Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[John F. Sowa]

Jon AS,

Peirce's definition of mathematics is consistent with
the mainstream
of mathematical thinking since antiquity.  There are
many versions
of the philosophy of mathematics, but Peirce's version
is still
at the forefront of modern research.

JAS>
anyone is free to disagree with Peirce's definition of
mathematics.

Nobody does.  Peirce's three branches (Formal
logic, discrete
mathematics, and continuous mathematics) are still
the backbone of
math today, but there have been some additions. 
There are, however,
controversies between nominalists and
realists.

Peirce adopted Aristotle's answer to Plato:  The
mathematical forms (or
patterns) are possibilities, which occur in
actuality only when
embodied.  But he went one step further:  he
defined three universes
of discourse, each of which is real in the
sense that they exist
independent of what anybody may think about
them:  mathematics is the
universe of all possibilities; actuality is
the universe of everything
that exists in space and time; the
necessitated is the universe of all
the laws that govern actuality,
including any aspect of it, no matter
how small or insisngificant.

JAS> Mathematical reasoning is always and only necessary
reasoning
about "creations of the mind,"

Yes. 
But every science, including phaneroscopy, is a creation of the
mind.  The elements of phaneroscopy -- the categories, hypoicons, and
all their possible combinations are the result of interpreting
experience in the phaneron in terms of mathematical patterns. 
Without
formal logic and other branches of mathematics, phaneroscopy
is
limited to a Hegelian style of speculation:

JAS> but
the hard facts of experience require probable reasoning,
which the
normative science of logic prescribes as induction.  There
is a
mathematical/deductive aspect to the latter, to be sure--"All
mathematical reasoning, even although it relates to probability, is
of
the nature of necessary reasoning" (CP 7.180, EP 2:82,
1901)--but this
is true of all reasoning in every science.

That quotation by Peirce contradicts what you said.  Peirce's
extensive writings about probability are purely deductive
mathematics.
Since phaneroscopy comes before normative science, it
depends only on
pure maathematics, especially formal logic.  Note the
following
quotations:

CSP:  Phenomenology is that branch
of scBience which is treated in
Hegel’s Phenomenologie des Geistes (a
work far too inaccurate to be
recommended to any but mature scholars,
though perhaps the most
profound ever written) in which the author
seeks to make out what are
the elements, or, if you please, the kinds
of elements, that are
invariably present in whatever is, in any
sense, in mind.  (EP 2:267,
1903)

Note that Peirce
considered formal logic essential to everything he
wrote that is of
any significance:

CSP:  The little that I have contributed to
pragmatism (or, for that
matter, to any other department of
philosophy), has been entirely the
fruit of this outgrowth from
formal logic, and is worth much more than
the small sum total of the
rest of my work, as time will show.  (CP
5.469, R318, 1907)

CSP:  My trichotomy is plainly of the family stock of Hegel’s three
stages of thought, — an idea that goes back to Kant, and I know not
how much further.  But the arbitrariness of Hegel’s procedure,
utterly
unavoidable at the time he lived, — and presumably, in less
degree,
unavoidable now, or at any future date, — is in great measure
avoided
by my taking care never to miss the solid support of
mathematically
exact formal logic beneath my feet  (EP 2:428,
R318, 1907)

Without mathematics, especially formal logic,
phaneroscopy cannot go
beyond Hegel.

John

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[PEIRCE-L] Announcement: James Liszka to give webinar on Peirce's Ethics 7/18

[Gary Richmond]

FYI: James Liszka is giving a seminar this Sunday, July 18th, on the
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To interested Peirce scholars:

I'm giving a webinar on the Development of Peirce's Normative Science of
Ethics, as part of the Smart Semiotics Series. The presentation is based on
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(Routledge). Discussants will be Richard Atkins, Boston College, Ron
Beadle, Northumbria University, and Cornelis de Waal, Editor-in-Chief of
the Peirce Transactions. It should be a lively discussion.
The webinar will be held this Sunday, July 18, 2pm Eastern standard time,
11am Pacific, 7pm UK, 8pm Europe.
For more information and registration, link to:
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Beauty and terror
Just keep going
No feeling is final”
― Rainer Maria Rilke

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
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Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[Jon Alan Schmidt]

Robert, List:

RM: I have just answered Gary F ... if you take up his criticism without
making sure of its validity, you are objectively in the same case as him ...


I agree with Gary F.'s "criticism," but there is nothing "malicious" about
simply pointing out that the statement, "The objects of Phaneroscopy are in
the inner world," is inaccurate or at best misleading. As he said, the only
science in Peirce's classification whose subject matter is *strictly *in
the inner world is mathematics. That is why it is not a *positive *science.

RM: For the second part, it seems to me that you are stating something very
close to what I am proposing when you write "both by manifesting
instantiations of them ..." This is what I am saying but in an unclear way.


In that case, maybe we are not so far apart after all. Routinely employing
technical terminology like "isomorphism," "poset," and "cryptomorphism"
might be helpful for communicating certain concepts to professional
mathematicians who are familiar with it, but not for discussion with the
rest of us if the goal is to foster genuine understanding and good-faith
engagement.

RM: The three categories are already in his mind and he is not surprised to
observe them in the phanerons.


Since the phaneron consists of whatever is or could be present to the mind
in any way, if "the three categories are already in his mind," then he is
already observing them in the phaneron. *Studying *relations
mathematically--i.e., hypothetically and deductively--is indeed good
preparation for *studying *the phaneron and recognizing that there are
exactly three irreducible elements in it.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Wed, Jul 14, 2021 at 11:45 AM robert marty 
wrote:

> Jon Alan, List,
> I have just answered Gary F ... if you take up his criticism without
> making sure of its validity, you are objectively in the same case as him ...
>
> For the second part, it seems to me that you are stating something very
> close to what I am proposing when you write "both by manifesting
> instantiations of them ..." This is what I am saying but in an unclear way.
> Indeed, if you have read me, you have seen that I define an isomorphism
> between forms found in the "mathematical repository" (a Poset) and forms
> that emerge from the observation of phanerons: another Poset. Simple but
> with important consequences. This is what supports the movement of Peirce's
> thought: "It is therefore not surprising to find that beyond the three
> elements of Firstness, Secondness, and Thirdness, there is nothing else to
> be found in the phenomenon". The three categories are already in his mind
> and he is not surprised to observe them in the phanerons. Perhaps you will
> admit that in your way of saying, the two isomorphic fields are mixed up.
> I don't ask for more. Besides, there is a concept that allows
> apprehending this mixture; I will use it soon: a cryptomorphism
> .
>
> Regards,
> RM
>
> Honorary Professor ; PhD Mathematics ; PhD Philosophy
> fr.wikipedia.org/wiki/Robert_Marty
> *https://martyrobert.academia.edu/ *
>
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Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[Gary Richmond]

Robert, Jon, Gary f,

Little of what you write below, Robert, pertains to phenomenology, but
rather to pure (vs applied) mathematics or to logic as semeiotic. For
example, Kenneth Ketner in two of the appendices of 'A Thief of Peirce'
suggests that the *reduction thesis* has its valental roots in mathematics
and its further development in logic as semeiotic, notably in existential
graphs. So I would agree that, as you wrote, "It is at the heart of his
[Peirce's]  "Logic of relatives'' and his "Existentials Graphs."

In my view, the reduction thesis functions in phenomenology primarily to
confirm that what is found there -- and necessarily *will be* found
there -- are
*only* *primans* (such as qualities), *secundans* (such as
actions-reactions), and *tertians* (such as thoughts about qualities and
action-reactions). There are no tetradic or higher number of correlates to
be found in the phaneron (or at least which can't be reduced to at most
triadic correlates). If, as you say, the reduction thesis (which, again,
asserts -adicity no higher than triadicity) is already there in the mind of
the mathematician then, *qua* phenomenologist, he can expect to find -- and
*does* find -- examples of *only* those three correlates. But what he does
*not* find are abstract 1ns, 2ns, and 3ns as such, and he does *not* find
bare -adicity. As Peirce writes in a 1905 letter to Giuliano Calderoni,
what one *does* find are, *primans, secundans, and tertians*:

The *Priman elements* of consciousness are the pure qualities of feeling,
red, green, the harmony of a chord, the quality of a tooth-ache, its
insistency being left out of account, the glow of a contemplation of any
situation, as mere quality. That wherein the perception of red and the
imagination or memory of red agree and are the same is Priman. As an
example of a *Secundan element*, take, effort, which can only be in so far
as there is a resistance to it. Without a counter-resistance there is no
effort. Also, the shock of a surprise is of this nature. In a long sea
voyage in the trade-winds, one day just like another,. . .The *Tertian
elements* are exemplified most clearly in the action of signs (in CP
 8.205-213 passim. Emphasis added).


In one place Peirce even goes so far as to suggest that the categories were
first *found*  in phaneroscopy and then *confirmed *retrospectively (from
the standpoint of his classification of the sciences) in mathematics. But
whatever the case may be (and I would tend to agree with you, Robert, that
-adicity would most likely be always-already in the mind of a polymath like
Peirce), in the phaneron one finds such elements as "the perception of red"
(1ns), the "effort" of pressing against a locked door and the
"counter-resistance" to that effort (2ns), and thoughts ("signs") about,
say, the unexpected resistance met when pressing my shoulder against that
red door (3ns). It is this sort of thing that I believe Peirce intends in
writing that "[i]t is therefore not surprising to find that beyond the
three elements of Firstness, Secondness, and Thirdness, there is nothing
else to be found in the phenomenon" (CP 1.347). He does *not*
mean -adity per se because monads, dyads, and triads are the stuff of what
Peirce calls the 'simplest mathematics' (in pure mathematics) and are
valentally employed primarily in EGs and *the logic of relative terms* in
logic as semeiotic.

And, btw, if I "follow" anyone it tends to be Peirce, not Gary f or Jon S.
However, I highly value critical thinking and 'so think for myself', as
they say. There are, for sure, points of agreement between us in
consideration of De Tienne's ppt presentation, for example. But we do not
think in anything like lockstep and disagree much more than you might
imagine (some of our off List exchanges regarding phenomenology in
preparing for this slow read would, I believe, demonstrate that clearly).
So, I believe it would be best for this slow read, and for participation on
the List generally, for contributors *not* to personalize matters but
rather to stick to argumentation, substantive discussion, etc. The first
rule of critical thinking is to criticize the argument, not the person.

Best,

Gary R

“Let everything happen to you
Beauty and terror
Just keep going
No feeling is final”
― Rainer Maria Rilke

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*







On Wed, Jul 14, 2021 at 5:46 AM robert marty 
wrote:

> Gary F., John Alan, Gary R., List,
>
>
> What you describe is right for the experimental sciences of nature, i.e.
> the knowledge of objects in the outer world. The objects of Phaneroscopy
> are in the inner world. It so happens that in this world, the relations
> between A preliminary mathematical result govern mathematics and
> Phaneroscopy that you never mention -and for a good reason- which is the
> Triadic Reduction Theorem.  I understand that it embarrasses you because it
> ruins all 

Aw: [PEIRCE-L] André De Tienne: Slow Read slide 14

[Helmut Raulien]

Jon. List

 

For the thing, why statistics is not pure mathemathics, I can only imagine, that its subject randomness is something external to mathematics. Is it? Randomness a phenomenon from other sciences like phaneroscopy? I cannot totally disagree with that view.

 

Being valid for an "ideal state of things" means, that parameters are limited to a number so that you can calculate with them.

But in chaos theory this limit is crossed. Again, you may say, that this is an influence from other sciences, or from experience.

 

I have, from the philosophical standpoint about classification of sciences no ready-made opinion about that. But on the other hand I have the feeling, that randomness and non-predictability of the outcome of nonlinear functions are experiences you can make without referring to other sciences, just by dealing with (e.g. complex, as you, Robert, said) numbers. That would be without leaving the range of mathematics. Somebody else might say, that randomness and losing the overview due too many parameters are influences from outside mathematics. But from where? Reality? Mathematical objects are by definition (of "reality") parts of reality too.

 

Best

Helmut

 
 

14. Juli 2021 um 19:47 Uhr
 "Jon Alan Schmidt" 
wrote:

 



Helmut, List:
 

Again, anyone is free to disagree with Peirce's definition of mathematics. However, the occurrence of surprises is perfectly consistent with its method being strictly deductive and its subject matter being strictly hypothetical, especially given the distinction that he draws between corollarial and theorematic reasoning.

 




CSP: Deductions are of two kinds, which I call corollarial and theorematic. The corollarial are those reasonings by which all corollaries and the majority of what are called theorems are deduced; the theorematic are those by which the major theorems are deduced. If you take the thesis of a corollary,--i.e. the proposition to be proved, and carefully analyze its meaning, by substituting for each term its definition, you will find that its truth follows, in a straightforward manner, from previous propositions similarly analyzed. But when it comes to proving a major theorem, you will very often find you have need of a lemma, which is a demonstrable proposition about something outside the subject of inquiry; and even if a lemma does not have to be demonstrated, it is necessary to introduce the definition of something which the thesis of the theorem does not contemplate. In the most remarkable cases, this is some abstraction; that is to say, a subject whose existence consists in some fact about other things. ...

Deduction, of course, relates exclusively to an ideal state of things. A hypothesis presents such an ideal state of things, and asserts that it is the icon, or analogue of an experience. (CP 7.204-205, EP 2:96, 1901)




 

Moreover, it seems to me that Peirce would not consider the discipline of statistics to fall within pure mathematics. Instead, it is an application of mathematics and thus belongs to the mathematical parts of other sciences. As I quoted him yesterday ...

 




CSP: What the mathematicians mean by a "hypothesis" is a proposition imagined to be strictly true of an ideal state of things. In this sense, it is only about hypotheses that necessary reasoning has any application; for, in regard to the real world, we have no right to presume that any given intelligible proposition is true in absolute strictness. On the other hand, probable reasoning deals with the ordinary course of experience; now, nothing like a course of experience exists for ideal hypotheses. Hence to say that mathematics busies itself in drawing necessary conclusions, and to say that it busies itself with hypotheses, are two statements which the logician perceives come to the same thing. (CP 3.558, 1898)




 

In other words, because the method of mathematics is strictly deductive, its subject matter must be strictly hypothetical. As Peirce writes elsewhere ...

 




CSP: Mathematics is not subject to logic. Logic depends on mathematics. The recognition of mathematical necessity is performed in a perfectly satisfactory manner antecedent to any study of logic. Mathematical reasoning derives no warrant from logic. It needs no warrant. It is evident in itself. It does not relate to any matter of fact, but merely to whether one supposition excludes another. Since we ourselves create these suppositions, we are competent to answer them. But it is when we pass out of the realm of pure hypothesis into that of hard fact that logic is called for. We then find that certain modes of reasoning are sound, because they must, by mathematical necessity, be sound, in whatever universe there may be in which there is such a thing as experience. ...

Mathematical reasoning holds. Why should it not? It relates only to the creations of the mind, concerning which there is no obstacle to our learning whatever is true of them. ... The only concern that logic 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[Jon Alan Schmidt]

Helmut, List:

Again, anyone is free to disagree with Peirce's definition of mathematics.
However, the occurrence of surprises is perfectly consistent with its
method being strictly deductive and its subject matter being strictly
hypothetical, especially given the distinction that he draws between
corollarial and theorematic reasoning.

CSP: Deductions are of two kinds, which I call *corollarial *and
*theorematic*. The corollarial are those reasonings by which all
corollaries and the majority of what are called theorems are deduced; the
theorematic are those by which the major theorems are deduced. If you take
the thesis of a corollary,--i.e. the proposition to be proved, and
carefully analyze its meaning, by substituting for each term its
definition, you will find that its truth follows, in a straightforward
manner, from previous propositions similarly analyzed. But when it comes to
proving a major theorem, you will very often find you have need of a *lemma*,
which is a demonstrable proposition about something outside the subject of
inquiry; and even if a lemma does not have to be demonstrated, it is
necessary to introduce the definition of something which the thesis of the
theorem does not contemplate. In the most remarkable cases, this is some
abstraction; that is to say, a subject whose existence consists in some
fact about other things. ...
Deduction, of course, relates exclusively to an ideal state of things. A
hypothesis presents such an ideal state of things, and asserts that it is
the icon, or analogue of an experience. (CP 7.204-205, EP 2:96, 1901)


Moreover, it seems to me that Peirce would not consider the discipline of
statistics to fall within *pure *mathematics. Instead, it is an *application
*of mathematics and thus belongs to the mathematical parts of *other *sciences.
As I quoted him yesterday ...

CSP: What the mathematicians mean by a "hypothesis" is a proposition
imagined to be strictly true of an ideal state of things. In this sense, it
is only about hypotheses that necessary reasoning has any application; for,
in regard to the real world, we have no right to presume that any given
intelligible proposition is true in absolute strictness. On the other hand,
probable reasoning deals with the ordinary course of experience; now,
nothing like *a course of experience* exists for ideal hypotheses. Hence to
say that mathematics busies itself in drawing necessary conclusions, and to
say that it busies itself with hypotheses, are two statements which the
logician perceives come to the same thing. (CP 3.558, 1898)


In other words, *because *the method of mathematics is strictly deductive,
its subject matter *must be* strictly hypothetical. As Peirce writes
elsewhere ...

CSP: Mathematics is not subject to logic. Logic depends on mathematics. The
recognition of mathematical necessity is performed in a perfectly
satisfactory manner antecedent to any study of logic. Mathematical
reasoning derives no warrant from logic. It needs no warrant. It is evident
in itself. It does not relate to any matter of fact, but merely to whether
one supposition excludes another. Since we ourselves create these
suppositions, we are competent to answer them. But it is when we pass out
of the realm of pure hypothesis into that of hard fact that logic is called
for. We then find that certain modes of reasoning are sound, because they
must, by mathematical necessity, be sound, in whatever universe there may
be in which there is such a thing as experience. ...
Mathematical reasoning holds. Why should it not? It relates only to the
creations of the mind, concerning which there is no obstacle to our
learning whatever is true of them. ... The only concern that logic has with
this sort of reasoning is to describe it.
That being settled, I propose, by purely mathematical reasoning, to show
that in any world in which there is such a thing as the course of
experience--an element which is absent from the world of pure
mathematics--in such world a certain kind of reasoning must be valid which
is not valid in the world of pure mathematics. (CP 2.191-193, 1902)


Mathematical reasoning is always and only *necessary *reasoning about
"creations of the mind," which the normative science of logic merely
*describes* as deduction; but the hard facts of experience require *probable
*reasoning, which the normative science of logic *prescribes* as induction.
There is a mathematical/deductive *aspect *to the latter, to be sure--"All
mathematical reasoning, even although it relates to probability, is of the
nature of necessary reasoning" (CP 7.180, EP 2:82, 1901)--but this is true
of all reasoning in *every *science.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Wed, Jul 14, 2021 at 11:29 AM Helmut Raulien  wrote:

> Jon, List
>
> I disagree with this "strictly hypothetical". In mathemathics,* mostly *there
> 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[robert marty]

Helmuth, List,
In algebra, the invention of complex numbers
 by Gerolamo Cardano is a
wonderful example that is not new! (1545 !) And so many others ...For
example, Peirce was interested in quaternions  CP 4.138  §10. THE ALGEBRA
OF REAL QUATERNIONS; CP 4.307
§4. TRICHOTOMIC MATHEMATICS) which are extensions of complex numbers ...
and even to onions ( CP 4.321) ...
Best regards,
Robert Marty

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



Le mer. 14 juil. 2021 à 18:29, Helmut Raulien  a écrit :

> Jon, List
>
> I disagree with this "strictly hypothetical". In mathemathics,* mostly *there
> are hypotheses at the beginning, presumtions, which then are deductively
> proven or refuted by disproof or failed to prove. But, as I said, in
> mathematics also are surprising phenomena for subject matters (e.g.
> attractors in chaos theory), and in statistics the subject matter is
> induction. But the rules of investigation are always (strictly) deductive,
> I think, so to "its method is strictly deductive" I don´t have a
> counterexample. But to "its suubject matter is strictly hypothetical" I
> disagree.
>
> Best
> Helmut
>
>
>  14. Juli 2021 um 17:28 Uhr
>  "Jon Alan Schmidt" 
> wrote:
>
> Robert, List:
>
>
> RM: What you describe is right for the experimental sciences of nature,
> i.e. the knowledge of objects in the outer world. The objects of
> Phaneroscopy are in the inner world.
>
>
> On the contrary, as Gary F. already pointed out, phaneroscopy does not
> concern itself with the distinction between the outer world and the inner
> world. It studies whatever is or could be present to the mind in any way.
>
>
> RM:  I understand that it [the Triadic Reduction Theorem] embarrasses you
> because it ruins all your arguments, as well as those of Gary F. and Gary
> R. who follows you.
>
>
> Nonsense, which arguments of mine does it supposedly "ruin"? In this
> particular thread, I provided nine quotations yesterday demonstrating that
> Peirce consistently defines mathematics as the science which draws
> necessary conclusions about hypothetical states of things, i.e., its method
> is strictly deductive and its subject matter is strictly hypothetical.
> Anyone is free to disagree with him about this, but no one can legitimately
> attribute a different view to him without providing a direct quotation
> where he explicitly repudiates it later.
>
>
> RM: But to make sure you read Peirce's thinking on it, I extract the
> following blunt quote because it is the core of my entire approach since
> 1977.
>
>
> CSP: And analysis will show that every relation which is *tetradic*,
> *pentadic*, or of any greater number of correlates is nothing but a
> compound of triadic relations. It is therefore not surprising to find that
> beyond the three elements of Firstness, Secondness, and Thirdness, there is
> nothing else to be found in the phenomenon. (CP 1.347, 1903)
>
>
> No one is disputing what Peirce states here. In fact, it is a good example
> of the two major principles underlying his *mature *classification of the
> sciences as summarized by André in the three slides that Gary F. posted
> this morning. Phaneroscopy depends on mathematics in the sense that it
> makes use of its general principles, both by manifesting instantiations of
> them and by providing critical and validating feedback. This reflects a
> considerably more developed understanding of the relationships among
> different sciences than his earlier description of "empirics" as "the study
> of phenomena with the purpose of identifying their forms with those
> mathematics has studied," especially since the latter encompasses not only
> phaneroscopy but also logic, metaphysics, and all the special sciences.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
> On Wed, Jul 14, 2021 at 4:46 AM robert marty 
> wrote:
>
>> Gary F., John Alan, Gary R., List,
>>
>>
>>
>> What you describe is right for the experimental sciences of nature, i.e.
>> the knowledge of objects in the outer world. The objects of Phaneroscopy
>> are in the inner world. It so happens that in this world, the relations
>> between A preliminary mathematical result govern mathematics and
>> Phaneroscopy that you never mention -and for a good reason- which is the
>> Triadic Reduction Theorem.  I understand that it embarrasses you because it
>> ruins all your arguments, as well as those of Gary F. and Gary R. who
>> follows you.  I do not fail to mention it in part 6.2 of my article on the
>> Podium of Universal Categories (concise) which I reproduce below. But to
>> make sure you read Peirce's thinking on it, I extract the following blunt
>> quote because it is the core of my entire approach since 1977.
>>

Aw: [PEIRCE-L] André De Tienne: Slow Read slide 14

[Helmut Raulien]

List,

 

Donot underestimate the power of words. I think it is very dangerous to ideationally seperate the world in two. Martin Luther did that, and the result were first ca. 75000 peasants slaughtered, and later a 30 years long war. An (epistemic) gap is not an impermeable border, and I think it is better to think about the bridges across it, than merely about its separating force. A beneficial idea by Peirce is the object, which is both external (dynamic) and internal (immediate). This for example is a bridge. The gap may anayway be a misunderstanding: Suggesting it may be imposing the part of logic that applies exclusively to tempospatial composition to functional composition (of the world). Don´t do that.

 

Best

Helmut

 
 

14. Juli 2021 um 18:13 Uhr
 "robert marty" 
wrote:

 


List,
 

Here is a malicious criticism from someone who obviously hasn't read what he is criticizing ... I won't say more ... except to tell those who read this thread to avoid reading the opinions of someone who makes you say the opposite of what you said without checking anything ...
But let's stay positive by quoting what I wrote on page 26 of the Podium section 9.1: 
 

 "The experience is thus fed by binary relations between the external world and the internal world (without forgetting that the second is imbricated in the first). The internal world captures the external world under the binary form of Secundans; they enter the mind by the door of Secondness. But Secondness involves Firstness, which at the same time brings in the Priman elements constituting each Secundan; moreover, we have seen that Secondness is eventually involved in Thirdness, which also captures the cases in which Secundans are involved in Tertians.  It  is the reason why Peirce can write: "The elements of every concept enter into logical thought at the gate of perception and make their exit at the gate of purposive action; and whatever cannot show its passports at both those two gates is to be arrested as unauthorized by reason." (CP 5.212).

 

As such, experience is thus a cumulative process in which every new experience concerns "facts accomplished" in the external world concerning the objects of knowledge added to previous experiences of these same objects whose aggregate is already structured. This addition may require changes in their general structure if the particular structures of the new entrants do not conform to the general form in use. The brute force that is exerted forces minds to make structural changes. Nevertheless, they force to proceed to modifications, even to radical changes of structure to preserve the structural unity of the aggregate, and so on,  because the process is iterative. It describes how knowledge invests external objects by continuously modifying the structures attributed to them and sometimes by reconsidering in a disruptive way these structural assets by substituting them with new adequate structures. We then speak of a change of paradigm."

