PEIRCE-L Digest 1275 -- January 27-28, 1998

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   From PEIRCE-L Forum, Jan 5, 1998, [name of author of message],
   "re: Peirce on Teleology"   

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Topics covered in this issue include:

  1) Re: "Oppositional Identity"
  2) Re: Peirce and the bootstrap
	by Joseph Ransdell 
  3) Re: Hookway's _Peirce_:Chapter I - Logic
	by Tom Anderson 
  4) Re: The Degeneracy of the Index and the Derivatives of "Determine"
	by piat[…] (Jim L Piat)
  5) Re: Peirce and the bootstrap
	by Thomas.Riese[…] (Thomas Riese)
  6) Re: "determines"
	by Leon Surette 
  7) Re: Peirce and the bootstrap
	by Joseph Ransdell 
  8) Re: "determines"                                               
	by Howard Callaway 
  9) Re: New List: Unity in muliplicity
	by BugDaddy[…] (BugDaddy)
 10) Re: slow reading: New List (paragraph 1)
	by BugDaddy[…] (BugDaddy)
 11) Hi! I have a question
	by Leonard Jacuzzo 
 12) FW: the problem with zero as a number
	by Leonard Jacuzzo 
 13) Re: The Degeneracy of the Index and the Derivatives of "Determine"
	by John Oller 


Date: Tue, 27 Jan 1998 17:23:55 +0100
To: peirce-l[…]
Subject: Re: "Oppositional Identity"

On Sun, 25 Jan 1998, David W. Low wrote:

> This is pretty much what I had in mind, Howard.  We might say the first
> variety is an oppositional identity built in the mode of secondness, the
> other, a semiotic identity built in the mode of thirdness, or as Joe
> Ransdell put it so well a while back on this thread, an identity that is
> "other than of mere otherness"('Context and Continuity' 9/1/98).
> Environmentalists who build an 'otherwise identity' are in secondness,
> while those who build a semiotic identity are 'other than otherwise', that
> is, thinking in the mode thirdness.  In the latter identity, I suggest, the
> environmentalist sees that it is not sufficient to be concerned with the
> visible opposition only (the 'stop this stop that' mode of action).  To
> oppose secondness with secondness merely displaces the environmental
> concern into another domain (temporally, geographically, politically or
> perhaps, most hard of all to detect, ideologically).  As Peirce explained,
> thirdness has a way of continually reappearing -- we just can't seem to get
> rid of it no matter how hard we try to transform the world into a machine.

Thanks for the clarification. I think we see eye to eye here.
I would elaborate, but you've said it pretty well, I think, and
in very Peircean terms. I think it might be mentioned, too, in
this connection that your point relates to Peirce's criticisms of
Hegel. At least I'm tempted to think that we might make a related
point. So Peirce criticizes Hegel, as I recall, for lack of emphasis
on 2ndness. But one way of looking at this is that the lack of
emphasis has the effect of assimilating 3rdness to 2ndness, covering
over the difference, as it were. But as you point out, it is just
this difference we've been dwelling on.

You quote my conclusion from a prior posting:

> >It is crucial to liberal democratic societies that they provide social
> >support to social criticism. It is equally crucial that the be able to
> >distinguish between criticism embedded in developed alternatives and
> >criticism which operates without contextual support.
> I find it interesting that you introduce the idea of professionalism. To
> work within social structures, we first have to see them, which is
> something that arises in the experience of opposition (being different can
> be very empowering in this sense).  Only in the semiotic identity,
> however, can we accept that authority not only exists, but that it can be
> consciously controlled (thought about) in the domain of legitimate public
> knowledge (thirdness). In other words, we can recognise the structure of
> authority as something general (ie., a sign), and perform intellectual
> experiments upon our conceptions of it.
> ...
> Perhaps the above has something to do with why Peirce uses the term
> 'semiotic' rather than 'semiotics'. Maybe he wanted to emphasise the
> semiotic of semiotic. The same idea might apply to 'authority' rather than
> 'authorities' if we place the emphasis on the general rather than the
> particular. I am inclined to think that this is the kind of progression in
> reasoning that enables us to distinguish between resemblance and
> contiguity, or abduction and induction. (Does this match up with your
> 'criticism without contextual support' and 'criticism embedded in
> developed alternatives' Howard?)

