RE: [PEIRCE-L] Peirce's categories

[Jeffrey Brian Downard]

Hello Ben, List,

I was particularly interested in the prospect of making a comparison between 
the hypotheses that we are working with in mathematics and the hypotheses that 
we are working with phenomenology.  There are good reasons to point out, as you 
have, that the hypotheses in phenomenology are based on something that is, in 
some sense prior.  Call them, if you will, particular discernments.

Having searched around a bit, I don't see a large number of places where Peirce 
uses this kind of language when talking about phenomenology.  Having said that, 
here is one:  "Philosophy has three grand divisions. The first is 
Phenomenology, which simply contemplates the Universal Phenomenon and discerns 
its ubiquitous elements" (CP 5.121)

There are interesting differences between the ways that we arrive at the 
hypotheses that serve as "starting points" for mathematical deduction, and ways 
that we arrive at the hypotheses that are being formulated in phenomenology.  
One reason I retained the language of "starting points" that was in the 
original questions that Peirce asked about mathematics is that hypotheses are, 
at heart, quite closely related to the questions that are guiding inquiry.  We 
normally think of hypotheses as explanations that can serve as possible answers 
to some questions.  In some cases, I think it might be better to think of the 
formulation of the questions were trying to answer as itself a kind of 
hypotheses..

We can ask the following kinds of questions about hypotheses in math, 
phenomenology, normative science and the like.  What are we drawing on when we 
formulate these hypotheses?  How should we develop the hypotheses from the 
"stuff" that we are drawing on so that the hypotheses we form will offer the 
greatest promise as we proceed in our inquiries. 

With these kinds of issues in mind, let me rephrase the questions about 
phenomenology so as to respond to the concern you've raised:

1. What are the different kinds of hypotheses that might be fruitful for 
phenomenological inquiry?
2. What are the general characters of these phenomenological hypotheses?
3. Why are not other phenomenological hypotheses possible, and the like?

--Jeff

Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354

From: Benjamin Udell [bud...@nyc.rr.com]
Sent: Friday, October 30, 2015 7:14 AM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Peirce's categories

Jeff, Clark, list,

I needed to look around till I found that you meant "The Logic of Mathematics: 
An Attempt to Develop My Categories from Within," and the three questions posed 
near its beginning. Here's an online version (sans italics, unfortunately)
http://web.archive.org/web/20090814011504/http://www.princeton.edu/~batke/peirce/cat_win_96.htm

In an earlier message you wrote,

[Begin quote]
1. What are the different systems of hypotheses from which mathematical 
deduction can set out?
2. What are their general characters?
3. Why are not other hypotheses possible, and the like?

Drawing on Peirce’s way of framing these questions about the starting points 
for mathematical inquiry, I’ve framed an analogous set of questions about 
inquiry in the phenomenological branch of cenoscopic science.  How might the 
normative sciences help us answer the following questions about phenomenology.

1. What are the different systems of hypotheses from which phenomenological 
inquiry can set out?
2. What are the general characters of these phenomenological hypotheses?
3. Why are not other phenomenological hypotheses possible, and the like?
[End quote]

I like that idea. I'm one for trying in an area to apply, in lockstep analogy, 
a proceeding taken from another area.

Yet - pure-mathematical deduction starts out from hypotheses, but does 
phaneroscopic (and, by extension, cenoscopic) analysis start out from 
hypotheses? Off the top of my head, and maybe I'm wrong about this, it seems to 
me that phaneroscopy a.k.a. phenomenology starts out from some sort of 
discernments, noticings, of positive phenomena in general. These discernments 
are not hypothetical suppositions or theoretical expectations. I'm not sure 
what to call the formulation of such a noticing or discernment, in the sense 
that a hypothesis formulates a supposition and a theory formulates expectations.

Still I'll try a revision of the three questions in order to apply them to 
phenomenology by lockstep analogy _mutatis mutandis_.

1. What are the different systems of discernments from which phenomenological 
inquiry can set out?
2. What are the general characters of these phenomenological discernments?
3. Why are not other phenomenological discernments possible, and the like?

