "moving pictures" from the very get-go,
have learned to see things somewhat differently.
https://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg
Regardez,
Jon
On 7/29/2021 5:27 AM, robert marty wrote:
Dear John, Edwina, List
Let me clarify my question:
The references in parentheses refer to the classification
<
https://www.academia.edu/5148127/The_outline_of_Peirces_classification_of_sciences_1902_1911_
compiled by Tommi Vehkavaara.
The classification of the Sciences of Discovery places Mathematics (AI)
ex-ante the Phaneroscopy; the whole mathematical activity is per se,
independent of any implementation and does not depend on anything, since
it
incorporates its own mathematics (of Logic) (AIa) as a constituent part
of
itself.
The discrete mathematics (so the algebra) (AIb) depend on it, and then
the
Mathematics of Continuum (AIc) depends on them.
The discrete mathematics (so the algebra) (AIb) depend on it, and then
the
Mathematics of Continuum (AIc) depends on these last ones.
In the ladder of dependencies that penetrate inside the "well of truth"
(Peirce's metaphor is a way of expressing his agreement with Auguste
Comte)
comes the (AII) Cenoscopy - Philosophia prima, which is only a generic
label covering all the positive sciences "which rests upon familiar,
general experience." At the first rank of them, the Phenomenology (AIIa),
the study of Universal Categories "all present in any phenomenon:
Firstness, Secondness, Thirdness." Indeed, any particular science of
nature
is the study of a phenomenology. We can see that it is at this level that
Peirce situates the elaboration of his universal categories.
I will stop here for a moment before addressing the question of the
Normative Sciences (AIIb) because you have referred three Universes of
Discourse.
JS >. " *In his three universes of** discourse -- possibilities,
actualities, and necessities – mathematics is first because it includes
every possible pattern of any kind.*"
In Universe of Discourse | Dictionary | Commens
<http://www.commens.org/dictionary/term/universe-of-discourse> there is
a
set of texts in which Peirce expresses himself on his conception of the
Universe of Discourse. I take one of them, which seems to me to be
representative (if this were not the case, you could indicate to me
whether
I am introducing any bias by this choice:
*"1903 | Graphs, Little Account [R] | MS [R] S27:9-10*
*…if one person is to convey any information to another, it must be upon
the basis of a common experience. They must not only have this common
experience, but each must know the other has it; and not only that but
each
must know the other knows that he knows the other has it; so that when
one
says ‘It is cold’ the other may know that he does not mean that it is
cold
in Iceland or in Laputa, but right here. In short it must be thoroughly
understood between them that they are talking about objects of a
collection
with which both have some familiarity. **The collection of objects to
which
it is mutually understood that the propositions refer is called by exact
logicians the universe of discourse." *[emphasize mine]
Then you consider the three universes of discourse which are
possibilities,
actualities, and necessities. In other words, the universe of discourse
discussed above is now divided into 3 collections of objects. It remains
to
know how this division occurs.