 

All this - and much more - is visualized in the Podium: Figure 2, 3 and 4.

 

Robert Marty

 




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

fr.wikipedia.org/wiki/Robert_Marty

https://martyrobert.academia.edu/

 






 


Le mer. 14 juil. 2021 à 17:05,  a écrit :




List,

 

CSP: ... every man inhabits two worlds. These are directly distinguishable by their different appearances. But the greatest difference between them, by far, is that one of these two worlds, the Inner World, exerts a comparatively slight compulsion upon us, though we can by direct efforts so slight as to be hardly noticeable, change it greatly, creating and destroying existent objects in it; while the other world, the Outer World, is full of irresistible compulsions for us, and we cannot modify it in the least, except by one peculiar kind of effort, muscular effort, and but very slightly even in that way. (CP 5.474)

 

RM: The objects of Phaneroscopy are in the inner world.

 

GF: We have already seen several of Peirce's definitions of phaneroscopy and of the phaneron. None of them say that phaneroscopy ignores objects in the outer world; on the contrary, the phaneron includes anything that appears or can appear in any way. Robert's statement above would be true enough if we changed the word “Phaneroscopy” to “Mathematics”; but as it stands, it is nonsense. (Just pointing this out to those who are trying to follow the thread, because it may not be obvious to everyone.)

 

Gary f.

 

 


From: peirce-l-requ...@list.iupui.edu  On Behalf Of robert marty
Sent: 14-Jul-21 05:46
 


 


Gary F., John Alan, Gary R., List,

 

What you describe is right for the experimental sciences of nature, i.e. the knowledge of objects in the outer world. The objects of Phaneroscopy are in the inner world. It so happens that in this world, the relations between A preliminary mathematical result govern mathematics and Phaneroscopy …



_ _ _ _ _ _ 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[robert marty]

Jon Alan, List,
I have just answered Gary F ... if you take up his criticism without making
sure of its validity, you are objectively in the same case as him ...

For the second part, it seems to me that you are stating something very
close to what I am proposing when you write "both by manifesting
instantiations of them ..." This is what I am saying but in an unclear way.
Indeed, if you have read me, you have seen that I define an isomorphism
between forms found in the "mathematical repository" (a Poset) and forms
that emerge from the observation of phanerons: another Poset. Simple but
with important consequences. This is what supports the movement of Peirce's
thought: "It is therefore not surprising to find that beyond the three
elements of Firstness, Secondness, and Thirdness, there is nothing else to
be found in the phenomenon". The three categories are already in his mind
and he is not surprised to observe them in the phanerons. Perhaps you will
admit that in your way of saying, the two isomorphic fields are mixed up.
I don't ask for more. Besides, there is a concept that allows
apprehending this mixture; I will use it soon: a cryptomorphism
.

Regards,
RM


Honorary Professor ; PhD Mathematics ; PhD Philosophy


fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le mer. 14 juil. 2021 à 17:28, Jon Alan Schmidt 
a écrit :

> Robert, List:
>
> RM: What you describe is right for the experimental sciences of nature,
> i.e. the knowledge of objects in the outer world. The objects of
> Phaneroscopy are in the inner world.
>
>
> On the contrary, as Gary F. already pointed out, phaneroscopy does not
> concern itself with the distinction between the outer world and the inner
> world. It studies whatever is or could be present to the mind in any way.
>
> RM:  I understand that it [the Triadic Reduction Theorem] embarrasses you
> because it ruins all your arguments, as well as those of Gary F. and Gary
> R. who follows you.
>
>
> Nonsense, which arguments of mine does it supposedly "ruin"? In this
> particular thread, I provided nine quotations yesterday demonstrating that
> Peirce consistently defines mathematics as the science which draws
> necessary conclusions about hypothetical states of things, i.e., its method
> is strictly deductive and its subject matter is strictly hypothetical.
> Anyone is free to disagree with him about this, but no one can legitimately
> attribute a different view to him without providing a direct quotation
> where he explicitly repudiates it later.
>
> RM: But to make sure you read Peirce's thinking on it, I extract the
> following blunt quote because it is the core of my entire approach since
> 1977.
>
>
> CSP: And analysis will show that every relation which is *tetradic*,
> *pentadic*, or of any greater number of correlates is nothing but a
> compound of triadic relations. It is therefore not surprising to find that
> beyond the three elements of Firstness, Secondness, and Thirdness, there is
> nothing else to be found in the phenomenon. (CP 1.347, 1903)
>
>
> No one is disputing what Peirce states here. In fact, it is a good example
> of the two major principles underlying his *mature *classification of the
> sciences as summarized by André in the three slides that Gary F. posted
> this morning. Phaneroscopy depends on mathematics in the sense that it
> makes use of its general principles, both by manifesting instantiations of
> them and by providing critical and validating feedback. This reflects a
> considerably more developed understanding of the relationships among
> different sciences than his earlier description of "empirics" as "the study
> of phenomena with the purpose of identifying their forms with those
> mathematics has studied," especially since the latter encompasses not only
> phaneroscopy but also logic, metaphysics, and all the special sciences.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Wed, Jul 14, 2021 at 4:46 AM robert marty 
> wrote:
>
>> Gary F., John Alan, Gary R., List,
>>
>>
>> What you describe is right for the experimental sciences of nature, i.e.
>> the knowledge of objects in the outer world. The objects of Phaneroscopy
>> are in the inner world. It so happens that in this world, the relations
>> between A preliminary mathematical result govern mathematics and
>> Phaneroscopy that you never mention -and for a good reason- which is the
>> Triadic Reduction Theorem.  I understand that it embarrasses you because it
>> ruins all your arguments, as well as those of Gary F. and Gary R. who
>> follows you.  I do not fail to mention it in part 6.2 of my article on the
>> Podium of Universal Categories (concise) which I reproduce below. But to
>> make sure you read Peirce's thinking on it, I extract the 

Aw: [PEIRCE-L] André De Tienne: Slow Read slide 14

[Helmut Raulien]

Jon, List

 

I disagree with this "strictly hypothetical". In mathemathics, mostly there are hypotheses at the beginning, presumtions, which then are deductively proven or refuted by disproof or failed to prove. But, as I said, in mathematics also are surprising phenomena for subject matters (e.g. attractors in chaos theory), and in statistics the subject matter is induction. But the rules of investigation are always (strictly) deductive, I think, so to "its method is strictly deductive" I don´t have a counterexample. But to "its suubject matter is strictly hypothetical" I disagree.