This seems to be a fairly complex question, but I'm inclined to answer
it affirmatively. Generally, I think that some criticisms or other is
always possible. So, if there are no proper limits on criticism, of
any sort (if we need no "contextual support"), then the range of critic-
ism becomes so broad that it becomes difficult to even sort them out.
So, I'm tempted to make an analogy with the idea of "genuine" doubt.
Genuine doubt, is something more that doubting for its own sake, and
when we doubt of something in particular, we always require some
contextual background to make sense of the problem, or propose 
solutions. Trying to doubt everything at once leads off into Descartes.

So, consider that the critic offers us reasons or grounds to doubt
something or other in particular. It seems to me that if no contextual
support is on offer, then we may end up not knowing how to go on with the 
problem, so that one criticism after another might be made, and we are no 
better off at the end of this than we were at the start. We need some 
prospect of a developed alternative in order to know how to make sense of 
a criticism. 

Though criticisms of a given point or position might be made from
the perspective of a wide variety of alternative views, still we
need some alternative in order to sympathetically deal with the
criticism. This seems similar to requiring that criticism be
constructive. By the same token, it suggests that criticism of
authority be constructive as well. You mention "professionalism,"
in this connection, and the conception of professionalism seems
positive, that involving the provision of some constructive
alternative. Contrast "deconstruction" with Deweyan "reconstruc-
tion." It seems to me that you are dwelling on the question of
the Peircean roots of Deweyan reconstruction.


H.G. Callaway
Seminar for Philosophy
University of Mainz


Date: Tue, 27 Jan 1998 10:40:33
From: Joseph Ransdell 
To: peirce-l[…]
Subject: Re: Peirce and the bootstrap
Message-ID: <[…]>

Thomas Riese says:

>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 
>This is my favorite bootstrap.
>What do you say,  Joe?

It's beyond my ability to say anything critically on it, Thomas, but if you
are up for another question about the same thing . . .  This arises in
wondering about the following:

=========quote from your (i.e. Thomas Riese's) post==============
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 ! [...]"

====================end of quotation========================

When the nonmathematician -- meaning by that a person without a special
talent for thinking mathematically (as distinct from a special talent for
computation) -- learns that zero is not a number but must nevertheless
enter into representations of number and numerical calculations just as if
it is a number, it is utterly baffling.  Consequently, it functions not as
a Socratic aporia -- an impasse of conflicting ideas that can set one on
the way of inquiry to find a way out, but functions instead to shut the
mind down because it seems to show that, whatever it is that mathematicians
do, they do not think in the same sense that the nonmathematician thinks or
possibly could think, since it seemingly involves such things as accepting
rather than trying to eliminate blatant contradiction and making movements
in thought that seem completely arbitrary in spirit or intent as well as in

This is, I believe, a crisis point in mathematical education -- a fork in
the road where the nonmathematicians abandon any attempt to understand math
and try to get by from that point on instead on the basis of whatever
calculative abilities they might have, while the talented pursue it
further, whether in pure math or in its applications in the sciences and
engineering.  The response of the mathematician is frequently to celebrate
this as a mark of distinction (thus taking a certain pride in it) and to
exaggerate rather than meliorate the seeming strangeness of the ways of
thinking of the mathematician, but it seems to me that it should be
possible to take another approach to it and say, in effect, that where this
sort of paradox is hit some kind of basic perspective shift is required
that converts it from a mind-deadening to a mind-stimulating aporia, and
that it may indicate further that the futile perspective that the
nonmathematician has at this point was mistaken from the beginning, though
it may have functioned well enough for some purposes (e.g. as a basis for
purely computational competence), and that mathematical pedagogy should
focus on identifying the alternative perspectives that, respectively,
enabled the mathematician to accept such a  seeming paradox as intelligible
and the nonmathematician to perceive it as hopelessly unintelligible.
Perhaps it would be possible even to work at eliminating that initial
perspective that led the one to the impasse of futility and at making as
clear as possible what that other and fruitful perspective is.