Does that make sense? Does it seem at all promising?

Best, Ben

On 10/29/2015 6:14 PM, Jeffrey Brian Downard wrote:

Hi Ben, Clark, List,

I'm working on an essay for the conference on P

Re: [PEIRCE-L] Peirce's categories

[Benjamin Udell]

by reflecting on the character of these 
precepts?  In what sense does the analysis of common experience involve 
precepts that govern what we should and shouldn't do by way of making 
observations?

Here is a particularly interesting passage (from a different time period) that 
appears to bear on this kind of question:

We have, thus far, supposed that although the selection of instances is not 
exactly regular, yet the precept followed is such that every unit of the lot 
would eventually get drawn. But very often it is impracticable so to draw our 
instances, for the reason that a part of the lot to be sampled is absolutely 
inaccessible to our powers of observation. If we want to know whether it will 
be profitable to open a mine, we sample the ore; but in advance of our mining 
operations, we can obtain only what ore lies near the surface. Then, simple 
induction becomes worthless, and another method must be resorted to. Suppose we 
wish to make an induction regarding a series of events extending from the 
distant past to the distant future; only those events of the series which occur 
within the period of time over which available history extends can be taken as 
instances. Within this period we may find that the events of the class in 
question present some uniform character; yet how do we know but this uniformity 
was suddenly established a little while before the history commenced, or will 
suddenly break up a little while after it terminates? Now, whether the 
uniformity observed consists (1) in a mere resemblance between all the 
phenomena, or (2) in their consisting of a disorderly mixture of two kinds in a 
certain constant proportion, or (3) in the character of the events being a 
mathematical function of the time of occurrence--in any of these cases we can 
make use of an apagoge from the following probable deduction:... (CP, 2.730)

This provides a really nice example of what it is to observe something like a 
uniformity.  It also provides some sense of how an analysis of the phenomena 
might enable us to sort out--as competing hypotheses--the possibilities 
represented in 1-3.  What is more, the elements provide us with guidance (they 
support the development of the precepts) needed to imagine the kinds of 
experiments that could be run to sort through the competing explanations.  
Stepping back from the particularities of the examples considered in this 
passage, I think we get a nice articulation of how a phenomenological account 
of the categories might supply us with the tools necessary to analyze the 
observations necessary to support, via an abductive argument, a set of 
conclusions in the normative theory of logic about what fair sampling really 
requires under different kinds of conditions.

--Jeff


Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354

From: Benjamin Udell [bud...@nyc.rr.com]
Sent: Thursday, October 29, 2015 1:10 PM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Peirce's categories

Jeff D., Clark, list,

I think it's important in this to get the quotes and dates. I recall
Peirce's views as changing, and partly it's his acceptance of changing
terminology. Earlier, he had regarded geometry as mathematically applied
science of space; later he accepted the idea that geometers were not
studying space as it is, but instead studying spaces as hypothetical
objects. Digging those quotes up is another little research project.

Best, Ben

On 10/29/2015 3:20 PM, Jeffrey Brian Downard wrote:

Clark, List,

You ask:  I wonder how we deal with things like quasi-empirical methods in 
mathematics (started I think by Putnam who clearly was influenced by Peirce in 
his approach). Admittedly the empirical isn’t the phenomenological (or at least 
it’s a complex relationship). I’m here thinking of mathematics as practiced in 
the 20th century and less Peirce’s tendency to follow Comte in a fascination 
with taxonomy.

Peirce draws on the distinction between pure and applied mathematics.  When it 
comes to geometry, for instance, only topology is pure mathematics.  Both 
projective geometry and all systems of metrical geometry import notions that 
are not part of pure mathematics, such as the conception of a ray, or a rigid 
bar.

When it comes to pure mathematics, he is just as concerned about getting 
straight about the the kinds of observations we can draw on as he is concerned 
about getting straight on this question for the purposes of a pure science of 
cenoscopic inquiry. He makes the following point:

The first is mathematics, which does not undertake to ascertain any matter of 
fact whatever, but merely posits hypotheses, and traces out their consequences. 
It is observational, in so far as it makes constructions in the imagination 
according to abstract precepts, and then observes these imaginary objects, 
finding in them relations of parts not specified in the precept of 
construction. This is truly observation, yet certa

Re: [PEIRCE-L] Peirce's categories

[Benjamin Udell]

Jon S., list

For all I know Peirce may agree with you but I'm doubtful of the idea 
itself.


