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PEIRCE-L Digest 1274 -- January 26-27, 1998
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From PEIRCE-L Forum, Jan 5, 1998, [name of author of message],
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Topics covered in this issue include:
1) On mind and matter and "determinations"
by John Oller
2) New List: Unity in muliplicity
by alan_manning[…]byu.edu (Alan Manning)
3) Re: Hypostatic Symbols (i.e., the concepts underlying the highest abstractions)
by John Oller
4) Re: "Oppositional Identity"
by piat[…]juno.com (Jim L Piat)
5) Re: Slow Reading the "New List" :paragraph 1
by piat[…]juno.com (Jim L Piat)
6) Peirce and the bootstrap
by Thomas.Riese[…]t-online.de (Thomas Riese)
7) Re: Hookway's _Peirce_:Chapter I - Logic
by Everdell[…]aol.com
8) Re: "determines"
by Leon Surette
9) Re: "determines"
by Howard Callaway
10) Re: Hookway's _Peirce_:Chapter I - Logic
by piat[…]juno.com (Jim L Piat)
11) Re: "determines"
by piat[…]juno.com (Jim L Piat)
12) Re: slow reading: New List (paragraph 1)
by "H.G.CALLAWAY"
13) The Degeneracy of the Index and the Derivatives of "Determine"
by John Oller
----------------------------------------------------------------------
Date: Mon, 26 Jan 1998 17:54:25 -0600
From: John Oller
To: peirce-l[…]ttacs6.ttu.edu
Subject: On mind and matter and "determinations"
Message-ID: <34CD2231.2634[…]usl.edu>
Naomi Cumming wrote:
> The everyday comprehension of spoken language involves a sensitivity to what
> might be called the "trivial" indices of vocal tension (softness,
> trumulousness etc.) in another's speech, which can lead to an iconic
> representation of the other-as-timid or other-as-anxious etc..
In most paradigms of linguistic studies devoted to conversational
analysis and functional ethnographic studies, we don't regard such
indices as "trivial" (per Jack S. Damico, Charles Goodwin, Irving
Goffman, Immanuel Schegloff, etc.) though I understand that you probably
mean "subtle" or "almost unnoticeable" or something like that and I
don't mean to split hairs. I think we agree on the intention.
> In cases
> like this, could not a "material event" (vocal tension) be read as
> exercising a perhaps involuntary "influence" over the significations
> produced through the speaker's mind?
Involuntary, yes. But essentially all events that we perceive impact us
through the powers of brute forces which are outside of our control. If
I find my own voice quavering and it signals to me that I am about to
cry, my perceptions are just as much outside of my direct volitional
control in this case as in any other. What confuses the matter is the
idea of being overwhelmed or surprised by one's own emotions, to
discover that something has made you sad, or angry, or fearful, etc.
through an observation as it were, of what your own body appears to be
doing. Since emotions are to some extent the product of energies
expended that come under volitional control they are a rather more mixed
bag than other kinds of perceptions or actions.
Speaking in an exploratory mode, here, and just for the sake of the
discussion, isn't it the case that emotional responses can be produced
in part by volitional concentration on thoughts and memories that will
generate the emotion (as in acting)? Yet, emotional reactions can also
be produced by events that overtake us and over which we have little or
no control. As the Cuban poet, Jose Marti wrote, "Cuando quiero llorar,
no lloro, y a veces lloro sin querer." [When I want to cry, I don't; and
at times I cry when I don't want to.] Or words close to these.
William James's point as I have understood him was to insist that
emotions are more subject to our actions than to our wills because the
former more than the latter are capable of producing changes in our
state of mind. My state of mind, and emotional state, is more subject to
my bodily actions (which I fairly well control most of the time) than to
my will which I know only indirectly through the actions I find myself
performing, or exerting myself to perform even if unsuccessfully.
> And could not the hearer's
> representation of "other-as-in-state X" involve something like physical
> empathy? I'm just not sure that the signs of a "material" body are always
> a matter of brute force, or that the symbolic functions of language manage
> entirely to cover the other dimensions of signification in an embodied
> setting (where visual and aural icons are involved). I would agree that
> 'our most abstract signs (the concepts underlying our discourse in words)
> are "relatively" less susceptible to such brute forces than are our material
> bodies,' but I wouldn't want to underestimate the complex
> psychophysiological phenomena, in which bodily states can at least _seem_ to
> be prior to an interpreted signification (hence James's "I cry and therefore
> I feel sad" - or something to that effect).
You make an important point, Naomi, but not one that is the least at
odds with the claim that brute forces are involved in the production of
emotions in ordinary bodily ways. If James is correct that crying can
cause sadness (or that singing a sad song can make us genuinely feel
sad, per Elton John's 1980s hit recommending that we should "Turn 'em
on! Turn on those sad songs!"), there is no conflict with the idea that
such causation involves physical forces impinging in the way that they
normally do. What complicates the issue is that abstract symbols
together with bodily actions (indices) interact with those brute forces
of external bodily events, and both the symbols and the indices we
produce through our actions come relatively more completely under our
control than sensations (including the emotions that we feel) do. But
the conventional symbols are known only (i.e., can only be acquired in
the first place or vested with any meaning), in fact, by virtue of
manifestations that involve bodily actions (e.g., movements of the
tongue in speech, or other articulators such as the hands as in signed
language systems). The upshot is that bodily actions are intrinsically
involved in the production of affect along the lines suggested by James.
