12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Saturday May 04, 2024
Jump to navigationJump to searchDirectory talk:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 21:24, 21 February 2017
, 21:24, 21 February 2017→Mathematical Demonstration and the Doctrine of Individuals: delete blog-formatted pieces
<p>(Peirce, CP 3.73).</p>
<p>(Peirce, CP 3.73).</p>
|}
|}
==Commentary Work Area==
==Commentary Work Area==
| height="80" |
| height="80" |
<math>
<math>
(\mathfrak{L} \mathfrak{W})_x ~=~
(\mathsf{L} \mathsf{W})_x ~=~
\sum_{p \in X} \mathfrak{L}_{xp} \mathfrak{W}_p
\sum_{p \in X} \mathsf{L}_{xp} \mathsf{W}_p
</math>
</math>
|}
|}
| height="80" |
| height="80" |
<math>
<math>
(\mathfrak{L} \mathfrak{W})_q ~=~
(\mathsf{L} \mathsf{W})_q ~=~
\sum_{p \in X} \mathfrak{L}_{qp} \mathfrak{W}_p
\sum_{p \in X} \mathsf{L}_{qp} \mathsf{W}_p
</math>
</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| height="80" |
| height="80" |
<math>(\mathfrak{L}^\mathfrak{W})_x ~=~
<math>(\mathsf{L}^\mathsf{W})_x ~=~
\prod_{p \in X} \mathfrak{L}_{xp}^{\mathfrak{W}_p}
\prod_{p \in X} \mathsf{L}_{xp}^{\mathsf{W}_p}
</math>
</math>
|}
|}
| height="80" |
| height="80" |
<math>
<math>
(\mathfrak{S}^\mathfrak{L})_{xy} ~=~
(\mathsf{S}^\mathsf{L})_{xy} ~=~
\prod_{p \in X} \mathfrak{S}_{xp}^{\mathfrak{L}_{py}}
\prod_{p \in X} \mathsf{S}_{xp}^{\mathsf{L}_{py}}
</math>
</math>
|}
|}
| height="80" |
| height="80" |
<math>
<math>
(\mathfrak{S}^\mathfrak{L})_{xp} ~=~
(\mathsf{S}^\mathsf{L})_{xp} ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}}
\prod_{q \in X} \mathsf{S}_{xq}^{\mathsf{L}_{qp}}
</math>
</math>
|}
|}
| height="80" |
| height="80" |
<math>
<math>
((\mathfrak{S}^\mathfrak{L})^\mathfrak{W})_x ~=~
((\mathsf{S}^\mathsf{L})^\mathsf{W})_x ~=~
(\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_x
(\mathsf{S}^{\mathsf{L}\mathsf{W}})_x
</math>
</math>
|}
|}
| height="80" |
| height="80" |
<math>
<math>
((\mathfrak{S}^\mathfrak{L})^\mathfrak{W})_x ~=~
((\mathsf{S}^\mathsf{L})^\mathsf{W})_x ~=~
\prod_{p \in X} (\mathfrak{S}^\mathfrak{L})_{xp}^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\mathsf{S}^\mathsf{L})_{xp}^{\mathsf{W}_p} ~=~
\prod_{p \in X} (\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}})^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\prod_{q \in X} \mathsf{S}_{xq}^{\mathsf{L}_{qp}})^{\mathsf{W}_p} ~=~
\prod_{p \in X} \prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}\mathfrak{W}_p}
\prod_{p \in X} \prod_{q \in X} \mathsf{S}_{xq}^{\mathsf{L}_{qp}\mathsf{W}_p}
</math>
</math>
|}
|}
| height="80" |
| height="80" |
<math>
<math>
(\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_x ~=~
(\mathsf{S}^{\mathsf{L}\mathsf{W}})_x ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{(\mathfrak{L}\mathfrak{W})_q} ~=~
\prod_{q \in X} \mathsf{S}_{xq}^{(\mathsf{L}\mathsf{W})_q} ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{\sum_{p \in X} \mathfrak{L}_{qp} \mathfrak{W}_p} ~=~
\prod_{q \in X} \mathsf{S}_{xq}^{\sum_{p \in X} \mathsf{L}_{qp} \mathsf{W}_p} ~=~
\prod_{q \in X} \prod_{p \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp} \mathfrak{W}_p}
\prod_{q \in X} \prod_{p \in X} \mathsf{S}_{xq}^{\mathsf{L}_{qp} \mathsf{W}_p}
</math>
</math>
|}
|}
===Commentary Note 12.6===
===Commentary Note 12.6===
Need a comment about the meaning of the sum <math>\sum_{p \in X} \mathfrak{L}_{qp} \mathfrak{W}_p</math> in the following equation:
Need a comment about the meaning of the sum <math>\sum_{p \in X} \mathsf{L}_{qp} \mathsf{W}_p\!</math> in the following equation:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
|
|
<math>
<math>
(\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_x ~=~
(\mathsf{S}^{\mathsf{L}\mathsf{W}})_x ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{(\mathfrak{L}\mathfrak{W})_q} ~=~
\prod_{q \in X} \mathsf{S}_{xq}^{(\mathsf{L}\mathsf{W})_q} ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{\sum_{p \in X} \mathfrak{L}_{qp} \mathfrak{W}_p} ~=~
\prod_{q \in X} \mathsf{S}_{xq}^{\sum_{p \in X} \mathsf{L}_{qp} \mathsf{W}_p} ~=~
\prod_{q \in X} \prod_{p \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp} \mathfrak{W}_p}
\prod_{q \in X} \prod_{p \in X} \mathsf{S}_{xq}^{\mathsf{L}_{qp} \mathsf{W}_p}\!
