[PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

[Jeffrey Brian Downard]

Jon Schmidt, List,


I'd like to take up the distinction between principles and laws.


Jon S:  "In other words, Peirce denies that excluded middle is an absolutely 
exceptionless law (NEM 4:xiii, no date), which is presumably why he typically 
prefers to call it a principle instead."


On its face, I believe this expresses some confusion about the differences 
between principles and laws. I think Peirce makes the following sort of 
distinction between the two. Consider the following argument, which is from the 
second section of Kant's Grounding for the Metaphysics of Morals:


Everything in nature works in accordance with laws. Only a rational being has 
the capacity to act in accordance with the representation of laws, that is, in 
accordance with principles, or has a will. Since reason is required for the 
derivation of actions from laws, the will is nothing other than practical 
reason. (Ak 412)


According to a neo-Kantian view of rational laws, a law of logic governs the 
relations between the facts expressed in the premisses and conclusion of an 
argument. A principle, on the other hand, is our representation of such a law.


A logic utens consists of the habits of inference that embody such principles. 
Those principles are subject to criticism precisely because they may not match 
up with the laws of logic themselves. The purpose of a philosophical theory of 
logic (i.e., a logica docens) is to build on the criticism of our common sense 
principles for the sake of arriving at a more adequate theoretical 
representation of the truth concerning the real laws that govern the logical 
relations between such facts.


As such, we can distinguish between the principles embodied in our logica utens 
and the principles embodied in a philosophical theory of logic--and either or 
both of these may deviate in some respects from the real laws of logic.


This distinction is at the root of the classification of genuine triadic 
relations in "The Logic of Mathematics, an attempt to develop my categories 
from within". In this classificatory scheme, the laws of logic function as laws 
of fact insofar as they govern those facts directly, and they are in a 
genuinely triadic relation to the actual facts and those that are possible 
(i.e., in the future).


The principles of logic, on the other hand, function as symbolic 
representations that govern the self-controlled growth of our understanding. 
The principles of logic, Peirce points out, do not govern brute facts with mere 
necessity. Rather, they function as imperatives that dictate how we ought to 
think. As such, the principles of logic differ from the laws of logic insofar 
as they are in thoroughly genuine triadic relations to the premisses and 
conclusions that are part of our inquiries. The principles that govern our 
deductive inferences are capable of growth even if the laws of deductive logic 
are, in some sense, necessary laws.


Yours,


Jeff




Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354



From: Jon Alan Schmidt 
Sent: Tuesday, August 4, 2020 6:59 PM
To: s...@bestweb.net
Cc: peirce-l@list.iupui.edu; ahti-veikko.pietari...@ttu.ee; 
francesco.belluc...@unibo.it; cdw...@iupui.edu; martin.irv...@georgetown.edu; 
Gary Richmond
Subject: [PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and 
final version of EGs)

John, All:

JFS:  I sent a complete analysis of these issues to you and others on the CC 
list.

Any analysis of these issues that treats cuts/shading as primitive in EGs, 
rather than derived from the scroll, is incomplete.  Peirce himself never 
claims in R 670 or in RL 231 to be giving a complete analysis or explanation of 
EGs.

JFS:  In response to the other comments in your recent note, I'll reply with a 
copy of Peirce's comments about scrolls in L231:  "  ", AKA silence.

An argument from silence is always logically weak, in this case especially so 
since Peirce elsewhere explicitly denies that a consequence is a composite of 
two negations and explicitly derives the cut from the scroll with a blackened 
inner close.  Again, I am not at all questioning the value of shading as a 
simpler and more iconic improvement over thin lines for representing these 
relations.  In fact, according to what seems to be Peirce's very first 
introduction of shading in EGs ("blue tint"), written five years earlier than R 
670 and RL 231, it is precisely what revealed to him that "if A then B" is not 
strictly equivalent to "not (A and not-B)."

CSP:  But I had better tell you that practically, I content myself with 
performing these cuts in my imagination, merely drawing a light line to 
represent the cut. The blue tint, however, of the area within the cut is a 
great aid to the understanding. How great I have only recently discovered. ...
The new discovery, which sheds such a light is simply that, as the main part of 
the sheet represen

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

[Gary Richmond]

Jon, Jeff, All,

JAS:  After all, *"when we have carried analysis so far as to leave only a
continuous predicate, we have carried it to its ultimate elements"* (SS 72,
1908 Dec 14).  Accordingly, my analysis of an EG is that *the names and
lines are subjects, respectively denoting abstract general concepts and
concrete indefinite individuals*, while *the syntax of their attachments
signifies the pure/continuous predicate*.[emphasis added: GR]

GR: I obviously agree.

Best.

Gary R

"Time is not a renewable resource." gnox

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








Virus-free.
www.avg.com

<#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>

On Wed, Aug 5, 2020 at 8:56 PM Jon Alan Schmidt 
wrote:

> Jeff, All:
>
> JD:  As far as I can see, the scroll is a special kind of iconic sign
> because it expresses the continuity in the relationship between antecedent
> and consequent of the conditional, and this mirrors the continuity in the
> relationship between premisses and conclusions in an argument.
>
>
> I agree; in fact, it expresses and mirrors not just the *continuity* of
> that relationship, but also its *asymmetry*.  All semeiosis is
> inferential process, a continuous hyperbolic sequence that always and only
> has one direction--from premiss to conclusion, from antecedent to
> consequent, from object to interpretant.
>
> I am in general agreement with your other comments, as well.  In
> particular, my interests here are primarily philosophical--as the subject
> line reflects--which is why I keep insisting on the derivative nature of
> negation while recognizing that treating it as a primitive does not
> necessarily affect the *appearance *of the resulting EGs.  As I just
> noted in my other post, it does make an important difference in the 
> *interpretation
> *of those EGs, which is why I believe that we should follow Peirce's
> advice to add a small darkened circle to a shaded area when it is intended
> to represent negation rather than the antecedent of a consequence.
>
> Another potential difference in interpretation is where we choose to draw
> the line between the subjects and predicate of a proposition.  I take
> Peirce seriously when he states that "the proper way in logic is to take as
> the subject whatever there is of which sufficient knowledge cannot be
> conveyed in the proposition itself, but collateral experience on the part
> of its interpreter is requisite ... leaving the *pure *predicate a mere
> form of connection" (NEM 3:885, 1908 Dec 5).  After all, "when we have
> carried analysis so far as to leave only a continuous predicate, we have
> carried it to its ultimate elements" (SS 72, 1908 Dec 14).  Accordingly, my
> analysis of an EG is that the names and lines are subjects, respectively
> denoting abstract general concepts and concrete indefinite individuals,
> while the syntax of their attachments signifies the pure/continuous
> predicate.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Tue, Aug 4, 2020 at 10:17 PM Jeffrey Brian Downard <
> jeffrey.down...@nau.edu> wrote:
>
>> Jon Schmidt, John Sowa, List,
>>
>> It might be helpful to make a clearer distinction between what is
>> advantageous for the purposes of developing the EGs as a formal system of
>> mathematical logic and what is advantageous for the purposes of developing
>> theories of philosophical logic.
>>
>> For the sake of illustrating the importance of the distinction, let me
>> take up the following assertion
>>
>> Jon Schmidt:  "Hence I continue to maintain that the cut for negation
>> must be *derived *from the scroll for consequence with a blackened inner
>> close, rather than treated as a primitive, even when shading is employed
>> instead."
>>
>> For the purposes of developing systems of mathematical logic, the
>> logician can adopt various starting points in setting up the logical
>> grammar for a given system. In symbolic systems, the rules determine what
>> does and does not count as a well-formed-formula. The same holds in the
>> case of the EGs. The grammatical rules determine what counts as a
>> well-formed-graph.
>>
>> Given all the work he has done on the symbolic systems of logic, Peirce
>> sees that there are a number of different ways of setting up the
>> grammatical rules that will, when taken together with the rules of
>> inference and transformation, yield consistent results. For the sake of the
>> EGs considered as a formal system, the scroll and two nested circles are
>> logically equivalent. What is more, it makes no difference for the beta
>> graphs

[PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

[Gary Richmond]

Jon, John, All,

JAS: [Peirce's] primary objective in developing both his logical algebras
and EGs is *not *"making a calculus which would turn out conclusions by a
regular routine."  It is "simply and solely the investigation of the theory
of logic," which requires "that the system devised for the investigation of
logic should be as analytical as possible" (CP 4.373, 1902).

JAS: EGs with shading, rather than cuts, satisfy this criterion as long as
the *derivation *of negation from the primitive of consequence, reflecting
the fundamental asymmetry of all semeiosis, is kept firmly in mind.
Accordingly, I agree with Peirce's "confession" that it is an "error" to
assume that "because the blackened Inner Close can be made indefinitely
small, therefore it can be struck out entirely like an infinitesimal" (CP
4.564n, c. 1906).  Instead, *when a shaded area is intended to represent
negation--not the antecedent of a consequence--it should have a darkened
circle within it, "however small, to represent iconically, the blackened
Inner Close"* (ibid).[emphasis added by GR]

QED (more or less),

Gary R

"Time is not a renewable resource." gnox

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








Virus-free.
www.avg.com

<#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>

On Wed, Aug 5, 2020 at 8:19 PM Jon Alan Schmidt 
wrote:

> John, All:
>
> JFS:  The beauty of eg1911, as specified in L231, is its brevity,
> simplicity, precision, and bare minimum of verbiage.
>
>
> Again, no one is disputing this.  Nevertheless, elsewhere Peirce
> explicitly (1) denies that a consequence is a composite of two negations,
> (2) derives the cut for negation from the scroll with a blackened inner
> close accordingly, and (3) states that shading any oddly enclosed area is
> what enabled him to perceive that it "represents a kind of possibility,"
> not just a denial of actuality.  One upshot of this "discovery" is the
> breakdown of the reasoning behind the widely accepted rule "that every
> conditional proposition whose antecedent does not happen to be realized is
> true," because the principle of excluded middle does not hold when that
> antecedent is a *real *possibility.  What conclusion does Peirce go on to
> draw from this?
>
> CSP:  I often think that we logicians are the most obtuse of men, and the
> most devoid of common sense. As soon as I saw that this strange rule, so
> foreign to the general idea of the System of Existential Graphs, could by
> no means be deduced from the other rules, nor from the general idea of the
> system, but has to be accepted, if at all, as an arbitrary first
> principle,--I ought to have poked myself, and should have asked myself if I
> had not been afflicted with the logician’s *bêtise*, What compels the
> adoption of this rule? The answer to that must have been that the
> *interpretation *requires it; and the inference of common sense from that
> answer would have been that the interpretation was too narrow. Yet I did
> not think of that until my operose method like that of a hydrographic
> surveyor sounding out a harbour, suddenly brought me up to the important
> truth that the *verso *of the sheet of Existential Graphs represents a
> universe of possibilities. This, taken in connection with other premisses
> led me back to the same conclusion to which my studies of Pragmatism had
> already brought me, the reality of some possibilities. (R 490:26-28, CP
> 4.581,1906)
>
>
> The restriction of the scroll to a consequence *ut nunc*--which, as
> Francesco Bellucci has explained (
> http://www.academia.edu/20434982/Charles_S._Peirce_and_the_Medieval_Doctrine_of_consequentiae
> ), Peirce seems to conflate with a conditional *de inesse* after 1896--cannot
> "be deduced from the other rules" for EGs.  Instead, it must be *imposed *as
> an additional "arbitrary first principle," like what is now known as
> Peirce's Law in the axiomatization of classical logic, which is absent from
> intuitionistic logic.  Why had he not noticed this previously?  For one
> thing ...
>
> JFS:  In terms of the semantics (endoporeutic) and permissions (rules of
> inference) of eg1911, a scroll is *indistinguishable* from a shaded area
> with a nested unshaded area.
>
> JFS:  Any EG drawn with a scroll would either be semantically identical
> to one with two ovals or it would be meaningless.
>
> JFS:  In the note I just sent, I was talking about the version of EGs in
> L231.  For that version of logic, there can be no difference in semantics
> between a scroll and a nest of two ovals.
>
>
> As Peirce himself ascertains, the relevant distinction is not to be found
> in the rules or general idea of EGs, but in the *interpretation *of a

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

[Jon Alan Schmidt]

Jeff, All:

JD:  As far as I can see, the scroll is a special kind of iconic sign
because it expresses the continuity in the relationship between antecedent
and consequent of the conditional, and this mirrors the continuity in the
relationship between premisses and conclusions in an argument.


I agree; in fact, it expresses and mirrors not just the *continuity* of
that relationship, but also its *asymmetry*.  All semeiosis is inferential
process, a continuous hyperbolic sequence that always and only has one
direction--from premiss to conclusion, from antecedent to consequent, from
object to interpretant.

I am in general agreement with your other comments, as well.  In
particular, my interests here are primarily philosophical--as the subject
line reflects--which is why I keep insisting on the derivative nature of
negation while recognizing that treating it as a primitive does not
necessarily affect the *appearance *of the resulting EGs.  As I just noted
in my other post, it does make an important difference in the *interpretation
*of those EGs, which is why I believe that we should follow Peirce's advice
to add a small darkened circle to a shaded area when it is intended to
represent negation rather than the antecedent of a consequence.

Another potential difference in interpretation is where we choose to draw
the line between the subjects and predicate of a proposition.  I take
Peirce seriously when he states that "the proper way in logic is to take as
the subject whatever there is of which sufficient knowledge cannot be
conveyed in the proposition itself, but collateral experience on the part
of its interpreter is requisite ... leaving the *pure *predicate a mere
form of connection" (NEM 3:885, 1908 Dec 5).  After all, "when we have
carried analysis so far as to leave only a continuous predicate, we have
carried it to its ultimate elements" (SS 72, 1908 Dec 14).  Accordingly, my
analysis of an EG is that the names and lines are subjects, respectively
denoting abstract general concepts and concrete indefinite individuals,
while the syntax of their attachments signifies the pure/continuous
predicate.

Regards,

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

On Tue, Aug 4, 2020 at 10:17 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon Schmidt, John Sowa, List,
>
> It might be helpful to make a clearer distinction between what is
> advantageous for the purposes of developing the EGs as a formal system of
> mathematical logic and what is advantageous for the purposes of developing
> theories of philosophical logic.
>
> For the sake of illustrating the importance of the distinction, let me
> take up the following assertion
>
> Jon Schmidt:  "Hence I continue to maintain that the cut for negation
> must be *derived *from the scroll for consequence with a blackened inner
> close, rather than treated as a primitive, even when shading is employed
> instead."
>
> For the purposes of developing systems of mathematical logic, the logician
> can adopt various starting points in setting up the logical grammar for a
> given system. In symbolic systems, the rules determine what does and does
> not count as a well-formed-formula. The same holds in the case of the EGs.
> The grammatical rules determine what counts as a well-formed-graph.
>
> Given all the work he has done on the symbolic systems of logic, Peirce
> sees that there are a number of different ways of setting up the
> grammatical rules that will, when taken together with the rules of
> inference and transformation, yield consistent results. For the sake of the
> EGs considered as a formal system, the scroll and two nested circles are
> logically equivalent. What is more, it makes no difference for the beta
> graphs whether the scroll (used to represent the conditional) or a shaded area
> within a boundary (used to represent negation) is taken as "primitive" in
> one sense or another.
>
> Having said that, I do think there is a special philosophical significance
> that Peirce attaches to the scroll as a representation of the conditional.
> I do not think that it is mere artifact of his early explorations of the
> graphs. As Peirce points out, the graphs can be used to express any sort of
> proposition. As such, they can be put to use in philosophical inquiry for
> the sake of analyzing the logical relationships between any set of
> premisses and conclusions.
>
> For the sake of giving a deeper philosophical analysis of the different
> classes of arguments we need to apply the EGs to the problem of analyzing
> synthetic forms of inference. In doing so, it will be helpful to have a
> variety of different icons that can be used to study the grounds of the
> validity of inductive and abductive inference. (MS 296, 499)
>
> As far as I can see, the scroll is a special kind of iconic sign because
> it expresses the continuity in the 

[PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

[Jon Alan Schmidt]

John, All:

JFS:  The beauty of eg1911, as specified in L231, is its brevity,
simplicity, precision, and bare minimum of verbiage.


Again, no one is disputing this.  Nevertheless, elsewhere Peirce explicitly
(1) denies that a consequence is a composite of two negations, (2) derives
the cut for negation from the scroll with a blackened inner close
accordingly, and (3) states that shading any oddly enclosed area is what
enabled him to perceive that it "represents a kind of possibility," not
just a denial of actuality.  One upshot of this "discovery" is the
breakdown of the reasoning behind the widely accepted rule "that every
conditional proposition whose antecedent does not happen to be realized is
true," because the principle of excluded middle does not hold when that
antecedent is a *real *possibility.  What conclusion does Peirce go on to
draw from this?

CSP:  I often think that we logicians are the most obtuse of men, and the
most devoid of common sense. As soon as I saw that this strange rule, so
foreign to the general idea of the System of Existential Graphs, could by
no means be deduced from the other rules, nor from the general idea of the
system, but has to be accepted, if at all, as an arbitrary first
principle,--I ought to have poked myself, and should have asked myself if I
had not been afflicted with the logician’s *bêtise*, What compels the
adoption of this rule? The answer to that must have been that the
*interpretation *requires it; and the inference of common sense from that
answer would have been that the interpretation was too narrow. Yet I did
not think of that until my operose method like that of a hydrographic
surveyor sounding out a harbour, suddenly brought me up to the important
truth that the *verso *of the sheet of Existential Graphs represents a
universe of possibilities. This, taken in connection with other premisses
led me back to the same conclusion to which my studies of Pragmatism had
already brought me, the reality of some possibilities. (R 490:26-28, CP
4.581,1906)


The restriction of the scroll to a consequence *ut nunc*--which, as
Francesco Bellucci has explained (
http://www.academia.edu/20434982/Charles_S._Peirce_and_the_Medieval_Doctrine_of_consequentiae
), Peirce seems to conflate with a conditional *de inesse* after 1896--cannot
"be deduced from the other rules" for EGs.  Instead, it must be *imposed *as
an additional "arbitrary first principle," like what is now known as
Peirce's Law in the axiomatization of classical logic, which is absent from
intuitionistic logic.  Why had he not noticed this previously?  For one
thing ...

JFS:  In terms of the semantics (endoporeutic) and permissions (rules of
inference) of eg1911, a scroll is *indistinguishable* from a shaded area
with a nested unshaded area.

JFS:  Any EG drawn with a scroll would either be semantically identical to
one with two ovals or it would be meaningless.

JFS:  In the note I just sent, I was talking about the version of EGs in
L231.  For that version of logic, there can be no difference in semantics
between a scroll and a nest of two ovals.


As Peirce himself ascertains, the relevant distinction is not to be found
in the rules or general idea of EGs, but in the *interpretation *of a
scroll--regardless of whether it appears as a single continuous line that
crosses itself once to form inner and outer loops, as one oval inside
another, or as a shaded area around an unshaded area.  The greater
iconicity of the last option is not primarily with respect to negation, but
because an oddly enclosed area is a different *surface* from an evenly
enclosed area, corresponding to a universe of possibility rather than that
of actuality.  Moreover ...

CSP:  This is a striking proof of the superiority of the System of
Existential Graphs to either of my algebras of logic. For in both of them
the incongruity of this strange rule is completely hidden behind the
superfluous machinery which is introduced in order to give an appearance of
symmetry to logical law, and in order to facilitate the working of these
algebras considered as reasoning machines. I cannot let this remark pass
without protesting, however, that in the construction of no algebra was the
idea of making a calculus which would turn out conclusions by a regular
routine other than a very secondary purpose. (R 490:28-29, CP 4.581)


This has important bearing on "the unsolved research problem from 1988" as
described in John's presentation slide (
https://list.iupui.edu/sympa/arc/peirce-l/2020-08/msg00017/ppe65.png).

JFS (off-List):  The reason why the problem by Larry Wos (1988) was
unsolved is that Gentzen assumed that an if-then statement was essential
for "illative transformations" (Peirce's term).  But an if-then statement
and any proofs that depend on it are not symmetric.  Peirce's EG rules,
which depend only on existence, conjunction, and negation, are simpler and
symmetric.


For Peirce, symmetry in logical laws is merely "an appearance," the pur

Aw: [PEIRCE-L] Re: Peirce's Methodology

[Helmut Raulien]

 

 
 

Supplement: Thank you, Jon, for this great metaphor of the two bins! I guess that a lot of "living experience"-affairs may be handled (I wont say analyzed) by applying this metaphor. But how is it logically? With mutually exclusive bins it is easy. It is XOR. XOR is "NOT (A AND B)", if you want to express it with EGs. Mutually nonexclusive bins on the other hand may be OR, AND, or Subset of one´s of the other. To express it with EGs becomes a bit complicated. Conclusion: Trying to abstract living experience with logic is hard and complicated somehow, but not doing it, avoiding it, is hazardous, because one will easily be a victim of one or the other fallacy. Fallacies are the most dangerous things at all, I think, because they are the fancy dresses common sense and populism are made of. Avoiding fallacies would make the world a better place, to put it pathetically. Pathos, however, is not illogical. Feeling does not work without logic: Both are not different categories, though they are two bins: 1ns and 3ns, but 1ns and 3ns are not two mutually exclusive bins... blahblahblah, bin the bin, or can the can (Suzie Quatro)...



Dear Jon, List,

 

I think, classification is justified, if the pair of bins really consists of two mutually exclusive bins. My bins "analysis" and "synthesis" really are mutually exclusive, I think. The hazard is on, I think, when two non-exclusive bins are treated like mutually exclusive ones. This is done all the time, here two examples: A young beautiful woman marries an old, rich guy. Now people argue, that she only marries him because of the money. But the bins "love" and "money" are not mutually exclusive, so nobody can justifiedly suggest, that she does not love him for real. Other example: The "Frontex" policy leads to the situation, that refugees in rubber boats are not rescued from the mediterranian sea, and drown. Politicians claim, that rather the reasons for fleeing should be overcome. But these bins are not mutually exclusive: On one bin is written: "Everybody in sea-distress must be rescued if possible". On the other bin is written: "Fleeing resons must be fought, but if people are rescued, more people will flee". But, as these bins are not mutually exclusive, a situation may fill both bins at the same time, and what happens in the second bin, does not make the first bin redundant. Everybody in sea-distress must be rescued if possible, period. Keeping people fom going into rubber boats must be achieved with other means than not rescuing. These examples show that it is ok to have two mutually exclusive bins: In one bin there are the pairs of mutually exclusive bins ("tertium non datur", classification), and in the other bin there are the pairs of mutually not exclusive bins (graduality, composition).

 

Best,

Helmut

 
 

 03. August 2020 um 23:00 Uhr
 "Jon Awbrey" 
wrote:

Dear Helmut,

It's one of the occupational hazards of the classifying mind
that one can start out consciously characterizing aspects of
real situations and end up unwittingly thinking we've gotten
everything under the sun sorted into mutually exclusive bins.

Once the idols of compartmentality and the illusions of autonomous
abstraction get their hold on our minds it is almost impossible to
reconstitute or synthesize what we've torn asunder, if only in our
own minds. The ounce of prevention here is always keeping in mind
that from which all abstractions are abstracted, living experience.

Regards,

Jon

On 8/3/2020 1:54 PM, Helmut Raulien wrote:
> List,
> with regard to this thread, but also to the classification of sciences, but also
> all inquiry, signs, objects, I am thinking about the distinction of analysis
> versus synthesis. To tell, whether a science, a sign, an inquiry is analytical
> or synthetical, I??d say, we have to tell whether the inquirer / interpreter is
> part or sufferer of the object or not. If he*she is not, he*she may have
> theoretc control over it, and the inquiry is analytical in the sense of "divide
> et impera". Analysis is virtual division. If the inquirer on the other hand is
> part or sufferer of the object, the object controls her*him to some extent, and
> the inquiry has to be partly synthetical.
> If a biochemist analyses some protein, it is analytic inquiry. If the climate
> change is the object, it is mostly synthetic inquiry. I think you can classify
> sciences or branches of sciences that way. Physics and chemistry are mostly
> analytic. Ecology, psychology, theology, metaphysics are mostly synthetic.
> Semiotics is kind of both, I think.
> I think, it is helpful, to analytically and synthetically look at the ways
> analysis and synthesis are subsequentially done. I think, many possibilities for
> fallacies are opening up, if analysis and synthesis are alternated in the wrong
> way, without me knowing yet, what in this respect a wrong and a justified way
> would be.
> I think, for example, that natural fallacy is something like that: First
> analysing a 

RE: [PEIRCE-L] Re: Peirce's methodology

[gnox]

Robert, answering your attack on a straw man would hardly be worthwhile, as it 
is apparently based on a misquotation of my post and your own hostile reaction 
to the word “imaginary.” Rather than unleash a barrage of quotes, i will just 
give one example where Peirce uses that word as i did in my paraphrase. This is 
from his classification of the “theoretical sciences,” CP 1.240 (1902):

 

[[ The first is mathematics, which does not undertake to ascertain any matter 
of fact whatever, but merely posits hypotheses, and traces out their 
consequences. It is observational, in so far as it makes constructions in the 
imagination according to abstract precepts, and then observes these imaginary 
objects, finding in them relations of parts not specified in the precept of 
construction. This is truly observation, yet certainly in a very peculiar 
sense; and no other kind of observation would at all answer the purpose of 
mathematics. ]]

 

Gary f.

 

From: robert marty  
Sent: 5-Aug-20 04:49



 

Gary F., Edwina, John, Auke, List

So you're sending mathematics back into the field of the imaginary. Peirce 
isn't as radical as you. He begins a simple and clear classification of science 
with:

- the mathematical sciences: "the study of ideal constructions without 
reference to their real existence",  

If we stopped reading it here, we wouldn't be so preoccupied with mathematics, 
as you seem to want us to be.

But as he goes on he writes:

-Empirical sciences: "the study of phenomena with the purpose of identifying 
their forms with those mathematics has studied"

which puts them back at the center of scientific thought and creates an 
obligation of scientific morality. In other words, what will you do with your 
"genuine indexes" if you do not have universal forms to support them. Will you 
prefer doctrines that have remained in an unformed state rather than having 
formalized theories that can be applied in the real world? By the way, Peirce 
ends his classification with :

- the pragmatic sciences, "the study of how we ought to behave in the ligth of 
the truths of empirics." (C.S. Peirce, 1976: NEM , vol III.2 1122, MS 1345)

which shows without question that pragmatism cannot do without even "imaginary" 
mathematics and even that they are the cornerstone of its pragmatism. 

To claim as you do that "theoretical reasoning is only a mathematical 
procedure, it leaves aside the experiential element of Peirce's methodology and 
his pragmatism" is an insult to Peirce himself and is in fact a certain 
negationism. I am not going to go into a recollection of the innumerable texts 
in which Peirce asserts the role he attributes to mathematics. I believe that 
the one I am quoting above is more than sufficient.

On the other hand, if you were not blinded by this kind of a priori rejection 
of mathematics you could have benefited from the lattice of the classes of 
signs, as noted by Edwina, which would have shown you that the dicent and 
rhematic indexical legisigns encapsulate the corresponding dicent and rhematic 
indexical sinsigns and furthermore that the legisigns themselves are 
encapsulated in dicent and rhematic symbols which combined using deductive or 
inductive arguments produce theories.

But as they say in French "il n'est pire sourd qui ne veut entendre"! (he's the 
worst deaf person who doesn't want to hear!)

Best regards

Robert Marty

Semiotics is a fighting sport

Honorary Professor ; PhD Mathematics ; PhD Philosophy 

fr.wikipedia.org/wiki/Robert_Marty  

 

 de.wikipedia.org/wiki/Robert_Fran%C3%A7ois_Raymond_Marty

 

 

 

Le lun. 3 août 2020 à 18:18, mailto:g...@gnusystems.ca> > 
a écrit :

Jon et al.,

The basic point of my post was that the interpreter of a sign can keep its 
dynamic object “in view” only by means of the indexical function of the sign, 
which connects it to actual experience. Diagrammatic signs are not so good at 
that.

The relevance to John's original post, as i see it, is this: if theorematic 
reasoning is only a mathematical procedure, it leaves out the experiential 
element of Peirce's methodology and his pragmatism. 

Mathematics is not a positive science, meaning that it involves no actual 
experience (other than the experience of doing mathematics, in which the 
universe of discourse is entirely imaginary). All positive sciences (including 
phaneroscopy, logic and semiotic) deal with what Peirce calls real relations as 
opposed to relations of reason (CP 1.365, for instance). A proposition in a 
positive science thus must employ a genuine Index 
 , as opposed to a degenerate index such 
as ‘the letters attached to a geometrical or other diagram’ (EP2:172).

Gary f.

_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to R

Re: [PEIRCE-L] Re: Peirce's methodology

[robert marty]

Gary F., Edwina, John, Auke, List

So you're sending mathematics back into the field of the imaginary. Peirce
isn't as radical as you. He begins a simple and clear classification of
science with:

- *the mathematical sciences*: "the study of ideal constructions without
reference to their real existence",

If we stopped reading it here, we wouldn't be so preoccupied with
mathematics, as you seem to want us to be.

But as he goes on he writes:

-*Empirical sciences*: "the study of phenomena with the purpose of
identifying their forms with those mathematics has studied"

which puts them back at the center of scientific thought and creates an
obligation of scientific morality. In other words, what will you do with
your "genuine indexes" if you do not have universal forms to support them.
Will you prefer doctrines that have remained in an unformed state rather
than having formalized theories that can be applied in the real world? By
the way, Peirce ends his classification with :

- *the pragmatic sciences*, "the study of how we ought to behave in the
ligth of the truths of empirics." (C.S. Peirce, 1976: NEM , vol III.2 1122,
MS 1345)

which shows without question that pragmatism cannot do without even
"imaginary" mathematics and even that they are the cornerstone of its
pragmatism.

To claim as you do that "theoretical reasoning is only a mathematical
procedure, it leaves aside the experiential element of Peirce's methodology
and his pragmatism" is an insult to Peirce himself and is in fact a certain
negationism. I am not going to go into a recollection of the innumerable
texts in which Peirce asserts the role he attributes to mathematics. I
believe that the one I am quoting above is more than sufficient.

On the other hand, if you were not blinded by this kind of a priori
rejection of mathematics you could have benefited from the lattice of the
classes of signs, as noted by Edwina, which would have shown you that the
dicent and rhematic indexical legisigns encapsulate the corresponding
dicent and rhematic indexical sinsigns and furthermore that the legisigns
themselves are encapsulated in dicent and rhematic symbols which combined
using deductive or inductive arguments produce theories.

But as they say in French "il n'est pire sourd qui ne veut entendre"! (he's
the worst deaf person who doesn't want to hear!)

Best regards

Robert Marty
Semiotics is a fighting sport
Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
de.wikipedia.org/wiki/Robert_Fran%C3%A7ois_Raymond_Marty




Le lun. 3 août 2020 à 18:18,  a écrit :

> Jon et al.,
>
> The basic point of my post was that the interpreter of a sign can keep its
> *dynamic* object “in view” only by means of the *indexical *function of
> the sign, which connects it to actual *experience*. Diagrammatic signs
> are not so good at that.
>
> The relevance to John's original post, as i see it, is this: if
> theorematic reasoning is *only *a *mathematical* procedure, it leaves out
> the *experiential *element of Peirce's methodology and his pragmatism.
>
> Mathematics is not a positive science, meaning that it involves no actual
> experience (other than the experience of doing mathematics, in which the
> universe of discourse is entirely imaginary). All positive sciences
> (including phaneroscopy, logic and semiotic) deal with what Peirce calls *real
> relations* as opposed to *relations of reason* (CP 1.365, for instance).
> A proposition in a positive science thus must employ a genuine Index
> , as opposed to a degenerate index
> such as ‘the letters attached to a geometrical or other diagram’ (EP2:172).
>
> Gary f.
>
> -Original Message-
> From: Jon Awbrey 
> Sent: 3-Aug-20 11:35
> To: Peirce List 
> Subject: [PEIRCE-L] Re: Pragma, Pragmata, Pragmatitude!
>
>
>
> Dear Gary, All ...
>
>
>
> I was obviously having a lot more fun with words in those days ...
>
> sigh, good times ... the point of it all being I always see the whole
> complex of meanings associated with the Greek root "pragma, pragmata"
> through the more threadbare veil of the Latin "object".
>
> That complex contains all the senses of aims, concerns, ends, goals,
> intentional objects, and purposes we tend to express more obliquely through
> the use of "object" to mean "objective".  Still, the latter use does have
> some currency in cybernetics, operations research, and systems theory, so
> it's a handy sense to keep in mind.
>
>
>
> Cf: Liddell & Scott
>
>
> http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dpra%3Dgma
>
>
>
> Regards,
>
>
>
> Jon
>
_ _ _ _ _ _ _ _ _ _
► 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 NO