Now, I don't have any concrete way of saying what I mean by a "perspective"
here and just assume that you will understand what I mean, much less any
way of describing the difference in the two particular perspectives that
show their difference in connection with the idea of zero as a number.  But
I seem to see in the form of Conway's account something of a likeness with
the seeming paradoxicality of Peirce's argment against intuition, which on
the positive side is acceptance as intelligible of the idea that before
every cognition there is a prior cognition. There are various ways in which
that latter can be made palatable once someone objects to it and indicates
why they find it objectionable, but it has a certain prima facie
paradoxicality that shuts a lot of minds down immediately.  (I think
something like this is true as regards the "ultimate opinion" issue which
seems to some an insurmountable self-contradiction while to others it is a
puzzle as to why people are so puzzled or disturbed about it, though that
is not quite the same paradoxicality as in the case of there being no
absolutely first cognition.) 

This is, I think, closely connected also with the idea of the generic sign
relation, which is defined in what I take to be a form akin to the form of
a mathematical recursive definition, which to the nonmathematician looks
like a pure case of question-begging but to the mathematician is no problem
at all. I don't myself find it intuitively problematic but I am not myself
a mathematician and am simply at a loss for words in trying to convey why
it is not problematic when someone complains that if an interpretant of a
sign is a sign, and indeed every element in the sequence of a semioss
process is a sign, then the definition of a sign is completely

My question is, I guess, as to whether you have any idea as to what it is
that the nonmathematician is thinking when he or she says "this just makes
no sense to me" in the case of zero as a number whereas the mathematician
says, as it were,"well, what is the problem about that? I don't get it."  I
think that is what you are already addressing when you speak of number as
being altogether relational, and in a couple of other remarks, but I can't
seem to get something into focus here that would illuminate this difference
in perspective I try to point at above.   

If this makes no sense to you as a problem, don't hesitate to say so,
Thomas, and I will try to articulate it another way.


Joseph Ransdell - joseph.ransdell[…]  
Dept of Philosophy - 806  742-3158  (FAX 742-0730) 
Texas Tech University - Lubbock, Texas 79409   USA (Peirce website - beta)


Date: Tue, 27 Jan 1998 11:53:43 -0800
From: Tom Anderson 
To: peirce-l[…]
Subject: Re: Hookway's _Peirce_:Chapter I - Logic
Message-ID: <34CE3B47.66F2AE14[…]>

Everdell[…] wrote:

> Jim Piat asks:  < between the nominalists and "universalist" is? Seems like much of Peirce's
> philosophy is an apology for his religious convictions. A theme Walker Percy
> (the novelist) whom I greatly admire took over the top as they say. Isn't
> there a Protestant sect called Unitarian Universalists.>>
> "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

  Peirce was brought up Unitarian -- I don't believe the Unitarians and
Universalists merged until recently.  Unitarianism actually began as one of the
first protestant sects, before Luther and Calvin, in Transylvania.  Originally,
the main theological principle was affirmation of the unity of God and denial of
the Trinity as, think, bordering on paganism.  I met a Unitarian minister who had
visited Unitarian churches in Transylvania, and found them very orthodox
religiously both in doctrine and ritual practice, except for the trinity, close
to catholicism.  Now, they are among the most liberal denominations -- many
members are atheist or agnostic.

Many of the Colonial and early American elite were Unitarians.

Tom Anderson


Date: Tue, 27 Jan 1998 13:24:19 -0500
From: piat[…] (Jim L Piat)
To: peirce-l[…]
Subject: Re: The Degeneracy of the Index and the Derivatives of "Determine"
Message-ID: <19980127.132421.13214.0.piat[…]>

On Tue, 27 Jan 1998 09:52:57 -0600 (CST) John Oller 

>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 
>than the awe inspiring impression the universe invariably makes upon 
>senses. Whereas the capacity to enjoy such inspiration is dependent 
>intelligence (semiosis), no analysis can outrank, in sheer force of
>impression, the uncriticized, unanalyzed, mere evidence provided by 
>senses. Nor can any logical argument hope to refute that evidence.
>Regards to all,
>John Oller


I've been enjoying your entertaining thought journeys.  How-ever, (is
that short for how-so-ever as in how could it ever be so?)  doesn't your
argument (something like: I know logic is inadequate, therefore...) saw
off the limb it's standing on?  Or is the argument "we (or I) hold these
truths to be self evident" without the "we hold".  In which case, it
seems to me,  we're down to "objects speak for themselves".  