</math>
</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>(\mathfrak{L}\mathfrak{W})_q ~=~ \sum_{p \in X} \mathfrak{L}_{qp} \mathfrak{W}_p</math>
| <math>(\mathsf{L}\mathsf{W})_q ~=~ \sum_{p \in X} \mathsf{L}_{qp} \mathsf{W}_p\!</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>(\mathfrak{L}\mathfrak{W})_x ~=~ \sum_{p \in X} \mathfrak{L}_{xp} \mathfrak{W}_p</math>
| <math>(\mathsf{L}\mathsf{W})_x ~=~ \sum_{p \in X} \mathsf{L}_{xp} \mathsf{W}_p\!</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>\mathrm{w} ~=~ \sum_{x \in X} \mathfrak{W}_x x \quad ?</math>
| <math>\mathrm{w} ~=~ \sum_{x \in X} \mathsf{W}_x x \quad ?\!</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>\mathrm{w} ~=~ \sum_\mathbf{1} \mathrm{w}_\mathrm{X} \mathrm{X} \quad ?</math>
| <math>\mathrm{w} ~=~ \sum_\mathbf{1} \mathrm{w}_\mathrm{X} \mathrm{X} \quad ?\!</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>S^L ~=~ \bigcap_{x \in \operatorname{proj}_1 L} \operatorname{proj}_1 (S \star x)</math>
| <math>S^L ~=~ \bigcap_{x \in \operatorname{proj}_1 L} \operatorname{proj}_1 (S \star x)\!</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>(\mathfrak{S}^\mathfrak{L})_{ab} ~=~ \prod_{x \in X} \mathfrak{S}_{ax}^{\mathfrak{L}_{xb}}</math>
| <math>(\mathsf{S}^\mathsf{L})_{ab} ~=~ \prod_{x \in X} \mathsf{S}_{ax}^{\mathsf{L}_{xb}}\!</math>
|}
|}
In other words, <math>(\mathfrak{S}^\mathfrak{L})_{ab} = 0</math> if and only if there exists an <math>x \in X</math> such that <math>\mathfrak{S}_{ax} = 0</math> and <math>\mathfrak{L}_{xb} = 1.</math>
In other words, <math>(\mathsf{S}^\mathsf{L})_{ab} = 0\!</math> if and only if there exists an <math>x \in X\!</math> such that <math>\mathsf{S}_{ax} = 0\!</math> and <math>\mathsf{L}_{xb} = 1.\!</math>
===Commentary on Selection 12 : Older Notes===
===Commentary on Selection 12 : Older Notes===
The term ''exponentiation'' is more generally used in mathematics for operations that involve taking a base to a power, and is slightly preferable to ''involution'' since the latter is used for different concepts in different contexts. Operations analogous to taking powers are widespread throughout mathematics and Peirce frequently makes use of them in a number of important applications, for example, in his theory of information. But that's another story.
The term ''exponentiation'' is more generally used in mathematics for operations that involve taking a base to a power, and is slightly preferable to ''involution'' since the latter is used for different concepts in different contexts. Operations analogous to taking powers are widespread throughout mathematics and Peirce frequently makes use of them in a number of important applications, for example, in his theory of information. But that's another story.
The ''function space'' <math>Y^X,\!</math> where <math>X\!</math> and <math>Y\!</math> are sets, is the set of all functions from <math>X\!</math> to <math>Y.\!</math> An alternative notation for <math>Y^X\!</math> is <math>(X \to Y).</math> Thus we have the following equivalents:
The ''function space'' <math>Y^X,\!</math> where <math>X\!</math> and <math>Y\!</math> are sets, is the set of all functions from <math>X\!</math> to <math>Y.\!</math> An alternative notation for <math>Y^X\!</math> is <math>(X \to Y).\!</math> Thus we have the following equivalents:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>\begin{matrix}Y^X & = & (X \to Y) & = & \{ f : X \to Y \}\end{matrix}</math>
| <math>\begin{matrix}Y^X & = & (X \to Y) & = & \{ f : X \to Y \}\end{matrix}\!</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>\begin{matrix}|Y^X| & = & |Y|^{|X|}\end{matrix}</math>
| <math>\begin{matrix}|Y^X| & = & |Y|^{|X|}\end{matrix}\!</math>
|}
|}
In the special case where <math>Y = \mathbb{B} = \{ 0, 1 \},</math> the function space <math>\mathbb{B}^X</math> is the set of functions <math>\{ f : X \to \mathbb{B} \}.</math> If the elements <math>0, 1 \in \mathbb{B}</math> are interpreted as the logical values <math>\operatorname{false}, \operatorname{true},</math> respectively, then a function of the type <math>X \to \mathbb{B}</math> may be interpreted as a ''proposition'' about the elements in <math>X.\!</math>
In the special case where <math>Y = \mathbb{B} = \{ 0, 1 \},\!</math> the function space <math>\mathbb{B}^X\!</math> is the set of functions <math>\{ f : X \to \mathbb{B} \}.\!</math> If the elements <math>0, 1 \in \mathbb{B}\!</math> are interpreted as the logical values <math>\mathrm{false}, \mathrm{true},\!</math> respectively, then a function of the type <math>X \to \mathbb{B}\!</math> may be interpreted as a ''proposition'' about the elements in <math>X.\!</math>
===Really Old Commentary Notes===
===Really Old Commentary Notes===
===Discussion Note 1===
===Discussion Note 1===
; Gary Richmond
: I wonder if the necessary “elementary triad” spoken of below isn't somehow implicated in those discussions “invoking a <i>closure principle</i>”.
; C.S. Peirce
: CP 1.292. It can further be said in advance, not, indeed, purely a priori but with the degree of apriority that is proper to logic, namely, as a necessary deduction from the fact that there are signs, that there must be an elementary triad. For were every element of the phaneron a monad or a dyad, without the relative of teridentity (which is, of course, a triad), it is evident that no triad could ever be built up. Now the relation of every sign to its object and interpretant is plainly a triad. A triad might be built up of pentads or of any higher perissad elements in many ways. But it can be proved — and really with extreme simplicity, though the statement of the general proof is confusing — that no element can have a higher valency than three.
; Gary Richmond
: (Of course this passage also directly relates to the recent thread on Identity and Teridentity.)
Yes, generally speaking, I think that there are deep formal principles here
; Jon Awbrey
that manifest themselves in these various guises: the levels of intention
: Yes, generally speaking, I think that there are deep formal principles here that manifest themselves in these various guises: the levels of intention or the orders of reflection, the sign relation, pragmatic conceivability, the generative sufficiency of 3-adic relations for all practical intents, and the irreducibility of continuous relations. I have run into themes in combinatorics, group theory, and Lie algebras that are tantalizingly reminiscent of the things that Peirce says here, but it will take me some time to investigate them far enough to see what's going on.
or the orders of reflection, the sign relation, pragmatic conceivability,
the generative sufficiency of 3-adic relations for all practical intents,
and the irreducibility of continuous relations. I have run into themes
in combinatorics, group theory, and Lie algebras that are tantalizingly
reminiscent of the things that Peirce says here, but it will take me
some time to investigate them far enough to see what's going on.
; Gary Richmond
: PS. I came upon the above passage last night reading through the Peirce selections in John J. Stuhr's <i>Classical American Philosophy : Essential Readings and Interpretive Essays</i>, Oxford University, 1987 (the passage above is found on pp. 61–62), readily available in paperback in a new edition, I believe.
: An aside: These excerpts in Sturh include versions of a fascinating “Intellectual Autobiography”, Peirce's summary of his scientific, especially, philosophic accomplishments. I've seen them published nowhere else.
===Discussion Note 2===
===Discussion Note 2===
; Benjamin Udell
: I'm in the process of moving back to NYC and have had little opportunity to do more than glance through posts during the past few weeks, but this struck me because it sounds something I really would like to know about, but I didn't understand it:
; Jon Awbrey
: Notice that Peirce follows the mathematician's usual practice, then and now, of making the status of being an "individual" or a "universal" relative to a discourse in progress. I have come to appreciate more and more of late how radically different this "patchwork" or "piecewise" approach to things is from the way of some philosophers who seem to be content with nothing less than many worlds domination, which means that they are never content and rarely get started toward the solution of any real problem. Just my observation, I hope you understand.