Perceptual judgments have general and qualitative elements, but have at 
least one foot firmly planted in the concrete haecceitous. They are such 
as "Socrates is standing outside the city" and "This stable contains no 
horses." Such judgments, perceptual recognitions of facts, a system of 
such judgments, seem more a starting point for idioscopic fields.


Peirce once said that a sensation differs from a feeling in that a 
sensation has a place and date. So far as I know, Peirce does not allow 
of a judgment, discernent or otherwise, by feeling, and I guess I'm 
straining in Peircean terms for such an idea.


Best, Ben

On 10/30/2015 12:56 PM, Jon Alan Schmidt wrote:


Ben, List:

Rather than "discernments" or some other novel term, should we maybe 
take the starting point for phaneroscopy to be perceptual judgments, 
especially given Peirce's characterization of these as acritical 
abductions?


Regards,

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


On Fri, Oct 30, 2015 at 9:14 AM, Benjamin Udell > wrote:


Jeff, Clark, list,

I needed to look around till I found that you meant "The Logic of
Mathematics: An Attempt to Develop My Categories from Within," and
the three questions posed near its beginning. Here's an online
version (sans italics, unfortunately)

http://web.archive.org/web/20090814011504/http://www.princeton.edu/~batke/peirce/cat_win_96.htm



In an earlier message you wrote,

[Begin quote]
1. What are the different systems of hypotheses from which
mathematical deduction can set out?
2. What are their general characters?
3. Why are not other hypotheses possible, and the like?

Drawing on Peirce’s way of framing these questions about the
starting points for mathematical inquiry, I’ve framed an
analogous set of questions about inquiry in the
phenomenological branch of cenoscopic science.  How might the
normative sciences help us answer the following questions
about phenomenology.

1. What are the different systems of hypotheses from which
phenomenological inquiry can set out?
2. What are the general characters of these phenomenological
hypotheses?
3. Why are not other phenomenological hypotheses possible, and
the like?
[End quote]

I like that idea. I'm one for trying in an area to apply, in
lockstep analogy, a proceeding taken from another area.

Yet - pure-mathematical deduction starts out from hypotheses, but
does phaneroscopic (and, by extension, cenoscopic) analysis start
out from hypotheses? Off the top of my head, and maybe I'm wrong
about this, it seems to me that phaneroscopy a.k.a. phenomenology
starts out from some sort of discernments, noticings, of positive
phenomena in general. These discernments are not hypothetical
suppositions or theoretical expectations. I'm not sure what to
call the formulation of such a noticing or discernment, in the
sense that a hypothesis formulates a supposition and a theory
formulates expectations.

Still I'll try a revision of the three questions in order to apply
them to phenomenology by lockstep analogy _/mutatis mutandis/_.

1. What are the different systems of discernments from which
phenomenological inquiry can set out?
2. What are the general characters of these phenomenological
discernments?
3. Why are not other phenomenological discernments possible, and
the like?

Does that make sense? Does it seem at all promising?

Best, Ben




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Re: [PEIRCE-L] Peirce's categories

[Clark Goble]

> On Oct 29, 2015, at 9:31 AM, Jeffrey Brian Downard  
> wrote:
> 
> In what sense can phenomenology "draw" things from logic?  If it can draw 
> something, what can it it draw?

An other question. We tend to think of logic as functional in its own right. 
For deduction and the mathematics of other types like Bayesian inference that’s 
true. It seems for abduction and perhaps types of induction that for the logic 
to function correct it can’t easily be separated from where it is applied. 
(There isn’t a way that I can see to talk about adductive inference without 
talking about the particular context of such inference for instance)

Does this relate to the question of phenomenology (in the Peircean sense) and 
logic?

The reason I ask is because you say:

> ...remember that phenomenology can draw its principles from mathematics, and 
> that the normative sciences can draw their principles from both math and 
> phenomenology--but not the other way around.

I wonder how we deal with things like quasi-empirical methods in mathematics 
(started I think by Putnam who clearly was influenced by Peirce in his 
approach). Admittedly the empirical isn’t the phenomenological (or at least 
it’s a complex relationship). I’m here thinking of mathematics as practiced in 
the 20th century and less Peirce’s tendency to follow Comte in a fascination 
with taxonomy.

My understanding is that we’re talking just about a hierarchy of abstract 
principles. As such mathematics as a category in the taxonomy is about 
generality of laws. In this sense an area of study is simply separate from the 
hierarchy in terms of principles. We have to then separate phenomenological 
principles from phenomenology in general which may indeed draw from logic. The 
analysis may then lead to discovery of general principles.

Of course for Peirce phenomenology is the study of the categories in their 
general form. His very inferences for why there must be three fundamental 
categories arises out of logic. At least it seems that way to me. Likewise when 
early only he switches from 5 categories to 3 (dropping Being and Substance) 
it’s because he sees them as unthinkable and irrelevant in a certain way. But 
that seems drawn from logic too. Jeffrey seems to say something similar when he 
talks about explanatory adequacy and observations. 

Apologies if I’m just missing the focus in this discussion. It just seems that 
if by “draw” we mean how particular laws are tied to more general laws then we 
can’t . If by “draw” we mean the method of analysis then of course we can and 
must. It just seems to me that while Peirce uses common terms like mathematics 
he means something subtle and nuanced about them such that his taxonomy of the 
sciences isn’t really a taxonomy of the sciences in any normal sense.
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Re: [PEIRCE-L] Peirce's categories

[Clark Goble]

> On Oct 29, 2015, at 1:20 PM, Jeffrey Brian Downard  
> wrote:
> 
> Peirce draws on the distinction between pure and applied mathematics.  When 
> it comes to geometry, for instance, only topology is pure mathematics.  Both 
> projective geometry and all systems of metrical geometry import notions that 
> are not part of pure mathematics, such as the conception of a ray, or a rigid 
> bar.

(Trying to remember my math classes - it’s been too long)

That’s really helpful though. Thank you.

Where does Peirce talk about this?  It’s not in anything I have handy. The 
places I find him discussing topology seem more related to his logical diagrams 
and logic of relations. Admittedly that got connections to mathematical 
topology as I remember it from my undergrad years. That is the issue is over 
set theory and how within sets relations take place. Which does seem quite tied 
to his general semiotics. 

Most of the geometry I did back in the day involved metric spaces and so not 
pure mathematics in Peirce’s sense. I’m just trying to get clear in my mind the 
dividing line. Is it fundamentally between set theory (and its relations) as 
opposed to use of set theory? 

I’m familiar with the quote you give later where math is about possibilities. 
We make premises and trace out implications. It’s imaginary in that sense.

I just don’t see how that leads to a divide between topology and metric 
geometry. The latter seems mathematical in this sense.

Forgive my ignorance here. Like I said it’s been more years than I care to 
admit. The days when Nirvana and Soundgarden were fresh and new. Thanks for 
getting at this though. It’s extremely helpful to me.

> So, I wonder, what kind of observation is it when a person observes the 
> relations between the parts of the imaginary (or diagrammed) objects and 
> learns something about the system that was not evident from the hypotheses 
> and abstract precepts that the reasoning took its start?

That bit about observation seems key. Peirce makes similar points in many 
places. It’s that reason I think Peirce is closer to Quine than Kant in this.

However I can imagine many things - some tied closer to the regular world than 
others. Geometry is the best example of this since circles, lines, rays and so 
forth seem precinded from regular phenomenal objects. I’d go so far as to say 
that’s true even of sets or continuity. 
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RE: [PEIRCE-L] Peirce's categories

[Jeffrey Brian Downard]

Clark, List,

You ask:  I wonder how we deal with things like quasi-empirical methods in 
mathematics (started I think by Putnam who clearly was influenced by Peirce in 
his approach). Admittedly the empirical isn’t the phenomenological (or at least 
it’s a complex relationship). I’m here thinking of mathematics as practiced in 
the 20th century and less Peirce’s tendency to follow Comte in a fascination 
with taxonomy.

Peirce draws on the distinction between pure and applied mathematics.  When it 
comes to geometry, for instance, only topology is pure mathematics.  Both 
projective geometry and all systems of metrical geometry import notions that 
are not part of pure mathematics, such as the conception of a ray, or a rigid 
bar.

When it comes to pure mathematics, he is just as concerned about getting 
straight about the the kinds of observations we can draw on as he is concerned 
about getting straight on this question for the purposes of a pure science of 
cenoscopic inquiry. He makes the following point:  

The first is mathematics, which does not undertake to ascertain any matter of 
fact whatever, but merely posits hypotheses, and traces out their consequences. 
It is observational, in so far as it makes constructions in the imagination 
according to abstract precepts, and then observes these imaginary objects, 
finding in them relations of parts not specified in the precept of 
construction. This is truly observation, yet certainly in a very peculiar 
sense; and no other kind of observation would at all answer the purpose of 
mathematics. CP 1.240 

So, I wonder, what kind of observation is it when a person observes the 
relations between the parts of the imaginary (or diagrammed) objects and learns 
something about the system that was not evident from the hypotheses and 
abstract precepts that the reasoning took its start?

--Jeff




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Re: [PEIRCE-L] Peirce's categories

[Benjamin Udell]

Jeff D., Clark, list,

I think it's important in this to get the quotes and dates. I recall 
Peirce's views as changing, and partly it's his acceptance of changing 
terminology. Earlier, he had regarded geometry as mathematically applied 
science of space; later he accepted the idea that geometers were not 
studying space as it is, but instead studying spaces as hypothetical 
objects. Digging those quotes up is another little research project.


Best, Ben

On 10/29/2015 3:20 PM, Jeffrey Brian Downard wrote:

Clark, List,

You ask:  I wonder how we deal with things like quasi-empirical methods in 
mathematics (started I think by Putnam who clearly was influenced by Peirce in 
his approach). Admittedly the empirical isn’t the phenomenological (or at least 
it’s a complex relationship). I’m here thinking of mathematics as practiced in 
the 20th century and less Peirce’s tendency to follow Comte in a fascination 
with taxonomy.

Peirce draws on the distinction between pure and applied mathematics.  When it 
comes to geometry, for instance, only topology is pure mathematics.  Both 
projective geometry and all systems of metrical geometry import notions that 
are not part of pure mathematics, such as the conception of a ray, or a rigid 
bar.

When it comes to pure mathematics, he is just as concerned about getting 
straight about the the kinds of observations we can draw on as he is concerned 
about getting straight on this question for the purposes of a pure science of 
cenoscopic inquiry. He makes the following point:

The first is mathematics, which does not undertake to ascertain any matter of 
fact whatever, but merely posits hypotheses, and traces out their consequences. 
It is observational, in so far as it makes constructions in the imagination 
according to abstract precepts, and then observes these imaginary objects, 
finding in them relations of parts not specified in the precept of 
construction. This is truly observation, yet certainly in a very peculiar 
sense; and no other kind of observation would at all answer the purpose of 
mathematics. CP 1.240

So, I wonder, what kind of observation is it when a person observes the 
relations between the parts of the imaginary (or diagrammed) objects and learns 
something about the system that was not evident from the hypotheses and 
abstract precepts that the reasoning took its start?

--Jeff






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Re: [PEIRCE-L] Peirce's categories

[Benjamin Udell]

In 1897 CP 4.218, Peirce makes his remarks that projective and metric 
geometries are not pure geometry, but goes on to say that they are so if 
the plane is defined so broadly as to make those geometries into 
chapters in topics (topology).


in 1901 in "Truth (and Falsity and Error)" 
http://www.gnusystems.ca/BaldwinPeirce.htm#Truth in the Baldwin 
Dictionary, Peirce wrote:


   CP 5.567. These characters equally apply to pure mathematics.
   Projective geometry is not pure mathematics, unless it be recognized
   that whatever is said of rays holds good of every family of curves
   of which there is one and one only through any two points, and any
   two of which have a point in common. But even then it is not pure
   mathematics until for points we put any complete determinations of
   any two-dimensional continuum. Nor will that be enough. A
   proposition is not a statement of perfectly pure mathematics until
   it is devoid of all definite meaning, and comes to this — that a
   property of a certain icon is pointed out and is declared to belong
   to anything like it, of which instances are given. The perfect truth
   cannot be stated, except in the sense that it confesses its
   imperfection. The pure mathematician deals exclusively with
   hypotheses. Whether or not there is any corresponding real thing, he
   does not care. His hypotheses are creatures of his own imagination;
   but he discovers in them relations which surprise him sometimes. A
   metaphysician may hold that this very forcing upon the
   mathematician's acceptance of propositions for which he was not
   prepared, proves, or even constitutes, a mode of being independent
   of the mathematician's thought, and so a reality. But whether there
   is any reality or not, the truth of the pure mathematical
   proposition is constituted by the impossibility of ever finding a
   case in which it fails. This, however, is only possible if we
   confess the impossibility of precisely defining it.
   [End quote]

I can't currently find the passage that I vaguely remember, where Peirce 
describes geometry as partly empirical, or something like that.


Best, Ben

On 10/29/2015 4:10 PM, Benjamin Udell wrote:

Jeff D., Clark, list,

I think it's important in this to get the quotes and dates. I recall 
Peirce's views as changing, and partly it's his acceptance of changing 
terminology. Earlier, he had regarded geometry as mathematically 
applied science of space; later he accepted the idea that geometers 
were not studying space as it is, but instead studying spaces as 
hypothetical objects. Digging those quotes up is another little 
research project.


Best, Ben

On 10/29/2015 3:20 PM, Jeffrey Brian Downard wrote:

Clark, List,

You ask:  I wonder how we deal with things like quasi-empirical 
methods in mathematics (started I think by Putnam who clearly was 
influenced by Peirce in his approach). Admittedly the empirical isn’t 
the phenomenological (or at least it’s a complex relationship). I’m 
here thinking of mathematics as practiced in the 20th century and 
less Peirce’s tendency to follow Comte in a fascination with taxonomy.


Peirce draws on the distinction between pure and applied 
mathematics.  When it comes to geometry, for instance, only topology 
is pure mathematics.  Both projective geometry and all systems of 
metrical geometry import notions that are not part of pure 
mathematics, such as the conception of a ray, or a rigid bar.


When it comes to pure mathematics, he is just as concerned about 
getting straight about the the kinds of observations we can draw on 
as he is concerned about getting straight on this question for the 
purposes of a pure science of cenoscopic inquiry. He makes the 
following point:


The first is mathematics, which does not undertake to ascertain any 
matter of fact whatever, but merely posits hypotheses, and traces out 
their consequences. It is observational, in so far as it makes 
constructions in the imagination according to abstract precepts, and 
then observes these imaginary objects, finding in them relations of 
parts not specified in the precept of construction. This is truly 
observation, yet certainly in a very peculiar sense; and no other 
kind of observation would at all answer the purpose of mathematics. 
CP 1.240


So, I wonder, what kind of observation is it when a person observes 
the relations between the parts of the imaginary (or diagrammed) 
objects and learns something about the system that was not evident 
from the hypotheses and abstract precepts that the reasoning took its 
start?


--Jeff








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RE: [PEIRCE-L] Peirce's categories

[Jeffrey Brian Downard]

w a phenomenological account 
of the categories might supply us with the tools necessary to analyze the 
observations necessary to support, via an abductive argument, a set of 
conclusions in the normative theory of logic about what fair sampling really 
requires under different kinds of conditions.