Hence, his special case is not so special after all, though it is, as
you suggest very important, nonetheless and not to be ignored or
neglected.
All of this, I think, bears on the question of what "determines" means
in Peirce's writings and in the most canonical uses elsewhere (or so I
believe). If we put all of the discussion together and seek a consistent
definition that is also as simple as possible and as comprehensive as
possible, I think we will find that determinations are made through
actions (indices) that involve symbols at their distal (or mental,
abnstract and conceptual) end and icons of some kind of event structure
consisting of bodily objects in space-time contexts at their proximal
(or concrete, empirical, perceptual) end. In between, linking these
symbolic abstractions to the bodily objects (always dynamic and in a
relative state of flux owing to the fact that the stars hold still for
no one) are bodily actions that give rise to the very indices that
constitute the links through the powers of brute forces. Some of those
brute forces come under our direct control (as when I move my fingers
over the keyboard), while others are quite independent of my volitional
control (such as the impression I get of the keyboard when I look at it
or touch it). My bodily movements, those particular indices that are
subject to my own muscular acts, are under my control to some extent,
but the sensations that even those movements give rise to are themselves
less subject to control (as Peirce argued so beautifully in the early
pages of volume II of the Hartshorne and Weiss Collected Papers of C.S.
Peirce and again in volume V on pragmaticism and related topics). More
accurately put, the sensations that I feel are subject to volitional
control only indirectly through exertions that initiate, intensify,
diminish, and arrest bodily movements.
Apart from such movements that come under our control, our sensations
are relatively beyond volitional control. (Here I will hedge a little by
saying that the efferent fibers of sensory neurons, as contrasted with
the afferent pathways, show that sensations can be deliberately attended
to more or less by exertions that come under volitional control. But
this too is a form of action and not an exceptional case. I am thinking
here of the auditory and visual cortex of the human brain and in
particular those neurocortical structures known to be especially
involved in language processing. In the inner ear there is evidence that
attention can actually turn up the volume of certain sounds. And similar
phenomena are observed in visual perception. Perceptual defense and
vigilance are pertinent phenomena in discourse dramatically showing
these features.)
As to the meaning of "determines" I think Peirce's whole view of the
subject (as seen in a careful and consistent reading of his vast work;
and here I aim to form an hypothesis rather than what will seem to be a
declaration) will show that he uses the term (1) with reference to
fixing in the sense that a sign (symbol) determines its object to be of
a particular kind; (2) with reference to causing something to be however
it may be just as I cause the letters of a certain word to appear on the
screen through an articulate sequence of actions (i.e., through indices
of particular kinds); (3) with reference to the manner in which brute
forces cause a percept of an object (say the keyboard and its
spatio-temporal setting) to appear as it does to a competent
observer/perceiver (as in iconic percepts).
However, upon closer examination, it will be found that it is not the
physical object that "causes" grass to appear green, but rather it is
the nature of the competence brought to the determination of the
green-ness of the grass by the sentient observer. Brute forces,
independently of mind and the signs (abstractions) that are formed by
intelligence (however meager that intellect may be), are powerless to
determine anything other than themselves. They (brute forces) do not
naturally produce signs of themselves nor do they have any power to
differentiate any part of the material continuum from any other part. To
draw in the lines and boundaries, to mark the colors and differentiate
the spectra, to find the surfaces and edges that mark off distinct parts
of the continuum and to produce the rich categories and grammatical
relations of material objects, even the dynamic structures that we call
distinct physical events, essentially requires the invocation of
intellect (mind) and its connections to matter through one or more
suitable bodies.
Peirce acknowledged all of this, I think, in his left-handed way (a
point which I make with great sympathy and, I think, a fair
comprehension of Peirce--and also with a nod of empathy towards Joe
Brent and his wonderful biographical annotations along this line) by
speaking of matter as "effete mind". Transformed into a right-handed
version, I think we come to the notion that only the power of mind freed
(though not utterly or entirely) from the constraints of brute forces
and from matter itself can attain to the creative freedoms we find
expressed most eloquently and undeniably in natural language systems and
the language capacity. Thus, if matter is "effete mind" then mind at its
best is also the source of fully empowered (non-effete) matter. By this
reckoning, even God requires a body, though not all matter is destined
to be fully empowered. Whence, then, whatever empowerment might be
attained by any material body? I should suppose the empowerment is owed
to something along the lines of "truth" in the most trivial and simple
sense of the TNR structures that we commonly find in our experience, and
as Peirce also noted in a quotation recently put up I think by Kelley
Wells.
To bring all this back to earth, I suppose that the freedoms of any
organism within its ecosystem are so utterly dependent on the
determinations of that ecosystem by the genetic specifications that
constitute the powers of the organism that if those determining signs
could be removed, the organism itself would cease to be viable within
that environment. This notion, I expect, is uncontroversial and quite
Peircean. However, there is an unanswered question that I believe
focuses the whole discussion of what "determines" means: it is whether
or not it is possible for matter to determine a sign to be however it
may be. In the case of conventional symbols, the most difficult ones to
explain, admittedly, I think the answer must be in the negative. The
material dog (or star burst or what-have-you) does not determine the
surface forms by which it shall be designated or signified in any given
language. Rather, the flow of determinacy (in all three of the cases
outlined above; I hypothesize) is always and only in the other
direction, from mind to matter, from abstract sign to concrete object.
