RE: [PEIRCE-L] André De Tienne: Slow Read slide 7

[gnox]

Robert, I can see how your Categorical Theoretic Structuralism is a way of
establishing the credentials of phaneroscopy as a science. But it doesn’t
explain why Peirce’s classification places it first among all positive
sciences, prior to logic and semiotic. Almost any positive science can call
on a mathematical theory and apply it to theorize about its observations;
but phaneroscopy is unique in this respect because it is supposed to
“dispense with preconceptions” and consider phenomena in their Firstness.
I’m hoping that the second part of André’s presentation on prescission will
help to show how phaneroscopy can be “pre-truth.” But I think we should wait
and see if there are any other comments or questions on slide 7 before we go
on to the next one.

 

Gary f.

 

From: peirce-l-requ...@list.iupui.edu  On
Behalf Of robert marty
Sent: 26-Jun-21 17:34

 

List,

My aim is not to differ from André's approach to discovering categories. I
do not want to engage in an endless philosophical debate about the reality
of mathematical objects and their complex relationship with experience. The
disagreements will come later because I assume a Categorical Theoretic
Structuralism position in mathematics. I extend it to phaneroscopy using an
isomorphism between an abstract mathematical object (Poset or Functor) and
the set of relations between Peirce's universal categories as he defines
them. It seems to me that this consolidates the scientific status of
phaneroscopy. Then - note that this is my conclusion - I point out all the
interest in considering these structures because they agree with Peirce's
objective idealism if we need a philosophical reference. 

Your quotation from Peirce introducing the question of truth is
enlightening in this respect: "And this truth like every truth must come to
us by the way of experience. No apriorist ever denied that.". Indeed,
whether you consider me as an apriorist or not, it will not destroy this
isomorphism. All means are good to reach the truth; let us not waste time in
vain quarrels. 

Sincerely,

Robert Marty

 

Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy 

 
fr.wikipedia.org/wiki/Robert_Marty

  https://martyrobert.academia.edu/

 

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Re: [PEIRCE-L] André De Tienne: Slow Read slide 7

[robert marty]

List,

My aim is not to differ from André's approach to discovering categories. I
do not want to engage in an endless philosophical debate about the reality
of mathematical objects and their complex relationship with experience. The
disagreements will come later because I assume a Categorical Theoretic
Structuralism position in mathematics. I extend it to phaneroscopy using an
isomorphism between an abstract mathematical object (Poset or Functor) and
the set of relations between Peirce's universal categories as he defines
them. It seems to me that this consolidates the scientific status of
phaneroscopy. Then - note that this is my conclusion - I point out all the
interest in considering these structures because they agree with Peirce's
objective idealism if we need a philosophical reference.

Your quotation from Peirce introducing the question of truth is
enlightening in this respect: *"And this truth like every truth must come
to us by the way of experience. No apriorist ever denied that*.". Indeed,
whether you consider me as an apriorist or not, it will not destroy this
isomorphism. All means are good to reach the truth; let us not waste time
in vain quarrels.

Sincerely,

Robert Marty


Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le sam. 26 juin 2021 à 15:07,  a écrit :

> List,
>
> Robert, except for a few inaccuracies (like the misspelling of
> *prescission*), your account of the discovery of the categories is very
> much in line with André’s, although the terminology is different. If I may
> focus on one sentence of your summary, I have a question about your usage
> of the term *a priori* here: “the act of precession is a simple
> observation that we can discover an organization a priori in the phaneron.”
> In most philosophical discourse (since Kant anyway), *a priori* means
> “prior to experience” (usually meaning *sense* experience). If you mean
> that we can discover this “organization” without relying on any
> *particular* sense experience, this is certainly true of phaneroscopic
> observation, because the phaneron includes that “organization” *as well
> as* sense experience. But obviously the discovery cannot be prior to
> observation of the phaneron. Once it has been formulated, mathematically or
> otherwise, the organization has been generalized *from the observation*,
> not the other way round. If you agree with that, your account is in
> agreement with André’s, as far as I can see.
>
> As for Peirce, one relevant comment on the issue is this one:
>
> CSP (CP 1.417,): [[ The questions which are here to be examined are, what
> are the different systems of hypotheses from which mathematical deduction
> can set out, what are their general characters, why are not other
> hypotheses possible, and the like. These are not problems which, like those
> of mathematics, repose upon clear and definite assumptions recognized at
> the outset; and yet, like mathematical problems, they are questions of
> possibility and necessity. What the nature of this necessity can be is one
> of the very matters to be discovered. This much, however, is indisputable:
> if there are really any such necessary characteristics of mathematical
> hypotheses as I have just declared in advance that we shall find that there
> [are], this necessity must spring from some truth so broad as to hold not
> only for the universe we know but for every world that poet could create.
> And this truth like every truth must come to us by the way of experience.
> No apriorist ever denied that. The first matters which it is pertinent to
> examine are the most universal categories of elements of all experience,
> natural or poetical. ]]
>
> Gary f.
>
> *From:* peirce-l-requ...@list.iupui.edu  *On
> Behalf Of *robert marty
> *Sent:* 26-Jun-21 04:08
>
> List,
>
> Since it is a slow read, we have the convenience of dealing with the
> questions one after the other.
>
> I observe that it is admitted in the previous slide that the reader is
> familiar with the categories.  They have a logical role, form a small set
> gradually ordered, participate in a step-by-step process that incorporates
> them. Each category is found inductively (in the phaneron, I suppose);
> finally, they are tested by precession.
>
>  I notice that no formal definition of the categories have been presented
> (like CP 8.328), nor any justification of their reduction to three
> (Reduction Thesis), and that the terms "mode of being" have not been
> mentioned so far.
>
>
>
> Slide 7 provides more details on testing.
>
> - it is an act of abstractive analysis (it is thus an operation of the
> mind on what is in front of it, i.e., a phaneron).
>
> - This operation seeks to identify (used as an intransitive verb) in this
> phaneron logically (sic) distinct components. The latter has the
> particularity of having non-reciprocal* dependency relations between them.
> 