--Jeff


Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354

From: Benjamin Udell [bud...@nyc.rr.com]
Sent: Thursday, October 29, 2015 1:10 PM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Peirce's categories

Jeff D., Clark, list,

I think it's important in this to get the quotes and dates. I recall
Peirce's views as changing, and partly it's his acceptance of changing
terminology. Earlier, he had regarded geometry as mathematically applied
science of space; later he accepted the idea that geometers were not
studying space as it is, but instead studying spaces as hypothetical
objects. Digging those quotes up is another little research project.

Best, Ben

On 10/29/2015 3:20 PM, Jeffrey Brian Downard wrote:
> Clark, List,
>
> You ask:  I wonder how we deal with things like quasi-empirical methods in 
> mathematics (started I think by Putnam who clearly was influenced by Peirce 
> in his approach). Admittedly the empirical isn’t the phenomenological (or at 
> least it’s a complex relationship). I’m here thinking of mathematics as 
> practiced in the 20th century and less Peirce’s tendency to follow Comte in a 
> fascination with taxonomy.
>
> Peirce draws on the distinction between pure and applied mathematics.  When 
> it comes to geometry, for instance, only topology is pure mathematics.  Both 
> projective geometry and all systems of metrical geometry import notions that 
> are not part of pure mathematics, such as the conception of a ray, or a rigid 
> bar.
>
> When it comes to pure mathematics, he is just as concerned about getting 
> straight about the the kinds of observations we can draw on as he is 
> concerned about getting straight on this question for the purposes of a pure 
> science of cenoscopic inquiry. He makes the following point:
>
> The first is mathematics, which does not undertake to ascertain any matter of 
> fact whatever, but merely posits hypotheses, and traces out their 
> consequences. It is observational, in so far as it makes constructions in the 
> imagination according to abstract precepts, and then observes these imaginary 
> objects, finding in them relations of parts not specified in the precept of 
> construction. This is truly observation, yet certainly in a very peculiar 
> sense; and no other kind of observation would at all answer the purpose of 
> mathematics. CP 1.240
>
> So, I wonder, what kind of observation is it when a person observes the 
> relations between the parts of the imaginary (or diagrammed) objects and 
> learns something about the system that was not evident from the hypotheses 
> and abstract precepts that the reasoning took its start?
>
> --Jeff
>
>
>

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Re: [PEIRCE-L] Peirce's categories

[Stephen C. Rose]

I think the most relevant way to see the triad is that Firsts are vague
beginnings related to the opening of consciousness and consideration.
Seconds are real barriers established to require a collision. The end
result, the Third, is the area at which actualization, continuity and
manifestation in the world are launched. In terms of Peirce I think
continuity might be included at any poiint he considers what a third is.

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On Wed, Oct 28, 2015 at 11:43 AM, Clark Goble  wrote:

>
>
> I hope that you will have patience with what may be a very ignorant
> question. In CP8.328, Perice defines thirdness as follows:
> Thirdness is the mode of being of that which is such as it is, in bringing
> a second and third into relation to each other.
>
> Now, I would have thought that thirdness brings a first and a second into
> relation to each other. Why would Peirce say that thirdness brings a second
> and a third into relation to each other? In which sense could thirdness
> bring a second into relation with itself? Or what am I missing here?
>
>
> I assume he means the relationship between quality/feeling and force in
> terms of phenomenology. At least that’s how I’ve always taken it.
>
> The other way to think of it is in the more ontological rather than
> phenomenological realm. That is the connection between actuality and
> potential. Firstness is pure potential while secondness is actuality.
> However the move from potential to actuality depends upon Peirce’s semiotic
> realism (or objective idealism). I’d again point to Kelly Parker’s “Peirce
> as a neoPlatonist” that I’ve referred to several times over the last week.
> While again I note there are a few problems in it, I think it does a
> fantastic job getting at how Peirce conceived of this ontologically. At
> least how he did in his early period.
>
> I’d love to read Jeffrey’s paper if he’s interested in sharing - although
> I won’t get to it until this weekend. Halloween and children being
> cooperative of course.
>
>
>
>
>
> -
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> .
>
>
>
>
>
>

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Re: [PEIRCE-L] Peirce's categories

[Stephen C. Rose]

I enlarged and hopefully clarified my response here.