Jimp Piat

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Date: Tue, 27 Jan 1998 22:31:56 +0100
From: Thomas.Riese[…] (Thomas Riese)
To: peirce-l[…]
Subject: Re: Peirce and the bootstrap

Dear Joe Ransdell,

thanks for your kind response. If what I have written is hard to 
understand then this is certainly my fault -- the irony  being 
that I just wanted to give a bare 'perspective' (I think I understand 
what you mean by that). Sorry! Please don't judge the subject matter 
from my email-message alone. 

But then: you can't tell me that you don't understand D.Knuth's book 
"Surreal Numbers". I simply don't believe you that :-)

The subtitle is "A numbertheoretic Genesis".  What if a mathematician 
read one of Peirce's papers on metaphysical cosmology -- I mean one 
of the "wild" ones with tabulae rasae determining themselves etc. and 
then this mathematician would, with all signs of excitedness jump out 
of his seat and say to himself: "Wow, it is remarkable that these few 
lines already define a real-closed Field with a very rich structure!" 
Would be o.k., wouldn't it?

By the way, Joe, professor Knuth (the above mentioned) writes in a 
footnote in volume 2 of his "The Art of Computer Programming 
/Seminumerical Algorithms (2nd edition)" on page 607 in another(!) 
though not unrelated thematical context: [...]"Peirce independently 
communicated this construction in a letter dated July 17, 1903, but 
never published it; and during the next few years he amused himself 
by making rather cryptic remarks about it without revealing the 
underlying mechanism". In another book Knuth even first named the 
structure in question "Stern-Peirce tree" and in a later edition of 
the same book changed this to "Stern-Brocot" without further notice. 
I tell you: Knuth suffers from Peirce ;-)

Seems to be difficult from both sides.
But imagine what could happen if philosophers and mathematicians 
would put their strengths together! Wasn't that Peirce's idea?!

Finally: there is indeed a difficulty and that is why not even for 
mathematicians these ideas are commonplace. It's not a "serious" 
difficulty but an apparent paradox which I think underlies 
Peirce's continuity, very similar to the difficulty to "understand" 
what the square-root of -1 "really" means. It is *very* similar to 
that. But today nobody anymore thinks that the square-root of -1 is a 
paradox or something like that. On the contrary: it is useful and 
widely used! But it's kind of strange, isn't it? A number multiplied 
with itself giving -1. Quite impossible, but it works.

Soon more (and hopefully more understandable!),



Date: Tue, 27 Jan 1998 21:51:58 -0500 (EST)
From: Leon Surette 
To: peirce-l[…]
Subject: Re: "determines"
Message-ID: <199801280251.VAA23406[…]>

Thanks Howard,
        The list seems even busier than heretofore. I can't begin to keep up.
Leon Surette					Home: 519-681-7787
Dept. of English				Fax:   519-661-3776
The University of Western Ontario		Email: lsurette[…]
London, Ontario
N6A 3K7


Date: Tue, 27 Jan 1998 22:02:45
From: Joseph Ransdell 
To: peirce-l[…]
Subject: Re: Peirce and the bootstrap
Message-ID: <[…]>

I think you misunderstood me, Thomas.  There is a lot that I don't
understand in this, but that isn't what I was intending to convey, and I
wasn't intending to suggest any defect in your account and observations.  I
only intended to say, first, that I don't have the kind of competence in
math that would enable me to respond in a genuinely critical way, but in
place of that I can perhaps raise further questions in connection with what
you say, for what it is worth.  I was hoping that others who are in
position to introduce a genuine critical perspective would be encouraged to
join in whenever they see fit. 

