RE: [PEIRCE-L] André De Tienne: Slow Read slide 6

[John F. Sowa]

Robert and Gary F,  
The issue you're debating is caused by the
ambiguity in Peirce's use of the word 'logic'.  In his 1903 classification
of the sciences, the word 'logic' appears in two places:  mathematics of
logic is the first of three branches of mathematics.  But logic proper is
a branch of normative science.
The logic that is used to derive the
categories and hypoicons is th logic of mathematics, AKA mathematical
logic, AKA formal logic.  The logic that scientists use to evaluate the
truth of their hypotheses is normative logic, which is misleadingly called
logic proper.
See the comments and quotations
below.
John

The
categories and hypoicons, the foundation for semeiotic, are
derived
from the phaneron by applying the three branches of pure
mathematics:  formal logic; discrete mathematics (arithmetic, graphs,
and discrete sets); and continuous mathematics (geometry, topology,
and uncountable sets).

We must also distinguish the term
formal logic, which occurs 119 times
in CP, from logic
proper, which occurs just 7 times in CP.  DeMorgan
coined the
term formal logic, and Peirce adopted it for every logic
notation
developed by himself or others.  Note its importance:

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
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RE: [PEIRCE-L] André De Tienne: Slow Read slide 6

[gnox]

Thank you, Robert, for providing two more Peirce quotes in confirmation of the 
three in my post, all clarifying the role of formal, mathematical, deductive 
logic in philosophy. Here is one more that might clarify it still further:

CSP: If the whole business of mathematics consists in deducing the properties 
of hypothetical constructions, mathematics is the one science to which a 
science of logic is not pertinent. For nothing can be more evident than its own 
unaided reasonings. On the contrary logic is an experiential, or positive, 
science. Not that it needs to make any special observations, but it does rest 
upon a part of our experience that is common to all men. Pure deductive logic, 
insofar as it is restricted to mathematical hypotheses, is, indeed, mere 
mathematics. But when logic tells us that we can reason about the real world in 
the same way with security, it tells us a positive fact about the universe. (CP 
7.524)

As I quoted the other day in reference to slide 9, Peirce says that “Normative 
science rests largely on phenomenology and on mathematics” (CP 1.186, 1902). 
The text that we are slow-reading is about phaneroscopy, including its 
relations with other positive sciences. If you have an opinion about that, we’d 
like to hear it; for one thing, we’d like to know how experience fits into the 
picture as you see it. That might help to explain why normative science rests 
largely on phenomenology as well as on mathematics.

Gary f.

 

From: peirce-l-requ...@list.iupui.edu  On 
Behalf Of robert marty
Sent: 6-Jul-21 12:13
To: Gary Fuhrman 
Cc: Peirce-L 
Subject: Re: [PEIRCE-L] André De Tienne: Slow Read slide 6

 

Gary F, List

 

My opinion is that Mathematics and Philosophy are best placed where Peirce 
himself put them :

 

Extract from  

 (26) (DOC) The "Podium" of Universal Categories and their degenerate cases | 
robert marty - Academia.edu

 

Section  1 Prolegomena on the role of mathematics in the classifications of 
sciences.

 

Carolyn Eisele, the editor of "The New Elements of Mathematics" of Peirce 
(1982), quoting Peirce, emphasized the importance of these principles for a 
proper understanding of Peirce's philosophy:

 

The doctrine of exact philosophy . . . is that all danger of error in 
philosophy will be reduced to a minimum by treating in philosophy will be 
reduced to a minimum by treating the problem as mathematically as possible, 
that is, by constructing some sort of a diagram representing that which is 
supposed to be open to the observation of every scientific intelligence, and 
thereupon mathematically . . . deducing the consequences of that hypothesis. 
(Peirce, NEM IV, x). 

