Re: [peirce-l] Doctrine Of Individuals

[Jon Awbrey]

Irving,

It would be impossible for me to tell you how much I value your contributions
on multiple scores without becoming effusive to the point of embarrassment,
and I'm sorry I didn't preface my list of links with a better explanation.
At any rate, I hope it's clear now that Peirce's treatment of individuals
is simply one of those open subjects that I revisit on a periodic basis,
and that all I was doing there was jumping at the chance to discuss the
old puzzles in hopes of new light being cast on them this time around.

Regards,

Jon

Irving Anellis wrote:

Jon, Auke, Jim W., list members,
 
My intention is and was not to withdraw from the list, but from the particular 
discussion regarding the role of individuals had played in Peirce's logic -- or, 
according to van Heijenoort had not played in Peirce's logic. My question was 
meant to sort out and distinguish my claims from van Heijenoort's, as it seemed 
-- to me, at least -- that the arsenal of quotations which Jon presented were 
designed to establish that the usual view, as enunciated by van Heijenoort, was 
incorrect. Indeed, van Heijenoort's claim that there are no individuals in 
Peirce's universe of discourse, as I myself have noted many times, is patently 
incorrect. But since the quotations were listed without explanation or 
qualification, it was unclear to me whether they were misdirected at me, or 
directed, and correctly so, at van Heijenoort. So my question was really 
intended to ascertain whether or not I had been misunderstood.
 
All this by way of explanation.
 
More crucially, I wish to thank all those who wrote to encourage me to continue 
on the lis, and to apololgize for the misunderstandings and confusions that 
ensued. I suppose we can take this as an example of one point at which I would 
agree with van Heijenoort, and probably most formal logicians: that natural or 
ordinary language embeds a vagueness that an ideal language is intended to override.
 
Once again, thanks to all for your encouragement!
 
I'm not planning on going anywhere.
 
Irving
 
 
Irving H. Anellis

Visiting Research Associate
Peirce Edition Project, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info


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Re: [peirce-l] Doctrine Of Individuals

[Irving Anellis]

Jon, Auke, Jim W., list members,
 
My intention is and was not to withdraw from the list, but from the particular discussion regarding the role of individuals had played in Peirce's logic -- or, according to van Heijenoort had not played in Peirce's logic. My question was meant to sort out and distinguish my claims from van Heijenoort's, as it seemed -- to me, at least -- that the arsenal of quotations which Jon presented were designed to establish that the usual view, as enunciated by van Heijenoort, was incorrect. Indeed, van Heijenoort's claim that there are no individuals in Peirce's universe of discourse, as I myself have noted many times, is patently incorrect. But since the quotations were listed without explanation or qualification, it was unclear to me whether they were misdirected at me, or directed, and correctly so, at van Heijenoort. So my question was really intended to ascertain whether or not I had been misunderstood.
 
All this by way of explanation.
 
More crucially, I wish to thank all those who wrote to encourage me to continue on the lis, and to apololgize for the misunderstandings and confusions that ensued. I suppose we can take this as an example of one point at which I would agree with van Heijenoort, and probably most formal logicians: that natural or ordinary language embeds a vagueness that an ideal language is intended to override.
 
Once again, thanks to all for your encouragement!
 
I'm not planning on going anywhere.
 
Irving
 
 
Irving H. AnellisVisiting Research AssociatePeirce Edition Project, Institute for American Thought902 W. New York St.Indiana University-Purdue University at IndianapolisIndianapolis, IN 46202-5159USAURL: http://www.irvinganellis.info 
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Re: [peirce-l] Doctrine Of Individuals

[Jon Awbrey]

Peircers,

Here's one gloss on what Peirce meant by the term "division" --

CSP: The moment, then, that we pass from nothing and the vacuity of being to
 any content or sphere, we come at once to a composite content and sphere.
 In fact, extension and comprehension — like space and time — are quantities
 which are not composed of ultimate elements; but every part however small 
is
 divisible.

CSP: The consequence of this fact is that when we wish to enumerate the sphere 
of a term —
 a process termed division — or when we wish to run over the content of a 
term —
 a process called definition — since we cannot take the elements of our 
enumeration
 singly but must take them in groups, there is danger that we shall take 
some element
 twice over, or that we shall omit some. Hence the extension and 
comprehension which we
 know will be somewhat indeterminate. But we must distinguish two kinds of 
these quantities.
 If we were to subtilize we might make other distinctions but I shall be 
content with two.
 They are the extension and comprehension relatively to our actual 
knowledge, and what these
 would be were our knowledge perfect.

CSP: Logicians have hitherto left the doctrine of extension and comprehension 
in a very imperfect
 state owing to the blinding influence of a psychological treatment of the 
matter. They have,
 therefore, not made this distinction and have reduced the comprehension of 
a term to what
 it would be if we had no knowledge of fact at all. I mention this because 
if you should
 come across the matter I am now discussing in any book, you would find the 
matter left
 in quite a different state.

CSP: Peirce 1866, Lowell Lecture 7, Chron. Ed. 1, p. 462.