And then, second, I wanted to articulate something about the intellectual
situation in respect to mathematical thinking that seems important in
connection particularly with Peirce but is a more general problem as well.
I had just been reading a paper by Ed Remler, a physicist, about the
pedagogical problem of conveying physics to nonphysicists in a university
course, e.g. in a so-called "physics for poets" course, thinking
particularly of people who cannot reasonably be expected to understand
physics as a physicist does, yet who shouldn't be written off as not worth
attempting to communicate with and given something misleading or useless in
its place. What can be done?  Part of the problem is, of course, that a lot
of what physics is is in the mathematics and can't be extracted from that
as a separate content that can be conveyed without recourse to the math.

You know how frequently Peirce complains that if people show interest in
this or that aspect of his work it quickly ends when he tries to introduce
the mathematical conceptions required to understand it. (This is voiced
again and again in his communication with James in particular.)  And I was
simply taking the occasion of the quotation from Conway to point out what I
take to be one of those places in the understanding of math at a basic
level where something becomes problematic in a stultifying rather than a
fruitful way for some people though not for others.  Puzzlement can either
drive inquiry or kill it.  What is the difference?  

I think you read me as raising objections to the way zero is regarded by
mathematicians or to treating it as a number, or implying that there must
be something wrong in doing so  since it seems paradoxical.  Your remarks
about the square root of -1 suggest that I shouldn't find it problematic
because it works, etc.  But  that wasn't what I was trying to say, Thomas.
What misled you was that you thought that when I talked about the
nonmathematician there it was a way of talking about myself, since I had
earlier said that I am not a mathematician.  But I wasn't talking about
myself or raising objections from my point of view but only trying to
articulate the problematics of mathematical pedagogy.  PLease re-read it
with that in mind when you have time and see if it makes more sense.  I
have to close this message now without trying to explain it further, but I
will take another try at articulating what I had in mind as soon as I get a

Best regards,

Joe Ransdell 

Joseph Ransdell - joseph.ransdell[…]  
Dept of Philosophy - 806  742-3158  (FAX 742-0730) 
Texas Tech University - Lubbock, Texas 79409   USA (Peirce website - beta)


Date: Wed, 28 Jan 1998 09:05:19 +0100 (MET)
From: Howard Callaway 
To: Multiple recipients of list 
Subject: Re: "determines"                                               

On Tue, 27 Jan 1998, Jim L Piat wrote:
(in reply to Ken Ketner)

> 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?


I want to focus on your question here: "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?"

This is an old and sometimes troubling kind of question for many a
philosopher --in other versions: does knowing change the object known?
Or, here, does interpreting alter the things interpreted? Again, con-
sider how these questions relate to Peirce's "realism" and his "idealism."

If we think of understanding something by means of our interpretation
of it, (perhaps most clearly in understanding what someone has said),
and at the same time think of understanding as a matter of preparation
for action, experimentation, etc., then the fact that what is inter-
preted enters into new systems of relations tells us that it has 
altered. But it seems clear too that not all such "alteration," is
going to be of great significance. For example, if I understand what
someone has said, then this may provide a way of dealing with it,
perhaps a more effective approach to interaction with the person and
with others holding similar views, but this is far from saying that
the the person who made the claim now has a distinct view. I cannot
straightforwardly attribute the new interpretation to the other

Likewise, to suggest an alteration via interpretation does not rule
out the idea that the object poses real limits on our interpretation
of it. So, for instance, I assume that (at any given time) there
are particular regularities in nature of the sort we may express by
means of physical laws. When we (successfully) interpret such 
regularities, the objects involved enter into new relationships (with
us), which is evident from the fact that understanding regularities
of nature allows us to do things (as in technological applications)
which we could not do before. But this is not to say that the 
regularities have changed, that physical laws have been modified.
We might want to say that the overall regularities of nature have
been altered, since (including ourselves as part of nature) new
regularities have arisen, as expressed in our behavior and its 
effects in the world. But this is far from saying that in expressing
a regularity of the natural world, by means of a physical law, we
have thereby altered the very regularity expressed in the statement
of the law.