As for brute forces, they are forceful and rach outward from themselves
with all the power that they possess. However, they have no power to
determine anything other than their own material selves. As to how they
come to be represented in signs, that is the fundamental riddle of the
Sphinx (as Peirce described it). That is the "miracle" of
comprehensibilty as Einstein put it in 1936 in his piece on "Physics and
Reality"--I think he was quoting Kant. It remains, to this day,
unresolved. Doesn't it?
Regards,
John Oller
***************************************
John W. Oller, Jr., Professor and Head
Department of Communicative Disorders
University of Southwestern Louisiana
P.O.Box 43170
Lafayette, LA 70504-3170
***************************************
------------------------------
Date: Mon, 26 Jan 1998 17:16:31 -0700
From: alan_manning[…]byu.edu (Alan Manning)
To: peirce-l[…]ttacs6.ttu.edu
Subject: New List: Unity in muliplicity
Message-ID:
Bill Overcamp asks (persistently):
"Why reduce multiplicity to mere unity?"
Let's all concede that multiplicity is fun and diverting and even
necessary, as found in (e.g.) Six flags rollercoaster rides, and in the
diverse sensualities of flower-smelling. Having thus conceded Bill's
point, it is nevertheless unavoidable, even for Bill Overcamp, that in
order to TALK about the fun of rollercoasters and flowers, one must REDUCE
(i.e. summarize, condense, determine) all of that experience with some few
word-signs that can only concisely express the conceptions of "flowers" or
"rollercoasters." Out of such conceptions, Bill, your audience is able to
recreate the diverse experiences you describe in a few brief words.
Even apart from language and communication, unified conceptions provide a
means for generating even more diversity, more diverse experiences, more
fun. Principles of physics and engineering and the single concept of
"rollercoaster" enable an architect to imagine and then create in fact
bigger and better rollercoasters. Part of the beauty of each flower lies
in it's conformity to our internalized concept of FLOWER, such that we can
perceive a "perfect" rose, a "perfect" lily, and so on: how can
perfection ever be perceived, except in terms of some conceptual, generally
unifying standard?
Put another way, put for example in Walker Percy's terms, our sensory
systems and physical environment provides us and every other animal with
immediate, multiple sensations, but only human beings (as far as we know)
have significant capacity to conceptualize, to create a world-UNIverse
beyond immediate experience. UNI-fying conceptions make that possible.
They provide the concise rules, the templates, the diagrams, out of which
an infinite number of specific instances, objects, and images (and even new
unifying concepts) can be generated, quite beyond our rather impoverished
(relatively-speaking) direct experience.
Three Thirdness cheers for conceptual unity! Peirce in the first
paragraph of the New List makes an incredibly insightful point.
Alan Manning
------------------------------
Date: Mon, 26 Jan 1998 18:14:59 -0600
From: John Oller
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Hypostatic Symbols (i.e., the concepts underlying the highest abstractions)
Message-ID: <34CD2703.3B61[…]usl.edu>
KWells2382 wrote:
> I agree with your metaphor that symbols are the "superconductors of meaning"
> in the sense that they extend or generalize meaning. But watch how your
> metaphor 'runs down' in this discussion.
Do you mean plays out? or rather loses steam? The latter I think, is
what you intend, but I can't see how the symbol itself is affected by my
poor efforts to get it across to you or anyone through my indexical acts
of putting up letters on this screen which are then transmitted all over
the place through the internet. Access to any symbol may be dependent on
indices which are subject to physical forces, but the symbol itself
remains, relatively, independent of such material accidents.
> Its extension comes at a price--for
> example, superconductors actually do follow the laws of physics. Now I am not
> trying to be thickheaded, here. I do understand the 'spirit' of your
> superconductor metaphor, and I think that it is excellent. But in order to
> achieve meaning extension, it must give off meaning entropy (the literalist
> confusion).
What is meant here by "the literalist confusion" and by "meaning
entropy"? I think I missed some antecedent. Sorry if I've been
inattentive.
>
> Moreover, I don't believe that Peirce would be comfortable with the implied
> dualism of symbols at their "hypostatic best." It also would run into great
> difficulties with P's "Incapacities" as well.
Could you be more explicit about the dualism you object to? My idea of
hypostasis involves a trichotomous distinction between it and
discrimination used in the usual way and prescission used in a
substantially modified way (detailed in part in the paper to appear in
the volume Bill Spinks is editing on the Semiotic Society of America
meeting of 1997). By the latter, prescission, I mean the mental
operation of literally removing an image (or a prescinded sign) from an
object while keeping that object (its discriminated percept, situated in
a particular space-time context) in view. Here, as Vincent Colapietro
noted at the SSA meeting, my definition of prescission is different from
Peirce's, but not, I think, in spirit. A hypostatic sign (the next
abstraction from a prescinded sign), on my reading, is one that achieves
full generality to a limit and applies to all possible contexts rather
than just the one or ones we may have happened to encounter up to any
given moment in time. In my view their is no objectionable duality, nor
can I imagine any conflict with the Incapacities paper with which I
believe I am in full agreement. (Yet willing to be instructed further!)
