Re: [PEIRCE-L] André De Tienne: Slow Read slide 25

[Gary Richmond]

Jon, Edwina, Gary F, List,

JAS: . . . Gary F. already noted [that] it is questionable whether
*all *hypotheses
are mathematically generated, although Peirce's broad definition of
mathematics as the science which draws necessary conclusions about
hypothetical states of things could arguably be construed that way.

In these ongoing reflections concerning the role that mathematics plays in
phaneroscopy it is, I think, important to consider several points, all of
which may be so obvious as to be easily forgotten or ignored:

(1) while mathematics undoubtedly offers principles to phaneroscopy, it
doesn't offer it *all* its principles (or phaneroscopy would constitute
something like a branch of mathematics);

(2) phaneroscopy also generates *its own principles, *as every discovery
science does;

(3) for phaneroscopy these include categoriality itself (which is *not*
equivalent to valency); that is, the three Universal Categories are
discerned in phaneroscopy; phaneroscopy can and does offer its principles
to sciences further down in the classification, for example, to semeiotic
grammar in its various trichotomic divisions in the classification of
signs: such as qualisign; sinsign, legisign; icon, index, symbol; rheme,
dicisign, argument;

(4) forms and examples of the three Universal Categories always appear in
the phaneron *together* so that while 1ns, 2ns, and 3ns (that is, examples
of these) may be prescinded from it, that prescision is an act of
abstraction and not the phaneronic appearance itself (which, again,
necessarily involves all three categories);

(5) while constituents of the phaneron may be assigned adicity (valency),
that too is an abstraction from, for example, the qualities (1ns),
interactions (2ns), and mediations (3ns) observed by the phaneroscopist.
For example, the color 'red' is not a mathematical entity.

Consequently, I obviously strongly agree with Gary F questioning whether "
*all *hypotheses are mathematically generated," and I strongly disagree,
and despite Peirce's "definition of mathematics as the science which draws
necessary conclusions about hypothetical states of things," that in
consideration of the hypotheses generated by phaneroscopy that it "could
arguably be construed that [exclusively mathematical] way."

In short, phaneroscopy *also* generates its own principles.

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 Thu, Aug 12, 2021 at 6:37 PM Jon Alan Schmidt 
wrote:

> Edwina, List:
>
> ET: That is - the 'methods for attaining truth include our own location
> within and examination of the real, factual world [the phaneron world] and
> coming up, abductively, via mathematical reasoning, with hypotheses that
> explain this world.
>
>
> As I keep pointing out, the phaneron as defined by Peirce is *not *coextensive
> with "the real, factual world." It encompasses *whatever *is or could be
> present to *any *mind in *any *way, including fictions that are as they
> are *only *because someone thinks about them that way. Moreover, as Gary
> F. already noted, it is questionable whether *all *hypotheses are
> mathematically generated, although Peirce's broad definition of mathematics
> as the science which draws necessary conclusions about hypothetical states
> of things could arguably be construed that way.
>
> ET: And - as Peirce pointed out - we must test these hypotheses for their
> validity. That is, we don't 'move on' from mathematics.
>
>
> Testing hypotheses about "the real, factual world" is *not *part of
> mathematics as defined by Peirce, since its reasoning method is strictly
> *deductive*. Even in his broad sense, mathematics can at most be employed
> only to *explicate *such hypotheses, i.e., determine what *would *necessarily
> follow from them if they *were *true. Instead, testing whether they *are *true
> by conducting further observations and experiments falls under metaphysics
> and the special sciences, because it requires *inductive *reasoning in
> accordance with the principles of the normative science of logic as
> semeiotic.
>
> ET: So- the two worlds, so to speak, matter and mind [phaneron and
> mathematics, fact and reason] are in a hylomorphic evolving correlation.
>
>
> This is a false parallel, because again the phaneron is defined by Peirce
> as whatever is or could be present to the *mind*. In accordance with his
> classification of the sciences, the distinction between matter and mind
> arises in metaphysics, not phaneroscopy, resulting in the division of the
> subsequent special sciences into physical and psychical branches.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Thu, Aug 12, 2021 at 1:37 PM 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 25

[Edwina Taborsky]

 

 BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}JAS, list

By factual world, I am referring to the sensate world of the
particular - and that includes the images in my mind. I don't mean,
by factual world, the quantitative alone but include the qualitative.
And I included the phrase 'the phaneron world' to locate this factual
world- and you may not believe me, but I am aware of the full
definition of the term. 

And Peirce was quite specific - "Every hypothesis  should be put to
the test by forcing it to make verifiable predictions. A hypothesis
on which no verifiable predictions can be based should never be
accepted, except with some mark attached to it to show that it is
regarded as a mere convenient vehicle of thought - a mere matter of
form" 5.599.

Who says that 'testing' is a 'part of mathematics'? I didn't say or
even imply this.  See the above quotation. Of course this testing is
inductive; - so - what is your point? The point I was making is that
these hypotheses - whether generated by abductive reasoning in
mathematics or logic or...have to then..be tested. 

As for my last paragraph - I stand by this, since I consider that
the LAWS of organization of matter [which is what our hypotheses are
seeking via mathematics ] and the actualization of these laws, [as
expressed in the phaneron]  co-evolve. That's an interesting -to me -
observation about our world; that the general Laws and the
instantiations - co-evolve. So, I think that these two 'realms'
should be in constant dialogic contact with each other. 