I'm not exactly sure that this will be helpful as regards your
question. But it does seem to me to be one direction we might go,
given the question you asked.



H.G. Callaway
Seminar for Philosophy
University of Mainz


Date: Wed, 28 Jan 1998 12:47:56 GMT
From: BugDaddy[…] (BugDaddy)
To: peirce-l[…]
Subject: Re: New List: Unity in muliplicity
Message-ID: <34d5282f.5142983[…]>

alan_manning[…] (Alan Manning) wrote:

>Three Thirdness cheers for conceptual unity!   Peirce in the first
>paragraph of the New List makes an incredibly insightful point.

Well, if we must have unity, then so be it.  But I plan to fight
it all the way to Thirdness.
Life is a miracle waiting to happen.

        Bill  Overcamp


Date: Wed, 28 Jan 1998 13:02:51 GMT
From: BugDaddy[…] (BugDaddy)
To: peirce-l[…]
Subject: Re: slow reading: New List (paragraph 1)
Message-ID: <34d729f4.5596310[…]>

"H.G.CALLAWAY"  wrote:

>I wonder if Bill will be happy with this answer.

>I like those flowers, Bill.

I like your answer.  One has needs to fulfill, goals to

But even if we didn't want to unite the manifold of experience,
we have *innate* mental filters that do the unification for us
regardless of our desire.  And society graciously gives us
culture to do more unification for us -- or to us.
Life is a miracle waiting to happen.

        Bill  Overcamp


Date: Wed, 28 Jan 1998 09:40:29 -0800
From: Leonard Jacuzzo 
To: "'peirce-l[…]'" 
Subject: Hi! I have a question
Message-ID: <01BD2BD0.C6721880[…]>

Dear Pierce list,

I am a new subscriber. My name is Leonard F Jacuzzo. I study philosophy at the University at Buffalo. I attended a seminar on pragmatism given by Dr. Peter Hare. My primary interest is in issues of necessary truth. I am currently attempting to understand and assess the peircian pragmatic account of the seeming necessity of logical laws. Unfortunately I have had little exposure to Peirce's writings (we focused upon contemporary literature in the pragmatist tradition). I am hoping that I can use this forum to become clear about what Peirce and those in that tradition think about logical truth.
	In my opinion a pragmatic justification for the laws of logic is roughly a reliablistic position. But I there seem to be many flaws in reliablistic thinking. It does not seem possible to base deductive laws upon inductive justification. Further, it seems that one cannot take a falliblistic stance towards the beliefs concerning logic seriously. In short, any supposed refutation of the logical laws based upon recalcitrant experience leads to inconsistency. 
For example, If logical theory 'T' implies that a particular experience cannot happen (say an experience of seeing something which is both red and blue all over) but that experience does happen, then one could justifiable assert the falsity of logical theory 'T'. But, if one denies the truth of the logical theory, the laws which sanctioned the implication between 'T' and the ruling out of the particular experience would be denied. But if one denies the implication, the recalcitrant experience does not have the falsifying force. In this case, the theory would be both falsified and not falsified. But that is ridiculous. Of course one could object by saying that the principle of non-contradiction does not always hold. But that would make the falsifying mechanism loose its force. 
The question is, what is wrong with my characterization of the pragmatic position on logical truth? Further, what is wrong with my argument against falliblism (reliablism) in regards to beliefs of a logical nature?
Thanks for your time, 
Leonard F Jacuzzo


Date: Wed, 28 Jan 1998 10:44:55 -0800
From: Leonard Jacuzzo 
To: "'peirce-l[…]'" 
Subject: FW: the problem with zero as a number
Message-ID: <01BD2BD9.C6212340[…]>

I'm new at this and I can't get it right. (It keeps bouncing back) . Here it is again

-----Original Message-----
From:	Leonard Jacuzzo [SMTP:jacuzzo[…]]
Sent:	Wednesday, January 28, 1998 10:24 AM
To:	'peice-l[…]'
Subject:	the problem with zero as a number

I hope this helps.
The question was raised as to the difference in perspective which allows a mathematician to be comfortable with zero as a number while those who have a mere computational prowess find the numerical status of zero problematic.

