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PEIRCE-L Digest 1316 - March 2-3, 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) RE: Logic Naturalized?
by Leonard Jacuzzo
2) Logic Naturalized?
by Howard Callaway
3) RE: Psychologism
by Howard Callaway
4) Re: Normative Element in Logic
by Charles Pyle
5) Re: Normative Element in Logic
by Howard Callaway
6) Re: Logic Naturalized?
by Tom Burke
7) RE: Logic Naturalized?
by Howard Callaway
8) Re: Normative Element in Logic
by Tom Burke
9) Re: Logic Naturalized?
by piat[…]juno.com (Jim L Piat)
10) Re: Logic Naturalized?
by piat[…]juno.com (Jim L Piat)
11) Re: The New List (paragraph 5)
by BugDaddy[…]cris.com (BugDaddy)
12) Re: The New List (Paragraph 5)
by piat[…]juno.com (Jim L Piat)
13) Re: Logic Naturalized?
by Howard Callaway
14) Re: The New List (Paragraph 4)
by Thomas.Riese[…]t-online.de (Thomas Riese)
----------------------------------------------------------------------
Date: Mon, 2 Mar 1998 13:37:29 -0800
From: Leonard Jacuzzo
To: "'peirce-l[…]ttacs6.ttu.edu'"
Subject: RE: Logic Naturalized?
Message-ID: <01BD45E0.5953D8E0[…]ubppp-248-019.ppp-net.buffalo.edu>
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What I meant by 'conflate' can be expressed with ' collapse', 'neglect', =
'disregard' or 'ignore'. The point is that I think what Mr. Callaway =
wrote did not recognize the distinction between the ontological status =
of logic laws and our grasp of them as epistemic agents.
I hope this helps,
Leonard F Jacuzzo=20
SUNY[…]Buffalo =20
-----Original Message-----
From: Thomas Riese [SMTP:Thomas.Riese[…]t-online.de]
Sent: Monday, March 02, 1998 8:26 AM
To: Multiple recipients of list
Subject: RE: Logic Naturalized?
In response to Leonard Jacuzzo
Mon, 2 Mar 1998 08:02:42 -0600 (CST)
Dear Leonard Jacuzzo, you wrote:
> Mr. Callaway's description of the evolution of logic is a prime =
example =3D
> of conflating the ontic\ epistemic distinction. =20
I am not familiar with the term "conflate", you use. In my dictionary=20
I could only find "verschmelzen". I think the meaning of this term is=20
decisive here for the argument and it's critic. Could you please=20
explain to me what "to conflate" exactly means (equivalence,=20
identity, ...?).=20
Kind regards,
Thomas Riese.
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------------------------------
Date: Mon, 2 Mar 1998 20:16:52 +0100 (MET)
From: Howard Callaway
To: peirce-l[…]ttacs6.ttu.edu
Subject: Logic Naturalized?
Message-ID:
(From the Dewey-l)
Tom, you bring up a question concerning the following
passage from my prior posting:
>> So, I agree with the anti-psychologism of Hookway's
>> exposition as far as holding that logic needs to contain
>> a normative element and should focus on linguistic
>> expression, rather than thought processes, and moreover
>> I've insisted that the validity or value of argumentation
>> does not reduce to the process of its production. I can
>> agree, too, that "whether an inference is a good one
>> simply concerns the real fact of whether, if the premises
>> are true, the conclusion is also."
You ask:
> This brings up a question that has puzzled me now and
> again for some time. What exactly is this "normative
> element" in logic?
The point is that logical generalizations are not simply a
description of the way that people actually do (or must)
reason. We are not to think of "logical laws" on the model
of physical laws governing the workings of thought or
reasoning. Thinking of them so, we leave no room for their
normative function. (J.S. Mill seems to be the chief target
of this kind of criticism.)
You continue:
> Norms reflect standards regarded as typical. How are these
> determined? You could just as well say, so far as logic is
> concerned, that they are averages which support inductive
> generalizations about what is valid argumentation and what
> is not. This is not incompatible with psychologism. Nor
> does it serve as any antidote to the genetic fallacy. In
> other words, to say that logic should contain a normative
> element really says very little.
To say that logic contains a normative element, or is suited
to perform a normative function, is to say that actual rea-
soning is not (always) governed by it to the exclusion of
illogical reasoning or thought. (Notice here the non-reduc-
tive relevancy of psychological generalization.)
This point is incompatible with a strong psychologism,
according to which logical generalizations simply are psy-
chology. I don't think we can look at logical generaliza-
tions as "averages" concerning actual reasoning, since such
averages are subject to (cultural) variations, while the
validity of logical forms is not subject to such variation.
Instead it's a matter, to quote Peirce, of "the real fact of
whether, if the premises are true, the conclusion is also."
I would emphasize, though, that this formula depends, in its
applications, upon knowing which premises and conclusions
are true, and this is to emphasize again, the continuity
between logical form and subject-matters.
You continue, further:
> Logic is more than just normative. It is in some sense
> merely descriptive -- not just of argumentation actually
> exercised, but of all possible argumentation (so far as we
> can remain open to the fact that the range of possibili-
> ties goes beyond what we have so far managed to exercise
> in our actual experience or in the whole history of human
> thought).