Edwina
 On Thu 12/08/21  6:37 PM , Jon Alan Schmidt jonalanschm...@gmail.com
sent:
 Edwina, List:
 ET: That is - the 'methods for attaining truth include our own
location within and examination of the real, factual world [the
phaneron world] and coming up, abductively, via mathematical
reasoning, with hypotheses that explain this world.
 As I keep pointing out, the phaneron as defined by Peirce is  not
coextensive with "the real, factual world." It encompasses whatever
is or could be present to any mind in any way, including fictions
that are as they are only because someone thinks about them that way.
Moreover, as Gary F. already noted, it is questionable whether all
hypotheses are mathematically generated, although Peirce's broad
definition of mathematics as the science which draws necessary
conclusions about hypothetical states of things could arguably be
construed that way. 
 ET: And - as Peirce pointed out - we must test these hypotheses for
their validity. That is, we don't 'move on' from mathematics.
 Testing hypotheses about "the real, factual world" is not part of
mathematics as defined by Peirce, since its reasoning method is
strictly deductive. Even in his broad sense, mathematics can at most
be employed only to  explicate such hypotheses, i.e., determine what
would necessarily follow from them if they were true. Instead,
testing whether they are true by conducting further observations and
experiments falls under metaphysics and the special sciences, because
it requires inductive reasoning in accordance with the principles of
the normative science of logic as semeiotic.
  ET: So- the two worlds, so to speak, matter and mind [phaneron and
mathematics, fact and reason] are in a hylomorphic evolving
correlation.
 This is a false parallel, because again the phaneron is defined by
Peirce as whatever is or could be present to the mind. In accordance
with his classification of the sciences, the distinction between
matter and mind arises in metaphysics, not phaneroscopy, resulting in
the division of the subsequent special sciences into physical and
psychical branches. 
 Regards,
Jon Alan Schmidt - Olathe, Kansas, USAStructural Engineer, Synechist
Philosopher, Lutheran Christianwww.LinkedIn.com/in/JonAlanSchmidt [1]
- twitter.com/JonAlanSchmidt [2] 
 On Thu, Aug 12, 2021 at 1:37 PM Edwina Taborsky  wrote:
Gary F, list

This is exactly what some of us have been saying - in our
questioning of the isolation by De Tienne of mathematics from the
Real World. And asking - if the practice of mathematics is so
cerebral, so detached from material reality, so isolated - then,
what's its point? And how and why should one 'move on' from
mathematics? What do we leave behind?

As I noted, in a previous post:  "We can see in the above, the
outline of  the 'methods for attaining truth' - which don't, to my
interpretation, reduce it to a singular foundation but instead,
present it as  a complex and very active, verifiable correlation of
'facts' and 'reason'. [emphasis added].

That is - the 'methods for attaining truth include our own location
within and examination of the real, factual world [the phaneron
world] and coming up, abductively, via mathematical reasoning, with
hypotheses that explain this world. And - as Peirce pointed out - we
must test these hypotheses for their validity. That is, we don't
'move 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 25

[Jon Alan Schmidt]

Edwina, List:

ET: That is - the 'methods for attaining truth include our own location
within and examination of the real, factual world [the phaneron world] and
coming up, abductively, via mathematical reasoning, with hypotheses that
explain this world.


As I keep pointing out, the phaneron as defined by Peirce is *not *coextensive
with "the real, factual world." It encompasses *whatever *is or could be
present to *any *mind in *any *way, including fictions that are as
they are *only
*because someone thinks about them that way. Moreover, as Gary F. already
noted, it is questionable whether *all *hypotheses are mathematically
generated, although Peirce's broad definition of mathematics as the science
which draws necessary conclusions about hypothetical states of things could
arguably be construed that way.

ET: And - as Peirce pointed out - we must test these hypotheses for their
validity. That is, we don't 'move on' from mathematics.


Testing hypotheses about "the real, factual world" is *not *part of
mathematics as defined by Peirce, since its reasoning method is strictly
*deductive*. Even in his broad sense, mathematics can at most be employed
only to *explicate *such hypotheses, i.e., determine what *would *necessarily
follow from them if they *were *true. Instead, testing whether they *are *true
by conducting further observations and experiments falls under metaphysics
and the special sciences, because it requires *inductive *reasoning in
accordance with the principles of the normative science of logic as
semeiotic.

ET: So- the two worlds, so to speak, matter and mind [phaneron and
mathematics, fact and reason] are in a hylomorphic evolving correlation.


This is a false parallel, because again the phaneron is defined by Peirce
as whatever is or could be present to the *mind*. In accordance with his
classification of the sciences, the distinction between matter and mind
arises in metaphysics, not phaneroscopy, resulting in the division of the
subsequent special sciences into physical and psychical branches.

Regards,

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

On Thu, Aug 12, 2021 at 1:37 PM Edwina Taborsky  wrote:

> Gary F, list
>
> This is exactly what some of us have been saying - in our questioning of
> the isolation by De Tienne of mathematics from the Real World. And asking -
> if the practice of mathematics is so cerebral, so detached from material
> reality, so isolated - then, what's its point? And how and why should one
> 'move on' from mathematics? What do we leave behind?
>
> As I noted, in a previous post:  "We can see in the above, the outline of
> the 'methods for attaining truth' - which don't, to my
> interpretation, reduce it to a singular foundation but instead, present it
> as a complex and very active, verifiable correlation of 'facts' and
> 'reason'. [emphasis added].
>
> That is - the 'methods for attaining truth include our own location within
> and examination of the real, factual world [the phaneron world] and coming
> up, abductively, via mathematical reasoning, with hypotheses that explain
> this world. And - as Peirce pointed out - we must test these hypotheses for
> their validity. That is, we don't 'move on' from mathematics.
>
> So- the two worlds, so to speak, matter and mind [phaneron and
> mathematics, fact and reason] are in a hylomorphic evolving correlation.
>
> Edwina
>
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Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Comment 3
https://inquiryintoinquiry.com/2021/08/12/semiotics-semiosis-sign-relations-comment-3/

All,

It helps me to compare sign relations with my other favorite class
of triadic relations, namely, groups.  Applications of mathematical
groups came up just recently in the Laws of Form discussion group,
so it will save a little formatting time to adapt the definition
used there.

Cf: Animated Logical Graphs • 60
https://inquiryintoinquiry.com/2021/02/21/animated-logical-graphs-60/

Definition 1.  A group (G, ∗) is a set G together with
a binary operation ∗ : G × G → G satisfying the following
three conditions.

1.  Associativity.
For any x, y, z in G, we have (x ∗ y) ∗ z  =  x ∗ (y ∗ z).

2.  Identity.

There is an identity element 1 in G such that for all g in G,
we have 1 ∗ g  =  g ∗ 1  =  g.

3.  Inverses.
Each element has an inverse, that is, for each g in G,
there is some h in G such that g ∗ h  =  h ∗ g  =  1.

Regards,

Jon

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Re: [PEIRCE-L] André De Tienne: Slow Read slide 25

[Edwina Taborsky]

 

Gary F, list

This is exactly what some of us have been saying - in our
questioning of the isolation by De Tienne of mathematics from the
Real World. And asking - if the practice of mathematics is so
cerebral, so detached from material reality, so isolated - then,
what's its point? And how and why should one 'move on' from
mathematics? What do we leave behind?

As I noted, in a previous post:  "We can see in the above, the
outline of  the 'methods for attaining truth' - which don't, to my
interpretation, reduce it to a singular foundation but instead,
present it as a complex and very active, verifiable correlation of
'facts' and 'reason'. [emphasis added].

That is - the 'methods for attaining truth include our own location
within and examination of the real, factual world [the phaneron
world] and coming up, abductively, via mathematical reasoning, with
hypotheses that explain this world. And - as Peirce pointed out - we
must test these hypotheses for their validity. That is, we don't
'move on' from mathematics. 

So- the two worlds, so to speak, matter and mind [phaneron and
mathematics, fact and reason] are in a hylomorphic evolving
correlation.

Edwina
 On Thu 12/08/21  1:29 PM , g...@gnusystems.ca sent:
Of all the slides I’ve posted here so far, this is the one I find
most questionable.

De Tienne here takes it as “given that mathematics is the 
“first” stage of research in the heuristic schema.” Now, there
is no question that mathematics comes first in the top-down hierarchy
of sciences as schematized in Peirce’s classification, which places
the most abstract at the top, the one that supplies “principles”
to all the sciences below it. But I see no reason to believe that
actual heuristic inquiry starts there “as a point of method.”

 I’ve argued in my book that the course of inquiry is generally
cyclical, implying that the choice of starting point is largely
arbitrary. (We might take it as the advent of a “surprising
phenomenon,” for instance, as that is what motivates a search for
some explanation of it.) Nevertheless, some of us do think of the
cycle broadly as abduction > deduction > induction, with abduction
(or retroduction) coming “first.” In the present context, this
would imply that abduction is essentially mathematical, or at least
that inquiry begins in the hypothetical realm. 

Based on my own limited experience, I very much doubt that inquiry
begins with mathematics, such that we need to “transition out of
it” in order to carry it further. I think, on the contrary, that
inquiry begins with a felt need to ‘make sense’ of some
experience, and then (in many cases) we bring in mathematical
thinking to suggest some principle which can help us organize our
guesses as to what might be going on. Often this involves using
deduction to render a hypothesis testable. But I very much doubt that
 all hypotheses are mathematically generated, as De Tienne would seem
to imply here.

Others may disagree, as indeed some already have, and I wouldn’t
want to prolong the debates about the working definition of
mathematics, which have been done to death already. I’m just
calling it as I see it, deplying the ordinary common-sense
signification of “mathematics.” 

Gary f.
From:  peirce-l-requ...@list.iupui.edu 

 On Behalf Of g...@gnusystems.ca
 Sent: 12-Aug-21 12:21
Continuing our slow read on phaneroscopy, here is the next slide of
André De Tienne’s slideshow posted on the  Peirce Edition Project
(iupui.edu) [1] site. 

Gary f.
Text: The Urge to Transition out of Mathematics

•  Given mathematics' unbounded search for formal
necessities,  we cannot count on mathematicians to help figure out
what goes on in experience.

•  Yet we cannot ignore the natural urge that pushes the
rest of us to figure out the all-too-real world that holds us under
its bondage. We want to sort out its laws, its structures, its
composition, its guises and disguises. 

•  As a point of method, however, given that mathematics
is the “first” stage of research in the heuristic schema, how do
we transition out of it into a concern no longer detached from but
attached to the conditions sustaining the cosmos, the world, nature,
life in general, our life?  


Links:
--
[1] https://peirce.iupui.edu/publications.html#presentations
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Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[robert marty]

Jon, List

  I am familiar with this type of confusion, and it is not because it has
been in Wikipedia for 15 years that it is validated. It existed in my
immediate environment that I finally break.  I will first make some remarks
and then ask you a question.

The remark: you spend without justification six different grammatical forms
allowing six different predicates to describe the same phaneron by linking
the letters A, B, C, in six ways to the six purely formal combinations of
the three letters S, O, and I. For each of the six combinations, which
predicate? A Y diagram with three free ends where the letters S, O, I
circulate might be the answer? (I can't think of any other, but you tell
me...) But then you spend from the six different ways given by Pierce to
express a single phaneron grammatically = the fact that an object in the
world has changed ownership (in all six grammatical cases, it is the same
fact that has happened in the real world) to the semiotic with six
combinations of three letters O, S, I which one wonders about the relation
with what precedes. Indeed, if O is the object of a sign, S the sign itself
(= the concrete thing that represents) and I the interpreter, that makes
three distinct elements possibly present to the mind according to the
focus, so three distinct phanerons, two out of mind and the third is a
determination of this mind. In passing, I note that you illustrate by
quotations from Peirce only three combinations (what about the other
three?) whose coherence is open to discussion.  Finally, you quote
2.228-229 (1902) and 2.230 (1910) from which it seems that Liszka would
have drawn (by observation?) four normative conditions that a sign should
fulfill, in which, if he retains that the sign determines the interpretant,
and represents the object thanks to ground, he still ignores that the
object determines the sign, although almost all the definitions after
1904-1905 expressly stipulate it.  Now, because we have a sign with three
elements, each of which can also be present in mind, Peirce can classify
the signs according to the categorial belonging of each of them (I have
modeled it).
So my question is: How will you get the 10 classes of signs, let alone the
28 (and I'm not talking about the 66 that are still not defined)? With OSI,
I presume? What will be the use of the 5 others?
  Best regards,
Robert Marty
NB: just now, I see that you had posted before I finished reacting. At
first glance, I see that the Cartesian product O x Sx I partially answers
my question above but does not inform me about the rest.
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le mer. 11 août 2021 à 01:15, Jon Awbrey  a écrit :