 

Best

Helmut

 
 

 14. Juli 2021 um 17:28 Uhr
 "Jon Alan Schmidt" 
wrote:

 




Robert, List:
 




RM: What you describe is right for the experimental sciences of nature, i.e. the knowledge of objects in the outer world. The objects of Phaneroscopy are in the inner world.




 

On the contrary, as Gary F. already pointed out, phaneroscopy does not concern itself with the distinction between the outer world and the inner world. It studies whatever is or could be present to the mind in any way.

 




RM:  I understand that it [the Triadic Reduction Theorem] embarrasses you because it ruins all your arguments, as well as those of Gary F. and Gary R. who follows you.




 

Nonsense, which arguments of mine does it supposedly "ruin"? In this particular thread, I provided nine quotations yesterday demonstrating that Peirce consistently defines mathematics as the science which draws necessary conclusions about hypothetical states of things, i.e., its method is strictly deductive and its subject matter is strictly hypothetical. Anyone is free to disagree with him about this, but no one can legitimately attribute a different view to him without providing a direct quotation where he explicitly repudiates it later.

 




RM: But to make sure you read Peirce's thinking on it, I extract the following blunt quote because it is the core of my entire approach since 1977.





 

CSP: And analysis will show that every relation which is tetradic, pentadic, or of any greater number of correlates is nothing but a compound of triadic relations. It is therefore not surprising to find that beyond the three elements of Firstness, Secondness, and Thirdness, there is nothing else to be found in the phenomenon. (CP 1.347, 1903)




 

No one is disputing what Peirce states here. In fact, it is a good example of the two major principles underlying his mature classification of the sciences as summarized by André in the three slides that Gary F. posted this morning. Phaneroscopy depends on mathematics in the sense that it makes use of its general principles, both by manifesting instantiations of them and by providing critical and validating feedback. This reflects a considerably more developed understanding of the relationships among different sciences than his earlier description of "empirics" as "the study of phenomena with the purpose of identifying their forms with those mathematics has studied," especially since the latter encompasses not only phaneroscopy but also logic, metaphysics, and all the special sciences.

 

Regards,

 







Jon Alan Schmidt - Olathe, Kansas, USA

Structural Engineer, Synechist Philosopher, Lutheran Christian

www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt








On Wed, Jul 14, 2021 at 4:46 AM robert marty  wrote:



Gary F., John Alan, Gary R., List,

 

What you describe is right for the experimental sciences of nature, i.e. the knowledge of objects in the outer world. The objects of Phaneroscopy are in the inner world. It so happens that in this world, the relations between A preliminary mathematical result govern mathematics and Phaneroscopy that you never mention -and for a good reason- which is the Triadic Reduction Theorem.  I understand that it embarrasses you because it ruins all your arguments, as well as those of Gary F. and Gary R. who follows you.  I do not fail to mention it in part 6.2 of my article on the Podium of Universal Categories (concise) which I reproduce below. But to make sure you read Peirce's thinking on it, I extract the following blunt quote because it is the core of my entire approach since 1977. 

 

And analysis will show that every relation which is tetradic, pentadic, or of any greater number of correlates is nothing but a compound of triadic relations. It is therefore not surprising to find that beyond the three elements of Firstness, Secondness, and Thirdness, there is nothing else to be found in the phenomenon. (CP 1.347) [ emphasize mine ]

 

In this case the dependency is native. It is based on the reduction of adicity justified by the fact that phanerons and the elements of phanerons are entities connected by their mode of being. So, as far as the observation of phanerons is concerned, Peirce and all those aware of this theorem can observe them with the categories already in their mind. The others tinker.

 

[ BEGINNING ]

 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[robert marty]

List,

Here is a malicious criticism from someone who obviously hasn't read what
he is criticizing ... I won't say more ... except to tell those who read
this thread to avoid reading the opinions of someone who makes you say the
opposite of what you said without checking anything ...
But let's stay positive by quoting what I wrote on page 26 of the Podium
section 9.1:

 "The experience is thus fed by binary relations between the external world
and the internal world (without forgetting that the second is imbricated in
the first). The internal world captures the external world under the binary
form of Secundans; they enter the mind by the door of Secondness. But
Secondness involves Firstness, which at the same time brings in the Priman
elements constituting each Secundan; moreover, we have seen that Secondness
is eventually involved in Thirdness, which also captures the cases in which
Secundans are involved in Tertians.  It  is the reason why Peirce can write:*
"**The elements of every concept enter into logical thought at the gate of
perception and make their exit at the gate of purposive action; and
whatever cannot show its passports at both those two gates is to be
arrested as unauthorized by reason**.*" (CP 5.212).



As such, experience is thus a cumulative process in which every new
experience concerns "facts accomplished" in the external world concerning
the objects of knowledge added to previous experiences of these same
objects whose aggregate is already structured. This addition may require
changes in their general structure if the particular structures of the new
entrants do not conform to the general form in use. The brute force that is
exerted forces minds to make structural changes. Nevertheless, they force
to proceed to modifications, even to radical changes of structure to
preserve the structural unity of the aggregate, and so on,  because the
process is iterative. It describes how knowledge invests external objects
by continuously modifying the structures attributed to them and sometimes
by reconsidering in a disruptive way these structural assets by
substituting them with new adequate structures. We then speak of a change
of paradigm."


All this - and much more - is visualized in the Podium: Figure 2, 3 and 4.