Cf: 
http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Information_%3D_Comprehension_%C3%97_Extension#Selection_12

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Re: [peirce-l] Doctrine Of Individuals

[Jim Willgoose]

Jerry, "Picturesque" was meant as a compliment. Logic doesn't pass judgement on 
whether there are individuals or not. Jim W
 > Date: Sun, 11 Dec 2011 11:06:10 -0500
> From: jerry_lr_chand...@me.com
> Subject: Re: [peirce-l] Doctrine Of Individuals
> To: PEIRCE-L@LISTSERV.IUPUI.EDU
> 
> Gary, Jim W., Ben, List:
> 
> Upon awakening this morning, I recognized that I should have been more 
> explicit in my comment last evening. Your prompt response eases my task.
> 
> The question is one of the distinction between semantics and syntax and 
> arithmetic operations on logical terms as well as the distinction between 
> arithmetic division and logical division. 
> 
> The logical point is one of the distinction between division as a separation 
> of a number into EQUAL parts and the separation of a logical term into 
> components.  
> 
> The quote from CSP is:
> 
> In reference to the doctrine of individuals, two distinctions should be
> | borne in mind.  The logical atom, or term not capable of logical division,
> | must be one of which every predicate may be universally affirmed or denied.
> | For, let 'A' be such a term.  Then, if it is neither true that all 'A' is 
> 'X'
> | nor that no 'A' is 'X', it must be true that some 'A' is 'X' and some 'A' is
> | not 'X';  and therefore 'A' may be divided into 'A' that is 'X' and 'A' that
> | is not 'X', which is contrary to its nature as a logical atom.
> |
> 
> For example, consider the the term of "my memory". 
> 
>  I hope this illustrates the grounding of feelings on this notion of the 
> usage of the term "individual".  :-)
> 
> BTW, this quote of CSP brings to my mind Bertrum Russell's famous paper "On 
> denotation" which, even though it has been twenty years since I first read 
> it, continues to give me a good chuckle.  Oh, how human it is to follow the 
> herd, philosophically or otherwise.
> 
> I would be delighted to learn of your rhetorical clarification of the 
> practical distinction between a logical atom, a mathematical atom and a 
> chemical atom; only the latter can be separated into parts (nucleus and 
> electrons - non-equal parts.) 
> 
>  The natural antecedence of unequal parts of chemical atoms was either not 
> known to or not accepted by CSP.  Consequently, he sought to use the logic of 
> chemistry to found a critical component of the over-all structure of his 
> pragmaticism.  (see EP2, #26, especially p362-363.)  
> 
> This mistaken judgment (either from ignorance or intent) killed the notion of 
> phaneroscopy within the natural sciences BECAUSE chemical valences of four, 
> five, six,... are not the same as the chemical valence of three  and the 
> things with higher valence are not the logical equivalence of things with 
> valence three. In other words, CSP's principle of "Thing-representation-form" 
> as represented in the diagrams of EP2, #26 FAILS for chemical valence.  In so 
> far as the logic of chemistry founded CSP's logic of phaneroscopy, it is not 
> supported by the perplexity of the mathematics of modern chemistry.  The 
> modern concept of chemical relations, such as between two strands of a DNA 
> molecule, is vastly richer than CSP's diagrams of p. 364 of EP2. 
> 
> Indeed, exactly the contrary exists in nature. As the number of relations 
> within a chemical molecule increases, the information content increases as a 
> consequence of the different sorts of parts. It is this increase in 
> information that becomes the natural source of DNA as the genetic material 
> and a component of our uniqueness as individual human beings.  Jim Willgoose 
> find this line of reasoning to be "picturesque".  In fact, it is among the 
> central concepts of molecular biology and the neurosciences.  
> 
> 
> Gary, you comment on an earlier post wrt to the usage of the term "special 
> sciences" by Ben.  I went on a business trip shortly after the posting and, 
> upon my return, decided that it was not worth re-opening the cold thread.  
> Ben does a very fine job of articulating historical ideas; my interests 
> reside in projecting historical concepts onto the present and hopefully, into 
> the future.
> 
> So, I am glad you brought it up.  I feel it is analogous to the exchange of 
> usage you and I had concerning the nature of community / communication / 
> communism / communion / and common.   Your argument of "convention" as a 
> standard of usage is applicable to Ben's usage.  I persist in maintaining 
> that one should, in professional disc

Re: [peirce-l] Doctrine Of Individuals

[Jerry LR Chandler]

to classifies the various 
manifestations of the mathematical sciences based on current usage and the 
hierarchical (categorical?) structures and scalings (size) of things. 

As for Deacon's usage, the social sciences are what they are - they deal with 
the community and are unique in that regard.  Such is the function of 
adjectives in creating sub-classes.

Cheers

Jerry






On Dec 11, 2011, at 9:51 AM, Gary Fuhrman wrote:

> Jerry, you wrote,
> 
> [[ One should also note the inexact usage of the term "division" when in fact 
> the meaning is "separation" (with respect to "logical atoms".) ]]
> 
> But i'm afraid it is your usage that is inexact. A logical atom (for Peirce 
> and every other logician that i know of) is defined by its Greek root, which 
> means exactly "indivisible". The current usage of "atom" in physics and 
> chemistry parted company with logic as soon as it was demonstrated that 
> physical "atoms" could be divided into component parts -- protons, neutrons, 
> electrons etc.
> 
> By the way, you also posted earlier about Peirce's usage of the term "special 
> sciences", saying that it is meaningless in contemporary science. Ben already 
> replied to that, but i'd like to add a comment or two. I had never heard this 
> term before i came across it in Peirce, but his usage is so handy and 
> straightforward that i've been using it myself ever since, in reference to 
> any non-cenoscopic science, in other words any science that studies a special 
> (limited) range of phenomena (and generally uses special apparatus to make 
> its observations). Physics, chemistry and psychology are all special sciences 
> in this sense. 
> 
> But i came across a very different sense while reading Terrence Deacon's 
> _Incomplete Nature_ -- thanks to Gary Richmond for pointing to it, and i hope 
> we can discuss it next year as Gary suggested, because it makes explicit use 
> of some important Peircean ideas. Deacon implies that the usage of "special 
> sciences" which he mentions is current within some (unspecified) academic or 
> scientific community with which he is familiar. On page 40, for instance, he 
> speaks of an "effort to include the special sciences (e.g., psychology, 
> sociology, economics) within the natural sciences." I gather that by this 
> usage, physics and chemistry are unequivocally "natural sciences", and 
> therefore *not* "special", while the three sciences named by Deacon are 
> "special" because their status as "natural" sciences is questionable. 
> Elsewhere in the book Deacon seems to distance himself from this usage by 
> referring to "the so-called special sciences". I recall using the terms 
> "hard" and "soft sciences" to make a distinction like that, but have never 
> heard the term "special sciences" used that way -- but then i don't move in 
> academic circles. I'm wondering whether anyone else on peirce-l has come 
> across this usage of the term.
> 
> Gary F.
> 
> } Once the whole is divided, the parts need names. There are already enough 
> names. One must know when to stop. [Tao Te Ching 32  (Feng/English)] {
> 
> www.gnusystems.ca/Peirce.htm }{ gnoxic studies: Peirce
> 
> -Original Message-
> From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On 
> Behalf Of Jerry LR Chandler
> Sent: December-10-11 11:32 PM
> To: PEIRCE-L@LISTSERV.IUPUI.EDU
> Subject: Re: [peirce-l] Doctrine Of Individuals
> 
> Jon, List:
> 
> Thanks for posting this set of fragments on individuals.
> 
> The writings are well worth studying, particularly if one is interested in 
> the leaps in CSP's mental development and his loss of correspondence with 
> modern chemical theories.
> 
> The changing views of the notion of "individual" is amusing.
> 
> One should also note the inexact usage of the term "division" when in fact 
> the meaning is "separation" (with respect to "logical atoms".)
> 
> One is forced to conclude that CSP's notion of a "logical atom" is remote 
> from any sort of relation to chemistry where the reference for an atom is an 
> atomic number and the signs from the indexical object.
> 
> It appears that he recognized this distinction and moved toward chemical 
> thinking in his developments of his versions of graph theory.
> 
> Cheers
> 
> Jerry 
> 
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Re: [peirce-l] Doctrine Of Individuals

[Jon Awbrey]

Re: Doctine Of Individuals
At: http://stderr.org/pipermail/inquiry/2011-December/003739.html

Jerry & All,

I apologize to all once again that other business and pleasures
of the season have prevented me from keeping up with the current
discussions. I'm not sure how the matter of individuals arose this
time -- I think it may have been questions that Jim Willgoose asked
about the relative power of various logical systems. Irving Anellis
then contributed an invaluable wealth of historiographic detail that
I can but digest mere fractions of at one or two sittings, much less
follow up with my own spare resources.  So we have to continue being
grateful to him for that.

For my part, my mental push-down stack lacks the capacity to keep up with
A's interpretation of B's interpretation of C's interpretation of D's ...,
so I have a tendency to flush the filters and return to reading the prime
source at hand, in this instance, what Peirce had to say about individuals,
individual terms, logical atoms, and so on.

When I have managed to focus on that, admittedly not an easy thing to do,
I find, or at least suspect to find, previously unsuspected, at least by
many, anticipations and hints of logical power of an utterly novel order.

So that is what I will try to keep focused on.

Regards,

Jon

JC = Jerry Chandler

JC: Thanks for posting this set of fragments on individuals.

JC: The writings are well worth studying, particularly if one is interested
in the leaps in CSP's mental development and his loss of correspondence
with modern chemical theories.

JC: The changing views of the notion of "individual" is amusing.

JC: One should also note the inexact usage of the term "division" when in
fact the meaning is "separation" (with respect to "logical atoms".)

JC: One is forced to conclude that CSP's notion of a "logical atom" is remote
from any sort of relation to chemistry where the reference for an atom is
an atomic number and the signs from the indexical object.

JC: It appears that he recognized this distinction and moved toward chemical
thinking in his developments of his versions of graph theory.

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Re: [peirce-l] Doctrine Of Individuals

[Benjamin Udell]

Gary F., Jerry,

When I first saw the phrase "special sciences" in Peirce, I was already 
acquainted with it in Neo-Thomistic writing, I think it was Maurice de Wulf 
ascribing the idea to medieval Schoolmen, but maybe also I read it in Gilson. 
In de Wulf's version - if I remember correctly - even mathematics is a 'special 
science'. (Comte and Peirce classed mathematics as the most general and basic 
science).  I've also seen the phrase "particular sciences" in the same sense. 

In de Wulf's view, a science studies a class of objects and "passes over" 
individual differences, and I rebelled at that idea. Darwin certainly wasn't 
passing over individual differences when he dissected pigeons since he needed 
to _find out_ which characteristics were common and which ones were 
idiosyncratic; also one seeks to understand the individual differences as 
reflecting combinations of rules, also of circumstances, etc.  Anyway the idea 
was that the first big step of abstraction was that of abstraction of classes 
from individual things, occurrences, etc.

De Wulf depicted the Scholastic view as being that the next big step of 
abstraction was that of abstraction from bodily change, leaving only quantity, 
studied by mathematicians. 

Next and last big step, the abstraction from quantity, leaving only substance 
in the philosophical sense of "substance", studied by metaphysics a.k.a. First 
Philosophy. (The phrase "First Philosophy" goes back to Aristotle, of course). 
I also seem to remember a Neo-Thomist - I think it was Maritain, though I can't 
swear to it - dividing the scientific subject matters into the supernatural 
(metaphysical), preternatural (mathematical), and natural (physical, material, 
biological, human/social). If such ideas (aside from some of the terminology) 
were common among the medieval Schoolmen, then Peirce was very likely familiar 
with them.

Best, Ben


- Original Message ----- 
From: "Gary Fuhrman" 
To: 
Sent: Sunday, December 11, 2011 9:51 AM
Subject: Re: [peirce-l] Doctrine Of Individuals

Jerry, you wrote,

[[ One should also note the inexact usage of the term "division" when in fact 
the meaning is "separation" (with respect to "logical atoms".) ]]

But i'm afraid it is your usage that is inexact. A logical atom (for Peirce and 
every other logician that i know of) is defined by its Greek root, which means 
exactly "indivisible". The current usage of "atom" in physics and chemistry 
parted company with logic as soon as it was demonstrated that physical "atoms" 
could be divided into component parts -- protons, neutrons, electrons etc.

By the way, you also posted earlier about Peirce's usage of the term "special 
sciences", saying that it is meaningless in contemporary science. Ben already 
replied to that, but i'd like to add a comment or two. I had never heard this 
term before i came across it in Peirce, but his usage is so handy and 
straightforward that i've been using it myself ever since, in reference to any 
non-cenoscopic science, in other words any science that studies a special 
(limited) range of phenomena (and generally uses special apparatus to make its 
observations). Physics, chemistry and psychology are all special sciences in 
this sense. 

But i came across a very different sense while reading Terrence Deacon's 
_Incomplete Nature_ -- thanks to Gary Richmond for pointing to it, and i hope 
we can discuss it next year as Gary suggested, because it makes explicit use of 
some important Peircean ideas. Deacon implies that the usage of "special 
sciences" which he mentions is current within some (unspecified) academic or 
scientific community with which he is familiar. On page 40, for instance, he 
speaks of an "effort to include the special sciences (e.g., psychology, 
sociology, economics) within the natural sciences." I gather that by this 
usage, physics and chemistry are unequivocally "natural sciences", and 
therefore *not* "special", while the three sciences named by Deacon are 
"special" because their status as "natural" sciences is questionable. Elsewhere 
in the book Deacon seems to distance himself from this usage by referring to 
"the so-called special sciences". I recall using the terms "hard" and "soft 
sciences" to make a distinction like that, but have never heard the term 
"special sciences" used that way -- but then i don't move in academic circles. 
I'm wondering whether anyone else on peirce-l has come across this usage of the 
term.

Gary F.

} Once the whole is divided, the parts need names. There are already enough 
names. One must know when to stop. [Tao Te Ching 32  (Feng/English)] {

www.gnusystems.ca/Peirce.htm }{ gnoxic studies: Pei

Re: [peirce-l] Doctrine Of Individuals

[Gary Fuhrman]

Jerry, you wrote,

[[ One should also note the inexact usage of the term "division" when in fact 
the meaning is "separation" (with respect to "logical atoms".) ]]

But i'm afraid it is your usage that is inexact. A logical atom (for Peirce and 
every other logician that i know of) is defined by its Greek root, which means 
exactly "indivisible". The current usage of "atom" in physics and chemistry 
parted company with logic as soon as it was demonstrated that physical "atoms" 
could be divided into component parts -- protons, neutrons, electrons etc.