Peirce gives us a well-known (but not exclusive) answer, as one could do
in
any observational science:
* "** Phaneroscopy is the description of the phaneron; and by the
phaneron
I mean the collective total of all that is in any way or in any sense
present to the mind, quite regardless of whether it corresponds to any
real
thing or not. If you ask present when, and to whose mind, I reply that I
leave these questions unanswered, never having entertained a doubt that
those features of the phaneron that I have found in my mind are present
at
all times and to all minds. So far as I have developed this science of
phaneroscopy, it is occupied with the formal elements of the
phaneron*"(CP
1.284) [emphasize mine]
It is well specified further on:
*" What I term phaneroscopy is that study which, supported by the direct
observation of **phanerons and generalizing its observations, signalizes
several very broad classes of **phanerons; describes the features of
each**;
shows that although they are so **inextricably mixed together that no one
can be isolated, yet it is manifest that their **characters are quite
disparate; then proves, beyond question, that a certain very short **list
comprises all of these broadest categories of phanerons there are; and
finally **proceeds to the laborious and difficult task of enumerating the
principal subdivisions **of those categories. *(CP 1.286, 1902)
[emphasize
mine]
That this answer is not exclusive, he showed it himself by having
recourse
to justify it, on many occasions, to the triadic reduction of polyadic
relations that he did not really establish himself. It was established
later, notably by Herzberger, Burch and more recently by Dau F., Correia
J.H. (2006 <https://link.springer.com/chapter/10.1007%2F11671404_7>)
*" A thorough study of the logic of relatives confirms the conclusions
which I had reached before going far in that study. It shows that logical
terms are either monads, dyads, or polyads, and that these last do not
introduce any radically different elements from those that are found in
triads. I therefore divide all objects into monads, dyads, and triads;
and
the first step in the present inquiry is to ascertain what are the
conceptions of the pure monad, free from all dyadic and triadic
admixtures;
of the dyad (which involves that of the monad) free from all triadic
contamination, and what it is that is peculiar which the dyad adds to the
monad; and of the triad (which involves those of the monad and dyad) and
what it is that is characteristic of the triad". *(CP 1.293 1894)
I note, moreover, that this text also contains the reasons that allow us
to
conclude that the categories are interdependent by involvements.
In any case, this answer is provided by Mathematics, which brings us
closer
to what is meant today by scientific theory and reassures us about the
possibility of really founding phaneroscopy as a normative science.
Indeed,
the difference with the observational posture is important when we think
about the claim to universality of the categories. Indeed, it isn't easy
to
grant universality to the former, which is rather an act of faith that
many
consider as an axiom. They can thus free themselves from any mathematical
reference and send them back to an unimportant level, rather cumbersome.
(but
this is another story).
As far as you are concerned, you place mathematics in the possibilities
(1ns); I conclude (you will tell me if I am wrong) that it is from 1ns
that
the two other categories 2ns and 3ns would be constituted as
complementary
sub-universes. We would then have an answer to the question of dependence
which would arise from the possibility contained in an original category
to
produce the two others, and it would perhaps also be necessary to grant
it
the possibility to produce itself in a self-referential way, as a
category
of possibility.
Indeed, there would be no conflict of views as you think: the poset 3 →2
-1, a syntactic mathematical structure of the external world would be
natively present as a possibility of semantic structure (model) in the
internal world, with the capacity to divide it into three encapsulated
sub-universes in the following way Thidness→Secondness →Firstness where
the
arrows represent relations of involvement (or presupposition) and the
isomorphism between the two posets would also be native.
This approach is very convenient for me because it certainly improves on
mine by explicitly capturing the implementation of the isomorphism
between
the two structures.
So my question is, "What about your own side? " ...
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*
Le mar. 27 juil. 2021 à 21:55, John F. Sowa <s...@bestweb.net> a écrit :
Robert> This leads me to a final question to be discussed: should the
classification of sciences according to Peirce be considered as a kind
of imperative to be respected or can phenomenology be approached from
the logic that depends on it according to this classification?
There is no conflict among any of those views. Peirce's classification
subsumes, relates, and clarifies all of them. In his three universes of
discourse -- possibilities, actualities, and necessities -- mathematics
is first because it includes every possible pattern of any kind. That
includes everything that any human or any living thing of any kind could
imagine -- plus all the possible patterns that no finite being could
imagine.
It's not possible for anybody to imagine any pattern that cannot be be
described and analyzed by mathematics (Alice in Wonderland, for example,
was imagined by a mathematician/logician).
Actuality consists of everything that exists in space and time. It's
what nominalists claim is everything. But they have no answer to the
mathematicians about the reality of mathematics. And they have no
answer to the nominalists about the reality of the laws of nature.
Peirce's three universes include Aristotle's answer to Plato:
mathematical forms are pure possibilities, which exist in actuality only
when embodied. But those forms are really real in the sense that they
exist independently of what anybody may think of them.
As for the scientific methodology in the Stanford article, that is an
example of Peirce's methodeutic for evaluating any proposed theory.
That is an example of normative logic, as distinguished from formal
logic, which is a branch of pure mathematics.
John
--