It is no wonder that in every classification of the sciences, mathematics heads 
every list, while philosophy, to be exact "must rest on mathematical 
principles. (Peirce, NEM IV, 273) [emphasize mine]

 

Robert Marty

Honorary Professor ; PhD Mathematics ; PhD Philosophy 

fr.wikipedia.org/wiki/Robert_Marty  

https://martyrobert.academia.edu/

 

 

 

Le mar. 6 juil. 2021 à 15:45, mailto:g...@gnusystems.ca> > 
a écrit :

Point of clarification:

CSP: Formal logic, however developed, is mathematics. Formal logic, however, is 
by no means the whole of logic, or even its principal part. It is hardly to be 
reckoned as a part of logic proper. Logic has to define its aim; and in doing 
so is even more dependent upon ethics, or the philosophy of aims, by far, than 
it is, in the methodeutic branch, upon mathematics. We shall soon come to 
understand how a student of ethics might well be tempted to make his science a 
branch of logic; as, indeed, it pretty nearly was in the mind of Socrates. But 
this would be no truer a view than the other. Logic depends upon mathematics; 
still more intimately upon ethics; but its proper concern is with truths beyond 
the purview of either. (CP 4.240, 1902)

CSP: 526. Logic is a branch of philosophy. That is to say it is an 
experiential, or positive science, but a science which rests on no special 
observations, made by special observational means, but on phenomena which lie 
open to the observation of every man, every day and hour. There are two main 
branches of philosophy, Logic, or the philosophy of thought, and Metaphysics, 
or the philosophy of being. Still more general than these is High Philosophy 
which brings to light certain truths applicable alike to logic and to 
metaphysics. It is with this high philosophy that we have at first to deal. (CP 
7.526, undated)

GF: In my opinion this “High Philosophy,” or first of the positive sciences, is 
essentially the same science that Peirce called “phenomenology” in 1902, and 
later “phaneroscopy”. It makes observations by direct experience and 
generalizes from them with the help of some kind of logica utens. After the 
categories have been prescinded, 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 6

[robert marty]

Gary F, List


My opinion is that Mathematics and Philosophy are best placed where Peirce
himself put them :


Extract from (26) (DOC) The "Podium" of Universal Categories and their
degenerate cases | robert marty - Academia.edu



Section  *1 Prolegomena on the role of mathematics in the classifications
of sciences**.*


Carolyn Eisele, the editor of "The New Elements of Mathematics" of Peirce
(1982), quoting Peirce, emphasized the importance of these principles for a
proper understanding of Peirce's philosophy:



*The doctrine of exact philosophy . . . is that all danger of error in
philosophy will be reduced to a minimum by treating in philosophy will be
reduced to a minimum by treating the problem as mathematically as possible,
that is, by constructing some sort of a diagram representing that which is
supposed to be open to the observation of every scientific intelligence,
and thereupon mathematically . . . deducing the consequences of that
hypothesis. *(Peirce, NEM IV, x).

*It is no wonder that in every classification of the sciences, mathematics
heads every list, while philosophy, to be exact "must rest on mathematical
principles**. *(Peirce, NEM IV, 273) [emphasize mine]


Robert Marty
Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le mar. 6 juil. 2021 à 15:45,  a écrit :

> Point of clarification:
>
> CSP: Formal logic, however developed, is mathematics. Formal logic,
> however, is by no means the whole of logic, or even its principal part. It
> is hardly to be reckoned as a part of logic proper. Logic has to define its
> aim; and in doing so is even more dependent upon ethics, or the philosophy
> of aims, by far, than it is, in the methodeutic branch, upon mathematics.
> We shall soon come to understand how a student of ethics might well be
> tempted to make his science a branch of logic; as, indeed, it pretty nearly
> was in the mind of Socrates. But this would be no truer a view than the
> other. Logic depends upon mathematics; still more intimately upon ethics;
> but its proper concern is with truths beyond the purview of either. (CP
> 4.240, 1902)
>
> CSP: 526. Logic is a branch of philosophy. That is to say it is an
> experiential, or positive science, but a science which rests on no special
> observations, made by special observational means, but on phenomena which
> lie open to the observation of every man, every day and hour. There are two
> main branches of philosophy, Logic, or the philosophy of thought, and
> Metaphysics, or the philosophy of being. Still more general than these is
> High Philosophy which brings to light certain truths applicable alike to
> logic and to metaphysics. It is with this high philosophy that we have at
> first to deal. (CP 7.526, undated)
>
> GF: In my opinion this “High Philosophy,” or first of the positive
> sciences, is essentially the same science that Peirce called
> “phenomenology” in 1902, and later “phaneroscopy”. It makes observations by
> direct experience and generalizes from them with the help of some kind of 
> *logica
> utens.* After the categories have been prescinded, named and
> conceptualized as a trichotomy, then we can use formal logic to apply them
> in other branches of philosophy.
>
> CSP: I have followed out this trichotomy into many other ramifications,
> and have uniformly found it to be a most useful polestar in my explorations
> into the different branches of philosophy. There is no fallacy in it; for
> it asserts nothing, but only offers suggestions…. 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. (EP2:428, 1907)
>
> Gary f.
>
>
>
> *From:* peirce-l-requ...@list.iupui.edu  *On
> Behalf Of *John F. Sowa
> *Sent:* 5-Jul-21 23:22
> Robert, List,
>
> I strongly agree with you:
>
> RM> My criticism is precisely about the fact that De Tienne starts with
> phaneroscopy and forgets that the formal structures he believes in
> discovering are inherited from mathematics on which they depend.
>
> At the end of this note is the opening section of my previous note on the
> elements of phaneroscopy.  These points are the prerequisites for
> understanding what Peirce wrote about phenomeology or phaneroscopy.  It's
> impossible to evaluate what anybody wrote about phaneroscopy without a
> solid understanding of Peirce's assumptions.
>
> John
>
> --
>
> The categories and
>
> hypoicons, the foundation for 