All the best,
John Oller
***************************************
John W. Oller, Jr., Professor and Head
Department of Communicative Disorders
University of Southwestern Louisiana
P.O.Box 43170
Lafayette, LA 70504-3170
***************************************
------------------------------
Date: Mon, 26 Jan 1998 22:58:14 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: "Oppositional Identity"
Message-ID: <19980126.225816.4382.1.piat[…]juno.com>
On Mon, 26 Jan 1998 01:24:26 -0600 (CST) David.Low[…]anu.edu.au (David W.
Low) writes:
>My encounter with the local water-board chemist is also pertinent. He
>was
>also trying to silence me in the 'voice of authority', so to get him
>to
>think in thirdness I asked him which of the chemical elements he
>thought we
>could intentionally make extinct.
David,
I don't know if this is an example of not thinking in thirdness, but I've
always found it amusing that career military folks were often such rabid
anti-communist. They seemed themselves pretty content making a career
(more than a career) in a very socialistic and totalitarian system.
Perhaps they've adopted an authoitarian identity. (I was a three year
enlistee myself so I guess I've earned the right not to vote if I want.)
Actually I think conservative vs liberal leanings are as fundamental as
religious views and that most of our other so called rational beliefs
are often just long winded rationalizations.
Jim Piat
_____________________________________________________________________
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------------------------------
Date: Mon, 26 Jan 1998 22:32:19 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Slow Reading the "New List" :paragraph 1
Message-ID: <19980126.225816.4382.0.piat[…]juno.com>
Tom Gollier: I thought I'd already sent this to you but I can't find a
record of having done so. So I'm sending it again. I apologize to all
if this is a duplicate.
>
On Fri, 23 Jan 1998 07:17:36 -0600 (CST) Tom Gollier
writes:
>Perhaps I'm too slow a reader for even the "slow reading" of the
>"New List", but I'm still stuck on Jim Piat's question regarding
>"conception," and a couple of other questions, in Section 1.
Tom, I'm so glad to have you weigh in here. I felt badly about not
responding to your last post on The New List. I found the exchange
between you Patrick and others very interesting. But frankly, I didn't
have the understanding to participate. One of those rare times I did have
the good manners to hold my tongue! Hopefully this slow read will give
me the understanding I seek.
>
>> >>This paper is based upon the theory already established,.. <<
>>
>> He's talking about Kant's Critique of Pure Reason?
>>
>> >> that the function of conceptions is to reduce the manifold of
>> sensuous impressions to unity,...<<
>>
>> What's Kant's notion of a conception?
>
>and while Peirce is not being specific about just what he means by
>"conception" my own take on that would be that it's intentional,
>that he seems to be talking about any conception of "conception,"
>that any such conception will be involved in reducing "the manifold
>of sensuous impressions to unity." Nor do I find it too
>troublesome that Peirce is not specific at this point about what he
>means by "conception," as this is what the essay seems to be in
>process of presenting, the details of his own conception of
>"conception."
Partly the point made byThomas Riese's as well, I believe.
>An analogous point which I find more troublesome in Section 1 is
>that the "sensuous manifold" is just as Kantian, just as
>ill-defined, just as integral to what is going on, but soon to
>disappear. The essay is not about the sensuous manifold, it is not
>in process of providing a definition of it, and in fact it will soon
>leave it behind -- on the other side of "Substance" defined as the
>"act of attention" -- and proceed without further reference, at
>least explicitly, to it. That I do find spelling "trouble down the
>line," not only in what Peirce is doing -- a characterization of
>concepts apart from what it is they unify -- but also in the
>interpretations which surreptitiously slip it back in to
>their characterizations of what Peirce is doing.>
Well, we shall see down the line. Let's see if we can spot if and when
the first (or next) bit of trouble does arise.
>Then there is the passage -- "that the validity of a conception
>consists in the impossibility of reducing the content of
>consciousness to unity without the introdution of it." If Peirce
>were saying conceptions in general are necessary to unifying the
>manifold, or that the validity of conceptions in general is that
>only conceptions are capable of unifiying the manifold, then it
>would be pretty innocuous. But he is saying the validity of "a
>conception" is its necessity, and this tip-toes along the edge of
>justifying something like saying there can be no mountains on the
>moon for it, being a heavenly body, must be perfectly spherical.
>Peirce is normally seen as integrating this kind of "necessity" into
>science as the "weakest" manner of inference, abduction, but here it
>appears to be the sole basis of inference; and the conclusion, if
>we're not to argue that Peirce is just indulging himself in a little
>metaphysical sport, must be that this essay is an abduction, nothing
>more.
This seems a very good point to me. I wonder what others think.
>And finally there is the substitution in this Section of the
>"content of consciousness" for the "sensuous manifold" as well as
>the assertion that concepts are "introduced" rather than derived or
>something like that which, for whatever affinities it creates with
>modern science, makes it feel like pretty idealistic ground we're
>walking on here.
Sounds a little like psychobabble as well! (Tom, this is what I had in
the original message that never got sent. My own comment sounds like
psycho-babble to me now. I'm leaving it in to spite myself ;)
Great fun, eh?
Jim Piat
>Tom Gollier
>
>
>
_____________________________________________________________________
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------------------------------
Date: Tue, 27 Jan 1998 13:22:43 +0100
From: Thomas.Riese[…]t-online.de (Thomas Riese)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Peirce and the bootstrap
Message-ID:
Dear Joe Ransdell,
Ken Ketner and Hilary Putnam in their introduction to "Reasoning and
the logic of things" compared Peirce's conception of continuity with
Dedekind's construction of the reals via "cuts" (see section on
"Peirce's Continuum" beginning with p.37). Among other things they
conclude from certain symmetry considerations that Peirce's conception
of a continuous line can't be (re-)constructed from Dedekind's cut
construction.