I agree that logic is more than a normative standard for
reasoning, but I don't agree that it is "merely descrip-
tive." I think we could maintain that there is a descriptive
element, in that we want to relate valid logical forms to
actual use in successful science and inquiry generally. But
I doubt that it helps to think of logic as descriptive of
"all possible argumentation." This would apparently mean it
is descriptive of all possible (valid) argumentation. But
given that we are allowing for the revision or extension of
logic, we have nothing left by reference to which to define
the intended "possibilities," (unless this be the mathema-
tics of continuity, of course). So, at the least, I don't
see that this notion of the descriptive character of logic
helps much. Far better to relate our actual logic to its
actual or historical exemplifications, so far as we are
concerned with its "descriptive" character.
Continuing on the "possibilities," you finish up the passage
as follows:
> That's what gives it it's objective character,
> i.e., that it deals with a realm of possibilities that is
> what it is independent of whatever current opinions we may
> have of it (to hark back to Peirce's scientific realism in
> "The Fixation of Belief"). What's important is that we do
> not make the mistake of thinking that the science of logic
> is "finished" (and start issuing blanket declarations of
> what's "normal" and what's not) just because we have found
> some kind of approach that seems to work in certain cases
> -- e.g., in the foundations of mathematics.
But I'm tempted to say here that basing the objectivity of
logic on an undefined conception of possibility may not help
much. As I understand Peirce, new possibilities continually
arise, and the fact that particular possibilities have ari-
sen may be the occasion for other possibilities being extin-
guished. Moreover, what possibilities obtain at a given time
depends on what we think, in some cases. This seems general-
ly the case with technological possibilities, as depending
on theoretical insight, e.g., and the technology may in turn
have its methodological roles, leading on to new tests and
new theories. This is not to say, thought, that particular
possibilities obtain simply because we think they do. But I
do not think we get any definitive account of possibilities
out of mathematics. Mathematics, too, has its advances.
You are certainly right that we shouldn't think of logic as
definitively "finished," since it may contain the potential
for elaboration or correction. But this doesn't prevent
looking to logic for norms of reasoning, so long as we view
the norms as subject to correction and elaboration in the
same way as logic itself.
This point is consistent with a considerable (defeasible)
conservativism about validity. It's not as though we turn up
new logical forms, or reject heretofore established forms,
every day or two. (If its not broken, don't try to fix it!)
Thanks for your comments, Tom, and thanks too for the cor-
rection of "genetic" for my "generic." Whoops.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Mon, 2 Mar 1998 20:35:36 +0100 (MET)
From: Howard Callaway
To: peirce-l[…]ttacs6.ttu.edu
Subject: RE: Psychologism
Message-ID:
Re-reading Nathan Houser's Introduction to _The Essential Peirce_,
I came across the following passage which seems relevant to my
criticism of Hookway's strong constual of "psychologism." Houser
quotes Peirce in a letter to President Gilman of Johns Hopkins:
When he sought the professorship of physics at
Johns Hopkins (before being appointed part-time
lecturer in logic), he wrote to President Dan-
iel C. Gilman that it was as a logician that he
sought to head that department and that he had
learned physics in his study of logic. "The data
for the generalizations of logic are the special
methods of the different sciences," he pointed
out, and "to penetrate these methods the logician
has to study various sciences rather profoundly"
(p. xxix).
This contrasts significantly, I believe, with Hookway's (apparent)
"denial that information from the sciences can have a bearing upon
logic or epistemology.
Of course, it is possible that Hookway is merely paraphrasing
(early) Peirce here (Hookway, p. 16). But in that case, the pas-
sage from Houser casts some doubt on Hookway's interpretation of
Peirce in relation to "psychologism."
In any case, I continue to maintain that there is a considerable
danger in interpreting psychologism too broadly.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Mon, 02 Mar 1998 15:31:38 -0500
From: Charles Pyle
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Normative Element in Logic
Message-ID: <34FB172A.E603C7D5[…]modempool.com>
Howard Callaway wrote:
> This brings up a question that has puzzled me now and
> again for some time. What exactly is this "normative
> element" in logic?
apparently this is quoted from a message from Tom, which I do not seem
to have received.
In regard to the question of the "normative element" in logic and to the
question of psychologism that has been touched on in recent discussions
I cite the following.
2.52 …Other authors, indeed, a large majority of logicians, without
citing results of scientific psychology in support of the principles of
logic, yet incessantly refer to data of psychology--or to what would
ordinarily be so considered, apparent self-observations that we think so
and so--as showing what the truths of logic are. All this is beside the
purpose. Logic is not the science of how we do think; but, in such sense
as it can be said to deal with thinking at all, it only determines how
we ought to think; nor how we ought to think in conformity with usage,
but how we ought to think in order to think what is true.
2.125. In the first place, you would not wish to study logic unless you
intended to reason; and you doubtless hold the purpose of reasoning to
be the ascertainment of the truth. So it appears that you belong to the
sect that maintains that there is such a thing as truth.