Robert Marty


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



Le mer. 14 juil. 2021 à 17:05,  a écrit :

> List,
>
>
>
> CSP: ... every man inhabits two worlds. These are directly distinguishable
> by their different appearances. But the greatest difference between them,
> by far, is that one of these two worlds, the Inner World, exerts a
> comparatively slight compulsion upon us, though we can by direct efforts so
> slight as to be hardly noticeable, change it greatly, creating and
> destroying existent objects in it; while the other world, the Outer World,
> is full of irresistible compulsions for us, and we cannot modify it in the
> least, except by one peculiar kind of effort, muscular effort, and but very
> slightly even in that way. (CP 5.474)
>
>
>
> RM: The objects of Phaneroscopy are in the inner world.
>
>
>
> GF: We have already seen several of Peirce's definitions of phaneroscopy
> and of the phaneron. None of them say that phaneroscopy ignores objects in
> the outer world; on the contrary, the phaneron includes anything that
> appears or can appear in any way. Robert's statement above would be true
> enough if we changed the word “Phaneroscopy” to “Mathematics”; but as it
> stands, it is nonsense. (Just pointing this out to those who are trying to
> follow the thread, because it may not be obvious to everyone.)
>
>
>
> Gary f.
>
>
>
>
>
> *From:* peirce-l-requ...@list.iupui.edu  *On
> Behalf Of *robert marty
> *Sent:* 14-Jul-21 05:46
>
>
>
> Gary F., John Alan, Gary R., List,
>
>
>
> What you describe is right for the experimental sciences of nature, i.e.
> the knowledge of objects in the outer world. The objects of Phaneroscopy
> are in the inner world. It so happens that in this world, the relations
> between A preliminary mathematical result govern mathematics and
> Phaneroscopy …
> _ _ _ _ _ _ _ _ _ _
> ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the
> message and nothing in the body.  More at
> https://list.iupui.edu/sympa/help/user-signoff.html .
> ► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and
> co-managed by him and Ben Udell.
>
_ _ _ _ _ _ _ _ _ _
► 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 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[Jon Alan Schmidt]

Robert, List:

RM: What you describe is right for the experimental sciences of nature,
i.e. the knowledge of objects in the outer world. The objects of
Phaneroscopy are in the inner world.


On the contrary, as Gary F. already pointed out, phaneroscopy does not
concern itself with the distinction between the outer world and the inner
world. It studies whatever is or could be present to the mind in any way.

RM:  I understand that it [the Triadic Reduction Theorem] embarrasses you
because it ruins all your arguments, as well as those of Gary F. and Gary
R. who follows you.


Nonsense, which arguments of mine does it supposedly "ruin"? In this
particular thread, I provided nine quotations yesterday demonstrating that
Peirce consistently defines mathematics as the science which draws
necessary conclusions about hypothetical states of things, i.e., its method
is strictly deductive and its subject matter is strictly hypothetical.
Anyone is free to disagree with him about this, but no one can legitimately
attribute a different view to him without providing a direct quotation
where he explicitly repudiates it later.

RM: But to make sure you read Peirce's thinking on it, I extract the
following blunt quote because it is the core of my entire approach since
1977.


CSP: And analysis will show that every relation which is *tetradic*,
*pentadic*, or of any greater number of correlates is nothing but a
compound of triadic relations. It is therefore not surprising to find that
beyond the three elements of Firstness, Secondness, and Thirdness, there is
nothing else to be found in the phenomenon. (CP 1.347, 1903)


No one is disputing what Peirce states here. In fact, it is a good example
of the two major principles underlying his *mature *classification of the
sciences as summarized by André in the three slides that Gary F. posted
this morning. Phaneroscopy depends on mathematics in the sense that it
makes use of its general principles, both by manifesting instantiations of
them and by providing critical and validating feedback. This reflects a
considerably more developed understanding of the relationships among
different sciences than his earlier description of "empirics" as "the study
of phenomena with the purpose of identifying their forms with those
mathematics has studied," especially since the latter encompasses not only
phaneroscopy but also logic, metaphysics, and all the special sciences.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Wed, Jul 14, 2021 at 4:46 AM robert marty 
wrote:

> Gary F., John Alan, Gary R., List,
>
>
> What you describe is right for the experimental sciences of nature, i.e.
> the knowledge of objects in the outer world. The objects of Phaneroscopy
> are in the inner world. It so happens that in this world, the relations
> between A preliminary mathematical result govern mathematics and
> Phaneroscopy that you never mention -and for a good reason- which is the
> Triadic Reduction Theorem.  I understand that it embarrasses you because it
> ruins all your arguments, as well as those of Gary F. and Gary R. who
> follows you.  I do not fail to mention it in part 6.2 of my article on the
> Podium of Universal Categories (concise) which I reproduce below. But to
> make sure you read Peirce's thinking on it, I extract the following blunt
> quote because it is the core of my entire approach since 1977.
>
>
>
> *And analysis will show that every relation which is tetradic, pentadic,
> or of any greater number of correlates is nothing but a compound of triadic
> relations. It is therefore not surprising to find that beyond the three
> elements of Firstness, Secondness, and Thirdness, there is nothing else to
> be found in the phenomenon. *(CP 1.347) [ emphasize mine ]
>
>
>
> In this case the dependency is native. It is based on the reduction of
> adicity justified by the fact that phanerons and the elements of phanerons
> are entities connected by their mode of being. So, as far as the
> observation of phanerons is concerned, Peirce and all those aware of this
> theorem can observe them with the categories already in their mind. The
> others tinker.
>
>
>
> *[ BEGINNING ]*
>
>
>
> *6.2 Why three categories and only three?*
>
>
>
> The answer is well known, but it is appropriate to recall it: is the
> "Reduction Thesis," a proof of which is given by Robert Burch in his
> Peircean Algebraic Logic (PAL). He states that all relations can be
> constructed from ternary relations in PAL but not from unary and binary
> relations. We also have two proofs established by and Joachim H. Correia
> and Reinhard Pöschel (2006) with less strong restrictions. Peirce often
> evokes this thesis, either as evidence drawn from the abstract observation
> of signs. He sometimes accompanies it with justifications limited to simple
> examples. It is at the heart of his "Logic of 

RE: [PEIRCE-L] André De Tienne: Slow Read slide 14

[gnox]

List,

 

CSP: ... every man inhabits two worlds. These are directly distinguishable by 
their different appearances. But the greatest difference between them, by far, 
is that one of these two worlds, the Inner World, exerts a comparatively slight 
compulsion upon us, though we can by direct efforts so slight as to be hardly 
noticeable, change it greatly, creating and destroying existent objects in it; 
while the other world, the Outer World, is full of irresistible compulsions for 
us, and we cannot modify it in the least, except by one peculiar kind of 
effort, muscular effort, and but very slightly even in that way. (CP 5.474)

 

RM: The objects of Phaneroscopy are in the inner world.

 

GF: We have already seen several of Peirce's definitions of phaneroscopy and of 
the phaneron. None of them say that phaneroscopy ignores objects in the outer 
world; on the contrary, the phaneron includes anything that appears or can 
appear in any way. Robert's statement above would be true enough if we changed 
the word “Phaneroscopy” to “Mathematics”; but as it stands, it is nonsense. 
(Just pointing this out to those who are trying to follow the thread, because 
it may not be obvious to everyone.)