; Benjamin Udell
: "Many worlds domination", "nothing less than many worlds domination" -- as opposed to the patchwork or piecewise approach. What is many worlds domination? When I hear "many worlds" I think of Everett's Many Worlds interpretation of quantum mechanics.
; Jon Awbrey
: Yes, it is a resonance of Edward, Everett, and All the Other Whos in Whoville, but that whole microcosm is itself but the frumious reverberation of Leibniz's Maenadolatry. More sequitur, though, this is an issue that has simmered beneath the surface of my consciousness for several decades now and only periodically percolates itself over the hyper-critical thrashold of expression. Let me see if I can a better job of it this time. The topic is itself a patchwork of infernally recurrent patterns. Here are a few pieces of it that I can remember arising recently:
{| align="center" cellspacing="6" width="90%"
| Zeroth Law Of Semantics
|
|
<p>
<b>Zeroth Law Of Semantics</b><br>
<br>
Meaning is a privilege not a right.<br>
Not all pictures depict.<br>
Not all signs denote.<br>
<br>
Never confuse a property of a sign,<br>
for instance, existence,<br>
with a sign of a property,<br>
for instance, existence.<br>
<br>
Taking a property of a sign,<br>
for a sign of a property,<br>
is the zeroth sign of<br>
nominal thinking,<br>
and the first<br>
mistake.<br>
<br>
Also Sprach 0*
</p>
|}
A less catchy way of saying "meaning is a privilege not a right"
: A less catchy way of saying "meaning is a privilege not a right" would most likely be "meaning is a contingency not a necessity". But if I reflect on that phrase, it does not quite satisfy me, since a deeper lying truth is that contingency and necessity, connections in fact and connections beyond the reach of fact, depend on a line of distinction that is itself drawn on the scene of observation from the embodied, material, physical, non-point massive, non-purely-spectrelative point of view of an agent or community of interpretation, a discursive universe, an engauged interpretant, a frame of at least partial self-reverence, a hermeneutics in progress, or a participant observer. In short, this distinction between the contingent and the necessary is itself contingent, which means, among other things, that signs are always indexical at some least quantum.
would most likely be "meaning is a contingency not a necessity".
But if I reflect on that phrase, it does not quite satisfy me,
since a deeper lying truth is that contingency and necessity,
connections in fact and connections beyond the reach of fact,
depend on a line of distinction that is itself drawn on the
scene of observation from the embodied, material, physical,
non-point massive, non-purely-spectrelative point of view
of an agent or community of interpretation, a discursive
universe, an engauged interpretant, a frame of at least
partial self-reverence, a hermeneutics in progress, or
a participant observer. In short, this distinction
between the contingent and the necessary is itself
contingent, which means, among other things, that
signs are always indexical at some least quantum.
===Discussion Note 3===
===Discussion Note 3===
; Joe Ransdell
: Would the Kripke conception of the "rigid designator" be an instance of the "many worlds domination"? I was struck by your speaking of the "patchwork or piecewise" approach as well in that it seemed to me you might be expressing the same general idea that I have usually thought of in terms of contextualism instead: I mean the limits it puts upon what you can say a priori if you really take contextualism seriously, which is the same as recognizing indexicality as incapable of elimination, I think.
; Jon Awbrey
: Yes, I think this is the same ballpark of topics. I can't really speak for what Kripke had in mind, but I have a practical acquaintance with the way that some people have been trying to put notions like this to work on the applied ontology scene, and it strikes me as a lot of nonsense. I love a good parallel worlds story as much as anybody, but it strikes me that many worlds philosophers have the least imagination of anybody as to what an alternative universe might really be like and so I prefer to read more creative writers when it comes to that. But serially, folks, I think that the reason why some people evidently feel the need for such outlandish schemes — and the vast majority of the literature on counterfactual conditionals falls into the same spaceboat as this — is simply that they have failed to absorb, through the fault of Principian filters, a quality that Peirce's logic is thoroughly steeped in, namely, the functional interpretation of logical terms, that is, as signs referring to patterns of contingencies. It is why he speaks more often, and certainly more sensibly and to greater effect, of “conditional generals” than of “modal subjunctives”. This is also bound up with that element of sensibility that got lost in the transition from Peircean to Fregean quantifiers. Peirce's apriorities are always hedged with risky bets.
Yes, I think this is the same ballpark of topics.
I can't really speak for what Kripke had in mind,
but I have a practical acquaintance with the way
that some people have been trying to put notions
like this to work on the applied ontology scene,
and it strikes me as a lot of nonsense. I love
a good parallel worlds story as much as anybody,
but it strikes me that many worlds philosophers
have the least imagination of anybody as to what
an alternative universe might really be like and
so I prefer to read more creative writers when it
comes to that. But serially, folks, I think that
the reason why some people evidently feel the need
for such outlandish schemes -- and the vast majority
of the literature on counterfactual conditionals falls
into the same spaceboat as this -- is simply that they
have failed to absorb, through the fault of Principian
filters, a quality that Peirce's logic is thoroughly
steeped in, namely, the functional interpretation
of logical terms, that is, as signs referring to
patterns of contingencies. It is why he speaks
more often, and certainly more sensibly and to
greater effect, of "conditional generals" than
of "modal subjunctives". This is also bound up
with that element of sensibility that got lost in
the transition from Peircean to Fregean quantifiers.
Peirce's apriorities are always hedged with risky bets.
===Discussion Note 4===
===Discussion Note 4===
; Benjamin Udell
: I wish I had more time to ponder the "many-worlds" issue (& that my books were not currently disappearing into heavily taped boxes). I had thought of the piecemeal approach's opposite as the attempt to build a kind of monolithic picture, e.g., to worry that there is not an infinite number of particles in the physical universe for the infinity integers. But maybe the business with rigid designators & domination of many worlds has somehow to do with monolithism.
Yes, that's another way of saying it. When I look to my own priorities,
; Jon Awbrey
my big worry is that logic as a discipline is not fulfilling its promise.
: Yes, that's another way of saying it. When I look to my own priorities, my big worry is that logic as a discipline is not fulfilling its promise. I have worked in too many settings where the qualitative researchers and the quantitative researchers could barely even talk to one an Other with any understanding, and this I recognized as a big block to inquiry since our first notice of salient facts and significant phenomena is usually in logical, natural language, or qualitative forms, while our eventual success in resolving anomalies and solving practical problems depends on our ability to formalize, operationalize, and quantify the issues, even if only to a very partial degree, as it generally turns out.