2.358. The view which pragmatic logic takes of the predicate, in
consequence of its assuming that the entire purpose of deductive logic
is to ascertain the necessary conditions of the truth of signs, without
any regard to the accidents of Indo-European grammar, will be here
briefly stated.
Charles Pyle
------------------------------
Date: Mon, 2 Mar 1998 22:09:18 +0100 (MET)
From: Howard Callaway
To: Multiple recipients of list
Subject: Re: Normative Element in Logic
Message-ID:
On Mon, 2 Mar 1998, Charles Pyle wrote:
> In regard to the question of the "normative element" in logic and to the
> question of psychologism that has been touched on in recent discussions
> I cite the following.
>
> 2.52 …Other authors, indeed, a large majority of logicians, without
> citing results of scientific psychology in support of the principles of
> logic, yet incessantly refer to data of psychology--or to what would
> ordinarily be so considered, apparent self-observations that we think
> so and so--as showing what the truths of logic are. All this is beside
> the purpose. Logic is not the science of how we do think; but, in such
> sense as it can be said to deal with thinking at all, it only determines
> how we ought to think; nor how we ought to think in conformity with
> usage, but how we ought to think in order to think what is true.
Thanks for the Peirce passage, Charles. I think it helps support the line
I've been defending, as regards psychologism and the normative function
of logic. "Logic is not the science of how we do think," Peirce says,
at best it only tells us "how we ought to think." In defending the claim
that special sciences can be of relevance of logic, I would point out
that saying that "logic is not the science of how we think," strongly
suggests that we do not always think logically. Saying that logic tells
us how we ought to think, again strongly suggests that we do not always
think logically.
Again, we, or some of us, teach logic. This seems to suppose that to
whatever degree students of logic already think logically, still its
worth some effort to improve the degree to which we or they think (or
are able to think) logically. Again this strongly suggests that people
do not, in general, inevitably think as logically as they might or
as logically as is desirable.
Coming from the psychological side of things, then, we seem to have
some grounds to support the claim that "logic is not the science
of how we do think." While this may not be the most central or
important characterization of logic, is does seem to be a character-
ization of logic --supported on the basis of a special science.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Mon, 2 Mar 1998 16:09:16 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized?
Message-ID:
At 1:17 PM -0600 3/2/98, Howard Callaway wrote:
>You ask:
>
>> This brings up a question that has puzzled me now and
>> again for some time. What exactly is this "normative
>> element" in logic?
>
>The point is that logical generalizations are not simply a
>description of the way that people actually do (or must)
>reason. We are not to think of "logical laws" on the model
>of physical laws governing the workings of thought or
>reasoning. Thinking of them so, we leave no room for their
>normative function. (J.S. Mill seems to be the chief target
>of this kind of criticism.)
But I think this is the wrong tack to take in characterizing what logic is
(despite the fact that it's the way the issues associated with
(anti-)psychologism are usually raised). Saying how logic applies to
actual reasoning -- whether it is in that sense descriptive or prescriptive
or neither or both -- doesn't by itself say much. Logic is descriptive in
the way that pure mathematics is descriptive -- not necessarily describing
anything beyond itself, but describing mathematical properties of certain
abstractions of a sort. E.g., "real analysis" is neither descriptive nor
prescriptive of actual physical motion, though it is addressed to
abstractions derived from physical kinematics and dynamics. It is
descriptive rather of the formal properties of these abstractions. That is
also the sense in which logic is simply descriptive. It is neither
prescriptive nor descriptive of the actual workings of thought or
reasoning, though it is addressed to (aims to describe formal properties
of) abstractions derived from ... what, actual reasoning? discourse?
speech? thought? inquiry? Yes: inquiry.
--TB
------------------------------
Date: Mon, 2 Mar 1998 22:26:22 +0100 (MET)
From: Howard Callaway
To: Multiple recipients of list
Subject: RE: Logic Naturalized?
Message-ID:
On Mon, 2 Mar 1998, Leonard Jacuzzo wrote:
> Mr. Callaway's description of the evolution of logic is a prime example
> of conflating the ontic\ epistemic distinction. Theories of logic have
> evolved. But logic itself has not. To claim that logic itself has
> evolved on the basis of the evolution of logical theories is to support
> psychologism. That is, if there is no distinction between logic and our
> means of recognizing and applying it, then there is no distinction
> between logic and psychology.
If you will tell me what "ontic/epistemic" distinction we ought to be
preserving here, then I'll be glad to try to answer your criticism.
But as it stands, I really have very little to go on.
You stipulate that theories of logic have evolved. But I take it that
logic "itself" is a kind of theory, an account of the better and
worse of drawing conclusions, or an account of the validity of
arguments. So, when you say, "logic itself has not [evolved]," its
not exactly clear what you have in mind. Nor is it clear to me why
you think it follows that if someone says that logic itself has evolved,
(as contrasted in some way with logic as a theory or science) then
psychologism follows from this.
I don't think (and nor did I claim) that there is no difference between
logic and our means of recognizing and applying it.
I hope this helps to clarify my position in connection with the issues
of your concern.