RE: [PEIRCE-L] André De Tienne: Slow Read slide 7

[gnox]

List,

Robert, except for a few inaccuracies (like the misspelling of prescission), 
your account of the discovery of the categories is very much in line with 
André’s, although the terminology is different. If I may focus on one sentence 
of your summary, I have a question about your usage of the term a priori here: 
“the act of precession is a simple observation that we can discover an 
organization a priori in the phaneron.” In most philosophical discourse (since 
Kant anyway), a priori means “prior to experience” (usually meaning sense 
experience). If you mean that we can discover this “organization” without 
relying on any particular sense experience, this is certainly true of 
phaneroscopic observation, because the phaneron includes that “organization” as 
well as sense experience. But obviously the discovery cannot be prior to 
observation of the phaneron. Once it has been formulated, mathematically or 
otherwise, the organization has been generalized from the observation, not the 
other way round. If you agree with that, your account is in agreement with 
André’s, as far as I can see.

As for Peirce, one relevant comment on the issue is this one:

CSP (CP 1.417,): [[ The questions which are here to be examined are, what are 
the different systems of hypotheses from which mathematical deduction can set 
out, what are their general characters, why are not other hypotheses possible, 
and the like. These are not problems which, like those of mathematics, repose 
upon clear and definite assumptions recognized at the outset; and yet, like 
mathematical problems, they are questions of possibility and necessity. What 
the nature of this necessity can be is one of the very matters to be 
discovered. This much, however, is indisputable: if there are really any such 
necessary characteristics of mathematical hypotheses as I have just declared in 
advance that we shall find that there [are], this necessity must spring from 
some truth so broad as to hold not only for the universe we know but for every 
world that poet could create. And this truth like every truth must come to us 
by the way of experience. No apriorist ever denied that. The first matters 
which it is pertinent to examine are the most universal categories of elements 
of all experience, natural or poetical. ]]

Gary f.

From: peirce-l-requ...@list.iupui.edu  On 
Behalf Of robert marty
Sent: 26-Jun-21 04:08



List,

Since it is a slow read, we have the convenience of dealing with the questions 
one after the other.

I observe that it is admitted in the previous slide that the reader is familiar 
with the categories.  They have a logical role, form a small set gradually 
ordered, participate in a step-by-step process that incorporates them. Each 
category is found inductively (in the phaneron, I suppose); finally, they are 
tested by precession.

 I notice that no formal definition of the categories have been presented (like 
CP 8.328), nor any justification of their reduction to three (Reduction 
Thesis), and that the terms "mode of being" have not been mentioned so far. 

 

Slide 7 provides more details on testing.

- it is an act of abstractive analysis (it is thus an operation of the mind on 
what is in front of it, i.e., a phaneron).

- This operation seeks to identify (used as an intransitive verb) in this 
phaneron logically (sic) distinct components. The latter has the particularity 
of having non-reciprocal* dependency relations between them. This is how sets 
of three components connected by these relations are formed, that an act of 
analysis has abstracted from the phaneron. 

The next two points introduce "active determinations" and particular rules (to 
be discussed later).

 

At this point, I summarize: the act of precession is a simple observation that 
we can discover an organization a priori in the phaneron. An organization that 
is already there. Now, in the mathematical repository, we find a very simple 
axiomatized structure (Partially Ordered Set, Poset) devoid of any empirical 
contamination which gathers in a single diagram (3-->2-->1) the totality of the 
information brought by De Tienne.  Why not extract this structure from the 
"cloudy manifold"? Everything would become so much simpler! Especially 
considering that Peirce advocates it in his Classification of Sciences (MS 
1345, CP 2.119):

 

 "[ … ]- mathematics, the study of ideal constructions without reference to 
their real existence,  

 - empirics, the study of phenomena with the purpose of identifying their forms 
with those mathematics has studied,

 - pragmatics, the study of how we ought to behave in the light of the truths 
of empirics."

(Peirce, MS 1345, undated, transcription 1976: NEM, III.2, 1122) [bold emphasis 
is mine]

 

*(i.e. whenever there is a relation of dependence between two components A and 
B, there is no relation of dependence between B and A)

 

Sincerely,

Robert Marty

 

Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy