Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jerry LR Chandler]

Jeff:

Parallelograms of forces about interacting electrical charges require a 
spherical mode of description. Correspondingly, an explanation of spherical 
forces requires categorial illations.

Can the diagram be extended to spheres?

Cheers

Jerry


> On Mar 17, 2017, at 10:19 AM, Jeffrey Brian Downard  
> wrote:
> 
> Jon A, John S, Jon S, Clark, List, 
> 
> I'd like to refer back to an earlier discussion of the last lecture in RLT in 
> order to take up the question of how we try to supply a diagram for better 
> understanding the relationship between truth and the starting and ending 
> points of inquiry. The diagram below is a sketch of how I would like to 
> develop the philosophical implications of what Peirce says about the 
> mathematics of projective relations. Let me know if you have suggestions for 
> making things clearer. 
> 
> Peirce argues that, in regard to the principle of movement from these two 
> points, only three types of philosophical positions are possible. Here are 
> the passages I'm trying to interpret:
> 
> 1.  Elliptic philosophy. Starting-point and stopping-point are not even 
> ideal. Movement of nature recedes from no point, advances towards no point, 
> has no definite tendency, but only flits from position to position.
> 2. Parabolic philosophy. Reason or nature develops itself according to one 
> universal formula; but the point toward which that development tends is the 
> very same nothingness from which it advances.
> 3. Hyperbolic philosophy. Reason marches from premisses to conclusion; nature 
> has ideal end different from its origin. (CP, 6.581-2)
>  
> Pierce argues that the conception of the absolute in philosophy “fulfills the 
> same function as the absolute in geometry. According as we suppose the 
> infinitely distant beginning and end of the universe are distinct,identical, 
> or nonexistent, we have three kinds of philosophy. What should determine our 
> choice of these? Observed Facts. These are all in favour of the first.” [W 
> 8.22; 1890], [CP 4.145; 1893])  Drawing on the series of mathematical 
> examples copied below, let's construct a diagram to illustrate Peirce's claim 
> that“[j]ust as geometry has its descriptive and its metrical portions, the 
> former considering whether points coincide or not, the latter measuring how 
> far distant from one another they are... so logic has first to decide whether 
> a proposition or reasoning to be true or false, and secondly in the latter 
> case, to measure the amount of its falsity” [W 4.241; 1881], [W 5.166; 1885]) 
> 
> 
> 
> While I'm not able to fit it into this diagram, one idea I'd like to capture 
> is that of the relations of proportion in quantitative inductive inferences 
> between what has been observed and what might observed in the future. In 
> order to understand the significance of picturing the horizon as hyperbolic 
> lines, see the discussion below.
> 
> --Jeff
> 
>  
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> 
> 
> From: Jeffrey Brian Downard  <mailto:jeffrey.down...@nau.edu>>
> Sent: Wednesday, November 16, 2016 10:04 AM
> Cc: peirce-l@list.iupui.edu <mailto:peirce-l@list.iupui.edu>
> Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
> Metaphysics and Nothing (was Peirce's Cosmology))
>  
> List,
> 
> Following up on Peirce's line of argument about the differences between 
> elliptical, parabolic and hyperbolic philosophies in Logic and Spiritualism 
> (from 1905, CP 6.581-585), I'd like to offer some relatively simple examples. 
> The purpose of the examples is to illustrate how ideas from perspective and 
> projective geometries can be used to clarify the points Peirce is making 
> about the formal differences between these different ways of orienting 
> ourselves with respect to the beginning and ending points of inquiry when we 
> go about the business of framing hypotheses.
> 
> For starters, let us draw out the analogy between the ending point of inquiry 
> and a point on the distant horizon. Like travelers who head off to the 
> horizon when they board different trains, different inquirers may try to 
> answer a question using different methods. What do we suppose might happen 
> when these different inquirers follow out these parallel lines of inquiry? 
> Should we suppose that such lines of inquiry will tend to converge on some 
> point of agreement--call it the truth--in the long run? 
> 
> I am interested in taking a closer look at what Peirce says about the analogy 
> between converging parallel lines in a perspective or a projective geometry 
> and converging li

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jeffrey Brian Downard]

deas in topology are offered by Peirce for the purposes of getting 
clearer about a number of key mathematical conceptions that he is putting to 
use in the development and refinement of the conception of continuity within 
the logical theory. Many of these conceptions are identified in italics in the 
text (e.g, completed aggregate, multitude brought to an end, potential, topical 
singularity, furcation, perissid, artiad, fornix, line, filament, surface, 
film, space, tripon, chorisis, cyclosis, immensity, ensemble, etc.), and he is 
applying these mathematical conceptions for the purpose of addressing the 
problem of how to clarify a logical conception of continuity that will be 
adequate for a normative theory of semiotics.

Peirce focuses on the evolution of more determinate dimensions from a vague 
potentiality in the account of the logical conception of continuity at 253-4 in 
RLT because he is trying to articulate an explanation of how the various 
dimensions of our thought might evolve. Those logical dimensions can be 
divided, in quite a fundamental way, according to three dimensions of yet 
further dimensions of possibles, existents and necessitants of signs, objects, 
interpretants and their relations within a growing system.

--Jeff



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



From: Jon Alan Schmidt 
Sent: Monday, November 14, 2016 3:17 PM
To: Jeffrey Brian Downard
Cc: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
Metaphysics and Nothing (was Peirce's Cosmology))

Jeff, List:

I am definitely interested, but it would be helpful to me if you could first 
outline where you see this ultimately going, and then proceed in smaller steps. 
 As you could probably tell, I had trouble making the connection between 
Desargues' theorem and Peirce's conception of continuity, not to mention the 
subsequent blackboard diagram; and my own intuition (or perhaps lack thereof) 
is such that discussing "the projective absolute" and "metrical relations in 
elliptical, parabolic or hyperbolic geometries" is not (at least so far) 
helping me understand your/Peirce's point "about the kind of hypothesis that is 
needed to make sense of ... the growth of order in the cosmos."  Also, I still 
believe that Peirce's "table of contents" in "A Neglected Argument" was for a 
future book that he had not yet written and never did manage to write, rather 
than anything specific in his previous material such as RLT.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> - 
twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt>

On Mon, Nov 14, 2016 at 3:45 PM, Jeffrey Brian Downard 
mailto:jeffrey.down...@nau.edu>> wrote:

Jon S, Gary R, Edwina, John S, List,

If others are interested, I'd like to continue the discussion of the last 
lecture on continuity in RLT. The goal, I took it, was to draw on it for the 
sake of filling in some the details in the "table of contents" for a larger set 
of inquiries that he sketched in "A Neglected Argument."

My proposal is to march through more of the mathematical examples he offers in 
the hopes of getting more clarity about the logical conception of continuity 
that he articulates. Then, the aim is to work up to the example of the lines on 
the blackboard and the way that he uses that example to frame some hypothesis 
in cosmological metaphysics.

Given the fact that my post on Desargues 6-point theorem did not generate much 
in the way of comments or questions, I am concerned that I overdid it and 
managed to smother some of the interest in the questions--both interpretative 
and philosophical--that we were considering. As such, I'm asking for feedback 
to make see if continued discussion of the mathematical examples is welcome.

Late last week, I thought of a way to illustrate Peirce's larger point about 
how the 6 point theorem is connected to the larger idea that Cayley and Klein 
make about the character of the projective absolute and how it provides the 
basis of any system of metrical relations in elliptical, parabolic or 
hyperbolic geometries. The illustration helps to see, in a more intuitive way, 
the point Peirce seems to be making about the kind of hypothesis that is needed 
to make sense of the possibility of progress with respect to the growth of our 
understanding or, more generally, with the growth of order in the cosmos.

So, let me ask if there are any takers for continuing the discussion of RLT 
along these lines?

--Jeff

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

-
P

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

I am definitely interested, but it would be helpful to me if you could
first outline where you see this ultimately going, and then proceed in
smaller steps.  As you could probably tell, I had trouble making the
connection between Desargues' theorem and Peirce's conception of
continuity, not to mention the subsequent blackboard diagram; and my own
intuition (or perhaps lack thereof) is such that discussing "the projective
absolute" and "metrical relations in elliptical, parabolic or hyperbolic
geometries" is not (at least so far) helping me understand your/Peirce's
point "about the kind of hypothesis that is needed to make sense of ... the
growth of order in the cosmos."  Also, I still believe that Peirce's "table
of contents" in "A Neglected Argument" was for a future book that he had
not yet written and never did manage to write, rather than anything
specific in his previous material such as RLT.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Mon, Nov 14, 2016 at 3:45 PM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S, Gary R, Edwina, John S, List,
>
> If others are interested, I'd like to continue the discussion of the last
> lecture on continuity in RLT. The goal, I took it, was to draw on it for
> the sake of filling in some the details in the "table of contents" for a
> larger set of inquiries that he sketched in "A Neglected Argument."
>
> My proposal is to march through more of the mathematical examples he
> offers in the hopes of getting more clarity about the logical conception of
> continuity that he articulates. Then, the aim is to work up to the example
> of the lines on the blackboard and the way that he uses that example to
> frame some hypothesis in cosmological metaphysics.
>
> Given the fact that my post on Desargues 6-point theorem did not generate
> much in the way of comments or questions, I am concerned that I overdid it
> and managed to smother some of the interest in the questions--both
> interpretative and philosophical--that we were considering. As such, I'm
> asking for feedback to make see if continued discussion of the mathematical
> examples is welcome.
>
> Late last week, I thought of a way to illustrate Peirce's larger point
> about how the 6 point theorem is connected to the larger idea that Cayley
> and Klein make about the character of the projective absolute and how it
> provides the basis of any system of metrical relations in elliptical,
> parabolic or hyperbolic geometries. The illustration helps to see, in a
> more intuitive way, the point Peirce seems to be making about the kind of
> hypothesis that is needed to make sense of the possibility of progress with
> respect to the growth of our understanding or, more generally, with the
> growth of order in the cosmos.
>
> So, let me ask if there are any takers for continuing the discussion of
> RLT along these lines?
>
> --Jeff
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
>

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Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jerry LR Chandler]

List, Jeffrey, John S.

First, I would support further discussion along these lines.

Of course, I would think that a degree of balance should be introduced into the 
nature of premises.  There are deep mathematical issues involved in this rather 
casual conversations.

With this regard, John S’s slides of 1 August 2015 provide a counter point. 
(see slides 4, 5, and 6.)

Cheers

Jerry


> On Nov 14, 2016, at 3:45 PM, Jeffrey Brian Downard  
> wrote:
> 
> Jon S, Gary R, Edwina, John S, List,
> 
> If others are interested, I'd like to continue the discussion of the last 
> lecture on continuity in RLT. The goal, I took it, was to draw on it for the 
> sake of filling in some the details in the "table of contents" for a larger 
> set of inquiries that he sketched in "A Neglected Argument."
> 
> My proposal is to march through more of the mathematical examples he offers 
> in the hopes of getting more clarity about the logical conception of 
> continuity that he articulates. Then, the aim is to work up to the example of 
> the lines on the blackboard and the way that he uses that example to frame 
> some hypothesis in cosmological metaphysics.
> 
> Given the fact that my post on Desargues 6-point theorem did not generate 
> much in the way of comments or questions, I am concerned that I overdid it 
> and managed to smother some of the interest in the questions--both 
> interpretative and philosophical--that we were considering. As such, I'm 
> asking for feedback to make see if continued discussion of the mathematical 
> examples is welcome.
> 
> Late last week, I thought of a way to illustrate Peirce's larger point about 
> how the 6 point theorem is connected to the larger idea that Cayley and Klein 
> make about the character of the projective absolute and how it provides the 
> basis of any system of metrical relations in elliptical, parabolic or 
> hyperbolic geometries. The illustration helps to see, in a more intuitive 
> way, the point Peirce seems to be making about the kind of hypothesis that is 
> needed to make sense of the possibility of progress with respect to the 
> growth of our understanding or, more generally, with the growth of order in 
> the cosmos.
> 
> So, let me ask if there are any takers for continuing the discussion of RLT 
> along these lines?
> 
> --Jeff
> 
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> 
> 
> From: Jon Alan Schmidt 
> Sent: Tuesday, November 8, 2016 10:55 AM
> To: Jeffrey Brian Downard
> Cc: peirce-l@list.iupui.edu
> Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
> Metaphysics and Nothing (was Peirce's Cosmology))
>  
> Jeff, List:
> 
> Did Peirce retain the notion of "the absolute" as he developed his conception 
> of a continuum in the last RLT lecture?
> 
> CSP:  The other rule that if A is r to B and B is r to C then A is r to C 
> leads to no contradiction, but it does lead to this, that there are two 
> possible exceptional individuals[,] one that is r to everything else and 
> another to which everything else is r.  This is like a limited line, where 
> every point is r that is, is to the right of every other or else that other 
> is to the right of it.  The generality of the case is destroyed by those two 
> points of discontinuity,--the extremities.  Thus, we see that no perfect 
> continuum can be defined by a dyadic relation.  But if we take instead the 
> triadic relation, and say A is r to B for C, say to fix our idea that 
> proceeding from A in a particular way, say to the right, you reach B before 
> C, it is quite evident, that a continuum will result like a self-returning 
> line with no discontinuity whatever. (RLT 250) 
> 
> Yesterday I came across an interesting paper by Nicholas Guardiano, "The 
> Categorial Logic of Peirce's Metaphysical Cosmogony" (The Pluralist 10:3, 
> Fall 2015, 313-334; early version at 
> http://www.american-philosophy.org/saap2014/openconf/modules/request.php?module=oc_program&action=view.php&id=28
>  
> <http://www.american-philosophy.org/saap2014/openconf/modules/request.php?module=oc_program&action=view.php&id=28>).
>   He describes Peirce's theory about the origin and development of the 
> universe from the standpoint of each Category, always in terms of three 
> stages.
> Secondness - chaos (1ns), reaction (2ns), regularity (3ns).
> Thirdness - spontaneity/chance/freedom (1ns), evolutionary process (3ns), 
> fixed end (2ns).
> Firstness - continuum (3ns), Platonic world of qualities (1ns), brute 
> existence (2ns).
> Guardiano thus presents the three most common in

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff:

Your comments about mathematics and phenomenology are well-taken.  I am
reminded of this remark by Peirce, which Guardiano omitted when quoting
what immediately followed.

CSP:  What is reality?  Perhaps there isn't any such thing at all.  As I
have repeatedly insisted, it is but a retroduction, a working hypothesis
which we try, our one desperate forlorn hope of knowing anything.  Again it
may be, and it would seem very bold to hope for anything, that the
hypothesis of reality though it answers pretty well, does not perfectly
correspond to what is.  But if there is any reality, then, so far as there
is any reality ... (NEM 4:343, RLT 161; 1898)


On the other hand, this thread is an offshoot from one about Metaphysics
and Nothing, which itself was an offshoot from one about Peirce's
Cosmology; so it seems to me that mathematics and phenomenology are
pertinent only to the extent that they inform our discussion of such
topics.  Hence if my questions about the "absolute" are not "on point,"
then it is unclear to me what the point actually is.

JD:  What is the advantage of taking different perspectives--where we are
highlighting what is predominately of the character of firstness,
secondness  or thirdness--when we seek to "comprehend the Reality of
Phenomena?"


Guardiano argues that the Categories have a fundamental role in grounding *any
*inquiry, and also sees his approach as "illuminating the rational or
logical coherence" of Peirce's cosmogony.  However, I am less interested in
the fact that he assigns each analysis to the "perspective" of one Category
than in the resulting descriptions, which concisely summarize the three
most common interpretations in terms of categorial sequence--1ns>2ns>3ns
vs. 1ns>3ns>2ns vs. 3ns>1ns>2ns.  In Gary R.'s vectorial terminology, this
is order vs. process vs. representation.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Tue, Nov 8, 2016 at 5:38 PM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Hello,
>
> Is Peirce a three category realist? Let me point out a few things that I
> take to be obvious. For the purposes of inquiry in both pure mathematics
> and phenomenology, Peirce was a no-category realist. For methodological
> reasons, Peirce holds that we should not import those kinds of
> metaphysical assertions about what is and isn't real into the way we go
> about answering questions in pure mathematics and in phenomenology.  On
> this point, I am in agreement with Peirce.
>
> When we get to the normative sciences, things get more complicated. What
> kinds of assertions can be warranted within the context of inquiry in the
> pure sciences of aesthetics, ethics and semiotics about the general
> features of what is and isn't really found in nature?
>
> The answer, I think, is rather complicated. In short, he is working to
> progressively to richer conceptions concerning what is real--as those are
> needed to justify claims about what kind of ideal is most attractive for
> its own sake, what kind of conduct is right, and what forms of inference are
> valid and modes of inquiry are best suited for different kinds of
> questions. While his position develops over time, most of the assertions
> about what is real that are made in the normative sciences are warranted
> as something akin to regulative principles that guide inquiry.
>
> In the context of metaphysics, is Peirce a three category realist? The
> answer, of course, is yes. Max Fisch is making a point that he takes to be
> obvious. Having said that, the questions of where each of the categories
> might really be found in nature and what shapes the categories might take
> when treated as metaphysical conceptions is something that has no easy
> answer--not even as a summary of the conclusions that he draws. Within the
> context of metaphysics, which of the assertions concerning the nature of
> what is are still "really" being made as something akin to a regulative
> principle and which general claims about what is real are being warranted
> on the bases of observational evidence that are sufficient to say that we
> can reasonably believe or know that it is literally true? In many cases,
> Peirce is arriving at his conclusions by showing that they are the best
> hypotheses--all things considered. In some cases, certain hypotheses can be
> rejected, but in most, what we are able to do is to delineate a space of
> plausible hypotheses--and then we can dicker over which are best within
> that space of possible explanations.
>
> Peirce's view, I think, is nicely summarized in the following passage:
>
> 121. Philosophy has three grand divisions. The first is Phenomenology,
> which simply contemplates the Universal Phenomenon and discerns its
> ubiquitous elements, Firstness, Secondness, and Thirdness, together
> perhaps with other series of categories.  The second grand divis

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Edwina, List:

ET:  So- at the moment, I don't see much difference, apart from semantics,
in the perspectives of Firstness and Secondness. Both 'begin' with
Firstness ...


On the contrary--according to Guardiano, the Firstness perspective does NOT
begin with Firstness, it begins with Thirdness.

NG:  Finally, there is the analysis from the perspective of the category of
firstness ... From this point of view, the essential feature that appears
to characterize the origin of the universe is its status as a continuum,
and this means that its character-defining category is thirdness ... the
continuum at the origin of the universe is special in that it is the master
continuum containing all possible and existing continua. That feature is
expressed in Peirce’s analogy of the blackboard. The blackboard when blank
describes a spatial continuum open to all kinds of possible figures that
may be drawn ... Peirce’s description of the origin as “pure zero” and
“nothing” is intended only in the sense that it consists in "no individual
thing, no compulsion, outward nor inward, no law. [Nevertheless, i]t is the
germinal nothing, in which the whole universe is involved or foreshadowed"
(CP 6.217). Hardly nothing in the common sense, then, it rather is possibly
*everything*, “the whole universe” in potential.


Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Tue, Nov 8, 2016 at 2:10 PM, Edwina Taborsky  wrote:

> Yes, an interesting article and must be read thoroughly. I'm not sure
> about an analysis of cosmological reality from the perspective of a
> Category...I don't know how one does such a thing!
>
> A few excerpts from the article that I so far find interesting.
>
> 1) In Max Fisch’s words, Peirce is nothing other than a “three-category
> realist”; he believes in “the triune Reality” whereby the categories are
> inherent, ubiquitous, and tripresent elements of the universe.[1] This is
> to say that the categories are more than the most general conceptual
> structures of experience and thought—as Kant’s categories are for him. They
> are that *and *the most general ontological or metaphysical structures of
> the universe.
>
> EDWINA: Exactly - my reading of Peirce is that one cannot privilege any
> category; cannot say that any are 'a priori' or operate alone; Peirce is a
> three -category realist.
>
>
>
> 2) “so far as there is any reality, what that reality consists in is this:
> that there is in the being of things something which corresponds to the
> process of reasoning, that the world *lives*, and *moves*, and *HAS ITS
> BEING*, in a logic of events. We all think of nature as syllogizing” (RLT
> 161
>
>
>
> EDWINA: And again, exactly - the world LIVES and MOVES...and nature does
> indeed 'syllogize'i.e., operate within the triadic semiosic Sign.  And this
> is also where one finds that commonality with George Spencer Brown, who
> also saw the world from the perspective of the active individual
> agent..rather than from a metaphysical analytic view.
>
>
>
> 3) In other words, they “are not merely mental in origin. They *are * part
> of the structure of our minds, but they are also part of the structure of
> reality itself” (ibid., 44). Thus, the categories have “ontological or
> cosmological import…. [in that they] designate, among other things, the
> modes of being and also the modes of the coming to be of the cosmos
> itself…. [They] designate both the irreducible modes of being and the
> ubiquitous traits of nature” (ibid., 43).
>
> [1] See EP1 121 and EP2 335.
>
>
>
> EDWINA: Again - the categories are NOT mental or theoretical constructs.
> They have ontological being...and do not merely 'designate' but FORM the
> 'modes of being'.
>
>
>
> 4) the ultimate origin of the universe that consists in a master continuum
> of the most abstract kind of potentiality. It is “the utter vagueness of
> completely undetermined and dimensionless potentiality,” or a vague
> potentiality of “everything in general but of nothing in particular.”[1]
>
>
>
> , it also is described as “pure zero” or “the germinal nothing, in which
> the whole universe is involved or foreshadowed. As such, it is absolutely
> undefined and unlimited possibility—boundless possibility. There is no
> compulsion and no law. It is boundless freedom.”[1]
>
> --
>
> [1] CP 6.217.
>
>
>
> EDWINA: Again, we can argue about pre and post 'Big Bang' [as well as
> whether there was ever such an event] - but the point is, that there was,
> as I read it,  a pre-categorical 'situation'. And afterwards, the three
> categories developed as matter/mind developed.
>
>
>
> 5)The first stage, he says, is like a blank blackboard, the forms of the
> second stage like individual lines drawn on the blackboard, and the third
> stage like the overlapping of lines that jointly create the curved shape of
> an oval.
>
>
>
> E

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Clark Goble]

> On Nov 8, 2016, at 10:55 AM, Jon Alan Schmidt  
> wrote:
> 
> Yesterday I came across an interesting paper by Nicholas Guardiano, "The 
> Categorial Logic of Peirce's Metaphysical Cosmogony" (The Pluralist 10:3, 
> Fall 2015, 313-334; early version at 
> http://www.american-philosophy.org/saap2014/openconf/modules/request.php?module=oc_program&action=view.php&id=28
>  
> ).
>   He describes Peirce's theory about the origin and development of the 
> universe from the standpoint of each Category, always in terms of three 
> stages.
> Secondness - chaos (1ns), reaction (2ns), regularity (3ns).
> Thirdness - spontaneity/chance/freedom (1ns), evolutionary process (3ns), 
> fixed end (2ns).
> Firstness - continuum (3ns), Platonic world of qualities (1ns), brute 
> existence (2ns).
> Guardiano thus presents the three most common interpretations, and does so in 
> this particular order.  I offer three observations about this, which may or 
> may not be significant.
> The Category that provides the point of view for the analysis always 
> corresponds to the second stage.
> The stage associated with Firstness always precedes the one associated with 
> Secondness.
> The stage associated with Thirdness moves from third to second to first in 
> the sequence.
> Gary R. and I have been advocating the Firstness perspective, while my 
> understanding is that Edwina primarily adopts the Secondness perspective.  
> The Thirdness perspective involves the hyperbolic absolute with two distinct 
> points, as Jeff described below.

That’s fascinating. I’ll definitely read that paper before commenting further. 
I’d not considered the idea that the types of analysis are from the perspective 
of particular categories.



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Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Edwina Taborsky]

Jeff, list:

Yes, I think that Peirce's rejection of Hegel's 'Absolute One' provides us with 
a richer, and more accurate outline of reality as complex - and I agree that  
Thirdness is relative. 

That relative nature refers to the operative nature of Thirdness, while the 
operative nature of both Firstness and Secondness is their capacity for 
non-relational interaction. Firstness is just 'absolute' as itself, while 
Secondness is a brute action that relies on no mediation.

 I am sure you are familiar with Spencer Brown's Laws of Form; his concept that 
'a universe comes into being when a space is severed or taken apart' 1972,v. 
And, Spencer Brown's four classes of statements: true, false, meaningless and 
imaginary. I wonder how these relate to the Categories, both genuine and 
degenerate and also, to theories of truth and logic. As Spencer-Brown writes, 
'If the weakness of present-day science is that it centres around existence, 
the weakness of present-day logic is that it centres around truth" [101].

That is "A theorem is no more proved by logic and computation than a sonnet is 
written by grammar and rhetoric" 102.

And, "we cannot escape the fact that the world we know is constructed in order 
[and thus in such as way as to be able] to see itselfBut in order to do so, 
evidently it must first cut itself up into at least one state which sees, and 
at least one other state which is seen. In this severed and mutilated 
condition, whatever it sees is only partially itself" 105. 

I don't mean to turn the thread to Spencer Brown, but his work [which does 
reference Peirce] seems to align with some of Peirce's focus on the metaphysics 
of the world. The paragraph above, to me, recalls 1.412, that 'explosion' of 
matter at the beginning of the universe; and also, the lines on the blackboard.

Edwina


  - Original Message - 
  From: Jeffrey Brian Downard 
  To: Edwina Taborsky ; peirce-l@list.iupui.edu 
  Sent: Monday, November 07, 2016 1:04 PM
  Subject: RE: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
Metaphysics and Nothing (was Peirce's Cosmology))


  Edwina, Jon S, Gary R, List

  Let's take up Peirce's rejoinder to Hegel about the character of the 
absolute.  He says: "Hegel is possessed with the idea that the Absolute is One. 
Three absolutes he would regard as a ludicrous contradiction in adjecto." (CP, 
5.91)

  Compare that remark about the three absolutes to what he says about two 
absolutes in "A Guess at the Riddle": 

  According to the mathematicians, when we measure along a line, were our 
yardstick replaced by a yard marked off on an infinitely long rigid bar, then 
in all the shiftings of it which we make for the purpose of applying it to 
successive portions of the line to be measured, two points on that bar would 
remain fixed and unmoved. To that pair of points, the mathematicians accord the 
title of the absolute; they are the points that are at an infinite distance one 
way and the other as measured by that yard. These points are either really 
distinct, coincident, or imaginary (in which case there is but a finite 
distance completely round the line), according to the relation of the mode of 
measurement to the nature of the line upon which the measurement is made. These 
two points are the absolute first and the absolute last or second, while every 
measurable point on the line is of the nature of a third. We have seen that the 
conception of the absolute first eludes every attempt to grasp it; and so in 
another sense does that of the absolute second; but there is no absolute third, 
for the third is of its own nature relative, and this is what we are always 
thinking, even when we aim at the first or second. The starting-point of the 
universe, God the Creator, is the Absolute First; the terminus of the universe, 
God completely revealed, is the Absolute Second; every state of the universe at 
a measurable point of time is the third. If you think the measurable is all 
there is, and deny it any definite tendency whence or whither, then you are 
considering the pair of points that makes the absolute to be imaginary and are 
an Epicurean. If you hold that there is a definite drift to the course of 
nature as a whole, but yet believe its absolute end is nothing but the Nirvana 
from which it set out, you make the two points of the absolute to be 
coincident, and are a pessimist. But if your creed is that the whole universe 
is approaching in the infinitely distant future a state having a general 
character different from that toward which we look back in the infinitely 
distant past, you make the absolute to consist in two distinct real points and 
are an evolutionist. This is one of the matters concerning which a man can only 
learn from his own reflections, but I believe that if my suggestions are 
followed out,

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

*math*., a locus whose projective relation to any two elements may be
> considered as constituting the metrical relation of these elements to one
> another. All measurement is made by successive super positions of a unit
> upon parts of the quantity to be measured. Now, in all shifting of the
> standard of measurement, if this be supposed to be rigidly connected with
> an unlimited continuum superposed upon that in which lies the measured
> quantity, there will be a certain locus which will always continue unmoved,
> and to which, therefore, the scale of measurement can never be applied.
> This is the absolute. In order to establish a system of measurement along a
> line, we first put a scale of numbers on the line in such a manner that to
> every point of the line corresponds one number, and to every number one
> point. If then we take any second scale of numbers related in this manner
> to the points of the line, to any number, *x*, of the first scale, will
> correspond just one number, *y*, of the second. If this correspondence
> extends to imaginary points, *x *and *y *will be connected by an equation
> linear in *x *and linear in *y*, which may be written thus: *xy + ax + by
> + c = 0. *The scale will thus be shifted from *x = 0 *to *y = 0 *or *x =
> -c/a*. In this shifting, two points of the scale remain unmoved, namely,
> those which satisfy the equation *x2 + (a + b) x + c =0*. This pair of
> points, which may be really distinct, coincident, or imaginary, constitute
> the absolute. For a plane, the absolute is a curve of the second order and
> second class. For three-dimensional space it is a quadric surface. For the
> ordinary system of measurement in space, producing the Euclidean geometry,
> the absolute consists of two coincident planes joined along an imaginary
> circle, which circle is itself usually termed the *absolute*.
>
> Let's try to apply these mathematical conceptions of the absolute to the
> philosophical questions that we are raising about the metaphysical
> absolute. The first steps in such an inquiry, I would think, would be to
> see how the conceptions might apply to the phenomenological questions, and
> then to the questions that arise in the normative semiotic. Once that is
> done, we will be in a better position to take up the questions
> in metaphysics.
>
> So, how might these mathematical conceptions of the absolute be used to
> shed some like on the phenomenon that we seek to explain with respect to
> the origins of the homogeneities of connectedness that we see within each
> of the universes of experience, between any two of them, and between all
> three taken together?
>
> --Jeff
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> 
> From: Edwina Taborsky [tabor...@primus.ca]
> Sent: Monday, November 7, 2016 7:23 AM
> To: peirce-l@list.iupui.edu
> Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was
> Metaphysics and Nothing (was Peirce's Cosmology))
>
> Jeff, list:
>
> Peirce considers this situation, as I read it, in his continued
> examination of the categories, see 5.90-92.
>
> He imagines a dissnter with an attack on his views:
>
> "We fully admit that you have proved, until we begin to doubt it, that
> Secondness is not involved in Firstness nor Thirdness in Secondness and
> Firstness. But you have entirely failed to prove that Firstness, Secondness
> and Thirdness are independent ideas for the obvious reason that it is as
> plain as the nose on your face that the idea of a triple involved the idea
> of pairs, and the idea of a pair the idea of units. Consequently, Thirdness
> is the one and sole category. This is substantially the idea of Hegel and
> unquestionably it contains a truth.
>
> Not only does Thirdness suppose and involve the ideas of Secondness and
> Firstness, but never will it be possible to find any Secondness or
> Firstness in the phenomenon that is not accompanied by Thirdness".
>
> This is the argument of ' The Dissenter' - who follows Hegel in positing
> the primacy of the continuous order of Thirdness.  Then, Peirce himself
> writes:
>
> 5.91 "If the Hegelians confined thmselves to that position they would find
> a hearty friend in my doctrine. But they do not. Hegel is possessed with
> the idea that the Absolute is One. Three absolutes he would regard as a
> ludicrous contradiction in adjecto. ..
>
> Peirce continues on [I only have time to write part of this long
> paragraph]..."Thirdness it is true involves Secondness and Firstness, in a
> sense. That is to say, if you have the idea of Thirdness you must have had
> the i

RE: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jeffrey Brian Downard]

n equation linear in x and linear in y, which may be written 
thus: xy + ax + by + c = 0. The scale will thus be shifted from x = 0 to y = 0 
or x = -c/a. In this shifting, two points of the scale remain unmoved, namely, 
those which satisfy the equation x2 + (a + b) x + c =0. This pair of points, 
which may be really distinct, coincident, or imaginary, constitute the 
absolute. For a plane, the absolute is a curve of the second order and second 
class. For three-dimensional space it is a quadric surface. For the ordinary 
system of measurement in space, producing the Euclidean geometry, the absolute 
consists of two coincident planes joined along an imaginary circle, which 
circle is itself usually termed the absolute.

Let's try to apply these mathematical conceptions of the absolute to the 
philosophical questions that we are raising about the metaphysical absolute. 
The first steps in such an inquiry, I would think, would be to see how the 
conceptions might apply to the phenomenological questions, and then to the 
questions that arise in the normative semiotic. Once that is done, we will be 
in a better position to take up the questions in metaphysics.

So, how might these mathematical conceptions of the absolute be used to shed 
some like on the phenomenon that we seek to explain with respect to the origins 
of the homogeneities of connectedness that we see within each of the universes 
of experience, between any two of them, and between all three taken together?

--Jeff







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

From: Edwina Taborsky [tabor...@primus.ca]
Sent: Monday, November 7, 2016 7:23 AM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
Metaphysics and Nothing (was Peirce's Cosmology))

Jeff, list:

Peirce considers this situation, as I read it, in his continued examination of 
the categories, see 5.90-92.

He imagines a dissnter with an attack on his views:

"We fully admit that you have proved, until we begin to doubt it, that 
Secondness is not involved in Firstness nor Thirdness in Secondness and 
Firstness. But you have entirely failed to prove that Firstness, Secondness and 
Thirdness are independent ideas for the obvious reason that it is as plain as 
the nose on your face that the idea of a triple involved the idea of pairs, and 
the idea of a pair the idea of units. Consequently, Thirdness is the one and 
sole category. This is substantially the idea of Hegel and unquestionably it 
contains a truth.

Not only does Thirdness suppose and involve the ideas of Secondness and 
Firstness, but never will it be possible to find any Secondness or Firstness in 
the phenomenon that is not accompanied by Thirdness".

This is the argument of ' The Dissenter' - who follows Hegel in positing the 
primacy of the continuous order of Thirdness.  Then, Peirce himself writes:

5.91 "If the Hegelians confined thmselves to that position they would find a 
hearty friend in my doctrine. But they do not. Hegel is possessed with the idea 
that the Absolute is One. Three absolutes he would regard as a ludicrous 
contradiction in adjecto. ..

Peirce continues on [I only have time to write part of this long 
paragraph]..."Thirdness it is true involves Secondness and Firstness, in a 
sense. That is to say, if you have the idea of Thirdness you must have had the 
ideas of Secondness and Firstness to build upone. But waht is required for the 
idea of a genuine Thirdness is an independent solid Secondness and not a 
Secondness that is a mere corollary of an unfounded and inconceivable 
Thirdness; and a similar remark may be made in reference to Firstness."

5.92 "Let the Universe be an evolution of Pure Reason if you will. Yet if, 
while you are walking in the street reflecting upon how everything is the pure 
distillate of Reason, a man carrying a heavy pole suddenly pokes you in the 
small of the back, you maythink there is something in the Universe that Pure 
Reason fails to account for; .you will be perhaps disposed to think 
that Quality and Reaction have their independent standing in the Universe".

My reading of the above is that two independent random points, the stick and a 
man's back can have no ordered relation - other than an accidental, unordered 
one. In addition, the power of chance and spontaneity in generating relations 
and thus evolving the habits - and these include novel habits-  of Thirdness 
is, I think, a powerful force within the Peircean semiosis.

Edwina



On Sun, Nov 6, 2016 at 8:15 PM, Jeffrey Brian Downard 
mailto:jeffrey.down...@nau.edu>> wrote:
Jon S, List,

For the sake of clarity, let me point out that the interpretative hypothesis I 
have been exploring is quite limited. The claim is that, on its face, it 
appears that some dyadic relations are n

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Edwina Taborsky]

Jeff, list:

Peirce considers this situation, as I read it, in his continued examination of 
the categories, see 5.90-92.

He imagines a dissnter with an attack on his views:

"We fully admit that you have proved, until we begin to doubt it, that 
Secondness is not involved in Firstness nor Thirdness in Secondness and 
Firstness. But you have entirely failed to prove that Firstness, Secondness and 
Thirdness are independent ideas for the obvious reason that it is as plain as 
the nose on your face that the idea of a triple involved the idea of pairs, and 
the idea of a pair the idea of units. Consequently, Thirdness is the one and 
sole category. This is substantially the idea of Hegel and unquestionably it 
contains a truth.

Not only does Thirdness suppose and involve the ideas of Secondness and 
Firstness, but never will it be possible to find any Secondness or Firstness in 
the phenomenon that is not accompanied by Thirdness".

This is the argument of ' The Dissenter' - who follows Hegel in positing the 
primacy of the continuous order of Thirdness.  Then, Peirce himself writes:

5.91 "If the Hegelians confined thmselves to that position they would find a 
hearty friend in my doctrine. But they do not. Hegel is possessed with the idea 
that the Absolute is One. Three absolutes he would regard as a ludicrous 
contradiction in adjecto. ..

Peirce continues on [I only have time to write part of this long 
paragraph]..."Thirdness it is true involves Secondness and Firstness, in a 
sense. That is to say, if you have the idea of Thirdness you must have had the 
ideas of Secondness and Firstness to build upone. But waht is required for the 
idea of a genuine Thirdness is an independent solid Secondness and not a 
Secondness that is a mere corollary of an unfounded and inconceivable 
Thirdness; and a similar remark may be made in reference to Firstness."

5.92 "Let the Universe be an evolution of Pure Reason if you will. Yet if, 
while you are walking in the street reflecting upon how everything is the pure 
distillate of Reason, a man carrying a heavy pole suddenly pokes you in the 
small of the back, you maythink there is something in the Universe that Pure 
Reason fails to account for; .you will be perhaps disposed to think 
that Quality and Reaction have their independent standing in the Universe".

My reading of the above is that two independent random points, the stick and a 
man's back can have no ordered relation - other than an accidental, unordered 
one. In addition, the power of chance and spontaneity in generating relations 
and thus evolving the habits - and these include novel habits-  of Thirdness 
is, I think, a powerful force within the Peircean semiosis.

Edwina



  On Sun, Nov 6, 2016 at 8:15 PM, Jeffrey Brian Downard 
 wrote:

Jon S, List,

For the sake of clarity, let me point out that the interpretative 
hypothesis I have been exploring is quite limited. The claim is that, on its 
face, it appears that some dyadic relations are not, in themselves, ordered. 
This is brought out in those that are classified as accidental and unordered 
(both materially and formally). I was extending the claim to degenerate triadic 
relations based on the general tenor of his remarks about such degenerate 
relations in "The Logic of Mathematics, an attempt..."

The points you are making about different sorts of collections and other 
kinds of groupings (including those that are based on some shared negative 
character) all seem to involve genuine triadic relations that apply to the 
collection as a whole. As far as I can tell, all such genuine triads 
essentially involve ordered relations.

So, to make the point clearer, a set consisting of members that are two 
distinct dots on a page is ordered if there is some general characteristic that 
applies to the set as a whole. Having said that, it does not follow that every 
sort of degenerate dyadic relation or degenerate triadic relation that holds 
between two dots is an ordered relation. The general property that makes the 
set the kind of thing that it is necessarily involves a genuine triadic 
relation. That is what is involved in all such generalities.

You seem to be claiming that every relation, regardless of how degenerate 
it may be, must involve some sort of order--otherwise the relation would not be 
intelligible. If this is your claim, you may be right, but I'm trying to 
explore a different line of interpretation.

--Jeff

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


--



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Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

Thanks for the clarification.  My understanding of Peirce's view is not
that order evolved from disorder, but that order--or rather, "super-order,"
the generalization of order and uniformity--is primordial.  "For all Being
involves some kind of super-order" (CP 6.490).

Regards,

Jon

On Mon, Nov 7, 2016 at 12:36 AM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S, List,
>
> If the aim is to explain how order might have evolved from states that
> were relatively disordered, it might help to get clearer about the
> different kinds of relations that are indicative of order and disorder. For
> the purposes of phenomenology, we seek to analyze those observations that
> seem to evince signs of different sorts of order and disorder and to
> correct for different sorts of observational errors. Analyzing the
> different classes of relations that might be part of our different
> observations will aid in this effort.
>
> --Jeff
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> 
> From: Jon Alan Schmidt [jonalanschm...@gmail.com]
> Sent: Sunday, November 6, 2016 8:43 PM
> To: Jeffrey Brian Downard; peirce-l@list.iupui.edu
> Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was
> Metaphysics and Nothing (was Peirce's Cosmology))
>
> Jeff, List:
>
> I thought that our objective in this thread was--at least eventually--to
> determine whether and how Peirce's mathematical and phenomenological
> discussions in the last RLT lecture might shed light on the subsequent
> metaphysical discussion (including the blackboard diagram), and especially
> the concept of "super-order" that he introduced in CP 6.490, or
> vice-versa.  Did I misunderstand?  So far, I am not seeing how your
> examination of ordered vs. unordered dyadic relations fits into that train
> of thought.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt<http://www.
> LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt p://twitter.com/JonAlanSchmidt>
>
> On Sun, Nov 6, 2016 at 8:15 PM, Jeffrey Brian Downard <
> jeffrey.down...@nau.edu<mailto:jeffrey.down...@nau.edu>> wrote:
> Jon S, List,
>
> For the sake of clarity, let me point out that the interpretative
> hypothesis I have been exploring is quite limited. The claim is that, on
> its face, it appears that some dyadic relations are not, in themselves,
> ordered. This is brought out in those that are classified as accidental and
> unordered (both materially and formally). I was extending the claim to
> degenerate triadic relations based on the general tenor of his remarks
> about such degenerate relations in "The Logic of Mathematics, an attempt..."
>
> The points you are making about different sorts of collections and other
> kinds of groupings (including those that are based on some shared negative
> character) all seem to involve genuine triadic relations that apply to the
> collection as a whole. As far as I can tell, all such genuine triads
> essentially involve ordered relations.
>
> So, to make the point clearer, a set consisting of members that are two
> distinct dots on a page is ordered if there is some general characteristic
> that applies to the set as a whole. Having said that, it does not follow
> that every sort of degenerate dyadic relation or degenerate triadic
> relation that holds between two dots is an ordered relation. The general
> property that makes the set the kind of thing that it is necessarily
> involves a genuine triadic relation. That is what is involved in all such
> generalities.
>
> You seem to be claiming that every relation, regardless of how degenerate
> it may be, must involve some sort of order--otherwise the relation would
> not be intelligible. If this is your claim, you may be right, but I'm
> trying to explore a different line of interpretation.
>
> --Jeff
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354

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Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

I thought that our objective in this thread was--at least eventually--to
determine whether and how Peirce's mathematical and phenomenological
discussions in the last RLT lecture might shed light on the subsequent
metaphysical discussion (including the blackboard diagram), and especially
the concept of "super-order" that he introduced in CP 6.490, or
vice-versa.  Did I misunderstand?  So far, I am not seeing how your
examination of ordered vs. unordered dyadic relations fits into that train
of thought.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sun, Nov 6, 2016 at 8:15 PM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S, List,
>
> For the sake of clarity, let me point out that the interpretative
> hypothesis I have been exploring is quite limited. The claim is that, on
> its face, it appears that some dyadic relations are not, in themselves,
> ordered. This is brought out in those that are classified as accidental and
> unordered (both materially and formally). I was extending the claim to
> degenerate triadic relations based on the general tenor of his remarks
> about such degenerate relations in "The Logic of Mathematics, an attempt..."
>
> The points you are making about different sorts of collections and other
> kinds of groupings (including those that are based on some shared negative
> character) all seem to involve genuine triadic relations that apply to the
> collection as a whole. As far as I can tell, all such genuine triads
> essentially involve ordered relations.
>
> So, to make the point clearer, a set consisting of members that are two
> distinct dots on a page is ordered if there is some general characteristic
> that applies to the set as a whole. Having said that, it does not follow
> that every sort of degenerate dyadic relation or degenerate triadic
> relation that holds between two dots is an ordered relation. The general
> property that makes the set the kind of thing that it is necessarily
> involves a genuine triadic relation. That is what is involved in all such
> generalities.
>
> You seem to be claiming that every relation, regardless of how degenerate
> it may be, must involve some sort of order--otherwise the relation would
> not be intelligible. If this is your claim, you may be right, but I'm
> trying to explore a different line of interpretation.
>
> --Jeff
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354

-
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L 
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Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jerry Rhee]

Jon, list:

Thank you for that.

I dare you all to think about this conversation NOT in context of CP 5.189.

one two three... C A B...
icon index symbol... Firstness Secondness Thirdness... esthetics ethics
logic
spiritedness desire reason... name definition essence... Father Son
Spirit...
abduction deduction induction...

Best,
Jerry R


On Sun, Nov 6, 2016 at 2:24 PM, Jon Alan Schmidt 
wrote:

> Jeff, List:
>
> At first, I was not sure how helpful CP 6.395&397 could be, since they are
> from an article published in 1878, 20 years before RLT and 30 years before
> "A Neglected Argument."  Leaving aside that concern, I read through the
> subsequent text and came to wonder if the "general characteristic of the
> universe" that Peirce said in CP 6.397 "would be of such singular
> assistance to us in all our future reasoning that it would deserve a place
> almost at the head of the principles of logic" is what he described a few
> paragraphs later.
>
> CSP:  ... while a certain amount of order exists in the world, it would
> seem that the world is not so orderly as it might be, and, for instance,
> not so much so as a world of pure chance would be. But we can never get to
> the bottom of this question until we take account of a highly-important
> logical principle which I now proceed to enounce. This principle is that
> any plurality or lot of objects whatever have some character in common (no
> matter how insignificant) which is peculiar to them and not shared by
> anything else. The word "character" here is taken in such a sense as to
> include negative characters ... (CP 6.401-402; 1878)
>
>
> He then proceeded to show that "any two things, *A* and *B*, have in
> common" the character of "un-*A*-*B*-lessness," and concluded, "It is
> obvious that what has thus been shown true of two things is *mutatis
> mutandis*, true of any number of things."  It seems to me that having
> something in common is a form of similarity; i.e., it entails a *relation* 
> between
> them.  Since any two (or more) objects have some character in common, it is
> also the case that any two (or more) objects have a relation between
> them--including two random spots on a page--and thus are intelligible, and
> thus manifest what Peirce (much later) called super-order.
>
> This is my current hypothesis about Peirce's position on "What sort of a
> conception we ought to have of the universe, how to think of the
> *ensemble* of things," especially when we translate it into the notion of
> continuity.  What you noticed in italics on page 259 of RLT is telling, I
> think.
>
> CSP:  We can hardly but suppose that those sense-qualities that we now
> experience ... are but the relics of an ancient ruined continuum of
> qualities, like a few columns standing here and there in testimony that
> here some old-world forum with its basilica and temples had once made a
> magnificent *ensemble*. (RLT:258-259)
>
>
> The ensemble corresponds to the original, most general continuum of *potential
> *qualities, out of which are determined the individual sense-qualities
> that *actually *occur--like the discrete columns that remain from the
> ancient (continuous) forum.
>
> Regards,
>
> Jon
>
> On Sun, Nov 6, 2016 at 8:59 AM, Jon Alan Schmidt  > wrote:
>
>> Jeff, List:
>>
>> I will try to take a closer look at this later.
>>
>> Thanks,
>>
>> Jon Alan Schmidt - Olathe, Kansas, USA
>> Professional Engineer, Amateur Philosopher, Lutheran Layman
>> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>>
>> On Sun, Nov 6, 2016 at 3:36 AM, Jeffrey Brian Downard <
>> jeffrey.down...@nau.edu> wrote:
>>
>>> Jon S, Gary R, List,
>>>
>>> Given our interest in providing a clearer meaning for the conceptions of
>>> order and Super-order, I think that these passages might be helpful.
>>>
>>> Any proposition whatever concerning the order of Nature must touch more
>>> or less upon religion. In our day, belief, even in these matters, depends
>>> more and more upon the observation of facts. If a remarkable and universal
>>> orderliness be found in the universe, there must be some cause for this
>>> regularity, and science has to consider what hypotheses might account for
>>> the phenomenon. One way of accounting for it, certainly, would be to
>>> suppose that the world is ordered by a superior power. But if there is
>>> nothing in the universal subjection of phenomena to laws, nor in the
>>> character of those laws themselves (as being benevolent, beautiful,
>>> economical, etc.), which goes to prove the existence of a governor of the
>>> universe, it is hardly to be anticipated that any other sort of evidence
>>> will be found to weigh very much with minds emancipated from the tyranny of
>>> tradition. (CP 6.395)
>>>
>>> And then, two paragraphs later:
>>>
>>> If we could find out any general characteristic of the universe, any
>>> mannerism in the ways of Nature, any law everywhere applicable and
>>> universally valid, such a discovery would be of such singul

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

At first, I was not sure how helpful CP 6.395&397 could be, since they are
from an article published in 1878, 20 years before RLT and 30 years before
"A Neglected Argument."  Leaving aside that concern, I read through the
subsequent text and came to wonder if the "general characteristic of the
universe" that Peirce said in CP 6.397 "would be of such singular
assistance to us in all our future reasoning that it would deserve a place
almost at the head of the principles of logic" is what he described a few
paragraphs later.

CSP:  ... while a certain amount of order exists in the world, it would
seem that the world is not so orderly as it might be, and, for instance,
not so much so as a world of pure chance would be. But we can never get to
the bottom of this question until we take account of a highly-important
logical principle which I now proceed to enounce. This principle is that
any plurality or lot of objects whatever have some character in common (no
matter how insignificant) which is peculiar to them and not shared by
anything else. The word "character" here is taken in such a sense as to
include negative characters ... (CP 6.401-402; 1878)


He then proceeded to show that "any two things, *A* and *B*, have in
common" the character of "un-*A*-*B*-lessness," and concluded, "It is
obvious that what has thus been shown true of two things is *mutatis
mutandis*, true of any number of things."  It seems to me that having
something in common is a form of similarity; i.e., it entails a
*relation* between
them.  Since any two (or more) objects have some character in common, it is
also the case that any two (or more) objects have a relation between
them--including two random spots on a page--and thus are intelligible, and
thus manifest what Peirce (much later) called super-order.

This is my current hypothesis about Peirce's position on "What sort of a
conception we ought to have of the universe, how to think of the *ensemble* of
things," especially when we translate it into the notion of continuity.
What you noticed in italics on page 259 of RLT is telling, I think.

CSP:  We can hardly but suppose that those sense-qualities that we now
experience ... are but the relics of an ancient ruined continuum of
qualities, like a few columns standing here and there in testimony that
here some old-world forum with its basilica and temples had once made a
magnificent *ensemble*. (RLT:258-259)


The ensemble corresponds to the original, most general continuum of *potential
*qualities, out of which are determined the individual sense-qualities
that *actually
*occur--like the discrete columns that remain from the ancient (continuous)
forum.

Regards,

Jon

On Sun, Nov 6, 2016 at 8:59 AM, Jon Alan Schmidt 
wrote:

> Jeff, List:
>
> I will try to take a closer look at this later.
>
> Thanks,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Sun, Nov 6, 2016 at 3:36 AM, Jeffrey Brian Downard <
> jeffrey.down...@nau.edu> wrote:
>
>> Jon S, Gary R, List,
>>
>> Given our interest in providing a clearer meaning for the conceptions of
>> order and Super-order, I think that these passages might be helpful.
>>
>> Any proposition whatever concerning the order of Nature must touch more
>> or less upon religion. In our day, belief, even in these matters, depends
>> more and more upon the observation of facts. If a remarkable and universal
>> orderliness be found in the universe, there must be some cause for this
>> regularity, and science has to consider what hypotheses might account for
>> the phenomenon. One way of accounting for it, certainly, would be to
>> suppose that the world is ordered by a superior power. But if there is
>> nothing in the universal subjection of phenomena to laws, nor in the
>> character of those laws themselves (as being benevolent, beautiful,
>> economical, etc.), which goes to prove the existence of a governor of the
>> universe, it is hardly to be anticipated that any other sort of evidence
>> will be found to weigh very much with minds emancipated from the tyranny of
>> tradition. (CP 6.395)
>>
>> And then, two paragraphs later:
>>
>> If we could find out any general characteristic of the universe, any
>> mannerism in the ways of Nature, any law everywhere applicable and
>> universally valid, such a discovery would be of such singular assistance to
>> us in all our future reasoning that it would deserve a place almost at the
>> head of the principles of logic. On the other hand, if it can be shown that
>> there is nothing of the sort to find out, but that every discoverable
>> regularity is of limited range, this again will be of logical importance.
>> What sort of a conception we ought to have of the universe, how to think of
>> the ensemble of things, is a fundamental problem in the theory of
>> reasoning. (CP 6.397)
>>
>> So, how should we "think of the ensemble

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Just a quick follow-up comment.

CSP:  Consequently, whether in time or not, the three universes must
actually be absolutely necessary results of a state of utter nothingness.
We cannot ourselves conceive of such a state of nility; but we can easily
conceive that there should be a mind that could conceive it, since, after
all, no contradiction can be involved in mere non-existence. A state in
which there should be absolutely no super-order whatsoever would be such a
state of nility. For all Being involves some kind of super-order. (CP 6.490)


This expresses what I mean by order as intelligibility--"We cannot
ourselves conceive of ... a state in which there should be no super-order
whatsoever."  Hence nothing that we *can *conceive *lacks *order in this
sense, including two random spots on a page.

Regards,

Jon

On Sun, Nov 6, 2016 at 8:57 AM, Jon Alan Schmidt 
wrote:

> John C., List:
>
> This is the equivocation to which I have been trying to call attention.
> When Jeff talks about "ordered" and "unordered" relations, I take him to be
> referring to your notion of "intrinsic priority."  When I talk about order
> as a prerequisite for existence, I have something different in mind; more
> like order in the sense of organization or, perhaps better,
> intelligibility.  I am evidently not doing a good job of defining it so far.
>
> The goal of this discussion is to shed light on what Peirce meant by
> "super-order" in CP 6.490.  It seems clear to me that what he described
> there was not order as "intrinsic priority," but rather as that which I am
> trying to articulate, since he said that both order and uniformity are
> particular varieties of super-order.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Sun, Nov 6, 2016 at 12:04 AM, John Collier  wrote:
>
>> Jon, List,
>>
>>
>>
>> I think your examples of order are irrelevant to whether the spots have
>> order. Relative to the blackboard alone there is no left or right or up and
>> down. These come from external conditions (gravity, space ship
>> acceleration) and our viewpoint. In three dimensional space we can have
>> true left and right handedness, the difference not depending on the
>> observer (right hand screw compared to left hand screw) – there is an
>> innate asymmetry. But it is not clear this gives and order, which I would
>> understand as one having a natural priority. I don’t see a grounds for that
>> even in your examples.
>>
>>
>>
>> Can any two things have an order that depends on intrinsic priority?
>> Well, larger, smaller might. One and two I think have an intrinsic order,
>> even without the number system, because there are two independent ways to
>> map two onto one (but the opposite is also true, for mapping one onto two)
>> that provide a direction. In the mappings, the two relations must meet at
>> one, and diverge to two. Is this priority? I am inclined to think it is,
>> but I can’t find an argument at 6:30 A< after only one cup of coffee.
>> Perhaps two cups would help
>>
>>
>>
>> John Collier
>>
>> Emeritus Professor and Senior Research Associate
>>
>> Philosophy, University of KwaZulu-Natal
>>
>> http://web.ncf.ca/collier
>>
>

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Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jerry Rhee]

Jeffrey, Jon, list:

You quoted Peirce saying:
"Any proposition whatever concerning the order of Nature must touch more or
less upon religion."

What a strange statement.
Would you accept that if I had said it instead of Peirce?

Best,
Jerry R

On Sun, Nov 6, 2016 at 8:59 AM, Jon Alan Schmidt 
wrote:

> Jeff, List:
>
> I will try to take a closer look at this later.
>
> Thanks,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Sun, Nov 6, 2016 at 3:36 AM, Jeffrey Brian Downard <
> jeffrey.down...@nau.edu> wrote:
>
>> Jon S, Gary R, List,
>>
>> Given our interest in providing a clearer meaning for the conceptions of
>> order and Super-order, I think that these passages might be helpful.
>>
>> Any proposition whatever concerning the order of Nature must touch more
>> or less upon religion. In our day, belief, even in these matters, depends
>> more and more upon the observation of facts. If a remarkable and universal
>> orderliness be found in the universe, there must be some cause for this
>> regularity, and science has to consider what hypotheses might account for
>> the phenomenon. One way of accounting for it, certainly, would be to
>> suppose that the world is ordered by a superior power. But if there is
>> nothing in the universal subjection of phenomena to laws, nor in the
>> character of those laws themselves (as being benevolent, beautiful,
>> economical, etc.), which goes to prove the existence of a governor of the
>> universe, it is hardly to be anticipated that any other sort of evidence
>> will be found to weigh very much with minds emancipated from the tyranny of
>> tradition. (CP 6.395)
>>
>> And then, two paragraphs later:
>>
>> If we could find out any general characteristic of the universe, any
>> mannerism in the ways of Nature, any law everywhere applicable and
>> universally valid, such a discovery would be of such singular assistance to
>> us in all our future reasoning that it would deserve a place almost at the
>> head of the principles of logic. On the other hand, if it can be shown that
>> there is nothing of the sort to find out, but that every discoverable
>> regularity is of limited range, this again will be of logical importance.
>> What sort of a conception we ought to have of the universe, how to think of
>> the ensemble of things, is a fundamental problem in the theory of
>> reasoning. (CP 6.397)
>>
>> So, how should we "think of the ensemble of things"? Peirce provides the
>> definition for "ensemble" in the Century Dictionary. In the second
>> definition of the term, he characterizes the mathematical use of the
>> conception. In that definition, he makes a distinction between an ensemble
>> of the first genus, the second genus, and a tout ensemble. It is clear, I
>> think, that he is talking about a tout ensemble at 6.397. What is more, I
>> believe that he is talking about a tout ensemble in RLT, when he puts the
>> word in italics on page 259. How should we think of order and Super-order
>> as they are applied to each of these three sorts of ensembles?
>>
>> He explicitly uses "tout ensemble" in the following passage:
>>
>> The division of modes of Being needs, for our purposes, to be carried a
>> little further. A feeling so long as it remains a mere feeling is
>> absolutely simple. For if it had parts, those parts would be something
>> different from the whole, in the presence of which the being of the whole
>> would consist. Consequently, the being of the feeling would consist of
>> something beside itself, and in a relation. Thus it would violate the
>> definition of feeling as that mode of consciousness whose being lies
>> wholly in itself and not in any relation to anything else. In short, a
>> pure feeling can be nothing but the total unanalyzed impression of the
>> tout ensemble of consciousness. Such a mode of being may be called simple
>> monadic Being. CP 6.345
>>
>> Given the fact that Peirce draws this meaning of "tout ensemble" from
>> mathematics, I'm wondering if some examples from topology, projective
>> geometry or metrical geometry might help to clarify the differences between
>> a tout ensemble and ensembles of the first and second genus. Peirce offers
>> the example of Desargues' theory of Involution and its use in the 6 point
>> theorem on page 245. How does the conception of an ensemble apply in this
>> case where we are looking at the intersection of these rays as they are
>> projected from their origins at Q and R?
>>
>> The upshot of this example is made clearer when he says that Cayley
>> showed that the whole of geometrical metric is but a special problem in
>> geometrical optic. The point Peirce is making is that the development of
>> the conception of a projective absolute as a locus in space was central for
>> thinking about the character of projective space as a whole--i.e., as a
>> tout ensemble. Taken

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

I will try to take a closer look at this later.

Thanks,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sun, Nov 6, 2016 at 3:36 AM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S, Gary R, List,
>
> Given our interest in providing a clearer meaning for the conceptions of
> order and Super-order, I think that these passages might be helpful.
>
> Any proposition whatever concerning the order of Nature must touch more or
> less upon religion. In our day, belief, even in these matters, depends more
> and more upon the observation of facts. If a remarkable and universal
> orderliness be found in the universe, there must be some cause for this
> regularity, and science has to consider what hypotheses might account for
> the phenomenon. One way of accounting for it, certainly, would be to
> suppose that the world is ordered by a superior power. But if there is
> nothing in the universal subjection of phenomena to laws, nor in the
> character of those laws themselves (as being benevolent, beautiful,
> economical, etc.), which goes to prove the existence of a governor of the
> universe, it is hardly to be anticipated that any other sort of evidence
> will be found to weigh very much with minds emancipated from the tyranny of
> tradition. (CP 6.395)
>
> And then, two paragraphs later:
>
> If we could find out any general characteristic of the universe, any
> mannerism in the ways of Nature, any law everywhere applicable and
> universally valid, such a discovery would be of such singular assistance to
> us in all our future reasoning that it would deserve a place almost at the
> head of the principles of logic. On the other hand, if it can be shown that
> there is nothing of the sort to find out, but that every discoverable
> regularity is of limited range, this again will be of logical importance.
> What sort of a conception we ought to have of the universe, how to think of
> the ensemble of things, is a fundamental problem in the theory of
> reasoning. (CP 6.397)
>
> So, how should we "think of the ensemble of things"? Peirce provides the
> definition for "ensemble" in the Century Dictionary. In the second
> definition of the term, he characterizes the mathematical use of the
> conception. In that definition, he makes a distinction between an ensemble
> of the first genus, the second genus, and a tout ensemble. It is clear, I
> think, that he is talking about a tout ensemble at 6.397. What is more, I
> believe that he is talking about a tout ensemble in RLT, when he puts the
> word in italics on page 259. How should we think of order and Super-order
> as they are applied to each of these three sorts of ensembles?
>
> He explicitly uses "tout ensemble" in the following passage:
>
> The division of modes of Being needs, for our purposes, to be carried a
> little further. A feeling so long as it remains a mere feeling is
> absolutely simple. For if it had parts, those parts would be something
> different from the whole, in the presence of which the being of the whole
> would consist. Consequently, the being of the feeling would consist of
> something beside itself, and in a relation. Thus it would violate the
> definition of feeling as that mode of consciousness whose being lies
> wholly in itself and not in any relation to anything else. In short, a
> pure feeling can be nothing but the total unanalyzed impression of the
> tout ensemble of consciousness. Such a mode of being may be called simple
> monadic Being. CP 6.345
>
> Given the fact that Peirce draws this meaning of "tout ensemble" from
> mathematics, I'm wondering if some examples from topology, projective
> geometry or metrical geometry might help to clarify the differences between
> a tout ensemble and ensembles of the first and second genus. Peirce offers
> the example of Desargues' theory of Involution and its use in the 6 point
> theorem on page 245. How does the conception of an ensemble apply in this
> case where we are looking at the intersection of these rays as they are
> projected from their origins at Q and R?
>
> The upshot of this example is made clearer when he says that Cayley showed
> that the whole of geometrical metric is but a special problem in
> geometrical optic. The point Peirce is making is that the development of
> the conception of a projective absolute as a locus in space was central for
> thinking about the character of projective space as a whole--i.e., as a
> tout ensemble. Taken as a whole, the topological character of the space is
> something that we study by a process of decomposition. That is, we cut it
> up and see how the parts are connected. In this way, we come to see what
> Listing numbers are for the Chorisis, Cyclosis, Periphraxis and Immensity
> of such a space. The Periphraxis and Immensity, I take it, are especially
> important in understanding the char

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

John C., List:

This is the equivocation to which I have been trying to call attention.
When Jeff talks about "ordered" and "unordered" relations, I take him to be
referring to your notion of "intrinsic priority."  When I talk about order
as a prerequisite for existence, I have something different in mind; more
like order in the sense of organization or, perhaps better,
intelligibility.  I am evidently not doing a good job of defining it so far.

The goal of this discussion is to shed light on what Peirce meant by
"super-order" in CP 6.490.  It seems clear to me that what he described
there was not order as "intrinsic priority," but rather as that which I am
trying to articulate, since he said that both order and uniformity are
particular varieties of super-order.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sun, Nov 6, 2016 at 12:04 AM, John Collier  wrote:

> Jon, List,
>
>
>
> I think your examples of order are irrelevant to whether the spots have
> order. Relative to the blackboard alone there is no left or right or up and
> down. These come from external conditions (gravity, space ship
> acceleration) and our viewpoint. In three dimensional space we can have
> true left and right handedness, the difference not depending on the
> observer (right hand screw compared to left hand screw) – there is an
> innate asymmetry. But it is not clear this gives and order, which I would
> understand as one having a natural priority. I don’t see a grounds for that
> even in your examples.
>
>
>
> Can any two things have an order that depends on intrinsic priority? Well,
> larger, smaller might. One and two I think have an intrinsic order, even
> without the number system, because there are two independent ways to map
> two onto one (but the opposite is also true, for mapping one onto two) that
> provide a direction. In the mappings, the two relations must meet at one,
> and diverge to two. Is this priority? I am inclined to think it is, but I
> can’t find an argument at 6:30 A< after only one cup of coffee. Perhaps two
> cups would help
>
>
>
> John Collier
>
> Emeritus Professor and Senior Research Associate
>
> Philosophy, University of KwaZulu-Natal
>
> http://web.ncf.ca/collier
>

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Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

I guess my point is that the only reason why we can *isolate *relate,
correlate, and the relation between them is because there is an underlying
order; that is what enables us to *distinguish *these things as individuals
at all.

I deliberately avoided using the relation of brother as an example because
it entails other relations--one is older, both A and B are in the relation
of son to some C, etc.

Left and right do require an observer for orientation, but "next to" does
not; likewise being on the same surface and similarity.  These relations
are not "ordered" in the sense of priority or sequence, but they do require
an underlying order, or we would not be able to pick them out at all.

Regards,

Jon

On Sun, Nov 6, 2016 at 12:03 AM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon, List,
>
> From a logical point of view, when we study some relation--such as the
> dyadic relation of A is brother of B--we are isolating the relate, the
> correlate, and the relation between them. We understand that the things
> standing in the position of relate and correlate will typically have many
> internal relations among the parts that make them up. We also understand
> that the things in the position of relate and correlate may stand in a
> variety of different external relations to other things. But, when we
> analyze this particular relation of being a brother, we ignore those other
> relations. That is, we ignore such things as the fact that one might be
> taller than another or that one might be more social than the other.
>
> We do the same thing, I take it, when we are engaged in a phenomenological
> analysis of something that has been observed. Phenomenological analysis
> works in manner that is analogous to logical analysis. Peirce explicitly
> says, for instance, that we do not attend to the parts of the spots. The
> fact that, in reality, the two spots on the page are arranged so that one
> is the left to the other brings in another kind of relation involving an
> observer. In relation to that observer, one is to the right and one is to
> the left really. But Peirce has isolated the relation of "being on the same
> surface."
>
> Let's consider a limiting kind of relation: C is similar to D. The
> relation of being on the same surface is a similarity, if I am not
> mistaken. Does such a relation of similarity involve some sort of order
> that holds between the relate and the correlate? There is a relation, but
> is it ordered?
>
> --Jeff
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> 
> From: Jon Alan Schmidt [jonalanschm...@gmail.com]
> Sent: Saturday, November 5, 2016 5:05 PM
> To: Jeffrey Brian Downard
> Cc: Peirce-L
> Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was
> Metaphysics and Nothing (was Peirce's Cosmology))
>
> Jeff, List:
>
> Just thinking out loud here ... Do two random spots on a page have a
> relation?  If not, then this example is not pertinent; but if so, is it
> accurate to say that they have no order?  Doesn't the fact that they occur
> on the same piece of paper--like, say, chalk marks on a blackboard--entail
> that there is order in some sense?  Again, I see that they are not
> "ordered" in terms of having a hierarchy or sequence, but in fact one will
> be to the left of the other, one will be above the other, etc.  If we
> rotate the page 180 degrees, then these relations will be reversed from our
> point of view, but the spots will still exhibit the same order because of
> the underlying paper.  As long as they are potential spots, they "cannot be
> placed in any particularly regular way," as Pierce said; but once they are
> actual spots, they now have been placed in a particularly regular way, and
> are distinguishable only because of the order that is manifested in their
> relations.
>
> Regards,
>
> Jon
>
> On Sat, Nov 5, 2016 at 6:10 PM, Jeffrey Brian Downard <
> jeffrey.down...@nau.edu<mailto:jeffrey.down...@nau.edu>> wrote:
>
> Jon, Gary R, List,
>
> First, let me point out that my comments were meant as interpretation of
> how Peirce is coming at these questions about the character of dyadic and
> triadic relations from the side of math (including formal logic),
> phenomenology and semiotics. I am not making any metaphysical claims about
> what, really presupposes what. My aim was to hold off on those sorts of
> questions--at least for now.
>
> In response to your claim that all dyads are, in some way or another,
> organized, I tend to disagree. Let's take one of Peirce's examples f

RE: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jeffrey Brian Downard]

g the diagram involving 
blackboard on pages 261-3. How might we draw them out?

--Jeff


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

From: Jeffrey Brian Downard [jeffrey.down...@nau.edu]
Sent: Saturday, November 5, 2016 10:03 PM
Cc: Peirce-L
Subject: RE: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
Metaphysics and Nothing (was Peirce's Cosmology))

Jon, List,

From a logical point of view, when we study some relation--such as the dyadic 
relation of A is brother of B--we are isolating the relate, the correlate, and 
the relation between them. We understand that the things standing in the 
position of relate and correlate will typically have many internal relations 
among the parts that make them up. We also understand that the things in the 
position of relate and correlate may stand in a variety of different external 
relations to other things. But, when we analyze this particular relation of 
being a brother, we ignore those other relations. That is, we ignore such 
things as the fact that one might be taller than another or that one might be 
more social than the other.

We do the same thing, I take it, when we are engaged in a phenomenological 
analysis of something that has been observed. Phenomenological analysis works 
in manner that is analogous to logical analysis. Peirce explicitly says, for 
instance, that we do not attend to the parts of the spots. The fact that, in 
reality, the two spots on the page are arranged so that one is the left to the 
other brings in another kind of relation involving an observer. In relation to 
that observer, one is to the right and one is to the left really. But Peirce 
has isolated the relation of "being on the same surface."

Let's consider a limiting kind of relation: C is similar to D. The relation of 
being on the same surface is a similarity, if I am not mistaken. Does such a 
relation of similarity involve some sort of order that holds between the relate 
and the correlate? There is a relation, but is it ordered?

--Jeff

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

From: Jon Alan Schmidt [jonalanschm...@gmail.com]
Sent: Saturday, November 5, 2016 5:05 PM
To: Jeffrey Brian Downard
Cc: Peirce-L
Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
Metaphysics and Nothing (was Peirce's Cosmology))

Jeff, List:

Just thinking out loud here ... Do two random spots on a page have a relation?  
If not, then this example is not pertinent; but if so, is it accurate to say 
that they have no order?  Doesn't the fact that they occur on the same piece of 
paper--like, say, chalk marks on a blackboard--entail that there is order in 
some sense?  Again, I see that they are not "ordered" in terms of having a 
hierarchy or sequence, but in fact one will be to the left of the other, one 
will be above the other, etc.  If we rotate the page 180 degrees, then these 
relations will be reversed from our point of view, but the spots will still 
exhibit the same order because of the underlying paper.  As long as they are 
potential spots, they "cannot be placed in any particularly regular way," as 
Pierce said; but once they are actual spots, they now have been placed in a 
particularly regular way, and are distinguishable only because of the order 
that is manifested in their relations.

Regards,

Jon

On Sat, Nov 5, 2016 at 6:10 PM, Jeffrey Brian Downard 
mailto:jeffrey.down...@nau.edu>> wrote:

Jon, Gary R, List,

First, let me point out that my comments were meant as interpretation of how 
Peirce is coming at these questions about the character of dyadic and triadic 
relations from the side of math (including formal logic), phenomenology and 
semiotics. I am not making any metaphysical claims about what, really 
presupposes what. My aim was to hold off on those sorts of questions--at least 
for now.

In response to your claim that all dyads are, in some way or another, 
organized, I tend to disagree. Let's take one of Peirce's examples from "The 
Logic of Mathematics" as a starting point. If you put two spots on a page, they 
are not ordered. As soon as you say that one is the left of the other, or that 
one is above the other, you are comparing them with respect to some third thing.

Here is the passage:  "Two phenomena, whose parts are not attended to, cannot 
display any law, or regularity. Three dots may be placed in a straight line, 
which is a kind of regularity; or they may be placed at the vertices of an 
equilateral triangle, which is another kind of regularity. But two dots cannot 
be placed in any particularly regular way, since there is but one way in which 
they can be placed, unless they were set together, when they would cease to be 
two. It 

RE: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jeffrey Brian Downard]

Jon, List,

>From a logical point of view, when we study some relation--such as the dyadic 
>relation of A is brother of B--we are isolating the relate, the correlate, and 
>the relation between them. We understand that the things standing in the 
>position of relate and correlate will typically have many internal relations 
>among the parts that make them up. We also understand that the things in the 
>position of relate and correlate may stand in a variety of different external 
>relations to other things. But, when we analyze this particular relation of 
>being a brother, we ignore those other relations. That is, we ignore such 
>things as the fact that one might be taller than another or that one might be 
>more social than the other.

We do the same thing, I take it, when we are engaged in a phenomenological 
analysis of something that has been observed. Phenomenological analysis works 
in manner that is analogous to logical analysis. Peirce explicitly says, for 
instance, that we do not attend to the parts of the spots. The fact that, in 
reality, the two spots on the page are arranged so that one is the left to the 
other brings in another kind of relation involving an observer. In relation to 
that observer, one is to the right and one is to the left really. But Peirce 
has isolated the relation of "being on the same surface."

Let's consider a limiting kind of relation: C is similar to D. The relation of 
being on the same surface is a similarity, if I am not mistaken. Does such a 
relation of similarity involve some sort of order that holds between the relate 
and the correlate? There is a relation, but is it ordered?

--Jeff

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

From: Jon Alan Schmidt [jonalanschm...@gmail.com]
Sent: Saturday, November 5, 2016 5:05 PM
To: Jeffrey Brian Downard
Cc: Peirce-L
Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was 
Metaphysics and Nothing (was Peirce's Cosmology))

Jeff, List:

Just thinking out loud here ... Do two random spots on a page have a relation?  
If not, then this example is not pertinent; but if so, is it accurate to say 
that they have no order?  Doesn't the fact that they occur on the same piece of 
paper--like, say, chalk marks on a blackboard--entail that there is order in 
some sense?  Again, I see that they are not "ordered" in terms of having a 
hierarchy or sequence, but in fact one will be to the left of the other, one 
will be above the other, etc.  If we rotate the page 180 degrees, then these 
relations will be reversed from our point of view, but the spots will still 
exhibit the same order because of the underlying paper.  As long as they are 
potential spots, they "cannot be placed in any particularly regular way," as 
Pierce said; but once they are actual spots, they now have been placed in a 
particularly regular way, and are distinguishable only because of the order 
that is manifested in their relations.

Regards,

Jon

On Sat, Nov 5, 2016 at 6:10 PM, Jeffrey Brian Downard 
mailto:jeffrey.down...@nau.edu>> wrote:

Jon, Gary R, List,

First, let me point out that my comments were meant as interpretation of how 
Peirce is coming at these questions about the character of dyadic and triadic 
relations from the side of math (including formal logic), phenomenology and 
semiotics. I am not making any metaphysical claims about what, really 
presupposes what. My aim was to hold off on those sorts of questions--at least 
for now.

In response to your claim that all dyads are, in some way or another, 
organized, I tend to disagree. Let's take one of Peirce's examples from "The 
Logic of Mathematics" as a starting point. If you put two spots on a page, they 
are not ordered. As soon as you say that one is the left of the other, or that 
one is above the other, you are comparing them with respect to some third thing.

Here is the passage:  "Two phenomena, whose parts are not attended to, cannot 
display any law, or regularity. Three dots may be placed in a straight line, 
which is a kind of regularity; or they may be placed at the vertices of an 
equilateral triangle, which is another kind of regularity. But two dots cannot 
be placed in any particularly regular way, since there is but one way in which 
they can be placed, unless they were set together, when they would cease to be 
two. It is true that on the earth two dots may be placed antipodally." (CP 
1.429)

If you take a pair of things as a collection within the mathematical system of 
set theory, the pair can be treated as an unordered set, or as an ordered set. 
The character of the set as a whole is, itself, some third thing. As such, the 
character of the set may be characterized in terms of a general rule of order 
between the members--or a set may no

Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

Just thinking out loud here ... Do two random spots on a page *have* a
relation?  If not, then this example is not pertinent; but if so, is it
accurate to say that they have no order?  Doesn't the fact that they occur
on the same piece of paper--like, say, chalk marks on a blackboard--entail
that there is order in some sense?  Again, I see that they are not
"ordered" in terms of having a hierarchy or sequence, but in fact one will
be to the left of the other, one will be above the other, etc.  If we
rotate the page 180 degrees, then these *relations* will be reversed from
our point of view, but the spots will still exhibit the same *order*
because of the underlying paper.  As long as they are *potential* spots,
they "cannot be placed in any particularly regular way," as Pierce said;
but once they are *actual* spots, they now *have been* placed in a
particularly regular way, and are distinguishable only *because* of the
order that is manifested in their relations.

Regards,

Jon

On Sat, Nov 5, 2016 at 6:10 PM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon, Gary R, List,
>
> First, let me point out that my comments were meant as interpretation of
> how Peirce is coming at these questions about the character of dyadic and
> triadic relations from the side of math (including formal logic),
> phenomenology and semiotics. I am not making any metaphysical claims about
> what, really presupposes what. My aim was to hold off on those sorts of
> questions--at least for now.
>
> In response to your claim that all dyads are, in some way or another,
> organized, I tend to disagree. Let's take one of Peirce's examples from
> "The Logic of Mathematics" as a starting point. If you put two spots on a
> page, they are not ordered. As soon as you say that one is the left of the
> other, or that one is above the other, you are comparing them with respect
> to some third thing.
>
> Here is the passage:  "Two phenomena, whose parts are not attended to,
> cannot display any law, or regularity. *Three *dots may be placed in a
> straight line, which is a kind of regularity; or they may be placed at the
> vertices of an equilateral triangle, which is another kind of regularity.
> But *two *dots cannot be placed in any particularly regular way, since
> there is but one way in which they can be placed, unless they were set
> together, when they would cease to be two. It is true that on the earth two
> dots may be placed antipodally." (CP 1.429)
>
> If you take a pair of things as a collection within the mathematical
> system of set theory, the pair can be treated as an unordered set, or as an
> ordered set. The character of the set as a whole is, itself, some third
> thing. As such, the character of the set may be characterized in terms of a
> general rule of order between the members--or a set may not impose such an
> ordered rule on its members.
>
> In the case of a dyad of identity, we have a dyad that consists of two
> instances of the same thing. Setting aside some temporal or spatial
> framework, the dyad of identity is unordered. Some mathematical collections
> allow multiple instances of the same thing (e.g., multiple instances of the
> number 1), but the postulates of most set theories do not allow
> multiple members that are identical.
>
> There is a short discussion within the context of formal logic of
> unordered collections of two or three things CP 4.345.  He calls such
> relations doublets and triplets, whereas he calls the ordered
> collections dyads and triads.
>
> I must admit that this pretty thin evidence for my claim that some dyads
> (or doublets in the context of the system of logic he is developing at
> 4.345) may not involve an ordered relation, but it is what I have to offer
> at this point. I don't see textual evidence for the claim that every sort
> of relation--of any kind--always involves some kind of order or another. 
> Having
> said that, Peirce is typically considering limiting kinds of cases in order
> to clarify some matter that is at hand. In order to get a better
> understanding of different sorts of order, considering relations that are
> unordered may be helpful.
>
> Looking ahead, preserving the conceptions of unordered relations may help
> us explain how things (e.g., some undifferentiated possibilities) which
> lack order might come to get ordered. After all, the presence of order--of
> any kind--is one of the things that needs to be explained.
>
> Given the fact that we're now looking at RLT, I think it makes sense to
> hold off on the Minute Logic--at least for now.
>
> --Jeff
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
>

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[PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology))

[Jon Alan Schmidt]

Jeff, List:

I see that Gary R. started a separate thread for this right after I did.
He suggested that I re-post my cosmological analysis of CP 6.490, but that
dives right into metaphysical matters, so I think that it would be better
just to stick with the text itself initially.

In what I quoted, Peirce defined "super-order" as "a character that is a
generalization of order ... something like uniformity ... that of which
order and uniformity are particular varieties ... Any general state of
things whatsoever would be a super-order and a super-habit."  Early in the
final RLT lecture, Peirce commented on what it means for something to be
general.

CSP:  That which is possible is in so far *general *and, as general, it
ceases to be individual. Hence, remembering that the word "potential"
means *indeterminate
yet capable of determination in any special case*, there may be a potential
aggregate of all the possibilities that are consistent with certain general
conditions ... But being a potential aggregate only, it does not contain
any individuals at all. It only contains general conditions which *permit *the
determination of individuals. (CP 6.185, RLT:247)


A super-order is thus a *potential *aggregate of all *particular *varieties
of order and uniformity; i.e., it contains the *general *conditions which
permit the determination of *individual *cases of order and uniformity.
Peirce went on to identify another property of a potential aggregate.

CSP:  A potential collection, more multitudinous than any collection of
distinct individuals can be, cannot be entirely vague. For the potentiality
supposes that the individuals are determinable in every multitude. That is,
they are determinable as distinct. But there cannot be a distinctive
quality for each individual; for these qualities would form a collection
too multitudinous for them to remain distinct. It must therefore be by
means of relations that the individuals are distinguishable from one
another. (CP 6.188, RLT:248)


Relations constitute a particular variety of order.  Hence there can be no
relations, and therefore no distinguishable individuals, without a
super-order that contains the general conditions which permit their
determination.  After giving the cave illustration, Peirce observed "that
nothing but a rigidly exact logic of relations can be your guide in such a
field," and that "when continua of higher dimensionality than 3 are
considered ... we begin to have systems of relations between the different
dimensions."  This is followed by a paragraph that Jeff quoted previously.

CSP:  A continuum may have any discrete multitude of dimensions whatsoever.
If the multitude of dimensions surpasses all discrete multitudes there
cease to be any distinct dimensions. I have not as yet obtained any
logically distinct conception of such a continuum. Provisionally, I
identify it with the *uralt *vague generality of the most abstract
potentiality. (RLT 253-254)


A continuum of "the multitude of dimensions that surpasses all discrete
multitudes" would be the ultimate potential aggregate, and thus the
ultimate super-order.  What does Peirce later say that "the clean
blackboard" (CP 6.203, RLT:261) represents?  "The original vague
potentiality ... a continuum of some indefinite multitude of dimensions
..."  I am guessing that Gary R. characterized the blackboard as
"*ur*-continuity"
precisely because Peirce here referred to "the *uralt* vague generality of
the most abstract potentiality."  He was talking about the same thing in
both passages, as well as in CP 6.490 when he discussed super-order.

CSP:  Now continuity is shown by the logic of relatives to be nothing but a
higher type of that which we know as generality. It is relational
generality ... we must suppose that as a rule the continuum has been
derived from a more general continuum, a continuum of higher generality.
(CP 6.190, RLT:258)


The source of *all *other continua is the continuum of the *highest
*generality,
a generality that exceeds all multitudes of discrete levels of relational
generality, a generalization of generality--in a word, a super-order.

Before we move on to "the questions of theological metaphysics" ... does
all of this seem to be on the right track?  Again, great suggestion.

Thanks,

Jon

On Fri, Nov 4, 2016 at 4:52 PM, Jon Alan Schmidt 
wrote:

> Jeff, List:
>
> Thank you for this very interesting suggestion.  In order to facilitate
> such a discussion (hopefully), here is the passage about "Super-order" from
> CP 6.490.
>
> CSP:  Order is simply thought embodied in arrangement; and thought
> embodied in any other way appears objectively as a character that is a
> generalization of order, and that, in the lack of any word for it, we may
> call for the nonce, "Super-order." It is something like uniformity. The
> idea may be caught if it is described as that of which order and uniformity
> are particular varieties ... A state in which there should be absolutely no
> super-order w