>From what I said in my message "Re: Dedekind and the bootstrap" on 22 Jan
there should follow
(1) that in Peirce's conception there must be a "branching process" if
he doesn't accept "similarity" as the fundamental relation
(2) that, if Dedekind's natural numbers are indeed natural numbers,
then in Peirce's conception the natural numbers should "stick
together" with other numbers, i.e. we can't have integers as an isolated system.
It is indeed possible to give a more general construction alternative
to Dedekind's cuts (and the variants of v.Neumann etc. which Ken
Ketner and Hilary Putnam mention) which fulfills the properties which
Peirce contended that the continuum has them.
What is more: we can thus generate integers, reals, certain well known
transfinites and much else in one continuous process -- they DO stick
together!
It was given by John Horton Conway (see his "On numbers and Games").
The construction is the following (Conway, p.4; I notate "greater or
equal" as ">=" ):
"If L,R are any two sets of numbers, and no member of L is >= any
member of R, then there is a number {L|R}. All numbers are constructed
in this way."
A number is smaller or equal than another number if and only if no
element of the left set of the first number is greater or equal than
the second number and no element of the right set of the second number
is smaller or equal than the first number.
That's all! -- It's all purely 'relative'.
Donald Knuth has written a very nice and readable account of it in his
wonderful booklet "Surreal Numbers"
Just to give an impression of how and why this works,
(I notate the empty set as "/O" and if x={L|R} I write xL for the typical
member of L and xR for the typical member of R.
I omit everything that is mathematically really decisive, i.e. the
definitions of equality, addition, multiplication etc. In truth the
numbers in an important sense are constructed exclusively from
operations, i.e. relations, see pp.5-6)
here is Conway (p.7):
"The number 0
According to the construction, every number has the form {L|R}, where
L and R are two sets of earlier constructed numbers. So how can the
system possibly get "off the ground", since initially there will be no
earlier constructed numbers?
The answer, of course, is that even before we have any numbers, we
have a certain _set_ of numbers, namely the _empty_set_ /O ! So the
earliest constructed number can only be {L|R} with both L=R=/O, or in
the simplified notation {|}. This number we call 0.
Is 0 a number? Yes, since we cannot have an inequality of the form
0L >= 0R, for there is neither a 0L nor a 0R ! [...]"
It is very clumsy to write this down here but if you have a look into
Conway's or Knuth's book you will see (and enjoy!) what a very strange
and very elegant system this is. Promised!
It is much more than just a cheap trick with the empty set!
Well, Conway uses the word "set" in a bit perverse way. If you compare
Conway's construction with Peirce's construction to prove Cantor's
theorem on power sets (Logic of things pp.155ff., esp.p.158) and _how_
he uses it.
It is this:
Let there be any set, the As.
The collection of As can be divided into two classes as
follows:
the first class contains the second class contains
every A which is every A to which is
assigned to a collection assigned a collection
which contains this A which doesn't contain this A
Peirce extensively discusses this in the various versions of his
'Prolegomena to an Apology for Pragmaticism' and the idea can be
traced back to his Harvard Lectures of 1865 where he said (W1, p.204):
"Now these questions may seem trifling and puerile; but I have no
hesitation in saying that I know of none upon the correct solution to
which man's happiness depends more; for the paradoxes which beset our
highest practical interest -- our religion -- the puzzles of free
will, of divinity, of immortality are precisely of such a character as
these." And indeed, as Ketner and Putnam put it in "Logic of Things", p.37:
these mathematical conceptions are important "for virtually all of
Peirce's larger metaphysical projects."
If you take only one of the two halfes of above construction alone you
will run into Russell's set-theoretic paradoxes (see my posting to
peirce-l on Tue, 20 May 1997). And Russell indeed talked, in the
letter of 24 June 1902 to Frege of imaginary logical values as the
alternative to type-theory. Well, I think forms like {|} are indeed
"complex logical values"!
Roughly speaking you get (as Peirce's proof shows) with the construction
for the proof of Cantor's theorem an ordering alternative to and more
general than Dedekind's 'chain' concept since whatever objects you
generate there will thereby be more relations between these objects
than there are objects which then via 'hypostatic abstraction' can be
considered as objects again and so on. (Mathematicians may forgive me
for this description; anyway it is best to experiment a bit with these
structures in order to perceive what Peirce means by 'real law'.)
I am on Robert Burch's side with what he says about "relation as
such", at least as long we have no better words. (anyway, according to
Conway it can be shown that (these) numbers are as much sort of
processes (or operations, relations) as they are objects -- may we
call it as we like)
I think there are many features which make apparent that this is
indeed Peirce's continuum though I can't show this here in all detail.
Just this (see Conway, p.5 and elsewhere): Natural numbers are
generated together with transfinites; the notion of equality is a
defined relation and thus apparently different definitions will
produce the same number, and we must distinguish between the _form_
{L|R} of a number and the number itself; all definitions are inductive etc.