> Cf: Semiotics, Semiosis, Sign Relations • Comment 2
>
> https://inquiryintoinquiry.com/2021/08/10/semiotics-semiosis-sign-relations-comment-2/
>
> Re: Semiotics, Semiosis, Sign Relations • Comment 1
>
> https://inquiryintoinquiry.com/2021/08/09/semiotics-semiosis-sign-relations-comment-1/
>
> All,
>
> Definitions tend to call on other terms in need of their own definitions,
> and so on till the process terminates at the level of primitive terms.
> The main two concepts requiring supplementation in Peirce's definition
> of a sign relation are the ideas of “correspondence” and “determination”.
> We can figure out fairly well what Peirce had in mind from things he wrote
> elsewhere, as I explained in the Sign Relation article I added to Wikipedia
> 15 years ago.
>
> Sign Relation
> https://en.wikipedia.org/w/index.php?title=Sign_relation=68541642
>
> Not daring to look at what's left of that, here's the relevant section
> from the OEIS Wiki fork.
>
> Sign Relation ( https://oeis.org/wiki/Sign_relation )
> • Definition ( https://oeis.org/wiki/Sign_relation#Definition )
>
> Regards,
>
> Jon
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Re: [PEIRCE-L] André De Tienne: Slow Read slide 23

[robert marty]

Helmut, List
In general algebra, we define particular types of structure formed by a set
with one or more "internal" laws of composition possessing certain
properties. I voluntarily leave aside the external laws with operator
domains on the set. The laws themselves are ways of associating any two
elements noted with conventional signs to obtain a third. Thus the sign "+"
has absolutely nothing to do with addition as you practice it in the real
world. The simplest structure consisting of a set of elements (without real
existence) and an internal law of composition that we can write as we want
(with "+" if we want) is called a magma... this abstract structure can be
implemented in a multitude of concrete sets in which we have observed that
the elements associate themselves two by two to form a third belonging to
the same set. For example, the set of natural integers (with or without the
zero) is a "magma." But it is more than that. It is also a semigroup as
soon as we establish that its law is associative, semigroup being a name
conventionally chosen to designate this more complex advanced type of
abstract structure. We can also say "associative magma." The natural
integers are still part of it. Now the set {1,2,3} consisting of the
numbers 1,2 and 3 alone is not a magma for the usual addition. On the other
hand, it has a structure of another kind, listed in the mathematical
repository, under the name of "total order structure" (so a fortiori it is
also a Poset = Partially Ordered Set) when we provide it with the natural
order relation. But if we call the three elements X, Y, and Z and if we
provide their set with an order relation defined in such a way as to "copy"
the previous relations by substituting X to 3, Y to 2, and Z to,1 we will
obtain an abstract structure which can be implemented in many other 3
elements sets, like for example (taken at random ;-) ) Peirce's categories
considered with their interdependence relations (involvement). This is why
your example of Aliens has no sense in algebra because the abstract
elements that we compose according to your addition is an "algebraic
unicorn." Indeed, the starting elements are fixed, unalterable, and all the
more unalterable because they have no real existence, even if the letters
that designate them are on Earth. If the Aliens want to call this way of
altering objects on their planet "+," they can, but they will not practice
the algebra that is practiced on Earth.
Best regards,
Robert Marty

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



Le jeu. 12 août 2021 à 16:45, Helmut Raulien  a écrit :

> Robert, Edwina, List
>
> The skeleton metaphor for a poset makes sense to me. Is it also a good
> metaphor for mathematics being the skeleton of all other sciences?
> I earlier wrote, that mathematics is based on axioms, and axioms are not
> hypothetical, but inducted. Edwina asked what I mean by axioms. I admit,
> that I donot understand the axiom- (inducted relation to the real world-)
> character of these things. For example, "a + b = b + a" is said to be an
> axiom. But to me it only seems to be a tautology of the definition of the
> plus-operator (summation). Summation is defined as a not temporal, and not
> sequential, only spatial connection. So where is the axiom? If axioms
> really exist, these are connections to the real world, which are not
> hypoteses (abductions), but experiences (inductions). This is how "axiom"
> is defined, I think. But I until now dont see the so-called axioms as
> axioms.
>
> Best,
> Helmut
>
>
> 12. August 2021 um 10:39 Uhr
>  "robert marty" 
> wrote:
>
>
> Helmut, List
>
>
> The case of Peirce's semiotics is different from that of the empirical
> sciences...it does not require induction to be verified and in this sense
> it can be said to be "robust" a priori. Indeed, the mathematical modeling
> by an abstract structure of Poset isomorphic to the organization of
> universal categories by involvements is purely qualitative and does not
> require any experimental verification. CP 3.559 has been quoted a lot but
> each one has drawn partial arguments from it. The part that I have
> personally underlined ( see Podium, p.4) does not suffer any dispute and
> leads us on the way to understanding this false debate between "formalists"
> and "empiricists" reformulated in a kind of will of power of mathematics on
> phaneroscopy. Here is this part: "*The skeletonization or
> diagrammatization of the problem serves more purposes than one; but its
> principal purpose is to strip the significant relations of all disguise*". The
> Poset is nothing else than "*the skeleton-set*" of all phanerons, a
> tri-relation of elements a priori in all that is present to any mind.  But
> there are many other things in the phaneron! The metaphors of the X-ray of
> the skeleton of a vertebrate allow us to illustrate this point
> 

Re: [PEIRCE-L] Relations & Their Relatives

[Jon Awbrey]

Cf: Relations & Their Relatives • Discussion 1
https://inquiryintoinquiry.com/2015/02/27/relations-their-relatives-discussion-1/

Re: Peirce List
https://web.archive.org/web/20150619134001/http://comments.gmane.org/gmane.science.philosophy.peirce/15704
::: Helmut Raulien
https://web.archive.org/web/20150619133003/http://permalink.gmane.org/gmane.science.philosophy.peirce/15719

The “divisor of” relation signified by x|y is a dyadic relation
on the set of positive integers M and thus may be understood as
a subset of the cartesian product M × M.  It is an example of
a “partial order”, while the “less than or equal to” relation
signified by x ≤ y is an example of a “total order” relation.

The mathematics of relations can be applied most felicitously
to semiotics but there we must bump the “adicity” or “arity”
up to three.  We take any sign relation L to be subset of a
cartesian product O × S × I, where O is the set of “objects”
under consideration in a given discussion, S is the set of
“signs”, and I is the set of “interpretant signs” involved
in the same discussion.

One thing we need to understand is the sign relation L ⊆ O × S × I
relevant to a given level of discussion may be rather more abstract
than what we would call a “sign process” proper, that is, a structure
extended through a dimension of time.  Indeed, many of the most powerful
sign relations generate sign processes through iteration or recursion
or similar operations.  In that event, the most penetrating analysis
of the sign process or semiosis in view is achieved through grasping
the generative sign relation at its core.

Regards,

Jon
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Aw: [PEIRCE-L] André De Tienne: Slow Read slide 23

[Helmut Raulien]

Robert, Edwina, List

 

The skeleton metaphor for a poset makes sense to me. Is it also a good metaphor for mathematics being the skeleton of all other sciences?

I earlier wrote, that mathematics is based on axioms, and axioms are not hypothetical, but inducted. Edwina asked what I mean by axioms. I admit, that I donot understand the axiom- (inducted relation to the real world-) character of these things. For example, "a + b = b + a" is said to be an axiom. But to me it only seems to be a tautology of the definition of the plus-operator (summation). Summation is defined as a not temporal, and not sequential, only spatial connection. So where is the axiom? If axioms really exist, these are connections to the real world, which are not hypoteses (abductions), but experiences (inductions). This is how "axiom" is defined, I think. But I until now dont see the so-called axioms as axioms.

 

Best,

Helmut

 
 

12. August 2021 um 10:39 Uhr
 "robert marty" 
wrote:

 

 


Helmut, List 
 
The case of Peirce's semiotics is different from that of the empirical sciences...it does not require induction to be verified and in this sense it can be said to be "robust" a priori. Indeed, the mathematical modeling by an abstract structure of Poset isomorphic to the organization of universal categories by involvements is purely qualitative and does not require any experimental verification. CP 3.559 has been quoted a lot but each one has drawn partial arguments from it. The part that I have personally underlined ( see Podium, p.4) does not suffer any dispute and leads us on the way to understanding this false debate between "formalists" and "empiricists" reformulated in a kind of will of power of mathematics on phaneroscopy. Here is this part: "The skeletonization or diagrammatization of the problem serves more purposes than one; but its principal purpose is to strip the significant relations of all disguise". The Poset is nothing else than "the skeleton-set" of all phanerons, a tri-relation of elements a priori in all that is present to any mind.  But there are many other things in the phaneron! The metaphors of the X-ray of the skeleton of a vertebrate allow us to illustrate this point (phaneroscopy vs. radioscopy): radioscopy reveals the skeleton by making it appear within an image.  The scanner, by taking over with the help of computers (tomodensidometry) can show it in three dimensions and from all angles. All the rest is obliterated and is part of the "disguise", i.e. all the rest in which it is immersed; the technique of X-rays allows the extraction of the skeleton (Wilhelm Röntgen, the first Nobel Prize of physics gave them the usual name of the unknown in mathematics, X! ). Continuing the metaphor, my "trichotomic machine" is a kind of scanner perfected to radiograph the signs based on the preliminary phaneroscopy of each of the elements of the sign but respecting the determinations of their tri-relation. 

Regards, 

Robert Marty
 





Honorary Professor ; PhD Mathematics ; PhD Philosophy 

fr.wikipedia.org/wiki/Robert_Marty

https://martyrobert.academia.edu/

 






 


Le jeu. 12 août 2021 à 00:08, Helmut Raulien  a écrit :




Edwina, List

 

I dont think that De Tienne "tells us that it is essentially detached and isolate from the Real World to be almost irrelevant". After all, mathematics is based on axioms, which come from the real world. These are premisses. What I donot understand is, why these are called "purely hypothetical" (in this thread). A hypothesis is a result of an abduction, but axioms are results of induction.

 

Now, how mathematics further deals with these premisses, is said to be deductively. I think so too. But you, with Peirce, call it "reasoning with specially constructed schemata". This to me seems completely different from pure deduction. I donot undertand what is meant by it. Can you give an example for such a constructed schema?

 

Best,

Helmut

 
 

11. August 2021 um 19:54 Uhr
"Edwina Taborsky" 
wrote:

 


Bernard, JAS, Gary F, Robert, list:

The problem I have with De Tienne's outline of mathematics is the intense focus he gives to its essential irrelevance to we who live in the real world. I don't think it can be ascribed to his sense of humour. He repeats it often enough that we must consider that he takes this view very seriously.

And - I don't agree with JAS's view that this focus is merely to differentiate 'pure' from 'applied' mathematics. We have to instead, ask WHY Peirce emphasized the role of pure mathematics in his SCIENCES. Surely it has a role in our scientific exploration and analysis of our Real World? Otherwise - why do it?

Yes, mathematics "deals exclusively with hypothetical states of things and asserts no matter of fact whatever, and further, that it is thus alone that the necessity of its conclusions explained" 4.232. And Peirce warns against what we can consider as the'induction' process as the sole sense of 

Aw: [PEIRCE-L] André De Tienne: Slow Read slide 23

[Helmut Raulien]

Supplement:

Ok, you may say, that it is a result of experience, that when you put two things together, for the sum it doesnt matter, which one you have first, and which one you then add. Now imagine an alien universe, in which it is so, that "a + b" is 90% of a and 110% of b, because the thing you have first, due to summation decreases to 90%, and the added thing increases to 110%. But the mathematics to handle this is the same mathematics like the one we have, just with this rule integrated. Also the aliens in that alien universe were able to calculate in our way. So, axiom or not, what I said was wrong: Axioms, if they exist, are not the basis for mathematics. Mathematics is everywhere the same, regardless of them.

 

Robert, Edwina, List

 

The skeleton metaphor for a poset makes sense to me. Is it also a good metaphor for mathematics being the skeleton of all other sciences?