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Mon, 2 Mar 1998 16:42:34 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Normative Element in Logic
Message-ID:
At 3:10 PM -0600 3/2/98, Howard Callaway wrote:
>On Mon, 2 Mar 1998, Charles Pyle wrote:
>
>> In regard to the question of the "normative element" in logic and to the
>> question of psychologism that has been touched on in recent discussions
>> I cite the following.
>>
>> 2.52 ÖOther authors, indeed, a large majority of logicians, without
>> citing results of scientific psychology in support of the principles of
>> logic, yet incessantly refer to data of psychology--or to what would
>> ordinarily be so considered, apparent self-observations that we think
>> so and so--as showing what the truths of logic are. All this is beside
>> the purpose. Logic is not the science of how we do think; but, in such
>> sense as it can be said to deal with thinking at all, it only determines
>> how we ought to think; nor how we ought to think in conformity with
>> usage, but how we ought to think in order to think what is true.
>
>Thanks for the Peirce passage, Charles. I think it helps support the line
>I've been defending, as regards psychologism and the normative function
>of logic. "Logic is not the science of how we do think," Peirce says,
>at best it only tells us "how we ought to think."
I would stress the clause you left out -- "in such sense as it can be said
to deal with thinking at all, it only determines ... how we ought to think
in order to think what is true" etc etc.
Charles's other quotes from Peirce are:
>2.125. In the first place, you would not wish to study logic unless you
>intended to reason; and you doubtless hold the purpose of reasoning to
>be the ascertainment of the truth. So it appears that you belong to the
>sect that maintains that there is such a thing as truth.
This is much like saying: "We would not study real analysis if we were not
interested in complex things like sending a person to the moon or
understanding why cannon balls do what they do when fired from a cannon."
But this is a far cry from saying that real analysis is just the physics of
motion at and about the Earth's surface. Likewise, we would not study
logic if we were not interested in correct reasoning, but this does not say
that logic is a study of correct reasoning. Logic may *determine* "how we
ought to think in order to think what is true", but that does not really
say what logic is. That simply puts constraints on it if and when it is
applied to how we think.
>2.358. The view which pragmatic logic takes of the predicate, in
>consequence of its assuming that the entire purpose of deductive logic
>is to ascertain the necessary conditions of the truth of signs, without
>any regard to the accidents of Indo-European grammar, will be here
>briefly stated.
This points to the abstract character of the subject matter of logic --
abstracted even from Indo-European grammar, not to mention actual reasoning
couched in languages which instantiate such grammars.
--TB
------------------------------
Date: Mon, 2 Mar 1998 17:54:28 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized?
Message-ID: <19980302.175429.3878.0.piat[…]juno.com>
Tom Burke asks,
> The question remains -- what
>then
>is the subject matter of logic if (given that, assuming that) it isn't
>the
>same as the subject matter of psychology or linguistics as such?
>
How about: logic is the study of the formal nature of how the knowable
is knowable. The nature of the knowable is the subject matter of
sciences. The formal nature of the knowable is the subject matter of
mathematics. The nature of how the knowable is knowable is the subject
matter of epistemology. The study of the formal nature of how the
knowable is knowable is logic. Logic is the ultimate form of how the
knowable is knowable. Math is the ultimate form of the knowable.
By the expression "the formal nature of how the knowable is knowable" I
mean the most basic form of the constraints that limit the way in which
reality can be known to us. I believe this is what Peirce is talking
about in The New List.
Where, you may ask does the nature of reasoning to correct conclusions
fit in here? Reasoning to correct conclusions (and in a sense there can
be no other) is an example or manifestation of the formal process of how
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knowledge of the knowable. (This is not well put and needs a bit of work
I admit. Not to say the rest is all the great either but I'm personally
more satisfied with it)
We take our most fundamental logical truths to be almost infallible. For
example something can not be both A and not A. We say this is
inconceivable, but perhaps it is not. In fact I'm already beginning to
suspect it is not.
Psychology is one of the sciences. Psychology studies one aspect of the
knowable which happens to include the knower. Psychology as science
emphasizes observation of human behavior to discern its underlying form
and regularities. Philosophy, of which the study of logic is a
traditional part, emphasizes reasoning about hypothetical circumstances
to discern there underlying form and regularities. But there is no rule
that the subject matter of logic can not be approached scientifically as
well as philosophically.
In my view, we simply do not know whether logic is fixed or not. Nor do
we know whether logic is best studied logically or scientifically. It
seems unlikely that our current beliefs regarding logic are fully
correct. Our basic beliefs about logic or what is logical seem
indisputable because they are the most universal and fundamental of our
knowledges. Indeed they are the very structure or foundation upon which
our knowledge is built. Logic itself teaches that the foundation is the
last to remain standing. But perhaps this too will pass and we will
ultimately reach the peace that passes understanding.
Ultimately science depends upon thinking up hypotheses to test and
philosophy depends upon the experimental testing of speculations. They
are flip sides of the same coin. By temperament philosophers abhor a
poorly reasoned experiment just as scientists by temperament decry an
untested guess.
Conclusion: I reject the premise. Linguistics and psychology do study
the subject matter of logic but they do it scientifically rather than
philosophically. Well, maybe its psychology, linguistics and philosophy
going from testing to thinking. Linguistics presently exemplifying the
best of both worlds.