By the way: if we have in mind what Peirce said on Dedekind's "relation of
similarity": translate this into Goedel's "primitive recursive
functions" and back again, have in mind the role they play in
Goedel's proof of essential incompleteness... I would say that Peirce
knew at least "virtually" that primitive recursive functions alone
won't do it ... ;-)
So we can extend, according to Goedel, our system with a "Goedelian
proposition" G or it's negation non-G "as a new axiom".
What is less well known is the fact that it is also possible to extend it with
(G v non-G) _considered_as_ a_form_.
Compare this to what Jaqueline Brunning writes in her paper "Charles S.
Peirce on Time" (in: Zeit und Zeichen; Schriften der Academie du Midi,
p.71):
"To get some idea of what formal construal of undecided is intended,
we need to look at Peirce's most explicit passage on the logical
status of future contingents.
' A certain event either will happen or it will not. There is nothing
now in existence to constitute the truth of its being about to happen,
or its being about not to happen, unless it be certain circumstances
to which only a law or uniformity can lend efficacy ... The most we
can say is that the disjunction is true, but neither of the
alternatives. If however, we admit that the law has real being, not
the mode of being an individual, but even more real, then the future
necessary consequent of a present state of things is as real and true
as that present state itself.'(CP 6.368)
It is difficult to understand what Peirce is claiming unless we first
distinguish between the Principle of Bivalence and the Law of Excluded
Middle. The Law of Excluded Middle is the claim that of any pair of
contradictories , p, non-p, exactly one is true. With many logical
systems it is difficult to distinguish these but there is a picture,
due to van Frassen, within which it is natural to distinguish them. [...]"
Jaqueline Brunning then proposes an interpretation in terms of
"supervaluations" etc.
Mmh, I think things are simpler here (though not easier to
understand). We indeed have to consider (p v non-p) _as_a_form_(of
relation). And again: some people call this modal logic which I think
is rather an extravagant a name for such fundamental a thing.
In order to end up with relational generality I think we have to start
right with a relation, i.e. a "split", "cut", "distinction" or kind of
logical "mitosis". I think much of what Robert Burch has done can be
simplified if we don't bind it back "Kripke-style" (to those who need
that detour things then will remain question-begging anyway).
Peirce, logically speaking, starts where others, in our century, left
off, i.e. he never engaged in certain detours. But historically this
can be very confusing indeed.
Well, I know what I say is worse than an abstract abstract of an
abstract. But if we want to get things "off the ground", what can I
do?
This is my favorite bootstrap.
What do you say, Joe?
Thomas.
------------------------------
Date: Tue, 27 Jan 1998 07:52:13 -0500 (EST)
From: Everdell[…]aol.com
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Hookway's _Peirce_:Chapter I - Logic
Message-ID: <980127075211_1414128772[…]mrin39.mx>
Jim Piat asks: <>
"Universalism" in theology means one who believes that everyone is saved, as
opposed to the Augustinian/Calvinist view that all are sinners, many are
called, and few chosen. It has no connection that I know of with
universalism in ontology. Peirce was surrounded by theological universalists
in Cambridge, but his own denomination, Episcopalian, was not so inclined. I
agree that the relation of Peirce's religion to his philosophy will bear more
exploration than it has had.
-Bill Everdell, Brooklyn
------------------------------
Date: Tue, 27 Jan 1998 08:52:58 -0500 (EST)
From: Leon Surette
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: "determines"
Message-ID: <199801271352.IAA09390[…]romeo.its.uwo.ca>
I have been away for a long time, and lurking for a short one, but
the "determine" discussion brought out the pedant in me.
On "determine," I thought it might be worthwhile to cite the OED. It
gives the following two definitions of "determine" as a verb, pointing out
its derivation from DETERMINARE, defined as "to bound or limit." It is from
TERMINARE "to place a limit on" or "end."
1. intrans. To put an end or limit to; to come to an end.
1. trans. To put an end to (in time); to bring to an end; to end, conclude,
terminate. (Now chiefly in Law.)
Thus the dictionary definition seems to cover the ground. To
determine something is to bound it, delimit it, identify it, give it a
label, sign or name. It is an ACT that causes or brings about a cognitive
condition in the sense that to determine something is to come to know it,
but not to bring it about, alter it, or cause it to cease to exist.
Leon Surette Home: 519-681-7787
Dept. of English Fax: 519-661-3776
The University of Western Ontario Email: lsurette[…]julian.uwo.ca
London, Ontario
N6A 3K7
------------------------------
Date: Tue, 27 Jan 1998 16:33:30 +0100 (MET)
From: Howard Callaway
To: Leon Surette
Subject: Re: "determines"
Message-ID:
Leon,
Greetings!
BTW: What you say sounds right to me.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Tue, 27 Jan 1998 11:20:12 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Hookway's _Peirce_:Chapter I - Logic
Message-ID: <19980127.113822.9030.0.piat[…]juno.com>
On Tue, 27 Jan 1998 06:52:44 -0600 (CST) Everdell[…]aol.com writes:
>"Universalism" in theology means one who believes that everyone is
>saved, as
>opposed to the Augustinian/Calvinist view that all are sinners, many
>are
>called, and few chosen. It has no connection that I know of with
>universalism in ontology. Peirce was surrounded by theological
>universalists
>in Cambridge, but his own denomination, Episcopalian, was not so
>inclined. I
>agree that the relation of Peirce's religion to his philosophy will
>bear more
>exploration than it has had.
