[peirce-l] Deacon's incompleteness and Peirce's infinity

2012-03-11 Thread Gary Fuhrman
Jon, Gary, Ben and List,

 

There's another part of the Minute Logic which may be related to the connection 
Jon is making between “objective logic” and “categories”. It is definitely 
related to the argument in Terrence Deacon's Incomplete Nature, which Gary R. 
suggested some time ago as worthy of study here. We haven't found a way to 
study it systematically, but maybe it's just as well to do it one post at a 
time. Or one thread at a time, if replies ensue.

 

The central part of Deacon's argument presents “a theory of emergent dynamics 
that shows how dynamical process can become organized around and with respect 
to possibilities not realized” (Deacon, p. 16). Depending on the context, he 
also refers to these “possibilities not realized” as “absential” or 
“ententional”. His argument is explicitly anti-nominalistic and acknowledges 
the reality of a kind of final causation in the physical universe 
(“teleodynamics”). It has a strong affinity with Peirce's argument for a mode 
of being which has its reality in futuro. In other words, he argues for the 
reality of Thirdness without calling it that – indeed without using Peirce's 
phaneroscopic categories at all. (Personally i doubt that he is familiar enough 
with them to use them fluently, but maybe he decided not to use them for some 
reason.)

 

“Incompleteness” is a crucial concept of what i might call Deaconian realism. 
In physical terms, it is connected with Prigogine's idea of dissipative 
structures (including organisms) as far from equilibrium in a universe where 
the spontaneous tendency is toward equilibrium, as the Second Law of 
thermodynamics would indicate. Teleodynamic processes take incompleteness to a 
higher level of complexity, but i don't propose to go into that now. Instead 
i'll present here a Peircean parallel to Deacon's “incompleteness”. The 
connection lies in the fact that incompleteness is etymologically – and perhaps 
mathematically? – equivalent to infinity.

 

First, we have this passage from Peirce's Minute Logic of 1902:

 

[[[ I doubt very much whether the Instinctive mind could ever develop into a 
Rational mind. I should expect the reverse process sooner. The Rational mind is 
the Progressive mind, and as such, by its very capacity for growth, seems more 
infantile than the Instinctive mind. Still, it would seem that Progressive 
minds must have, in some mysterious way, probably by arrested development, 
grown from Instinctive minds; and they are certainly enormously higher. The 
Deity of the Théodicée of Leibniz is as high an Instinctive mind as can well be 
imagined; but it impresses a scientific reader as distinctly inferior to the 
human mind. It reminds one of the view of the Greeks that Infinitude is a 
defect; for although Leibniz imagines that he is making the Divine Mind 
infinite, by making its knowledge Perfect and Complete, he fails to see that in 
thus refusing it the powers of thought and the possibility of improvement he is 
in fact taking away something far higher than knowledge. It is the human mind 
that is infinite. One of the most remarkable distinctions between the 
Instinctive mind of animals and the Rational mind of man is that animals rarely 
make mistakes, while the human mind almost invariably blunders at first, and 
repeatedly, where it is really exercised in the manner that is distinctive of 
it. If you look upon this as a defect, you ought to find an Instinctive mind 
higher than a Rational one, and probably, if you cross-examine yourself, you 
will find you do. The greatness of the human mind lies in its ability to 
discover truth notwithstanding its not having Instincts strong enough to exempt 
it from error. ]] CP 7.380 ]

 

This suggests to me that fallibility – which not even Peirce attributes to God 
– is a highly developed species of incompleteness. The connection with 
infinity, and with Thirdness, is further brought out in Peirce's Harvard 
Lecture of 1903 “On Phenomenology”:

 

[[[ The third category of which I come now to speak is precisely that whose 
reality is denied by nominalism. For although nominalism is not credited with 
any extraordinarily lofty appreciation of the powers of the human soul, yet it 
attributes to it a power of originating a kind of ideas the like of which 
Omnipotence has failed to create as real objects, and those general conceptions 
which men will never cease to consider the glory of the human intellect must, 
according to any consistent nominalism, be entirely wanting in the mind of 
Deity. Leibniz, the modern nominalist par excellence, will not admit that God 
has the faculty of Reason; and it seems impossible to avoid that conclusion 
upon nominalistic principles.

 

But it is not in Nominalism alone that modern thought has attributed to the 
human mind the miraculous power of originating a category of thought that has 
no counterpart at all in Heaven or Earth. Already in that strangely influential 
hodge-podge, the salad of 

Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition

2012-03-11 Thread Irving

Ben Udell asked:


Do you think that your theoretical - computational distinction and
likewise Pratt's creator - consumer distinction between kinds of
mathematics could be expressed in terms of Peirce's theorematic -
corollarial distinction?


Given that Peirce wrote at MS L75:35-39 that:

Deduction is only of value in tracing out the consequences of
hypotheses, which it regards as pure, or unfounded, hypotheses.
Deduction is divisible into sub-classes in various ways, of which the
most important is into corollarial and theorematic. Corollarial
deduction is where it is only necessary to imagine any case in which
the premisses are true in order to perceive immediately that the
conclusion holds in that case. Ordinary syllogisms and some deductions
in the logic of relatives belong to this class. Theorematic deduction
is deduction in which it is necessary to experiment in the imagination
upon the image of the premiss in order from the result of such
experiment to make corollarial deductions to the truth of the
conclusion. The subdivisions of theorematic deduction are of very high
theoretical importance. But I cannot go into them in this statement.

the answer to the question would appear to be: no.

Whereas Peirce's characterization of theorematic and corrolarial
deduction would seem, on the basis of this quote, to have to do with
whether the presumption that the premises of a deductive argument or
proof are true versus whether they require to be established to be
true, and seems more akin, at least peripherally, to the
categorical/hypothetical status of the premises, the distinctions
theoretical - computational which I suggested and likewise Pratt's
creator - consumer are not at all about the deriving theorems or the
what is assumed about the truth of the premises. Rather the distinction
between creator-theoretician vs. consumer-practitioner is a distinction
in which the former is concerned (in the main) to develop new
mathematics on the basis of the mathematics that has already been
established, whereas the consumer practitioner borrows and utilizes
already established mathematics for purposes other than establishing
new mathematical results. The example which I cited, of Riemann and
Minkowski vs. Einstein is applicable here. Riemann expanded known
mathematical results regarding three-dimensional geometries to
n-dimensional geometries (Riemann manifolds) and contributed to the
development of non-Euclidean geometries, and Minkowski starting from
non-Euclidean geometries, in particular parabolic and hyperbolic,
arrived at his saddle-shaped space, and Minkowski taught Einstein the
mathematics of Riemannin and Minkowski geometry, who used it to work
out the details of relativity, but, unlike Riemann or Minkowski, did
not create any new mathematics, just utilized the already given
mathematics of Riemann and Minkowski to mathematically solve a
particular problem in physics. I think most would agree with the
proposition that Einstein was a physicist, rather than a mathematician,
albeit unassailably a mathematical physicist, who employed already
established mathematics and mathematical equations to advance physics,
and along those same lines, I think most would likewise agree with the
proposition that Einstein was not a mathematician. This does not, of
course, take away from his status as a physicist.

By the same token, Newton can be credited as both a mathematician, for
his fluxional caculus as well as a physicist, although his invention --
and I would not want to get into the Newton-Leibniz battle here -- of
the calculus was developed in large measure for the purpose of doing
physics. But the fact that Newton (although he used geometry rather
than the calculus in the mathematics of the Principia) obtained the
fluxional calculus in part to advance mathematics (a major advance over
Cavalieri's ponderous method of indivisibles, and in part to work out
and express mathematically the laws of gravity and of terrestrial and
celestial mechanics, illustrates that a theoretical/ applied
distinction is somewhat artificial as compared with the theoretical -
computational distinction and creator - consumer distinction.


- Message from bud...@nyc.rr.com -
   Date: Wed, 7 Mar 2012 14:41:08 -0500
   From: Benjamin Udell bud...@nyc.rr.com
Reply-To: Benjamin Udell bud...@nyc.rr.com
Subject: Re: [peirce-l] Mathematical terminology, was, review of
Moore's Peirce edition
 To: PEIRCE-L@LISTSERV.IUPUI.EDU



Irving,

Do you think that your theoretical - computational distinction and
likewise Pratt's creator - consumer distinction between kinds of
mathematics could be expressed in terms of Peirce's theorematic -
corollarial distinction? That identification seems not without
issues but still pretty appealing to me, but maybe I've missed
something. (For readers unfamiliar with Peirce's way of
distinguishing theormatic from corollarial, see further below where
I've copied my Wikipedia summary with reference links in the

Re: [peirce-l] Categorical Aspects of Abduction, Deduction, Induction

2012-03-11 Thread Benjamin Udell
Dear Steven,

In your previous post, you said,

  Although the dialogic makes these passages a little difficult to read, it 
seems very clear to me that Peirce, in CP 4.549, is explicitly not referring to 
his own categories as predicated predicates, or assertions on assertions. 

  I think the question of what is a category is clearly addressed earlier, 
in CP 4.544, Peirce says:

  ... of superior importance in Logic is the use of Indices to denote 
Categories and Universes, which are classes that, being enormously large, very 
promiscuous, and known but in small part, cannot be satisfactorily defined, and 
therefore can only be denoted by Indices.
Now you say, 

  After some consideration I think this is an incorrect interpretation Ben.