I have a sinking feeling that all of the above is very sophomoric; but,
truth be told-- as it can not otherwise be...
Jim Piat
_____________________________________________________________________
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------------------------------
Date: Mon, 2 Mar 1998 21:24:28 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized?
Message-ID: <19980302.212434.4294.0.piat[…]juno.com>
>Where, you may ask does the nature of reasoning to correct conclusions
>fit in here? Reasoning to correct conclusions (and in a sense there
>can
>be no other) is an example or manifestation of the formal process of
>how
>knowledge of the knowable. (This is not well put and needs a bit of
>work
>I admit. Not to say the rest is all the great either but I'm
>personally
>more satisfied with it)
It's me again taking another try at this. I think I lost my way the
first time and also left out part of the above paragraph to boot.
Perhaps what I'm calling logic is really the science of signs. But as
for the paragraph above, the second sentence should read. Reasoning to
correct conclusions is merely an example or manifestation of the formal
process of how knowledge of the knowable is applied. Or in plain
English, reasoning to correct conclusions is merely an example of applied
logic. Actually I like Tom Burke's statement much better:
>>Logic may *determine* "how we ought to think what is true", but that
doesn't really say what logic is. That simply puts constraints on it if
and when it is applied to how we think.<<
Of course stealing Tom's thought doesn't mean he agrees with my
application of it or anything else I've said.
One other second thought. I've suggested that math is the syntax of
reality and that logic was the syntax of how we know reality. So if our
knowing reality is also part of reality than math is more fundamental
than logic (not vice versa as is commonly thought). However it could
also be argued that logic puts limits on our knowledge of reality.
Therefore even though math is the syntax of reality, the math we can know
is limited by the syntax or logic of our knowing. So we have math which
includes logic which limits the math we can know. Like the proverbial
onion maybe the form of "form within form" is the ultimate nature of
reality.
Jim Piat
_____________________________________________________________________
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------------------------------
Date: Tue, 03 Mar 1998 02:37:02 GMT
From: BugDaddy[…]cris.com (BugDaddy)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: The New List (paragraph 5)
Message-ID: <34ff63cd.2069757[…]pop3.cris.com>
piat[…]juno.com (Jim L Piat) wrote:
>1. We can separate them by ESSENCE according to the principle:
> ------- is the essence of ---------.
I assume you mean "is *not* the essence of."
>2. We can separate them by PRESENCE according to the principle:
> -------can be imagined present without ------also imagined being
>present.
I think the word *understood* seems more appropriate than
*imagined.*
>3. We can separate them simultaneously by both Essence and Presence
>according to the principle :
> -----can actually be known without actual knowledge of ------
>4. Peirce calls these three principles of separation Discrimination,
>Precision and Dissociation. Discrimination is based upon separation by
>pragmatic meaning, precision is based upon separation by selective
>attention, and dissociation is based upon separation by consciousness.
>5. Notice that Essence is the most basic of the three principles by
>which reality is divided at the joints. Next comes Presence and last
>comes Consciousness or Knowledge. Again we have predicate (or essence)
>and subject (or that which is actually present) joined together to
>produce a proposition or knowledge.
>6. We can discriminate red from blue, space from color and color from
>space but not red from color because color is the essence of red.
I certainly *do* discriminate RED from COLOR. RED is a
particular example of COLOR. The two words simply do not mean
the same thing.
>7. We can prescind red from blue and space from color, but not color
>from space nor red from color because we can not imagine color present
>without also imagining space present nor imagine red present without also
>acknowledging color present.
The word *imagine* is horribly psychological for a work on logic.
I believe color is necessarily a property of a body. Bodies, of
course, occupy space. This understanding has nothing to do with
mere *imagination.*
>8. We can dissociate red from blue, but not space from color, color from
>space, nor red from color because we cannot actually know or be conscious
>of a space which is colorless, a color which is spaceless or a colorless
>red. There may in principle be space which is colorless but we have no
>or consciousness of it.
A blind man can understand space without understanding color.
Therefore, *I,* who can see, understand space without any
necessary association with color. Mathematicians are able to
prove numerous theorems about space without any reference to
color. Thus a blind man may apply Euclid's geometry with
complete confidence that it will work *for him.*
>9. In summary:
> We can discriminate, prescind and dissociate red from blue.
> We can discriminate and prescind (but not dissociate) space from
> color.
> We can discriminate (but not prescind or dissociate) color from
> space.
Really?
----------------------------------------------------------
The light which puts out our eyes is darkness to us.
Only that day dawns to which we are awake. There is more day to
dawn. The sun is but a morning star.