RE: [PEIRCE-L] André De Tienne: Slow Read slide 6

[gnox]

Point of clarification:

CSP: Formal logic, however developed, is mathematics. Formal logic, however,
is by no means the whole of logic, or even its principal part. It is hardly
to be reckoned as a part of logic proper. Logic has to define its aim; and
in doing so is even more dependent upon ethics, or the philosophy of aims,
by far, than it is, in the methodeutic branch, upon mathematics. We shall
soon come to understand how a student of ethics might well be tempted to
make his science a branch of logic; as, indeed, it pretty nearly was in the
mind of Socrates. But this would be no truer a view than the other. Logic
depends upon mathematics; still more intimately upon ethics; but its proper
concern is with truths beyond the purview of either. (CP 4.240, 1902)

CSP: 526. Logic is a branch of philosophy. That is to say it is an
experiential, or positive science, but a science which rests on no special
observations, made by special observational means, but on phenomena which
lie open to the observation of every man, every day and hour. There are two
main branches of philosophy, Logic, or the philosophy of thought, and
Metaphysics, or the philosophy of being. Still more general than these is
High Philosophy which brings to light certain truths applicable alike to
logic and to metaphysics. It is with this high philosophy that we have at
first to deal. (CP 7.526, undated)

GF: In my opinion this “High Philosophy,” or first of the positive sciences,
is essentially the same science that Peirce called “phenomenology” in 1902,
and later “phaneroscopy”. It makes observations by direct experience and
generalizes from them with the help of some kind of logica utens. After the
categories have been prescinded, named and conceptualized as a trichotomy,
then we can use formal logic to apply them in other branches of philosophy.

CSP: I have followed out this trichotomy into many other ramifications, and
have uniformly found it to be a most useful polestar in my explorations into
the different branches of philosophy. There is no fallacy in it; for it
asserts nothing, but only offers suggestions…. 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. (EP2:428, 1907)

Gary f.

 

From: peirce-l-requ...@list.iupui.edu  On
Behalf Of John F. Sowa
Sent: 5-Jul-21 23:22
Robert, List,

I strongly agree with you:

RM> My criticism is precisely about the fact that De Tienne starts with
phaneroscopy and forgets that the formal structures he believes in
discovering are inherited from mathematics on which they depend. 

At the end of this note is the opening section of my previous note on the
elements of phaneroscopy.  These points are the prerequisites for
understanding what Peirce wrote about phenomeology or phaneroscopy.  It's
impossible to evaluate what anybody wrote about phaneroscopy without a solid
understanding of Peirce's assumptions.

John

--

The categories and
hypoicons, the foundation for semeiotic, are derived
from the phaneron by applying the
three branches of pure mathematics:
formal logic; discrete mathematics
(arithmetic, graphs, and discrete sets); 
and continuous mathematics (geometry,
topology, and uncountable sets).  
See the diagram of Peirce’s
classification of the sciences (attached in the 
file CSPscience.jpg).
 
We must also distinguish the term
formal logic, which occurs 119 times
in CP, from logic proper, which
occurs just 7 times in CP.   DeMorgan
coined the term formal
logic, and Peirce adopted it for every logic
notation developed by himself or
others.  Note its importance:
 
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)
_ _ _ _ _ _ _ _ _ _
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