I have worked in too many settings where the qualitative researchers and
the quantitative researchers could barely even talk to one an Other with
any understanding, and this I recognized as a big block to inquiry since
our first notice of salient facts and significant phenomena is usually
in logical, natural language, or qualitative forms, while our eventual
success in resolving anomalies and solving practical problems depends
on our ability to formalize, operationalize, and quantify the issues,
even if only to a very partial degree, as it generally turns out.
When I look to the history of how logic has been deployed in mathematics,
: When I look to the history of how logic has been deployed in mathematics, and through those media in science generally, it seems to me that the Piece Train started to go off track with the <i>Principia Mathematica</i>. All pokes in the rib aside, however, I tend to regard this event more as the symptom of a localized cultural phenomenon than as the root cause of the broader malaise.
and through those media in science generally, it seems to me that the
Piece Train started to go off track with the 'Principia Mathematica'.
All pokes in the rib aside, however, I tend to regard this event
more as the symptom of a localized cultural phenomenon than as
the root cause of the broader malaise.
===Discussion Note 5===
===Discussion Note 5===
; C.S. Peirce
{| align="center" cellspacing="6" width="90%"
| For example,
|-
| align="center" | <math>\mathrm{f} + \mathrm{u}\!</math>
|-
| means all Frenchmen besides all violinists, and, therefore, considered as a logical term, implies that all French violinists are <i>besides themselves</i>.
|}
; Clark Goble
: Could you clarify your use of “besides”?
: I think I am following your thinking in that you don't want the logical terms to be considered to have any necessary identity between them. Is that right?
I use vertical sidebars "|" for long quotations, so this
; Jon Awbrey
is me quoting Peirce at CP 3.67 who is explaining in an
: I use vertical sidebars "|" for long quotations, so this is me quoting Peirce at CP 3.67 who is explaining in an idiomatic way Boole's use of the plus sign for a logical operation that is strictly speaking limited to terms for mutually exclusive classes. The operation would normally be extended to signify the “symmetric difference” operator. But Peirce is saying that he prefers to use the sign <math>{}^{\backprime\backprime} +\!\!, {}^{\prime\prime}</math> for inclusive disjunction, corresponding to the union of the associated classes. Peirce calls Boole's operation “invertible” because it amounts to the sum operation in a field, whereas the inclusive disjunction or union is “non-invertible”, since knowing that <math>A \cup B = C\!</math> does not allow one to say determinately that <math>A = C - B.\!</math> I can't recall if Boole uses this “besides” idiom, but will check later.
idiomatic way Boole's use of the plus sign for a logical
operation that is strictly speaking limited to terms for
mutually exclusive classes. The operation would normally
be extended to signify the "symmetric difference" operator.
But Peirce is saying that he prefers to use the sign "+,"
for inclusive disjunction, corresponding to the union of
the associated classes. Peirce calls Boole's operation
a field, whereas the inclusive disjunction or union is
not allow one to say determinately that A = C - B.
I can't recall if Boole uses this 'besides' idiom,
but will check later.
===Discussion Note 6===
===Discussion Note 6===
; Jon Awbrey
: I use vertical sidebars “|” for long quotations, so this is me quoting Peirce at CP 3.67 who is explaining in an idiomatic way Boole's use of the plus sign for a logical operation that is strictly speaking limited to terms for mutually exclusive classes.
; Clark Goble
: Is that essay related to any of the essays in the two volume <i>Essential Peirce</i>? I'm rather interested in how he speaks there.
; Jon Awbrey
: No, the EP volumes are extremely weak on logical selections. I see nothing there that deals with the logic of relatives.
: But Peirce is saying that he prefers to use the sign <math>{}^{\backprime\backprime} +\!\!, {}^{\prime\prime}</math> for inclusive disjunction, corresponding to the union of the associated classes.
; Clark Goble
: The reason I asked was more because it seemed somewhat interesting in light of the logic of operators in quantum mechanics. I was curious if the use of “beside” might relate to that. But from what you say it probably was just me reading too much into the quote. The issue of significance was whether the operation entailed the necessity of mutual exclusivity or whether some relationship between the classes might be possible. I kind of latched on to Peirce's odd statement about “all French violinists are <i>beside themselves</i>”.
: Did Peirce have anything to say about what we'd call non-commuting operators?
; Jon Awbrey
: In general, 2-adic relative terms are non-commutative. For example, a brother of a mother is not identical to a mother of a brother.
In general, 2-adic relative terms are non-commutative.
For example, a brother of a mother is not identical to
a mother of a brother.
===Discussion Note 7===
===Discussion Note 7===
; Gary Richmond
: I am very much enjoying, which is to say, learning from your interlacing commentary on Peirce's 1870 “Logic of Relatives” paper.
: What an extraordinary paper the 1870 “LOR” is! Your notes helped me appreciate the importance of the unanticipated proposal of P's to “assign to all logical terms, numbers”. On the other hand, the excerpts suggested to we why Peirce finally framed his Logic of Relatives into graphical form. Still, I think that a thorough examination of the 1970 paper might serve as propaedeutic (and of course, much more) for the study of the alpha and beta graphs.
Yes, there's gold in them thar early logic papers that has been "panned"
; Jon Awbrey
but nowhere near mined in depth yet. The whole quiver of arrows between
: Yes, there's gold in them thar early logic papers that has been “panned” but nowhere near mined in depth yet. The whole quiver of arrows between terms and numbers harks back to the <i>numeri characteristici</i> of Leibniz, of course, but Leibniz attended more on the intensional chains of being while Peirce will here start to “escavate” the extensional hierarchies.
terms and numbers harks back to the 'numeri characteristici' of Leibniz,
of course, but Leibniz attended more on the intensional chains of being
while Peirce will here start to "escavate" the extensional hierarchies.
I consider myself rewarded that you see the incipient impulse toward
: I consider myself rewarded that you see the incipient impulse toward logical graphs, as one of the most striking things to me about this paper is to see these precursory seeds already planted here within it and yet to know how long it will take them to sprout and bloom.
logical graphs, as one of the most striking things to me about this
paper is to see these precursory seeds already planted here within
it and yet to know how long it will take them to sprout and bloom.
Peirce is obviously struggling to stay within the linotyper's art --
: Peirce is obviously struggling to stay within the linotyper's art — a thing that we, for all our exorbitant hype about markable text, are still curiously saddled with — but I do not believe that it is possible for any mind equipped with a geometrical imagination to entertain these schemes for connecting up terminological hubs with their terminological terminals without perforce stretching imaginary strings between the imaginary gumdrops.
a thing that we, for all our exorbitant hype about markable text,
are still curiously saddled with -- but I do not believe that it
is possible for any mind equipped with a geometrical imagination
to entertain these schemes for connecting up terminological hubs
with their terminological terminals without perforce stretching
imaginary strings between the imaginary gumdrops.