Henry David Thoreau, *Walden*
http://www.cris.com/~bugdaddy/sophia
-----------------------------------
Life is a miracle waiting to happen.
http://www.cris.com/~bugdaddy/life.htm
-----------------------------------
Bill Overcamp
-----------------------------------
------------------------------
Date: Tue, 3 Mar 1998 00:01:52 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: The New List (Paragraph 5)
Message-ID: <19980303.000157.4310.0.piat[…]juno.com>
Joe Ransdell wrote:
>I don't know what to make of it, but there is at least a vague
>correlation between the three modes of separation -- discrimination,
>dissociation, and prescision -- and the Kantian distinction between,
>respectively, the analytic a priori (= true or false by definition),
>the
>synthetic a posteriori (= true or false in virtue of the content of
>experience), and the synthetic a priori (= true or false in virtue of
>the a priori structure of experience), in terms of which Kant poses
>the
>guiding question of the Critique of Pure Reason: How is synthetic a
>priori knowledge possible?
Been thinking about this and agree there does seem to be a correspondence
of concerns. Peirce describes precision as intermediate between
discrimination and dissociation just as synthetic a priori seems to be
intermediate between analytic a priori and synthetic a posteriori (Not
that this observation adds much, if anything, to what you've already
said).
Of course it makes sense that there would be a connection given the
Peirce's acknowledged debt to Kant and his avowed starting point for The
New List.
Peirce appears to be attempting to rework and improve upon Kant's ideas
and concerns.
Jim Piat
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------------------------------
Date: Tue, 3 Mar 1998 10:56:14 +0100 (MET)
From: Howard Callaway
To: Multiple recipients of list
Subject: Re: Logic Naturalized?
Message-ID:
On Mon, 2 Mar 1998, Jim L Piat wrote:
> It's me again taking another try at this. I think I lost my way the
> first time and also left out part of the above paragraph to boot.
> Perhaps what I'm calling logic is really the science of signs. But as
> for the paragraph above, the second sentence should read. Reasoning to
> correct conclusions is merely an example or manifestation of the formal
> process of how knowledge of the knowable is applied. Or in plain
> English, reasoning to correct conclusions is merely an example of applied
> logic. Actually I like Tom Burke's statement much better:
>
> >>Logic may *determine* "how we ought to think what is true", but that
> doesn't really say what logic is. That simply puts constraints on it if
> and when it is applied to how we think.<<
I also have no objection to this formulation from Tom. Stating an
anti-psychologistic thesis is not a substitute for trying to define
what logic is in its own terms. But I take it that stating an
anti-psychologistic thesis is not incompatible with plausible
accounts of what logic is either.
> One other second thought. I've suggested that math is the syntax of
> reality and that logic was the syntax of how we know reality. So if our
> knowing reality is also part of reality than math is more fundamental
> than logic (not vice versa as is commonly thought). However it could
> also be argued that logic puts limits on our knowledge of reality.
> Therefore even though math is the syntax of reality, the math we can know
> is limited by the syntax or logic of our knowing. So we have math which
> includes logic which limits the math we can know. Like the proverbial
> onion maybe the form of "form within form" is the ultimate nature of
> reality.
Here I'm inclined to re-emphasize the point that we get a better grasp
of the "descriptive" character of logic by relating it to its actual
and historical exemplifications in use. This is not to deny the pos-
sibility of revising logic, improving it with reference to new
applications and developments, of course. The idea of revising or
developing logic does plausibly rely on mathematics of one sort or
another. But it seems to me that merely mathematical exemplification
of forms of inference are less interesting than non-mathematical
applications. So, perhaps we could say that the typical result of
mathematical logic is to produce speculative extensions/revisions
of more or less standard logics. In fact most such speculative
extensions/revisions won't leave the pages of technical journals.
But its always possible that some particular variation will find
wider application. A plausible example might be the proposals for
"quantum logics." In any case, there are lots of recent discussions
of proposals to revise standard logics. These could certainly be
drawn upon to say something further.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Tue, 3 Mar 1998 14:04:43 +0100
From: Thomas.Riese[…]t-online.de (Thomas Riese)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: The New List (Paragraph 4)
Message-ID:
In response to Bernard Morand, Thu, 26 Feb 10:17:05 -0600 (CST)
Dear Bernard Morand,
I agree with you that the Categories can't be used as a 'rigid'
classification scheme. If that were possible they were just predicates
and not Categories.
Nevertheless I believe that to try and use them whenever possible is
very useful for gaining experience with these excessively general
structures, even if this can't be completely successful.
My little steam-engine is of course far too simplistic and I think in
order to understand what we called 'collapsing' more fully one would
have perhaps better to use mathematical models, for example the
relation of hypercomplex number systems and their algebras. This is
substantially what Peirce himself has done, i.e. his "logic of (dual)
relatives", under a different name. I think this would go too far
here, but a hypercomplex number system can be understood as a
projection of an (linear associative) algebra. One of the problems
with the New List certainly is that the logical process in a certain
sense has three dimensions _logically_.
'Collapsing' would then be geometrically 'projection' and logically
'hypostatic abstraction'.
I think I do understand immediately what you mean by "pli" ('fold',
'crease', etc), Bernard!
I have, over the years, followed with great interest the work of
Isabelle Stengers and Ilya Prigogine and others, as e.g. also Murray
Gell-Mann with his Santa Fe group. Prigogine has written a very
clear-sighted foreword to a collection of Peirce papers on natural
science ('Naturordnung und Zeichenprozess', ed. H.Pape).