By the way, you also posted earlier about Peirce's usage of the term "special 
sciences", saying that it is meaningless in contemporary science. Ben already 
replied to that, but i'd like to add a comment or two. I had never heard this 
term before i came across it in Peirce, but his usage is so handy and 
straightforward that i've been using it myself ever since, in reference to any 
non-cenoscopic science, in other words any science that studies a special 
(limited) range of phenomena (and generally uses special apparatus to make its 
observations). Physics, chemistry and psychology are all special sciences in 
this sense. 

But i came across a very different sense while reading Terrence Deacon's 
_Incomplete Nature_ -- thanks to Gary Richmond for pointing to it, and i hope 
we can discuss it next year as Gary suggested, because it makes explicit use of 
some important Peircean ideas. Deacon implies that the usage of "special 
sciences" which he mentions is current within some (unspecified) academic or 
scientific community with which he is familiar. On page 40, for instance, he 
speaks of an "effort to include the special sciences (e.g., psychology, 
sociology, economics) within the natural sciences." I gather that by this 
usage, physics and chemistry are unequivocally "natural sciences", and 
therefore *not* "special", while the three sciences named by Deacon are 
"special" because their status as "natural" sciences is questionable. Elsewhere 
in the book Deacon seems to distance himself from this usage by referring to 
"the so-called special sciences". I recall using the terms "hard" and "soft 
sciences" to make a distinction like that, but have never heard the term 
"special sciences" used that way -- but then i don't move in academic circles. 
I'm wondering whether anyone else on peirce-l has come across this usage of the 
term.

Gary F.

} Once the whole is divided, the parts need names. There are already enough 
names. One must know when to stop. [Tao Te Ching 32  (Feng/English)] {

www.gnusystems.ca/Peirce.htm }{ gnoxic studies: Peirce

-Original Message-
From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On Behalf 
Of Jerry LR Chandler
Sent: December-10-11 11:32 PM
To: PEIRCE-L@LISTSERV.IUPUI.EDU
Subject: Re: [peirce-l] Doctrine Of Individuals

Jon, List:

Thanks for posting this set of fragments on individuals.

The writings are well worth studying, particularly if one is interested in the 
leaps in CSP's mental development and his loss of correspondence with modern 
chemical theories.

The changing views of the notion of "individual" is amusing.

One should also note the inexact usage of the term "division" when in fact the 
meaning is "separation" (with respect to "logical atoms".)

One is forced to conclude that CSP's notion of a "logical atom" is remote from 
any sort of relation to chemistry where the reference for an atom is an atomic 
number and the signs from the indexical object.

It appears that he recognized this distinction and moved toward chemical 
thinking in his developments of his versions of graph theory.

Cheers

Jerry 

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Re: [peirce-l] Doctrine Of Individuals

[Jerry LR Chandler]

Jon, List:

Thanks for posting this set of fragments on individuals.

The writings are well worth studying, particularly if one is interested in the 
leaps in CSP's mental development and his loss of correspondence with modern 
chemical theories.

The changing views of the notion of "individual" is amusing.

One should also note the inexact usage of the term "division" when in fact the 
meaning is "separation" (with respect to "logical atoms".)

One is forced to conclude that CSP's notion of a "logical atom" is remote from 
any sort of relation to chemistry where the reference for an atom is an atomic 
number and the signs from the indexical object.

It appears that he recognized this distinction and moved toward chemical 
thinking in his developments of his versions of graph theory.

Cheers

Jerry 


On Dec 8, 2011, at 5:25 PM, Jon Awbrey wrote:

> Peircers,
> 
> Writing "in reference to the doctrine of individuals" in his
> "Description of a Notation for the Logic of Relatives" (1870),
> Peirce's approach is, in its basic principles, so far ahead of
> his time that it overleaps the dustbin of Logical Atomism and
> anticipates ideas about element-free set theory that will not
> come into their own until the latter part of the 20th Century.
> 
> Here is a collection of excerpts that I gathered for
> several previous occasions, here and elsewhere, when
> the topic of Peirce's approach to individuals arose.
> 
> o~o~o~o~o~o
> 
> DOI.  Doctrine Of Individuals
> 
> o~o~o~o~o~o
> 
> DOI.  Note 1
> 
> o~o~o~o~o~o
> 
> | In reference to the doctrine of individuals, two distinctions should be
> | borne in mind.  The logical atom, or term not capable of logical division,
> | must be one of which every predicate may be universally affirmed or denied.
> | For, let 'A' be such a term.  Then, if it is neither true that all 'A' is 
> 'X'
> | nor that no 'A' is 'X', it must be true that some 'A' is 'X' and some 'A' is
> | not 'X';  and therefore 'A' may be divided into 'A' that is 'X' and 'A' that
> | is not 'X', which is contrary to its nature as a logical atom.
> |
> | Such a term can be realized neither in thought nor in sense.
> |
> | Not in sense, because our organs of sense are special -- the eye,
> | for example, not immediately informing us of taste, so that an image
> | on the retina is indeterminate in respect to sweetUess and non-sweetness.
> | When I see a thing, I do not see that it is not sweet, nor do I see that it
> | is sweet;  and therefore what I see is capable of logical division into the
> | sweet and the not sweet.  It is customary to assume that visual images are
> | absolutely determinate in respect to color, but even this may be doubted.
> | I know of no facts which prove that there is never the least vagueness
> | in the immediate sensation.
> |
> | In thought, an absolutely determinate term cannot be realized,
> | because, not being given by sense, such a concept would have to
> | be formed by synthesis, and there would be no end to the synthesis
> | because there is no limit to the number of possible predicates.
> |
> | A logical atom, then, like a point in space, would involve for
> | its precise determination an endless process.  We can only say,
> | in a general way, that a term, however determinate, may be made
> | more determinate still, but not that it can be made absolutely
> | determinate.  Such a term as "the second Philip of Macedon" is
> | still capable of logical division -- into Philip drunk and
> | Philip sober, for example;  but we call it individual because
> | that which is denoted by it is in only one place at one time.
> | It is a term not 'absolutely' indivisible, but indivisible as
> | long as we neglect differences of time and the differences which
> | accompany them.  Such differences we habitually disregard in the
> | logical division of substances.  In the division of relations,
> | etc., we do not, of course, disregard these differences, but we
> | disregard some others.  There is nothing to prevent almost any
> | sort of difference from being conventionally neglected in some
> | discourse, and if 'I' be a term which in consequence of such
> | neglect becomes indivisible in that discourse, we have in
> | that discourse,
> |
> |['I'] = 1.
> |
> | This distinction between the absolutely indivisible and that which
> | is one in number from a particular point of view is shadowed forth
> | in the two words 'individual' ('to atomon') and 'singular' ('to kath
> | ekaston');  but as those who have used the word 'individual' have not
> | been aware that absolute individuality is merely ideal, it has come to
> | be used in a more general sense.
> |
> | C.S. Peirce, 'Collected Papers', CP 3.93
> 
> Peirce defines the "number" ['t'] of a logical term 't' as follows:
> 
> | I propose to assign to all logical terms, numbers;  to an absolute term,
> | the numbe

Re: [peirce-l] Doctrine Of Individuals

[Jon Awbrey]

Irving (& All),

I hope you didn't think any of that was directed at you specifically.
To be perfectly honest, I haven't even caught up with that branch of
the discussion well enough yet to digest the details of what various
participants were asserting or not. I was merely recalling a text to
which I periodically return whenever that whole complex of questions
cycling around individual existence, individual terms, logical atoms,
Leibniz indiscernibles, and even just nominalism v. realism comes up.

Regards,

Jon

Irving Anellis wrote:
>

The sample quotes from Peirce regarding individuals are much appreciated.
 
Nevertheless: ...
 
Did Anellis claim that there are no individuals in Peirce's logical system? No.
 
Did Anellis say that van Heijenoort claim that there are no individuals in 
Peirce's logical system? Yes.
 
Did Anellis say that Bertrand Russell claimed that there are no individuals in 
Schroeder's logic? Yes.
 
Did Bertrand Russell tell Norbert Wiener that he  had judged that Peano's logic 
was better than Schroeder's because Peano was able to refer to individuals in 
his system (had a notation for 'the'), whereas Schroeder's did not? Yes.
 
Did Anellis claim that it was Bertrand Russell (and by implication also van 
Heijenoort, had he known of Russell's account of that discussion with Wiener) 
who denied that there are individuals in the classical Boole-Schroeder calculus? Yes
 
Did Anellis claim that there are no individuals in Schroeder's logic? No.
 
Is it perhaps time for Anellis to withdraw from the discussion? Yes? / No?
 
 
 
Dec 8, 2011 05:28:41 PM, jawb...@att.net  wrote:


Peircers,

Writing "in reference to the doctrine of individuals" in his
"Description of a Notation for the Logic of Relatives" (1870),
Peirce's approach is, in its basic principles, so far ahead of
his time that it overleaps the dustbin of Logical Atomism and
anticipates ideas about element-free set theory that will not
come into their own until the latter part of the 20th Century.

Here is a collection of excerpts that I gathered for
several previous occasions, here and elsewhere, when
the topic of Peirce's approach to individuals arose.