I earlier wrote, that mathematics is based on axioms, and axioms are not hypothetical, but inducted. Edwina asked what I mean by axioms. I admit, that I donot understand the axiom- (inducted relation to the real world-) character of these things. For example, "a + b = b + a" is said to be an axiom. But to me it only seems to be a tautology of the definition of the plus-operator (summation). Summation is defined as a not temporal, and not sequential, only spatial connection. So where is the axiom? If axioms really exist, these are connections to the real world, which are not hypoteses (abductions), but experiences (inductions). This is how "axiom" is defined, I think. But I until now dont see the so-called axioms as axioms.

 

Best,

Helmut

 
 

12. August 2021 um 10:39 Uhr
 "robert marty" 
wrote:

 

 


Helmut, List 
 
The case of Peirce's semiotics is different from that of the empirical sciences...it does not require induction to be verified and in this sense it can be said to be "robust" a priori. Indeed, the mathematical modeling by an abstract structure of Poset isomorphic to the organization of universal categories by involvements is purely qualitative and does not require any experimental verification. CP 3.559 has been quoted a lot but each one has drawn partial arguments from it. The part that I have personally underlined ( see Podium, p.4) does not suffer any dispute and leads us on the way to understanding this false debate between "formalists" and "empiricists" reformulated in a kind of will of power of mathematics on phaneroscopy. Here is this part: "The skeletonization or diagrammatization of the problem serves more purposes than one; but its principal purpose is to strip the significant relations of all disguise". The Poset is nothing else than "the skeleton-set" of all phanerons, a tri-relation of elements a priori in all that is present to any mind.  But there are many other things in the phaneron! The metaphors of the X-ray of the skeleton of a vertebrate allow us to illustrate this point (phaneroscopy vs. radioscopy): radioscopy reveals the skeleton by making it appear within an image.  The scanner, by taking over with the help of computers (tomodensidometry) can show it in three dimensions and from all angles. All the rest is obliterated and is part of the "disguise", i.e. all the rest in which it is immersed; the technique of X-rays allows the extraction of the skeleton (Wilhelm Röntgen, the first Nobel Prize of physics gave them the usual name of the unknown in mathematics, X! ). Continuing the metaphor, my "trichotomic machine" is a kind of scanner perfected to radiograph the signs based on the preliminary phaneroscopy of each of the elements of the sign but respecting the determinations of their tri-relation. 

Regards, 

Robert Marty
 





Honorary Professor ; PhD Mathematics ; PhD Philosophy 

fr.wikipedia.org/wiki/Robert_Marty

https://martyrobert.academia.edu/

 






 


Le jeu. 12 août 2021 à 00:08, Helmut Raulien  a écrit :




Edwina, List

 

I dont think that De Tienne "tells us that it is essentially detached and isolate from the Real World to be almost irrelevant". After all, mathematics is based on axioms, which come from the real world. These are premisses. What I donot understand is, why these are called "purely hypothetical" (in this thread). A hypothesis is a result of an abduction, but axioms are results of induction.

 

Now, how mathematics further deals with these premisses, is said to be deductively. I think so too. But you, with Peirce, call it "reasoning with specially constructed schemata". This to me seems completely different from pure deduction. I donot undertand what is meant by it. Can you give an example for such a constructed schema?

 

Best,

Helmut

 
 

11. August 2021 um 19:54 Uhr
"Edwina Taborsky" 
wrote:

 


Bernard, JAS, Gary F, Robert, list:

The problem I have with De Tienne's outline of mathematics is the intense focus he gives to its essential irrelevance to we who live in the real world. I don't think it can be 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 23

[Jon Alan Schmidt]

Bernard, List:

We cannot answer the question of "how we ought to practice the science of
phaneroscopy today" without first establishing what the science of
phaneroscopy *is*, which according to Peirce requires carefully
distinguishing it from mathematics as a strictly hypothetical science and
from all the other positive sciences.

Regards,

Jon S.

On Thu, Aug 12, 2021 at 4:23 AM Bernard Morand 
wrote:

> Le 12/08/2021 à 02:10, Jon Alan Schmidt a écrit :
>
> Bernard, List:
>
> BM: The main difficulty for me is the doctrinal turn of the exchanges that
> consist most often in some kind of gloss of Peirce's writings, as if they
> were gospels.
>
>
> JAS: Peirce's writings are our only definitive source for ascertaining
> what *his *views were, in this case *his *definition of mathematics as
> distinguished from phaneroscopy and all the other sciences in *his 
> *classification.
> Anyone is free to disagree with it, but not to attribute a *different 
> *definition
> to him.
>
> Agreed, but your statement doesn't exhaust the subject (the actuality of
> Peirce, including his classification of sciences)
>
> BM: In fact this his what has happened to my arguments refering to the
> concrete and daily activity of mathematicians.
>
>
> JAS: It may well be the case that Peirce's definition of mathematics is
> inconsistent with the actual practice of the people who call themselves
> mathematicians today. That is irrelevant to the primary topic at hand,
> which is the science of phaneroscopy as *he *defined and practiced it.
>
> if it was really inconsistent, there would be something to look for.
>
> Your primary topic is not the same as mine.  Mine is: how we ought to
> practice the science of phaneroscopy today.
>
> BM: The only response has been to quote Peirce, out of context, who wrote
> one century before (and you know the extend to which I hold his merits)
>
>
> JAS: Any quotation of any author is removed from its original context, so
> an argument is needed to demonstrate that a *particular *quotation is
> being interpreted and presented in a way that somehow misrepresents its
> author's original intent.
>
> Agreed, but I prefer in place of your's to terminate with :  a
> particular quotation is being interpreted and presented in a way that
> somehow attests of its pertinence for the actual state of things, otherwise
> characterized.
>
> Evidently this little modification changes everything in making us pass
> from comment to living science.
>
> As regards to the author's intend I agree with what Edwina and John Sowa
> have already written.
>
> Bernard Morand
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Wed, Aug 11, 2021 at 1:38 PM Bernard Morand 
> wrote:
>
>> Gary R, list
>>
>> I agree with you that the materials used for the slow read  are only
>> supports for public presentations and not research papers.
>>
>> I had noticed this straight from the beginning of the slow read and I
>> thought that to use publicly such materials was not a good service made to
>> their author. As you say we remain ignorant of his oral presentation itself.
>>
>> Nevertheless, the direction of the argument that he is developing on pure
>> maths is as clear as erroneous. And I maintain my strong desagreement with
>> it.
>>
>> Despite the so-called sense of humor (which I have never experienced with
>> this author),  it leads his assertions as far as becoming false and abusing
>> his audience as well. One can laugh of everything but not with everybody
>> says the maxim.
>>
>> As regard to my participation to the list I will probably return to the
>> state of lurker. The main difficulty for me is the doctrinal turn of the
>> exchanges that consist most often in some kind of  gloss of Peirce's
>> writings, as if they were gospels.
>>
>> In fact this his what has happened to my arguments refering to the
>> concrete and daily activity of  mathematicians.  The only response has been
>> to quote Peirce, out of context, who wrote one century before (and you know
>> the extend to which I hold his merits)
>>
>> Regards
>>
>> Bernard
>>
>
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Re: [PEIRCE-L] Relations & Their Relatives

[robert marty]

Dear Jon, List

 You evoke many concepts with their relations, the explanation of which
would take a considerable amount of time, to the point that you are reduced
to answering yourself. I want to question you on the point that interests
me particularly, which concerns your entry into Peirce's semiotics. I found
it among all your links here: https://oeis.org/wiki/Sign_relation
 and also here: Sign relation -
Wikipedia . You will tell me
if this is the right reference. If it is so, then I think you have made a
bad choice, and of course, I explain myself...To be clear and precise, I
must reproduce the entirety of your "Definition" paragraph:

JA >  "One of Peirce's clearest and most complete definitions of a sign is
one he gives in the context of providing a definition for *logic*, and so
it is informative to view it in that setting.

Logic will here be defined as *formal semiotic*. A definition of a sign
will be given which no more refers to human thought than does the
definition of a line as the place which a particle occupies, part by part,
during a lapse of time. Namely, a sign is something, *A*, which brings
something, *B*, its *interpretant* sign determined or created by it, into
the same sort of correspondence with something, *C*, its *object*, as that
in which itself stands to *C*. It is from this definition, together with a
definition of “formal,” that I deduce mathematically the principles of
logic. I also make a historical review of all the definitions and
conceptions of logic, and show, not merely that my definition is no
novelty, but that my non-psychological conception of logic has *virtually* been
quite generally held, though not generally recognized. (C.S. Peirce, NEM 4,
20–21).

In the general discussion of diverse theories of signs, the question
frequently arises whether signhood is an absolute, essential, indelible, or
*ontological* property of a thing, or whether it is a relational,
interpretive, and mutable role that a thing can be said to have only within
a particular context of relationships.

Peirce's definition of a *sign* defines it in relation to its *object* and
its *interpretant sign*, and thus it defines signhood in *relative terms
*, by means of a predicate with
three places. In this definition, signhood is a role in a triadic relation
, a role that a thing bears or
plays in a given context of relationships — it is not an *absolute*,
*non-relative* property of a thing-in-itself, one that it possesses
independently of all relationships to other things.

Some of the terms that Peirce uses in his definition of a sign may need to
be elaborated for the contemporary reader.

   - *Correspondence.* From the way that Peirce uses this term throughout
   his work, it is clear that he means what he elsewhere calls a “triple
   correspondence”, and thus this is just another way of referring to the
   whole triadic sign relation itself. In particular, his use of this term
   should not be taken to imply a dyadic correspondence, like the kinds of
   “mirror image” correspondence between realities and representations that
   are bandied about in contemporary controversies about “correspondence
   theories of truth”.


   - *Determination.* Peirce's concept of determination is broader in
   several directions than the sense of the word that refers to strictly
   deterministic causal-temporal processes. First, and especially in this
   context, he is invoking a more general concept of determination, what is
   called a *formal* or *informational* determination, as in saying “two
   points determine a line”, rather than the more special cases of causal and
   temporal determinisms. Second, he characteristically allows for what is
   called *determination in measure*, that is, an order of determinism that
   admits a full spectrum of more and less determined relationships.


   - *Non-psychological.* Peirce's “non-psychological conception of logic”
   must be distinguished from any variety of *anti-psychologism*. He was
   quite interested in matters of psychology and had much of import to say
   about them. But logic and psychology operate on different planes of study
   even when they have occasion to view the same data, as logic is a *normative
   science
   *
where
   psychology is a *descriptive science
   
*,
   and so they have very different aims, methods, and rationales.


RM > I could not find the term "signhood" in any dictionary, nor in the pdf
of Peirce at my disposal, but the making of the term allowed me, I think to
get an exact idea of it: it is a kind of container of triadic signs, a free
predicate with three places, that is three loose ends. I base my challenge
on the fact that you have not 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 23

[Bernard Morand]

Le 12/08/2021 à 02:10, Jon Alan Schmidt a écrit :

Bernard, List:

BM: The main difficulty for me is the doctrinal turn of the
exchanges that consist most often in some kind of gloss of
Peirce's writings, as if they were gospels.


JAS: Peirce's writings are our only definitive source for ascertaining 
what /his /views were, in this case /his /definition of mathematics as 
distinguished from phaneroscopy and all the other sciences in /his 
/classification. Anyone is free to disagree with it, but not to 
attribute a /different /definition to him.
Agreed, but your statement doesn't exhaust the subject (the actuality of 
Peirce, including his classification of sciences)


BM: In fact this his what has happened to my arguments refering to
the concrete and daily activity of mathematicians.


JAS: It may well be the case that Peirce's definition of mathematics 
is inconsistent with the actual practice of the people who call 
themselves mathematicians today. That is irrelevant to the primary 
topic at hand, which is the science of phaneroscopy as /he /defined 
and practiced it.


if it was really inconsistent, there would be something to look for.

Your primary topic is not the same as mine.  Mine is: how we ought to 
practice the science of phaneroscopy today.




BM: The only response has been to quote Peirce, out of context,
who wrote one century before (and you know the extend to which I
hold his merits)


JAS: Any quotation of any author is removed from its original context, 
so an argument is needed to demonstrate that a /particular /quotation 
is being interpreted and presented in a way that somehow misrepresents 
its author's original intent.


Agreed, but I prefer in place of your's to terminate with :  a 
particular quotation is being interpreted  and presented in a way that 
somehow attests of its pertinence for the actual state of things, 
otherwise characterized.


Evidently this little modification changes everything in making us pass 
from  comment to living science.


As regards to the author's intend I agree with what Edwina and John Sowa 
have already written.


Bernard Morand


Regards,

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


On Wed, Aug 11, 2021 at 1:38 PM Bernard Morand > wrote:


Gary R, list

I agree with you that the materials used for the slow read  are
only supports for public presentations and not research papers.

I had noticed this straight from the beginning of the slow read
and I thought that to use publicly such materials was not a good
service made to their author. As you say we remain ignorant of his
oral presentation itself.

Nevertheless, the direction of the argument that he is developing
on pure maths is as clear as erroneous. And I maintain my strong
desagreement with it.

Despite the so-called sense of humor (which I have never
experienced with this author),  it leads his assertions as far as
becoming false and abusing his audience as well. One can laugh of
everything but not with everybody says the maxim.

As regard to my participation to the list I will probably return
to the state of lurker. The main difficulty for me is the
doctrinal turn of the exchanges that consist most often in some
kind of  gloss of Peirce's writings, as if they were gospels.

In fact this his what has happened to my arguments refering to the
concrete and daily activity of mathematicians.  The only response
has been to quote Peirce, out of context, who wrote one century
before (and you know the extend to which I hold his merits)

Regards

Bernard


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Re: [PEIRCE-L] André De Tienne: Slow Read slide 23

[robert marty]

Helmut, List

The case of Peirce's semiotics is different from that of the empirical
sciences...it does not require induction to be verified and in this sense
it can be said to be "robust" a priori. Indeed, the mathematical modeling
by an abstract structure of Poset isomorphic to the organization of
universal categories by involvements is purely qualitative and does not
require any experimental verification. CP 3.559 has been quoted a lot but
each one has drawn partial arguments from it. The part that I have
personally underlined ( see Podium, p.4) does not suffer any dispute and
leads us on the way to understanding this false debate between "formalists"
and "empiricists" reformulated in a kind of will of power of mathematics on
phaneroscopy. Here is this part: "*The skeletonization or diagrammatization
of the problem serves more purposes than one; but its principal purpose is
to strip the significant relations of all disguise*". The Poset is nothing
else than "*the skeleton-set*" of all phanerons, a tri-relation of elements
a priori in all that is present to any mind.  But there are many other
things in the phaneron! The metaphors of the X-ray of the skeleton of a
vertebrate allow us to illustrate this point (phaneroscopy vs. radioscopy):
radioscopy reveals the skeleton by making it appear within an image.  The
scanner, by taking over with the help of computers (tomodensidometry) can
show it in three dimensions and from all angles. All the rest is
obliterated and is part of the "disguise", i.e. all the rest in which it is
immersed; the technique of X-rays allows the extraction of the skeleton
(Wilhelm Röntgen, the first Nobel Prize of physics gave them the usual name
of the unknown in mathematics, X! ). Continuing the metaphor, my
"trichotomic machine" is a kind of scanner perfected to radiograph the
signs based on the preliminary phaneroscopy of each of the elements of the
sign but respecting the determinations of their tri-relation.

Regards,

Robert Marty

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



Le jeu. 12 août 2021 à 00:08, Helmut Raulien  a écrit :

> Edwina, List
>
> I dont think that De Tienne "tells us that it is essentially detached and
> isolate from the Real World to be almost irrelevant". After all,
> mathematics is based on axioms, which come from the real world. These are
> premisses. What I donot understand is, why these are called "purely
> hypothetical" (in this thread). A hypothesis is a result of an abduction,
> but axioms are results of induction.
>
> Now, how mathematics further deals with these premisses, is said to be
> deductively. I think so too. But you, with Peirce, call it "reasoning with
> specially constructed schemata". This to me seems completely different from
> pure deduction. I donot undertand what is meant by it. Can you give an
> example for such a constructed schema?
>
> Best,
> Helmut
>
>
> 11. August 2021 um 19:54 Uhr
> "Edwina Taborsky" 
> wrote:
>
>
> Bernard, JAS, Gary F, Robert, list:
>
> The problem I have with De Tienne's outline of mathematics is the intense
> focus he gives to its essential irrelevance to we who live in the real
> world. I don't think it can be ascribed to his sense of humour. He repeats
> it often enough that we must consider that he takes this view very
> seriously.
>
> And - I don't agree with JAS's view that this focus is merely to
> differentiate 'pure' from 'applied' mathematics. We have to instead, ask
> WHY Peirce emphasized the role of pure mathematics in his SCIENCES. Surely
> it has a role in our scientific exploration and analysis of our Real World?
> Otherwise - why do it?
>
> Yes, mathematics "deals exclusively with hypothetical states of things and
> asserts no matter of fact whatever, and further, that it is thus alone that
> the necessity of its conclusions explained" 4.232. And Peirce warns against
> what we can consider as the'induction' process as the sole sense of
> information, with his comment "to assert that any source of information
> that is restricted to actual facts could afford us a necessary knowledge,
> that is, knowledge relating to a whole general range of possibility, would
> be a flat contradiction in terms" 4.232.
>
> And he moves, not into applied mathematics but into phenomenology, for
> 'Thinking in general terms is not enough. It is necessary that something
> should be DONE. In geometry, subsidiary lines are drawn. In algebra
> permissible transformations are made. Thereupon the faculty of observation
> is called into play...Theorematic reasoning invariably depends upon
> experimentation with individual schemata...theorematic or mathematical
> reasoning proper, is reasoning with specially constructed schemata" 4.233.
>
> And "phenomenology, which does not depend upon any other positive science,
> nevertheless must, if it is to be properly grounded, be made to depend upon
> the