  Peirce is indeed referring to his own categories (it is difficult to read 
the dialogic and to see how he is not) and he answers the question concerning 
predicates of predicates' in the text of the Prolegomena to which I referred 
earlier.

  The categories stand alone in his view, independent and identifiable, i.e., 
they are indices, we can point to them and they cannot be decomposed. 

Peirce doesn't say in Prolegomena (CP 4.530-572) that categories _are_ 
indices, instead he says that, for categories are denotable only by indices, 
and the reason that he gives is not indecomposibility, but instead their being 
enormously large, very promiscuous, and known but in small part such that 
they cannot be satisfactorily defined..  But the supposed indecomposibility 
of Prolegomena-categories was the only specific positive reason you give for 
thinking that by Category in Prolegomena he means the same that he means by 
Category pretty much everywhere else. Meanwhile you've left untouched the 
positive reasons for thinking that it is not the same Category as everywhere 
else:

1. He says: I will now say a few words about what you have called Categories 
but for which I prefer the designation Predicaments and which you have 
explained as predicates of predicates. Peirce usually calls his own categories 
Categories, not Predicaments, and usually uses Predicaments as an 
alternate term for Aristotle's categories (substance, quantity, relation, 
quality, position (attitude), state, time (when), place, action, passion 
(undergoing).

2. He calls Modes of Being three things whose terms, as the CP editors note, 
he often enough uses as terms for his own categories - Actuality, Possibility, 
and Destiny (or Freedom from Destiny) - that is, Secondness, Firstness, and 
Thirdness, respectively.

3. He says that the divisions so obtained - i.e., 1st-intentional, 
2nd-intentional, 3rd-intentional - must not be confounded with the different 
Modes of Being: Actuality, Possibility, Destiny (or Freedom from Destiny). On 
the contrary, the succession of Predicates of Predicates - i.e., the 
Prolegomena-categories - is different in the different Modes of Being. And on 
those successions, he says, and remember the year is 1906, his thoughts are 
not yet harvested. Seems unlikely indeed that the Prolegomena-categories are 
the same Categories that he has been discussing since 1867.

Best, Ben

- Original Message - 
From: Steven Ericsson-Zenith 
To: PEIRCE-L@LISTSERV.IUPUI.EDU 
Cc: Benjamin Udell 
Sent: Sunday, March 11, 2012 5:20 PM 
Subject: Re: [peirce-l] Categorical Aspects of Abduction, Deduction, Induction 

Dear Ben,

After some consideration I think this is an incorrect interpretation Ben. 

Peirce is indeed referring to his own categories (it is difficult to read the 
dialogic and to see how he is not) and he answers the question concerning 
predicates of predicates' in the text of the Prolegomena to which I referred 
earlier. The categories stand alone in his view, independent and identifiable, 
i.e., they are indices, we can point to them and they cannot be decomposed. 

In my terms, Peirce argues that they are necessary distinctions. The world 
forces them upon us, we do not force them upon the world.

With respect,
Steven

--
Dr. Steven Ericsson-Zenith 
Institute for Advanced Science  Engineering 
http://iase.info

On Mar 9, 2012, at 2:44 PM, Benjamin Udell wrote:

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Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition

2012-03-11 Thread malgosia askanas
Irving wrote, quoting Peirce MS L75:35-39:

Deduction is only of value in tracing out the consequences of
hypotheses, which it regards as pure, or unfounded, hypotheses.
Deduction is divisible into sub-classes in various ways, of which the
most important is into corollarial and theorematic. Corollarial
deduction is where it is only necessary to imagine any case in which
the premisses are true in order to perceive immediately that the
conclusion holds in that case. Ordinary syllogisms and some deductions
in the logic of relatives belong to this class. Theorematic deduction
is deduction in which it is necessary to experiment in the imagination
upon the image of the premiss in order from the result of such
experiment to make corollarial deductions to the truth of the
conclusion. The subdivisions of theorematic deduction are of very high
theoretical importance. But I cannot go into them in this statement.


[...] Peirce's characterization of theorematic and corrolarial
deduction would seem, on the basis of this quote, to have to do with
whether the presumption that the premises of a deductive argument or
proof are true versus whether they require to be established to be
true [...]

I would disagree with this reading of the Peirce passage.  It seems
to me that the distinction he is making is, rather, between (1) the case
where the conclusion can be seen to follow from the premisses
by virtue of the logical form alone, as in A function which is continuous
on a closed interval is continuous on any subinterval of that interval
(whose truth is obvious without requiring us to imagine any continuous
function or any interval), and (2) the case where the deduction of the
conclusions from the premisses requires turning one's imagination
upon, and experimenting with, the actual mathematical objects
of which the theorem speaks, as in A function which is continuous
on a closed interval is bounded on that interval.