o~o~o~o~o~o

DOI. Doctrine Of Individuals

o~o~o~o~o~o

DOI. Note 1

o~o~o~o~o~o

| In reference to the doctrine of individuals, two distinctions should be
| borne in mind. The logical atom, or term not capable of logical division,
| must be one of which every predicate may be universally affirmed or 
denied.
| For, let 'A' be such a term. Then, if it is neither true that all 'A' is 
'X'
| nor that no 'A' is 'X', it must be true that some 'A' is 'X' and some 'A' 
is
| not 'X'; and therefore 'A' may be divided into 'A' that is 'X' and 'A' 
that
| is not 'X', which is contrary to its nature as a logical atom.
|
| Such a term can be realized neither in thought nor in sense.
|
| Not in sense, because our organs of sense are special -- the eye,
| for example, not immediately informing us of taste, so that an image
| on the retina is indeterminate in respect to sweetUess and non-sweetness.
| When I see a thing, I do not see that it is not sweet, nor do I see that 
it
| is sweet; and therefore what I see is capable of logical division into the
| sweet and the not sweet. It is customary to assume that visual images are
| absolutely determinate in respect to color, but even this may be doubted.
| I know of no facts which prove that there is never the least vagueness
| in the immediate sensation.
|
| In thought, an absolutely determinate term cannot be realized,
| because, not being given by sense, such a concept would have to
| be formed by synthesis, and there would be no end to the synthesis
| because there is no limit to the number of possible predicates.
|
| A logical atom, then, like a point in space, would involve for
| its precise determination an endless process. We can only say,
| in a general way, that a term, however determinate, may be made
| more determinate still, but not that it can be made absolutely
| determinate. Such a term as "the second Philip of Macedon" is
| still capable of logical division -- into Philip drunk and
| Philip sober, for example; but we call it individual because
| that which is denoted by it is in only one place at one time.
| It is a term not 'absolutely' indivisible, but indivisible as
| long as we neglect differences of time and the differences which
| accompany them. Such differences we habitually disregard in the
| logical division of substances. In the division of relations,
| etc., we do not, of course, disregard these differences, but we
| disregard some others. There is nothing to prevent

Re: [peirce-l] Doctrine Of Individuals

[Irving Anellis]

The sample quotes from Peirce regarding individuals are much appreciated.
 
Nevertheless: ...
 
Did Anellis claim that there are no individuals in Peirce's logical system? No.
 
Did Anellis say that van Heijenoort claim that there are no individuals in Peirce's logical system? Yes.
 
Did Anellis say that Bertrand Russell claimed that there are no individuals in Schroeder's logic? Yes.
 
Did Bertrand Russell tell Norbert Wiener that he  had judged that Peano's logic was better than Schroeder's because Peano was able to refer to individuals in his system (had a notation for 'the'), whereas Schroeder's did not? Yes.
 
Did Anellis claim that it was Bertrand Russell (and by implication also van Heijenoort, had he known of Russell's account of that discussion with Wiener) who denied that there are individuals in the classical Boole-Schroeder calculus? Yes
 
Did Anellis claim that there are no individuals in Schroeder's logic? No.
 
Is it perhaps time for Anellis to withdraw from the discussion? Yes? / No?
 
 
 
Dec 8, 2011 05:28:41 PM, jawb...@att.net wrote:
Peircers,Writing "in reference to the doctrine of individuals" in his"Description of a Notation for the Logic of Relatives" (1870),Peirce's approach is, in its basic principles, so far ahead ofhis time that it overleaps the dustbin of Logical Atomism andanticipates ideas about element-free set theory that will notcome into their own until the latter part of the 20th Century.Here is a collection of excerpts that I gathered forseveral previous occasions, here and elsewhere, whenthe topic of Peirce's approach to individuals arose.o~o~o~o~o~oDOI. Doctrine Of Individualso~o~o~o~o~oDOI. Note 1o~o~o~o~o~o| In reference to the doctrine of individuals, two distinctions should be| borne in mind. The logical atom, or term not capable of logical division,| must be one of which every predicate may be universally affirmed or denied.| For, let 'A' be such a term. Then, if it is neither true that all 'A' is 'X'| nor that no 'A' is 'X', it must be true that some 'A' is 'X' and some 'A' is| not 'X'; and therefore 'A' may be divided into 'A' that is 'X' and 'A' that| is not 'X', which is contrary to its nature as a logical atom.|| Such a term can be realized neither in thought nor in sense.|| Not in sense, because our organs of sense are special -- the eye,| for example, not immediately informing us of taste, so that an image| on the retina is indeterminate in respect to sweetUess and non-sweetness.| When I see a thing, I do not see that it is not sweet, nor do I see that it| is sweet; and therefore what I see is capable of logical division into the| sweet and the not sweet. It is customary to assume that visual images are| absolutely determinate in respect to color, but even this may be doubted.| I know of no facts which prove that there is never the least vagueness| in the immediate sensation.|| In thought, an absolutely determinate term cannot be realized,| because, not being given by sense, such a concept would have to| be formed by synthesis, and there would be no end to the synthesis| because there is no limit to the number of possible predicates.|| A logical atom, then, like a point in space, would involve for| its precise determination an endless process. We can only say,| in a general way, that a term, however determinate, may be made| more determinate still, but not that it can be made absolutely| determinate. Such a term as "the second Philip of Macedon" is| still capable of logical division -- into Philip drunk and| Philip sober, for example; but we call it individual because| that which is denoted by it is in only one place at one time.| It is a term not 'absolutely' indivisible, but indivisible as| long as we neglect differences of time and the differences which| accompany them. Such differences we habitually disregard in the| logical division of substances. In the division of relations,| etc., we do not, of course, disregard these differences, but we| disregard some others. There is nothing to prevent almost any| sort of difference from being conventionally neglected in some| discourse, and if 'I' be a term which in consequence of such| neglect becomes indivisible in that discourse, we have in| that discourse,|| ['I'] = 1.|| This distinction between the absolutely indivisible and that which| is one in number from a particular point of view is shadowed forth| in the two words 'individual' ('to atomon') and 'singular' ('to kath| ekaston'); but as those who have used the word 'individual' have not| been aware that absolute individuality is merely ideal, it has come to| be used in a more general sense.|| C.S. Peirce, 'Collected Papers', CP 3.93Peirce defines the "number" ['t'] of a logical term 't' as follows:| I propose to assign to all logical terms, numbers; to an absolute term,| the number of individuals it denotes; to a relative term, the av