; Gary Richmond
: I must say though that the pace at which you've been throwing this at us is not to be kept up with by anyone I know “in person or by reputation”. I took notes on the first 5 or 6 Notes, but can now just barely find time to read through your posts.
Oh, I was trying to burrow as fast as I could toward the more untapped veins --
; Jon Awbrey
I am guessing that things will probably "descalate" a bit over the next week,
: Oh, I was trying to burrow as fast as I could toward the more untapped veins — I am guessing that things will probably “descalate” a bit over the next week, but then, so will our attention spans …
but then, so will our attention spans ...
Speaking of which, I will have to break here, and pick up the rest later ...
: Speaking of which, I will have to break here, and pick up the rest later …
===Discussion Note 8===
===Discussion Note 8===
; Gary Richmond
: In any event, I wish that you'd comment on Note 5 more directly (though you do obliquely in your own diagramming of “every [US] Vice-President(s) … [who is] every President(s) of the US Senate”.
; Jon Awbrey
: There are several layers of things to say about that, and I think that it would be better to illustrate the issues by way of the examples that Peirce will soon be getting to, but I will see what I can speak to for now.
; Gary Richmond
and I think that it would be better to illustrate the
: But what interested me even more in LOR, Note 5, was the sign <math>{}^{\backprime\backprime} < {}^{\prime\prime}\!</math> (“less than” joined to the sign of identity <math>{}^{\backprime\backprime} = {}^{\prime\prime}\!</math> to yield Peirce's famous sign <math>{}^{\backprime\backprime} \texttt{-}\!\texttt{<} {}^{\prime\prime}\!</math> (or more clearly, <math>{}^{\backprime\backprime} \texttt{=}\!\texttt{<} {}^{\prime\prime}\!</math>) of inference, which combines the two (so that <math>{}^{\backprime\backprime} \texttt{-}\!\texttt{<} {}^{\prime\prime}\!</math> (literally, “as small as”) means “is”. I must say I both “get” this and don't quite (Peirce's example(s) of the frenchman helped a little). Perhaps your considerably more mathematical mind can help clarify this for a non-mathematician such as myself. (My sense is that “as small as” narrows the terms so that “everything that occurs in the conclusion is already contained in the premise”.) I hope I'm not being obtuse here. I'm sure it's “all too simple for words”.
; Jon Awbrey
: Then let us draw a picture.
: The proposition <math>\texttt{(} F ~ \texttt{(} G \texttt{))},\!</math> read as <math>{}^{\backprime\backprime} \mathrm{not}~ F ~\mathrm{without}~ G {}^{\prime\prime},\!</math> states that the region indicated by <math>F ~ \texttt{(} G \texttt{)},\!</math> in other words, where <math>F ~\mathrm{and~not}~ G\!</math> holds true, is the only region exempted from the occupation of being in this universe:
is the only region exempted from the occupation of being in this universe:
{| align="center" cellspacing="6"
|
<pre>
o-----------------------------------------------------------o
o-----------------------------------------------------------o
|`X`````````````````````````````````````````````````````````|
|`X`````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
o-----------------------------------------------------------o
o-----------------------------------------------------------o
</pre>
|}
Collapsing the vacuous region like soapfilm popping on a wire frame,
: Collapsing the vacuous region like soapfilm popping on a wire frame, we draw the constraint <math>\texttt{(} F ~ \texttt{(} G \texttt{))}\!</math> in the following alternative fashion:
we draw the constraint (F (G)) in the following alternative fashion:
{| align="center" cellspacing="6"
|
<pre>
o-----------------------------------------------------------o
o-----------------------------------------------------------o
|`X`````````````````````````````````````````````````````````|
|`X`````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
o-----------------------------------------------------------o
o-----------------------------------------------------------o
</pre>
|}
So, "(F (G))", "F => G", "F =< G", "F -< G", "F c G",
: So all of the following expressions, under suitable mutations of interpretation, are just so many ways of saying that the denotation of <math>{}^{\backprime\backprime} F {}^{\prime\prime}\!</math> is contained within the denotation of <math>{}^{\backprime\backprime} G {}^{\prime\prime}.\!</math>
under suitable mutations of interpretation, are just
so many ways of saying that the denotation of "F" is
contained within the denotation of "G".
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{l}
\texttt{(} F ~ \texttt{(} G \texttt{))}
\\[4pt]
F \Rightarrow G
\\[4pt]
F ~\texttt{=}\!\texttt{<}~ G
\\[4pt]
F ~\texttt{-}\!\texttt{<}~ G
\\[4pt]
F \subseteq G
\end{array}\!</math>
|}
: Let us now look to the “characteristic functions” or “indicator functions” of the various regions of being. It is frequently convenient to use the same letters for them and merely to keep a variant interpretation “en-thy-meme”, but let us be more meticulous here, and reserve the corresponding lower case letters <math>f\!</math> and <math>g\!</math> to denote the indicator functions of the regions <math>F\!</math> and <math>G,\!</math> respectively.
: Taking <math>\mathbb{B} = \{ 0, 1 \}~\!</math> as the boolean domain, we have:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{lcl}
f, g : X & \to & \mathbb{B}
\\[4pt]
f^{-1}(1) & = & F
\\[4pt]
g^{-1}(1) & = & G
\end{array}\!</math>
|}
: In general, for a proposition <math>h : X \to \mathbb{B},\!</math> an expression like <math>h^{-1}(1)\!</math> can be read as “the inverse of <math>h\!</math> evaluated at <math>1\!</math>”, in effect, denoting the set of points in <math>X\!</math> where <math>h\!</math> evaluates to <math>\mathrm{true}.\!</math> This is called the “fiber of truth” under <math>h,\!</math> and I have gotten where I like to abbreviate it as <math>[|h|].\!</math>
: Accordingly, we have:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{*{7}{l}}
F & = & [|f|] & = & f^{-1}(1) & \subseteq & X
\\[4pt]
G & = & [|g|] & = & g^{-1}(1) & \subseteq & X
\end{array}\!</math>
|}
: This brings us to the question, what sort of “functional equation” between <math>f\!</math> and <math>g\!</math> goes with the regional constraint <math>\texttt{(} F ~ \texttt{(} G \texttt{))}\!</math>?
: Just this, that <math>f(x) ~\texttt{=}\!\texttt{<}~ g(x)\!</math> for all <math>x\!</math> in <math>X,\!</math> where the <math>{}^{\backprime\backprime} \texttt{=}\!\texttt{<} {}^{\prime\prime}\!</math> relation on the values in <math>\mathbb{B}\!</math> has the following operational table for the pairing <math>{}^{\backprime\backprime} \mathrm{row~head} ~\texttt{=}\!\texttt{<}~ \mathrm{column~head} {}^{\prime\prime}.\!</math>
{| align="center" cellspacing="6"
|
<math>\begin{array}{|c||cc|}
\hline
\texttt{=}\!\texttt{<} & 0 & 1 \\
\hline\hline
0 & 1 & 1 \\
1 & 0 & 1 \\
\hline
\end{array}\!</math>
|}
And this, of course, is the same thing as the truth table
: And this, of course, is the same thing as the truth table for the conditional connective or the implication relation.
for the conditional connective or the implication relation.