For me there are these important points: I think that a theory of
signs has to explain 'atomicity' in general, i.e. the fact that our
universe has physically an atomistic structure, that there are more or
less clearly separated animal species, words, concepts, human beings
etc etc. This can't be taken for granted here. These are very
important facts which amount to saying that information is at all
possible!
To explain atomicity of course means to go a step beyond atomicity and
consider the structure of continuity. In order to explain my ideas, my
plan of work, concerning what you call "pli", I have to step out a
bit:
There are several indications that for the questions we have now
reached in science our tools are simply insufficient. To run into
increasing complexity for me is a signal that it is time for
backtracking. The main tool in science is certainly calculus. Calculus
as we know it today is not particularly suited for processes of growth
and decay. This is perhaps most clearly seen from the fact that
according to Liouville's theorem phase-space volume does not change
with the evolution of time. This is one of the sources of extreme
complexities -- in calculus;-)
And, by the way, this, again, has the same consequences as Peirce
claimed in the Harvard Lectures CP 5.71, we had this recently on
peirce-l (also comp. Roger Penrose, The Emperor's New Mind, e.g
p.343): We have despite all the complexity just one single point on a
continuious map. These things nicely fit together even over seemingly
uncoordinated and widely separated fields:-) It's logically one and
the same problem. And that's why people in physics are unable to unify
the great theories:-) It's the idea of complex unity. In logic! It
works the same miracles as complex numbers in analysis but people are
seemingly unable to grasp this. They want something _absolute_. That's
nonsense. If the beginning of the universe, physical or other, is just
a single point, well, what is the surrounding space then:-)
Psychologically this seems to be an insurmountable difficulty.
Logically it is certainly not so. But this leads too far away...
I think we have to expand the idea of COORDINATION. Rene Descartes'
"cogito ergo sum" is not only akin to Dedekind's construction of the
natural numbers, as is immediately obvious from inspection of the
central proposition 66 in Dedekind's paper 'Was sind und was sollen
die Zahlen'. Further: self-referential systems form only a relatively
'small' domain and the idea of 'general transitivity', expansion by
restriction, potentially applies to Descartes as well as Dedekind.
What is pertinent here is Descartes' idea of a 'coordinate system' and
his discovery of a link between geometry and algebra which has proved
to be so important that today we tend to take this completely for
granted. And further than that: it cannot be overestimated how heavily
(Newton's) calculus, as we know it today, is dependent on this
Cartesian idea of a coordinate system -- logically.
So the task is to expand the idea of coordination and thus to find a
new, more general link between geometry and algebra. This was
substantially the project of Peirce's Existential Graphs.
Implicit in Descartes' idea is that only two things at a time can and
must be coordinated. I think Peirce showed that more than two elements
"at a time" can and must be coordinated for a coordinate system in the
general sense. And here we are at the roots of mathematics and physics
and of the question of representation and of what a system in the
sense of the social sciences could be.
I think it is necessary to go back to Newton's 'Principia',
particularly the central Lemma II in Book Two
(e.g.:
http://www.maths.tcd.ie/pub/HistMath/People/Newton/Principia/Bk2Lem2/)
and it is particularly interesting to read bishop Berkeley's criticism
thereof ('The Analyst: A Discourse addressed to an Infidel
Mathematician'
(e.g.: http://www.knuten.liu.se/~bjoch509/works/berkeley/analyst.html)
(This exercise of going back to the original texts seems to me also to
be particularly revealing in that it shows how certain curious,
seemingly nonsensical and intuitively hardly understandable texts can
sometimes have astonishing consequences -- _practically_, i.e. flying
to the moon and such things!)
I think it is one of the ironies of the history of philosophy that
Berkeley is quite right in his criticism -- but in such a way that he
doesn't destroy Newton's metaphysics, but on the contrary, he flately
and apparently without perceiving this, _fully_confirms_it_. (Somehow
Berkeley seems to have been a specialist in such manoeuvres)
Berkeley should have had a look into Duns Scotus' "De Primo Principio"
and his idea of 'complex unity'. But to go back to Aristotle and the
Scholastics, who were perhaps as 'out' as anybody could be in those
days, would have been far too "conservative", even for a theologician.
Well, Berkeley simply was not "radical" enough;-)
Leibniz, by the way, shows rather directly how important the idea of
coordination in this field is: his monads 'conspire' and at the same
time they have no 'windows'.
So in the mean time the logic of calculus has been stretched beyond
the limits as can also be seen from the absurd sounding project of
"continuous geometries" John von Neumann in his later years had.
On the other hand it _is_ possible to fit _calculus_ into a more
general idea of coordination: Saunders MacLane has shown that the
directional derivative of a function along a path can be developed
from the "product" of the gradient of the function by the tangent
vector to the path, so that gradients (cotangent vectors) are thereby
linear functions of the tangent vectors and vice versa. Dual spaces!
(see MacLane, "Mathematics -- Form and Function", p.193).
By the way: I have visited your web pages at
http://www.iutc3.unicaen.fr/~moranb/
and I would like to say that this was an aethetic and intellectual
pleasure for me.
So more down to earth: I have some practical and/or theoretical
experience with the design of information systems for intensive-care
units and technical monitoring systems for large underground
coal-mines.