 

Gary f.

 

 

From: peirce-l-requ...@list.iupui.edu  On 
Behalf Of robert marty
Sent: 14-Jul-21 05:46



 

Gary F., John Alan, Gary R., List,

 

What you describe is right for the experimental sciences of nature, i.e. the 
knowledge of objects in the outer world. The objects of Phaneroscopy are in the 
inner world. It so happens that in this world, the relations between A 
preliminary mathematical result govern mathematics and Phaneroscopy …

_ _ _ _ _ _ _ _ _ _
► 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 
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► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

[PEIRCE-L] André De Tienne: Slow Read slide 16

[gnox]

Continuing our slow read, here is the next slide of André De Tienne’s
slideshow posted on the Peirce Edition Project (iupui.edu)
  site. Comments,
questions and counter-arguments are welcome. (Personal attacks are not. This
is peirce-l, not Facebook.)

 

Gary f.

 



 

Text:

1. The principle of principle-dependency

Any heuristic science discovers and expresses a number of general
fundamental principles that find applications not only across its whole
range but also in other sciences or fields of research. 

Any science that would make use of general principles originating in another
science is said to depend on that other science and thus to follow it as a
matter of prescissive classification. 

This order of subsequence therefore moves from the more abstract or
theoretical science to the more concrete or applied science in phylogenetic
fashion.

_ _ _ _ _ _ _ _ _ _
► 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 . 
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► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

[PEIRCE-L] André De Tienne: Slow Read slide 15

[gnox]

Continuing our slow read, here is the next slide of André De Tienne’s
slideshow posted on the Peirce Edition Project (iupui.edu)
  site. Here
begins Part 3 of the presentation. The next two slides will follow shortly.

 

Gary f.

 



 

Text:

This is not the place to discuss the long history of the development of
Peirces classification of the sciences. Be it known, however, that in its
mature form it was subtended by two major principles.

_ _ _ _ _ _ _ _ _ _
► 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 . 
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co-managed by him and Ben Udell.

Re: [PEIRCE-L] André De Tienne: Slow Read slide 14

[robert marty]

Gary F., John Alan, Gary R., List,


What you describe is right for the experimental sciences of nature, i.e.
the knowledge of objects in the outer world. The objects of Phaneroscopy
are in the inner world. It so happens that in this world, the relations
between A preliminary mathematical result govern mathematics and
Phaneroscopy that you never mention -and for a good reason- which is the
Triadic Reduction Theorem.  I understand that it embarrasses you because it
ruins all your arguments, as well as those of Gary F. and Gary R. who
follows you.  I do not fail to mention it in part 6.2 of my article on the
Podium of Universal Categories (concise) which I reproduce below. But to
make sure you read Peirce's thinking on it, I extract the following blunt
quote because it is the core of my entire approach since 1977.



*And analysis will show that every relation which is tetradic, pentadic, or
of any greater number of correlates is nothing but a compound of triadic
relations. It is therefore not surprising to find that beyond the three
elements of Firstness, Secondness, and Thirdness, there is nothing else to
be found in the phenomenon. *(CP 1.347) [ emphasize mine ]



In this case the dependency is native. It is based on the reduction of
adicity justified by the fact that phanerons and the elements of phanerons
are entities connected by their mode of being. So, as far as the
observation of phanerons is concerned, Peirce and all those aware of this
theorem can observe them with the categories already in their mind. The
others tinker.



*[ BEGINNING ]*



*6.2 Why three categories and only three?*



The answer is well known, but it is appropriate to recall it: is the
"Reduction Thesis," a proof of which is given by Robert Burch in his
Peircean Algebraic Logic (PAL). He states that all relations can be
constructed from ternary relations in PAL but not from unary and binary
relations. We also have two proofs established by and Joachim H. Correia
and Reinhard Pöschel (2006) with less strong restrictions. Peirce often
evokes this thesis, either as evidence drawn from the abstract observation
of signs. He sometimes accompanies it with justifications limited to simple
examples. It is at the heart of his "Logic of relatives" and his
"Existentials Graphs." There is abundant literature on this subject. It is
a separate issue that I do not deal with here.



Peirce considers that everyone can get this result from the observation of
phanerons. Even if he did not provide mathematical proof himself, he
nevertheless reinforced the credibility of the reduction by a sketch of
inductive reasoning, which starts with the easy reduction of a 4-unary
relation and goes on to assert that it would be the same for 5-unary,
6-unary, etc. relations (CP 1.347, 1.294-299).



*And analysis will show that every relation which is tetradic, pentadic, or
of any greater number of correlates is nothing but a compound of triadic
relations. It is therefore not surprising to find that beyond the three
elements of Firstness, Secondness, and Thirdness, there is nothing else to
be found in the phenomenon. *(CP 1.347)



In Peirce's eyes, it is a justification that one can adopt the reduction as
a postulate. He then presents the study of phanerons or phaneroscopy, as
one would an experimental science-based, in this case, on a postulate drew
by abstractive observation of the functioning of signs in social life.
Consequently, he affirms (CP 1.284) that the direct observation allows
isolating pure forms (1.287) characterized by features that lead to a
division in three big categories (CP 1.286) whose explanatory value entrust
to readers who are as many potential reviewers (CP 1.287).



*[ END OF QUOTE ]*

Moreover, Peirce informs his reader (including you, I hope) of this
structural dependence; here are some significant excerpts from MS 908, "The
basis of Pragmaticism in Phaneroscopy," 1905, EP2: 360) chosen so as to
highlight the 13-point plan of Peirce's argument. Point 9 in particular,
considerably increases the scope of the assertions of CP 1.347 above (It
may concern you personally):

*1-  **"I invite the reader to join me in a little survey of the
Phaneron (which will be sufficiently identical for him and for me) in order
to discover what different forms of indecomposable elements it contains.
[...] This ... will be a work of observation. But in order that a work of
observation should bring in any considerable harvest, there must always be
a preparation of thought, a consideration as definite as may be, of what it
is possible that observation should disclose. That is a principe familiar
to every observer. Even if one is destined to be quite surprised, the
preparation will be of mighty aid."*

*2-  **"We are to consider what forms are possible rather than kinds
are possible, because it is universally admitted, in all sorts of
inquiries, that the most important divisions are divisions according to
form, and not according to the qualities