[peirce-l] Doctrine Of Individuals

[Jon Awbrey]

Peircers,

Writing "in reference to the doctrine of individuals" in his
"Description of a Notation for the Logic of Relatives" (1870),
Peirce's approach is, in its basic principles, so far ahead of
his time that it overleaps the dustbin of Logical Atomism and
anticipates ideas about element-free set theory that will not
come into their own until the latter part of the 20th Century.

Here is a collection of excerpts that I gathered for
several previous occasions, here and elsewhere, when
the topic of Peirce's approach to individuals arose.

o~o~o~o~o~o

DOI.  Doctrine Of Individuals

o~o~o~o~o~o

DOI.  Note 1

o~o~o~o~o~o

| In reference to the doctrine of individuals, two distinctions should be
| borne in mind.  The logical atom, or term not capable of logical division,
| must be one of which every predicate may be universally affirmed or denied.
| For, let 'A' be such a term.  Then, if it is neither true that all 'A' is 'X'
| nor that no 'A' is 'X', it must be true that some 'A' is 'X' and some 'A' is
| not 'X';  and therefore 'A' may be divided into 'A' that is 'X' and 'A' that
| is not 'X', which is contrary to its nature as a logical atom.
|
| Such a term can be realized neither in thought nor in sense.
|
| Not in sense, because our organs of sense are special -- the eye,
| for example, not immediately informing us of taste, so that an image
| on the retina is indeterminate in respect to sweetUess and non-sweetness.
| When I see a thing, I do not see that it is not sweet, nor do I see that it
| is sweet;  and therefore what I see is capable of logical division into the
| sweet and the not sweet.  It is customary to assume that visual images are
| absolutely determinate in respect to color, but even this may be doubted.
| I know of no facts which prove that there is never the least vagueness
| in the immediate sensation.
|
| In thought, an absolutely determinate term cannot be realized,
| because, not being given by sense, such a concept would have to
| be formed by synthesis, and there would be no end to the synthesis
| because there is no limit to the number of possible predicates.
|
| A logical atom, then, like a point in space, would involve for
| its precise determination an endless process.  We can only say,
| in a general way, that a term, however determinate, may be made
| more determinate still, but not that it can be made absolutely
| determinate.  Such a term as "the second Philip of Macedon" is
| still capable of logical division -- into Philip drunk and
| Philip sober, for example;  but we call it individual because
| that which is denoted by it is in only one place at one time.
| It is a term not 'absolutely' indivisible, but indivisible as
| long as we neglect differences of time and the differences which
| accompany them.  Such differences we habitually disregard in the
| logical division of substances.  In the division of relations,
| etc., we do not, of course, disregard these differences, but we
| disregard some others.  There is nothing to prevent almost any
| sort of difference from being conventionally neglected in some
| discourse, and if 'I' be a term which in consequence of such
| neglect becomes indivisible in that discourse, we have in
| that discourse,
|
|['I'] = 1.
|
| This distinction between the absolutely indivisible and that which
| is one in number from a particular point of view is shadowed forth
| in the two words 'individual' ('to atomon') and 'singular' ('to kath
| ekaston');  but as those who have used the word 'individual' have not
| been aware that absolute individuality is merely ideal, it has come to
| be used in a more general sense.
|
| C.S. Peirce, 'Collected Papers', CP 3.93

Peirce defines the "number" ['t'] of a logical term 't' as follows:

| I propose to assign to all logical terms, numbers;  to an absolute term,
| the number of individuals it denotes;  to a relative term, the average
| number of things so related to one individual.  Thus in a universe of
| perfect men ('men'), the number of "tooth of" would be 32.  The number
| of a relative with two correlates would be the average number of things
| so related to a pair of individuals;  and so on for relatives of higher
| numbers of correlates.  I propose to denote the number of a logical term
| by enclosing the term in square brackets, thus ['t'].
|
| C.S. Peirce, 'Collected Papers', CP 3.65

The "number" of an absolute term, as in the case of 'I',
is defined as the number of individuals that it denotes.

o~o~o~o~o~o

DOI.  Note 2

o~o~o~o~o~o

| The old logics distinguish between 'individuum signatum' and 'individuum 
vagum'.
| "Julius Caesar" is an example of the former;  "a certain man", of the latter.
| The 'individuum vagum', in the days when such conceptions were exactly
| investigated, occasi