I'm no psychologist, but I think the difference in perspective is the same as that which allows people with a philosophical disposition to wonder about personhood while those who lack such a disposition think that the concept is as non-problematic as what counts as a scrambled egg. 
Those who are merely comptutational have only been exposed to the concept of number only in so far as it facilitates learning how to compute. In those cases a number is correlated with the presence of fingers. So, the absence of fingers is not a number. There is nothing correlated with a closed fist. On the other hand, those unfortunate enough to puzzle over mathematics and the relations between numbers need to have list of properties essential to being a number. Once this list is generated, it becomes apparent that zero is not only a number, but it is an even number.
In my first year of graduate school I had the opportunity to argue over this subject at length with a dorm-mate. I was of the opinion that zero was the absence of number. But, after further education in and reflection upon subjects of a mathematical nature, it is now apparent to me that zero is a number. The convincing factor was considering the necessary and sufficient conditions of being a number. 
Maybe I've missed the point of the question, but I hope this helps
Leonard F Jacuzzo


Date: Wed, 28 Jan 1998 09:43:49 -0600
From: John Oller 
To: peirce-l[…]
Subject: Re: The Degeneracy of the Index and the Derivatives of "Determine"
Message-ID: <34CF5235.4C4E[…]>

Jim L Piat wrote:

> I've been enjoying your entertaining thought journeys.  How-ever, (is
> that short for how-so-ever as in how could it ever be so?)  doesn't your
> argument (something like: I know logic is inadequate, therefore...) saw
> off the limb it's standing on?  Or is the argument "we (or I) hold these
> truths to be self evident" without the "we hold".  In which case, it
> seems to me,  we're down to "objects speak for themselves".
> Jimp Piat

Thanks Jim for your reaction. I've thought about it quite a lot trying
to see how it might have been gathered from what I said. I've not come
to any solution there, yet. But, I see another way to say what I was
getting at yesterday. Here is an illustration. 

Suppose someone witnesses certain amazing and beautiful phenomena along
with some other events that are utterly horrible, but for some reason
does not believe his or her own senses. Let us suppose for the sake of
the argument that the events were real and correctly reported by the
senses of the witness who rejects the report of his or her own senses.
What sort of syllogism or logic is likely to convince the person in
question that the amazing events really occurred?

I am very far from saying that events or things have all the value they
can get apart from representations. On the contrary, objects and events
without being represented in signs by any observer are barely above
nothing at all. But that small distance between nothing and something is
sufficient to squeeze a universe through, just as the physical present,
though logically unextended, is sufficiently wide in its infinitesimal
breadth for the whole universe at every instant to be evident within it.
(This, of course, can only be inferred from the phenomenal present which
as I demonstrated logically in an earlier post, months ago, must be a
time smear with indefinitely expandable edges, and which is necessarily
extended--by contrast with the instantaneous physical present which
logically cannot be extended.)

Now there is that "miracle" of the perpetual present again. But suppose
I deny what I am in the process of witnessing at every instant. What
logic will convince me or, as we say, "bring me to my senses"? 

A mere corroborating report (the "foolishness of preaching" as it were)
of what I have already witnessed, or previously may have heard about,
may persuade me to take another look, to reflect on the perceptual
reports and perhaps corroborating reports that I have (we are supposing
just for the sake of argument) already suppressed. However, an argument
from logic is unapt to move me in such a case because the force of
abstract ideas is generally much less than that of concrete events. Nor
is an additional report from another eyewitness likely to persuade me of
events that I have already placed in the category of fiction. 

Peirce illustrated all of this beautifully in his remarks (which I
cannot turn to at the moment for want of the right books) about the
relative difficulty of physical manipulations (empirical experiments) as
contrasted with mental experiments through the power of thought. Yet if
those thought experiments do not lead us (eventually or at least
potentially) back to the material realities where our perceptual
experience is always occurring, they will be of little use. If they have
no connection at all to the material world, as Peirce showed in a
variety of ways, and as the theory of true narrative representations
also shows straightforwardly, representations approach the limit of
utter meaningless emptiness. They come to naught.