; Gary Richmond
: By the way, in the semiosis implied by the modal gamma graphs, could <math>{}^{\backprime\backprime} \texttt{-}\!\texttt{<} {}^{\prime\prime}\!</math> (were it used there, which of course it is not) ever be taken to mean “leads to” or “becomes” or “evolves into”? I informally use it that way myself, using the ordinary arrow for implication.
I am a bit insensitive to the need for modal logic,
; Jon Awbrey
since necessity in mathematics always seems to come
: I am a bit insensitive to the need for modal logic, since necessity in mathematics always seems to come down to being a matter of truth for all actual cases, if under an expanded sense of actuality that makes it indiscernible from possibility, so I must beg off here. But there are places where Peirce makes a big deal about the advisability of drawing the <math>{}^{\backprime\backprime} \texttt{-}\!\texttt{<} {}^{\prime\prime}\!</math> symbol in one fell stroke of the pen, kind of like a “lazy gamma” — an old texican cattle brand — and I have seen another place where he reads <math>A ~\texttt{-}\!\texttt{<}~ B\!</math> as <math>{}^{\backprime\backprime} A, ~\text{in every way that it can be, is}~ B {}^{\prime\prime},\!</math> as if this <math>{}^{\backprime\backprime} \texttt{-}\!\texttt{<} {}^{\prime\prime}\!</math> fork in the road led into a veritable garden of branching paths.
down to being a matter of truth for all actual cases,
if under an expanded sense of actuality that makes it
indiscernible from possibility, so I must beg off here.
But there are places where Peirce makes a big deal about
the advisability of drawing the '-<' symbol in one fell
stroke of the pen, kind of like a "lazy gamma" -- an old
texican cattle brand -- and I have seen another place where
he reads "A -< B" as "A, in every way that it can be, is B",
as if this '-<' fork in the road led into a veritable garden
of branching paths.
And out again ...
: And out again …
===Discussion Note 9===
===Discussion Note 9===
; Jon Awbrey
: I am a bit insensitive to the need for modal logic, since necessity in mathematics always seems to come down to being a matter of truth for all actual cases, if under an expanded sense of actuality that makes it indiscernible from possibility, so I must beg off here.
; Gary Richmond
: I cannot agree with you regarding modal logic. Personally I feel that the gamma part of the EGs is of the greatest interest and potential importance, and as Jay Zeman has made clear in his dissertation, Peirce certainly thought this as well.
You disagree that I am insensitive? Well, certainly nobody has ever done that before!
; Jon Awbrey
No, I phrased it that way to emphasize the circumstance that it ever hardly comes up
: You disagree that I am insensitive? Well, certainly nobody has ever done that before! No, I phrased it that way to emphasize the circumstance that it ever hardly comes up as an issue within the limited purview of my experience, and when it does — as in topo-logical boundary situations — it seems to require a sort of analysis that doesn't comport all that well with the classical modes and natural figures of speech about it. Then again, I spent thirty years trying to motorize Alpha, have only a few good clues how I would go about Beta, and so Gamma doesn't look like one of those items on my plate.
as an issue within the limited purview of my experience, and when it does -- as in
topo-logical boundary situations -- it seems to require a sort of analysis that
doesn't comport all that well with the classical modes and natural figures of
speech about it. Then again, I spent thirty years trying to motorize Alpha,
have only a few good clues how I would go about Beta, and so Gamma doesn't
look like one of those items on my plate.
Speeching Of Which ---
: Speeching Of Which ---
Best Of The Season ...
: Best Of The Season ...
And Happy Trailing ...
: And Happy Trailing ...
===Discussion Note 10===
===Discussion Note 10===
; Bernard Morand
: Thanks for your very informative talk. There is a point that I did not understand in Note 35:
; Jon Awbrey
: If we operate in accordance with Peirce's example of <math>\mathfrak{g}\mathit{o}\mathrm{h}</math> as the “giver of a horse to an owner of that horse”, then we may assume that the associative law and the distributive law are by default in force, allowing us to derive this equation:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{lll}
\mathit{l},\!\mathit{s}\mathrm{w}
& = &
\mathit{l},\!\mathit{s}(\mathrm{B} ~~+\!\!,~~ \mathrm{D} ~~+\!\!,~~ \mathrm{E})
\\[6pt]
& = &
\mathit{l},\!\mathit{s}\mathrm{B} ~~+\!\!,~~ \mathit{l},\!\mathit{s}\mathrm{D} ~~+\!\!,~~ \mathit{l},\!\mathit{s}\mathrm{E}
\end{array}</math>
|}
; Bernard Morand
: May be because language or more probably my lack of training in logic, what does mean that “associative law and distributive law are by default in force”?
; Jon Awbrey
: Those were some tricky Peirces, and I was trying to dodge them as artful as could be, but now you have fastly apprehended me!
: It may be partly that I left out the initial sections of this paper where Peirce discusses how he will regard the ordinarily applicable principles in the process of trying to extend and generalize them (CP 3.45–62), but there may be also an ambiguity in Peirce's use of the phrase “absolute conditions” (CP 3.62–68). Does he mean “absolutely necessary”, “indispensable”, “inviolate”, or does he mean “the conditions applying to the logic of absolute terms”, in which latter case we would expect to alter them sooner or later?
: We lose the commutative law, <math>xy = yx,\!</math> as soon as we extend to 2-adic relations, but keep the associative law, <math>x(yz) = (xy)z,\!</math> as the multiplication of 2-adics is the logical analogue of ordinary matrix multiplication, and Peirce like most mathematicians treats the double distributive law, <math>x(y + z) = xy + xz\!</math> and <math>(x + y)z = xz + yz,\!</math> and as something that must be striven to preserve as far as possible.
: Strictly speaking, Peirce is already using a principle that goes beyond the ordinary associative law, but that is recognizably analogous to it, for example, in the modified Othello case, where <math>(\mathrm{J}\!:\!\mathrm{J}\!:\!\mathrm{D})(\mathrm{J}\!:\!\mathrm{D})(\mathrm{D}) = \mathrm{J}.\!</math>
: If it were strictly associative, then we would have the following:
If it were strictly associative, then we would have the following:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{lcccc}
(J:J:D)((J:D)(D)) & = & (J:J:D)(J) & = & 0?
\\[4pt]
((J:J:D)(J:D))(D) & = & (J)(D) & = & 0?
\end{array}</math>
|}
In other words, the intended relational linkage would be broken.