 Brief Notion of The Triad — Everything Comes — Medium
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On Wed, Oct 28, 2015 at 12:00 PM, Clark Goble  wrote:

>
> On Oct 28, 2015, at 9:52 AM, Stephen C. Rose  wrote:
>
> I think the most relevant way to see the triad is that Firsts are vague
> beginnings related to the opening of consciousness and consideration.
> Seconds are real barriers established to require a collision. The end
> result, the Third, is the area at which actualization, continuity and
> manifestation in the world are launched. In terms of Peirce I think
> continuity might be included at any poiint he considers what a third is.
>
>
> Yes, I don’t think we can understand Peirce’s logic of vagueness in any of
> its areas without understanding this basic conception of firstness,
> secondness and thirdness. As I’ve mentioned I’m a bit skeptical of taking
> Peirce’s early conceptions as a way of understanding his mature views such
> as in the Welby letter. However it is interesting when we do so.
>
> I should add that it’s somewhat interesting reading the Timaeus here
> relative to Peirce’s categories. In particular there’s an interesting
> connection to the rise of elements in that work of Plato. There the forms
> and space (khora) engender the elements. It’s hard not to see some of the
> categories in that discussion. Although at best I suspect that might have
> been only an early catalyst to how Peirce rethought Kant. But the forms
> would be firstness, the elements secondness, while space/receptical are
> thirdness.
>
>
>
>
>
>
> -
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> .
>
>
>
>
>
>

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Re: [PEIRCE-L] Peirce's categories

[Clark Goble]

> On Oct 28, 2015, at 9:52 AM, Stephen C. Rose  wrote:
> 
> I think the most relevant way to see the triad is that Firsts are vague 
> beginnings related to the opening of consciousness and consideration. Seconds 
> are real barriers established to require a collision. The end result, the 
> Third, is the area at which actualization, continuity and manifestation in 
> the world are launched. In terms of Peirce I think continuity might be 
> included at any poiint he considers what a third is.

Yes, I don’t think we can understand Peirce’s logic of vagueness in any of its 
areas without understanding this basic conception of firstness, secondness and 
thirdness. As I’ve mentioned I’m a bit skeptical of taking Peirce’s early 
conceptions as a way of understanding his mature views such as in the Welby 
letter. However it is interesting when we do so.

I should add that it’s somewhat interesting reading the Timaeus here relative 
to Peirce’s categories. In particular there’s an interesting connection to the 
rise of elements in that work of Plato. There the forms and space (khora) 
engender the elements. It’s hard not to see some of the categories in that 
discussion. Although at best I suspect that might have been only an early 
catalyst to how Peirce rethought Kant. But the forms would be firstness, the 
elements secondness, while space/receptical are thirdness.





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Re: [PEIRCE-L] Peirce's categories

[Clark Goble]

> 
> I hope that you will have patience with what may be a very ignorant question. 
> In CP8.328, Perice defines thirdness as follows:
> Thirdness is the mode of being of that which is such as it is, in bringing a 
> second and third into relation to each other.
> 
> Now, I would have thought that thirdness brings a first and a second into 
> relation to each other. Why would Peirce say that thirdness brings a second 
> and a third into relation to each other? In which sense could thirdness bring 
> a second into relation with itself? Or what am I missing here?

I assume he means the relationship between quality/feeling and force in terms 
of phenomenology. At least that’s how I’ve always taken it. 

The other way to think of it is in the more ontological rather than 
phenomenological realm. That is the connection between actuality and potential. 
Firstness is pure potential while secondness is actuality. However the move 
from potential to actuality depends upon Peirce’s semiotic realism (or 
objective idealism). I’d again point to Kelly Parker’s “Peirce as a 
neoPlatonist” that I’ve referred to several times over the last week. While 
again I note there are a few problems in it, I think it does a fantastic job 
getting at how Peirce conceived of this ontologically. At least how he did in 
his early period.

I’d love to read Jeffrey’s paper if he’s interested in sharing - although I 
won’t get to it until this weekend. Halloween and children being cooperative of 
course.




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