You may ask, but what of the idea of nothing itself? What of zero in
mathematics? Where does this notion find an empirical touch point? In
fact it finds none at all, and this is just the meaning of no-thing.
That meaning is everywhere evident in the fact that no-thing can be
found everywhere. Does this puzzle us? Sure. But not because it is such
a hard concept. A three year old can get the gist of it. One of my sons,
Stephen, now 18, at age three said upon a failed search for something or
other, "I can't find it everywhere." (The word "everywhere" had that
extreme high falling intonation suggesting that he had really turned
over every possible stone and had come up empty on all tries.)

The idea of nothing is surely one of the most beautiful and thoroughly
useful fictions ever constructed. It is also forever destined to remain
void of material content. Wittgenstein puzzled about this and produced
no satisfactory (on my reading) account of what was really meant by the
typewriter that was "not" on the desk. Yet the straightforward
distinctions between true narrative representations (TNRs)--ones that
have all three of the requisite sign elements, a. valid sensations of
material events, b. actions of one or more observers coordinated with
those events, and c. articulate conventional signs mapped onto the
events through the actions of the one or more observers--as contrasted
with fictions which are deficient in element a, errors deficient in both
a and c, and lies deficient in a, b, and c, readily produces the desired
(and much needed) distinction between the laptop on the desk but no
longer in the bag. It also handles the distinctions between the laptop
perceived on the desk here and now as contrasted with the laptop
remembered in the bag where it is not located now. And it easily
accounts for the laptop being put back in the bag to take it home later
on today. The latter being a representation of the anticipatory kind.
The memory of the laptop in the bag is a fiction now (as the laptop is
now on the desk) but it was a TNR when the laptop was in the bag.
Similarly the anticipation of putting it back in the carrying case may
turn out to be a TNR at a future time, but right now it is only a

If I think I put the computer in the bag, but discover that it is not
there, I commit an error. If I know that it is not there but tell
someone it is there, I lie.

Other than these possibilities, Jim, there is only the case of generals
which do not purport to be about any determinate particular at hand but
about all (or none) of a given kind (genera). Yet those (generals) are
like fictions except that the latter purport to be particular. We
pretend or imagine that there might be a typewriter on the table and
either finding it not to be there or knowing that it is elsewhere we
acknowlege that the argument (the typewriter) is purely fictional in
that context by using the linguistic and logical device of negation (no

That device (negation) is critically linked to the underlying structure
of a fiction, just as the notion of "zero" or "nothing" is so linked.
Between particulars and generals we might expect to find multitudes of
other possibilities, but this does not occur. We find only pluralities
that can be counted or pointed to in some way or other, which are
strictly particulars, and ones that are generalized fictions. Other than
these there are no multitudes that can be designated, for if they be
designated they shall either be particulars that are in principle
countable, or ones that are not countable. If countable in principle,
then that counting if executed would make them particular, if not
countable in principle, then not particular and therefore general.
Hence, no middle ground exists between particulars and generals. 

Was I saying that logic is unneeded? No. Do objects and events speak for
themselves? No. If they speak at all, they speak for someone to someone.
The question is could it be that the words were spoken unto me or unto
thee? And by whom? I didn't know whether to weep or laugh when I read in
Bertrand Russell's "Why I am not a Christian" and his other
autobiographical essays (somewhere in one of those) that the heat death
of the universe (a notion to which he subscribed) put us in the spot of
a person trapped in a valley of desperation between two mountain peaks
of insurmountably high probabilities, the attitude toward which, he
avowed, was one of "unyielding despair". Since he was defending his
atheism, I thought of Wittgestein and the "no typewriter" problem and
wondered, whence this word "unyielding" from Mr. Russell? "Unyielding"
to whom or what? 

Uh, concerning the etymology of "however", perhaps we may return at a
later date to reflect on its coming out.

Kindest to all,

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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Last modified January 28, 1998 — J.R.
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