In both cases the decisive problem seems to me to be the question what
is, in a given interval of time, 'atomic', i.e. irreducible
information (or, perhaps even better: what should be introduced as
such). This can change dramatically in time and at the same time, I
think, we have to take this 'reduction to atomicity' serious. Ideas,
concepts can be extremely stable, even over hundreds of years. Even
when there are radical changes, they reappear, perhaps in different
disguise, again. Just these phenomena we know if people try to effect
changes in social systems.
On the other hand there have been careful statistical studies which
have shown that though we are able to monitor and influence
physiological processes microbiologically even down to the molecular
level, that does not necessarily mean increased medical success. Not
even in the strictly technical sense. I think then it might be a
question of the economy of research whether a point of view stressing
social and informational factors might not be indicated now.
Especially if we should be able to apply at least as sophisticated
tools as in the natural sciences themselves. If not more so. But
hitherto the really hard questions were simply too difficult. Perhaps
that's why these other fields have been called 'soft'. Funny use of
language.
And coal-mines, where everything up to the size of a truck can
completely disappear in mist and mud are true nightmares if one tries
any rigid classification scheme (we tried to set up a catalog of
possible causes for production stillstands -- our phantasy was never
sufficient:-))
There are very large gaps indeed between kicking certain molecules and
gently touching a human being -- both can be equally important.
Today still far too often either data graveyards or high tech hells
which consist in not much else but false alarms are constructed, I
believe. I think even the usual ideas of control and automation, even
second order cybernetics and such things, are still insufficient.
Philosophy seems to me to be highly important here: when the
straightforward control is too rigid, mere relativism won't do either.
A sequence of managment fashions is not yet a culture, I believe. We
need a viable theory of truth. Norms which are extremely general
without being empty. Perhaps an idea what 'cultural health' might be.
One of the toys I currently have for playing around with atomicity and
transitivity are Wedderburn's structure theorems for abstract
algebras. I don't know whether this is in the mathematics textbooks,
but the ensemble of these algebraic structures seems to me to be at
the same time an abstract projective geometry _and_, as far as I know
a total matrix algebra is a projective geometry too.
Perhaps they are general enough for a mathematical model and at the
same time near enough to purposes of quantitative measurement and
sufficiently akin to Peirce's several systems of logical notation:
Division algebras // subject to further distinction/classification //
~first
Idempotent algebras // directly decidable/decided/boolean // ~second
Total matrix algbras // tools for further inquiry // ~third
Just a VERY ROUGH idea! But I think here it is particularly obvious
that Categories are certainly no very straightforward 'labels'. If
everything works fine, then somehow the number ten (for the different
classes of signs) should come out of this structure.
A nice semiformal description of the ideas behind Wedderburn's
theorems can be found in Edna Kramer's "The Nature and Growth of
Modern Mathematics, Princeton U Press, pp. 679-680. I think the true
potential of these structures isn't yet discovered.
It might fit to what you say on one of your web-pages concerning
"Analyse et Conception des Systemes d'Information" and geometry and at
the same time it is a 'dynamical' system, since every representation
is itself only a sort of 'projection'. Perhaps it was something like
that what v.Neumann had in mind with his 'continuous geometries'.
Such a geometrical model for information systems would have several
immediate advantages. One is that a 'change of bases' is evidently
often very useful -- just the effect we know from engineering
mathematics. On the other hand people all too often disagree though
there is nothing to disagree about. To show that a 'basis
transformation' is possible can be very far from easy. Even the
geometrical idea of a 'norm' makes sense. And of course that does
_not_ mean that all people have to have the same "point of view".
In modelling there is often the idea that the model should necessarily
in all stages have a direct similarity to what is modelled. I think it
is obvious that we often have to introduce new elements. These are
just what is usually called "tricks of the trade". On the other hand
people often get into difficulties since it is not always possible to
justify such ideas immediately in any pictorial, intuitive fashion.
That's one of the reasons why I believe that the idea of coordination
has to be expanded. Coordination does not mean that all involved
people do see and believe the same things in a simplistic
straightforward way.
I do not wish to propose a new method 'more geometrico' in the sense
of an 'automaton' or something. It's only that people should
understand that logic is much more than a simple 'goat and sheep'
business or only consists of empty tautologies, the 'selling' of
preconceived ideas. It's a matter of generation and degeneration,
growth and decay too.
Why do I say this all? -- I started with your idea of a "pli" and
stepped out a bit... Wait: you translated pli into English "crease"
and my eyes, when seeing this immediately slipped into "grease",
lubricant. No joke, this was indeed the case. I had to have a look
into my dictionary:-)
Well, there is indeed a lot in them, in these, let's say folds. We
should go on unfolding this.
Thomas.
P.S. One of the constant experiences of my counselling practice is
that people in trouble vehemently explain to you why it is so
decisively important to be in trouble (and, for heaven's sake, stay
there!). At the same time they usually show you themselves the
solution very immediately and in all desirable iconicity. _Their_
solution! I took me a long time to understand why this must be so in
the case of the more insistent problems.
At the same time this is exactly the fun in counseling (same with
mathematics):-) That's information business too.
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