-malgosia

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Re: [peirce-l] Categorical Aspects of Abduction, Deduction, Induction

2012-03-11 Thread Steven Ericsson-Zenith
Dear Ben,

There is no inconsistency as I see it, though I may not have stated the case 
clearly enough. In the first I said Peirce is not referring to his categories 
AS predicates of predicates, not that he is not referring to his categories.

As index I am referring to the category itself, not its elements. A category 
stands apart from the elements that it may select by virtue of its properties. 
Apprehended, denoted, the category is indexed; 1st, 2nd, 3rd. You object to my 
saying that a category IS an index, by which I mean that it has the properties 
of an index. You appear to suggest that indices has another level of being, 
that will lead to an infinite recurse. 

Again:

... of superior importance in Logic is the use of Indices to denote Categories 
and Universes, which are classes that, being enormously large, very 
promiscuous, and known but in small part, cannot be satisfactorily defined, and 
therefore can only be denoted by Indices.

A year earlier, in 1866, Peirce wrote On A Method Of Searching For The 
Categories in which he lists the categories as Quality, Relation, 
Representation. So it seems clear that in this period he already had his 
categories and is referring to them here.

See p. 520 and p. 524 of the first volume of the chronological edition 
Writings of CSP.

On they cannot be decomposed, in CP 1.299 Peirce writes:

We find then a priori that there are three categories of undecomposable 
elements to be expected in the phaneron: those which are simply positive 
totals, those which involve dependence but not combination, those which involve 
combination.

Predicaments are predicates of predicates for Peirce, Aristotle's 
Categories.

With respect,
Steven


--
Dr. Steven Ericsson-Zenith
Institute for Advanced Science  Engineering
http://iase.info







On Mar 11, 2012, at 4:35 PM, Benjamin Udell wrote:

 Dear Steven,
 
 In your previous post, you said,
 
 Although the dialogic makes these passages a little difficult to read, it 
 seems very clear to me that Peirce, in CP 4.549, is explicitly not referring 
 to his own categories as predicated predicates, or assertions on assertions. 
 
 I think the question of what is a category is clearly addressed earlier, 
 in CP 4.544, Peirce says:
 
 ... of superior importance in Logic is the use of Indices to denote 
 Categories and Universes, which are classes that, being enormously large, 
 very promiscuous, and known but in small part, cannot be satisfactorily 
 defined, and therefore can only be denoted by Indices.
 Now you say,
 
 After some consideration I think this is an incorrect interpretation Ben.
 
 Peirce is indeed referring to his own categories (it is difficult to read 
 the dialogic and to see how he is not) and he answers the question 
 concerning predicates of predicates' in the text of the Prolegomena to 
 which I referred earlier.
 
 The categories stand alone in his view, independent and identifiable, i.e., 
 they are indices, we can point to them and they cannot be decomposed.
 
 Peirce doesn't say in Prolegomena (CP 4.530-572) that categories _are_ 
 indices, instead he says that, for categories are denotable only by indices, 
 and the reason that he gives is not indecomposibility, but instead their 
 being enormously large, very promiscuous, and known but in small part such 
 that they cannot be satisfactorily defined..  But the supposed 
 indecomposibility of Prolegomena-categories was the only specific positive 
 reason you give for thinking that by Category in Prolegomena he means the 
 same that he means by Category pretty much everywhere else. Meanwhile 
 you've left untouched the positive reasons for thinking that it is not the 
 same Category as everywhere else:
 
 1. He says: I will now say a few words about what you have called Categories 
 but for which I prefer the designation Predicaments and which you have 
 explained as predicates of predicates. Peirce usually calls his own 
 categories Categories, not Predicaments, and usually uses Predicaments 
 as an alternate term for Aristotle's categories (substance, quantity, 
 relation, quality, position (attitude), state, time (when), place, action, 
 passion (undergoing).
 
 2. He calls Modes of Being three things whose terms, as the CP editors 
 note, he often enough uses as terms for his own categories - Actuality, 
 Possibility, and Destiny (or Freedom from Destiny) - that is, Secondness, 
 Firstness, and Thirdness, respectively.
 
 3. He says that the divisions so obtained - i.e., 1st-intentional, 
 2nd-intentional, 3rd-intentional - must not be confounded with the different 
 Modes of Being: Actuality, Possibility, Destiny (or Freedom from Destiny). On 
 the contrary, the succession of Predicates of Predicates - i.e., the 
 Prolegomena-categories - is different in the different Modes of Being. And 
 on those successions, he says, and remember the year is 1906, his thoughts 
 are not yet harvested. Seems unlikely indeed that the