: In other words, the intended relational linkage would be broken. However, the type of product that Peirce is taking for granted in this situation often occurs in mathematics in just this way. There is another location where he comments more fully on this, but I have the sense that it was a late retrospective remark, and I do not recall if it was in CP or in the microfilm MSs that I read it.
However, the type of product that Peirce is taking for granted
in this situation often occurs in mathematics in just this way.
There is another location where he comments more fully on this,
but I have the sense that it was a late retrospective remark,
and I do not recall if it was in CP or in the microfilm MS's
that I read it.
By "default" conditions I am referring more or less to what
: By “default” conditions I am referring more or less to what Peirce says at the end of CP 3.69, where he use an argument based on the distributive principle to rationalize the idea that “<i>A term multiplied by two relatives shows that the same individual is in the two relations.</i>” This means, for example, that one can let <math>{}^{\backprime\backprime} \mathfrak{g}\mathit{o}\mathrm{h} {}^{\prime\prime}\!</math>, without subjacent marks or numbers, be interpreted on the default convention of “overlapping scopes”, where the two correlates of <math>\mathfrak{g}\!</math> are given by the next two terms in line, namely, <math>\mathit{o}\!</math> and <math>\mathrm{h},\!</math> and the single correlate of <math>\mathit{o}\!</math> is given by the very next term in line, namely, <math>\mathrm{h}.\!</math> Thus, it is only when this natural scoping cannot convey the intended sense that we have to use more explicit mark-up devices.
Peirce says at the end of CP 3.69, where he use an argument
based on the distributive principle to rationalize the idea
that 'A term multiplied by two relatives shows that the same
individual is in the two relations'. This means, for example,
that one can let "`g`'o'h", without subjacent marks or numbers,
be interpreted on the default convention of "overlapping scopes",
where the two correlates of `g` are given by the next two terms
in line, namely, 'o' and h, and the single correlate of 'o' is
given by the very next term in line, namely, h. Thus, it is
only when this natural scoping cannot convey the intended
sense that we have to use more explicit mark-up devices.
; Bernard Morand
: About another point: do you think that the LOR could be of some help to solve the puzzle of the “second way of dividing signs” where CSP concludes that 66 classes could be made out of the 10 divisions (Letters to lady Welby)? (As I see them, the ten divisions involve a mix of relative terms, dyadic relations, and a triadic one. In order to make 66 classes it is clear that these 10 divisions have to be stated under some linear order. The nature of this order is at the bottom of the disagreements on the subject).
This topic requires a longer excuse from me
; Jon Awbrey
than I am able to make right now, but maybe
: This topic requires a longer excuse from me than I am able to make right now, but maybe I'll get back to it later today or tomorrow.
I'll get back to it later today or tomorrow.
===Discussion Note 11===
===Discussion Note 11===
; Bernard Morand
: About another point: do you think that the LOR could be of some help to solve the puzzle of the "second way of dividing signs" where CSP concludes that 66 classes could be made out of the 10 divisions (Letters to lady Welby)? (As I see them, the ten divisions involve a mix of relative terms, dyadic relations and a triadic one. In order to make 66 classes it is clear that these 10 divisions have to be stated under some linear order. The nature of this order is at the bottom of the disagreements on the subject).
Yes. At any rate, I have a pretty clear sense from reading Peirce's work
; Jon Awbrey
in the period 1865-1870 that the need to understand the function of signs
: Yes. At any rate, I have a pretty clear sense from reading Peirce's work in the period 1865–1870 that the need to understand the function of signs in scientific inquiry is one of the main reasons he found himself forced to develop both the theory of information and the logic of relatives.
in scientific inquiry is one of the main reasons he found himself forced
to develop both the theory of information and the logic of relatives.
Peirce's work of this period is evenly distributed across the extensional
: Peirce's work of this period is evenly distributed across the extensional and intensional pans of the balance in a way that is very difficult for us to follow anymore. I remember when I started looking into this I thought of myself as more of an "intensional, synthetic" than an "extensional, analytic" type of thinker, but that seems like a long time ago, as it soon became clear that much less work had been done in the Peirce community on the extensional side of things, while that was the very facet that needed to be polished up in order to reconnect logic with empirical research and mathematical models. So I fear that I must be content that other able people are working on the intensional classification of sign relations.
and intensional pans of the balance in a way that is very difficult for us
to follow anymore. I remember when I started looking into this I thought of
myself as more of an "intensional, synthetic" than an "extensional, analytic"
type of thinker, but that seems like a long time ago, as it soon became clear
that much less work had been done in the Peirce community on the extensional
side of things, while that was the very facet that needed to be polished up
in order to reconnect logic with empirical research and mathematical models.
So I fear that I must be content that other able people are working on the
intensional classification of sign relations.
Still, the way that you pose the question is very enticing,
: Still, the way that you pose the question is very enticing, so maybe it is time for me to start thinking about this aspect of sign relations again, if you could say more about it.
so maybe it is time for me to start thinking about this
aspect of sign relations again, if you could say more
about it.
===Discussion Note 12===
===Discussion Note 12===
; Bernard Morand
: The pairing “intensional, synthetic” against the other “extensional, analytic” is not one that I would have thought so. I would have paired synthetic with extensional because synthesis consists in adding new facts to an already made conception. On the other side analysis looks to be the determination of features while neglecting facts. But may be there is something like a symmetry effect leading to the same view from two different points.
Oh, it's not too important, as I don't put a lot of faith in such divisions,
; Jon Awbrey
and the problem for me is always how to integrate the facets of the object,
: Oh, it's not too important, as I don't put a lot of faith in such divisions, and the problem for me is always how to integrate the facets of the object, or the faculties of the mind — but there I go being synthetic again!
or the faculties of the mind -- but there I go being synthetic again!
I was only thinking of a conventional contrast that used to be drawn
: I was only thinking of a conventional contrast that used to be drawn between different styles of thinking in mathematics, typically one points to Descartes, and the extensionality of analytic geometry, versus Desargues, and the intensionality of synthetic geometry.
between different styles of thinking in mathematics, typically one
points to Descartes, and the extensionality of analytic geometry,
versus Desargues, and the intensionality of synthetic geometry.
It may appear that one has side-stepped the issue of empiricism
: It may appear that one has side-stepped the issue of empiricism that way, but then all that stuff about the synthetic à priori raises its head, and we have Peirce's insight that mathematics is observational and even experimental, and so I must trail off into uncoordinated elliptical thoughts …
that way, but then all that stuff about the synthetic a priori
raises its head, and we have Peirce's insight that mathematics
is observational and even experimental, and so I must trail off
into uncoordinated elliptical thoughts ...
The rest I have to work at a while, and maybe go back to the Welby letters.
: The rest I have to work at a while, and maybe go back to the Welby letters.