>
Bill, thanks! In his introduction, speaking of Peirce, Hookway states,
"...he was confirmed an Episcopalian and acknowledged the Trinity. His
early attempts to develop a Kantian system of three categories are given
a context which suggest that he is attempting to relate them to the
Trinity."
Jim Piat
_____________________________________________________________________
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------------------------------
Date: Tue, 27 Jan 1998 11:38:20 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: "determines"
Message-ID: <19980127.113822.9030.1.piat[…]juno.com>
On Mon, 26 Jan 1998 10:46:43 -0600 (CST) Ken Ketner
writes:
>I would hazard to say that there is no fundamental entity, a person.
> So
>a likely hypothesis, it seems to me, about 'determined', is that x
>determines
>y if x "fixes" y more meaningfully. If some approach like that is
>
>sustainable, then 'determine' in the sense that CSP uses it, is a word
>on the
>side of interpreting, instead of being an efficiently causal word on
>the
>side of the object (object causes or determines something). That is, I
>suspect
>that Peirce's use of 'determine' is not at all the typical causal
>sense.
Thanks, this helps although I'm still struggling with trying to
understand in what sense the object limits the interpretant verses the
sense in which the sign or interpetant side of the sign determines the
object. Do you or others suppose it is accurate to say the sign fixes
(selects) an interpretation of the object but that the real object as
such is not altered by this process? And that -if we want to be real
about it- the object poses real limits to how it might be determined?
Jim Piat
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------------------------------
Date: Tue, 27 Jan 1998 16:48:47 +0100
From: "H.G.CALLAWAY"
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: slow reading: New List (paragraph 1)
On Sun, 25 Jan 1998, BugDaddy wrote:
> There are two lessons to be learned from the flowers. First that
> we must slow down to smell them. The second is more hidden in
> their manifold beauty. But no one has answered my question: Why
> reduce multiplicity to mere unity?
>
Bill repeats his question here. I think he's basically looking for a
common-sense type answer, which may be a very good idea. Looking at
the question in that way, I want to say, well, of course we don't
want to reduce multiplicity to mere unity everywhere and always.
We only want to do so if there is some problem to solve which might
be solved in that way.
So, it strikes me that we might be able to transform the question:
Why do we want to unify the manifold in judgement? What general sort
of purpose does this serve? What general sort of problem does this
solve? The answer that suggests itself is that it helps in deciding
how to act. Given a goal, we want to act in the same way in all
those situations where acting in a particular way will tend toward
reaching the goal. But if the situations are different then we
may need to act in some other way. So, we need to know which situ-
ations are the same, in reference to our goals and means, and which
are different.
I wonder if Bill will be happy with this answer.
I like those flowers, Bill.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Tue, 27 Jan 1998 09:48:48 -0600
From: John Oller
To: peirce-l[…]ttacs6.ttu.edu
Subject: The Degeneracy of the Index and the Derivatives of "Determine"
Message-ID: <34CE01E0.7F00[…]usl.edu>
To Everdell and Overcamp,
Uh, sorry Bill Everdell for the reference to the "miracle" you were
waiting for, it was Bill Overcamp, that I intended to refer to.
It is only dimly relevant, I suppose, and a poor rationalization that
"ever" and "over" are a little alike phonologically and that "dell" and
"camp" have vague semantic resemblances. We may also note that the
number of syllables in each of the words, "Overcamp" and "Everdell", are
also the same and that the rhythms (as I pronounce them) are also
identical. There is also a morphological similarity in the elements
"ever" and "over" which can be seen dimly in the "-er". So we can find
various phonological, morphological, lexical, and semantic elements in
common. Pragmatically both names are commonly seen in Peirce-L and
syntactically both are proper names--i.e., those special referring terms
that are associated with what can only be designated otherwise by a
phrase involving a determinative element with a "th-" in it ("this",
"that", "these", "those"), the most reduced form of which is "the".
Now I ask, what object without a name or without being designated in the
manner captured linguistically by a demonstrative (determinative) term
is capable of "determining" anything?
An investigation of this question all the way to the bottom will show
that there is none (no object) whatever that can determine a sign in the
requisite sense. Only a sign can determine such an object and it
requires a special kind of sign at that. A mere index alone cannot
accomplish the objective on account mainly of the universal degeneracy
of icons (supplemented by that of indices laid on top of or within
them).
That is, every situation in which any given object might be found, and
every object which might be found in any of those situations, is so like
so many others that indices together with icons cannot enable the
determination of any object or of any situation. An index not already
anchored in a determinate object (e.g., in an observer with a proper
name--with a conventionalized symbol attached) is hardly more
determinate than whatever object(s) it may be connected with. In the
larger perspective every index is part of a dynamic icon, and cannot be
more determinate than that larger dynamic icon.
How then is this problem of the "the" itself (determination) solvable?
(And isn't it interesting that this should turn out to be the crux of
the language acquisition problem? Who'd have thought that "the" could be
a very important word?)
In infant development the key can be summed up in Leibniz's principle of
the identity of indiscernibles (the flip side being the non-identity of
discernibles)--all of which is merely a restatement in a more general
form of Ockham's razor. The infant evidently applies a more abstracted
version as a kind of double-edged sword and pointer in a most effective
manner. Whatever is not discernibly different from whatever else there
may be shall be regarded as the same as that other on account of the
fact that the infant cannot find a basis for maintaining a distinction.
But, whatever is evidently different from whatever else may be
encountered, the infant must regard as distinct from that whatever else
unless and until the difference can be so fully accounted for as to be
removed. (Apropos of Wittgenstein's suggestion that a problem solved is
effectively erased by its solution.)
Yet these operations applied to the problem of determining identities
(e.g., Sherlock's problem posed to Watson, if I remember, to go and see
who a certain individual might be as brought up by Piat? and reacted to
by Ketner? and others or was it the other way around? no matter), will
not quite cut the mustard. If Watson were a preverbal infant, he could
not solve the problem that Sherlock has posed. More than icons and
indices are needed.
What is wanted, to solve the problem of determining anything, is the
sort of conventional sign supplied by one or more other observers
relative to the object(s) to be determined. If those object should be
events and event sequences of great complexity, the problem will
nonetheless demand conventional signs to make any determination.
(Etymology is only distantly relevant, but consider the morpheme
"-term-" in "determination".)
The structure and nature of such a conventional sign (a symbol in the
Peircean system; and a communally supplied determining word to the
infant) will turn out to be so much richer and more abstract and more
general than any given icon or index that it will be applicable
eventually to an "entity" so continuously across its various contexts,
and it will be sufficiently powerful in consort with its fellows (i.e.,
with other symbols as used by the sign community the infant is joining
up with) so as to differentiate the various contexts so adequately (to a
limit of diminishing returns) that it will enable the required
determination of the "id-entity" of that particular "entity" as distinct
from all others (to such a degree of certainty that we may speak of it
as perfectly well-determined relative to ordinary concerns).
Does this lead to a doctrine of infallibility? No, but it does lead to a
point of determinacy that is essential to the finding out (to a limit of
reasonable certainty or the virtual removal of all rational doubt) of
any given identity of any given object which is the very essence, I
think, of the determinacy problem. I did not always see it that way, but
after working intensively with the theory of abstraction now for
approximately four years, this is the way the problem has defined itself
empirically.
Now, I believe, it is this same determinacy issue that is tied up in the
very mystery of our own individual and collective existences. How do we,
or how can we, if we do, know who and what we are? How can we know from
whence we came? Is our history discoverable? And what of our future? The
very essence of determining anything, I suppose, is the "miracle" that
Einstein referred to (vis a vis comprehension and comprehensibility of
the universe) and that Overcamp is hoping will someday occur (sorry,
Bill Everdell). Has it occurred? Will it? Can it? Upon these little
questions all the degrees of skepticism and belief, I suppose, can be
sorted into a finely graded array.
What is most amazing to me, and captivating, is that the very problem of
the individual soul (the self) should merge so completely and evidently
perfectly with the problem of the determinacy of any object (up to and
including the whole of the universe as we know it). The miracle of
existence is not waiting to happen, I suppose, Bill Overcamp, but is
perpetually happening in the present tense of every sentient observer.
It is so perfectly evident in the stars of the night sky, not to mention
the broad daylight, that to wait for it to happen (as if it were not
happening now) is to deny or essay to doubt (in some way) what is so
entirely necessary as a prerequisite to that doubt or denial as to make
the claim of doubtfulness a kind of imploding black hole from which only
a self-defeated absurdity can escape to its own ruination. Our power to
understand the slightest thing about any object, i.e., to determine any
of its characters adequately or to know it as an identity, is already
evidence that intelligence exists.
Today is the day and now is the time. If this here and this now can be
known at all, if any "th- ___" is known relative to any particular
observer(s), let us rejoice in this present fact and with Mr. Peirce,
apropos of his conclusion to one of the Harvard lectures, let us
recognize that such a convergence of remarkable unlikelihoods must be
evidence of the benevolence of an Intelligent Creator.
As Peirce argued, semiotic capacity out-reaches logic and the intellect
itself. If beauty is not evidence of an external world, and of the
existence of truth, goodness, and intelligence, no logic, will serve to
convince us. In the conclusion to his third Lowell Lecture on logic at
Harvard University in 1866 Peirce said:
********************************************************************
"If this most goodly frame the earth, and this most excellent canopy the
air, look you, this brave o'rehanging firmament, this majestical roof
fretted with golden fire, will not prove that God is good, think you
that any syllogism which is at best a bare turning about of what we
already know is going to do it? Fie! There is no sense in such a
thought." (in Fisch, et al., 1982, p. 407).
********************************************************************
(For the literati among us, it is worth noting that the self-same
argument posed by Peirce in the foregoing lines was put by David in
Psalm 19 and in the first and second chapters of Romans in the New
Testament by Paul, formerly, Saul of Tarsus.)
In other words, no mere invention of the mind (e.g., logical syllogism
or theology) can conceivably serve better to prove the reality of
goodness (which is at its root indistinguishable from truth and beauty)
than the awe inspiring impression the universe invariably makes upon the
senses. Whereas the capacity to enjoy such inspiration is dependent upon
intelligence (semiosis), no analysis can outrank, in sheer force of
impression, the uncriticized, unanalyzed, mere evidence provided by the
senses. Nor can any logical argument hope to refute that evidence.
Regards to all,
John Oller
***************************************
John W. Oller, Jr., Professor and Head
Department of Communicative Disorders
University of Southwestern Louisiana
P.O.Box 43170
Lafayette, LA 70504-3170
***************************************
------------------------------
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