===Discussion Note 13===
===Discussion Note 13===
; Bernard Morand
: I will try to make clear the matter, at least as far as I understand it for now. We can summarize in a table the 10 divisions with their number in a first column, their title in current (peircean) language in the second and some kind of logical notation in the third. The sources come mainly from the letters to Lady Welby. While the titles come from CP 8.344, the third column comes from my own interpretation.
: So we get:
{| align="center" cellspacing="6"
|
<pre>
I - According to the Mode of Apprehension of the Sign itself - S
I - According to the Mode of Apprehension of the Sign itself - S
II - According to the Mode of Presentation of the Immediate Object - Oi
II - According to the Mode of Presentation of the Immediate Object - Oi
X - According to the Triadic Relation of the Sign to its Dynamical Object
X - According to the Triadic Relation of the Sign to its Dynamical Object
and to its Normal Interpretant - S-Od-If
and to its Normal Interpretant - S-Od-If
</pre>
|}
For my future study, I will reformat the table in a way that I can muse upon.
; Jon Awbrey
I hope the roman numerals have not become canonical, as I cannot abide them.
: For my future study, I will reformat the table in a way that I can muse upon. I hope the roman numerals have not become canonical, as I cannot abide them.
{| align="center" cellspacing="6"
|
<pre>
Table. Ten Divisions of Signs (Peirce, Morand)
Table. Ten Divisions of Signs (Peirce, Morand)
o---o---------------o------------------o------------------o---------------o
o---o---------------o------------------o------------------o---------------o
| | | | & Normal Interp | S : O_d : I_f |
| | | | & Normal Interp | S : O_d : I_f |
o---o---------------o------------------o------------------o---------------o
o---o---------------o------------------o------------------o---------------o
</pre>
|}
Just as I have always feared, this classification mania
: Just as I have always feared, this classification mania appears to be communicable! But now I must definitely review the Welby correspondence, as all this stuff was a blur to my sensibilities the last 10 times I read it.
appears to be communicable! But now I must definitely
review the Welby correspondence, as all this stuff was
a blur to my sensibilities the last 10 times I read it.
===Discussion Note 14===
===Discussion Note 14===
; Jon Awbrey
{| align="center" cellspacing="6"
|
<pre>
<pre>
Table. Ten Divisions of Signs (Peirce, Morand)
o---o---------------o------------------o------------------o---------------o
| | According To: | Of: | To: | |
o===o===============o==================o==================o===============o
| 1 | Apprehension | Sign Itself | | S |
| 2 | Presentation | Immediate Object | | O_i |
| 3 | Being | Dynamical Object | | O_d |
| 4 | Relation | Sign | Dynamical Object | S : O_d |
o---o---------------o------------------o------------------o---------------o
| 5 | Presentation | Immediate Interp | | I_i |
| 6 | Being | Dynamical Interp | | I_d |
| 7 | Relation | Sign | Dynamical Interp | S : I_d |
o---o---------------o------------------o------------------o---------------o
| 8 | Nature | Normal Interp | | I_f |
| 9 | Relation | Sign | Normal Interp | S : I_f |
o---o---------------o------------------o------------------o---------------o
| A | Relation | Sign | Dynamical Object | |
| | | | & Normal Interp | S : O_d : I_f |
o---o---------------o------------------o------------------o---------------o
</pre>
|}
; Bernard Morand
: Yes this is clearer (in particular in expressing relations with “:”)
This is what Peirce used to form elementary relatives, for example,
; Jon Awbrey
o:s:i = <o, s, i>, and I find it utterly ubertous in a wide variety
: This is what Peirce used to form elementary relatives, for example, <math>o\!:\!s\!:\!i = (o, s, i),\!</math> and I find it utterly ubertous in a wide variety of syntactic circumstances.
of syntactic circumstances.
; Bernard Morand
: I suggest making a correction to myself if the table is destinate to become canonic.
Hah! Good one!
; Jon Awbrey
: Hah! Good one!
; Bernard Morand
: I probably made a too quick jump from Normal Interpretant to Final Interpretant. As we know, the final interpretant, the ultimate one is not a sign for Peirce but a habit. So for the sake of things to come it would be more careful to retain <math>\mathrm{I_n}\!</math> in place of <math>\mathrm{I_f}\!</math> for now.
This accords with my understanding of how the word is used in mathematics.
; Jon Awbrey
In my own work it has been necessary to distinguish many different species
: This accords with my understanding of how the word is used in mathematics. In my own work it has been necessary to distinguish many different species of expressions along somewhat similar lines, for example: arbitrary, basic, canonical, decidable, normal, periodic, persistent, prototypical, recurrent, representative, stable, typical, and so on. So I will make the changes below:
of expressions along somewhat similar lines, for example: arbitrary, basic,
canonical, decidable, normal, periodic, persistent, prototypical, recurrent,
representative, stable, typical, and so on. So I will make the changes below:
{| align="center" cellspacing="6"
|
<pre>
Table. Ten Divisions of Signs (Peirce, Morand)
Table. Ten Divisions of Signs (Peirce, Morand)
o---o---------------o------------------o------------------o---------------o
o---o---------------o------------------o------------------o---------------o
| | | | & Normal Interp | S : O_d : I_n |
| | | | & Normal Interp | S : O_d : I_n |
o---o---------------o------------------o------------------o---------------o
o---o---------------o------------------o------------------o---------------o
</pre>
|}
; Bernard Morand
: Peirce gives the following definition (CP 8.343).
; C.S. Peirce
: It is likewise requisite to distinguish the <i>Immediate Interpretant</i>, i.e. the Interpretant represented or signified in the Sign, from the <i>Dynamic Interpretant</i>, or effect actually produced on the mind by the Sign; and both of these from the <i>Normal Interpretant</i>, or effect that would be produced on the mind by the Sign after sufficient development of thought. (<i>Collected Papers</i>, CP 8.343).
; Jon Awbrey
: Well, you've really tossed me in the middle of the briar patch now! I must continue with my reading from the 1870 LOR, but now I have to add to my do-list the problems of comparing the whole variorum of letters and drafts of letters to Lady Welby. I have only the CP 8 and Wiener versions here, so I will depend on you for ample excerpts from the Lieb volume.
Well, you've really tossed me in the middle of the briar patch now!
I must continue with my reading from the 1870 LOR, but now I have
to add to my do-list the problems of comparing the whole variorum
of letters and drafts of letters to Lady Welby. I only have the
CP 8 and Wiener versions here, so I will depend on you for ample
excerpts from the Lieb volume.
===Discussion Note 15===
===Discussion Note 15===
; Jon Awbrey
I will need to go back and pick up the broader contexts of your quotes.
: I will need to go back and pick up the broader contexts of your quotes. For ease of study I break Peirce's long paragraphs into smaller pieces.
For ease of study I break Peirce's long paragraphs into smaller pieces.
; C.S. Peirce
{| align="center" width="90%"
| of the concepts of the science.
|
|
<p>It seems to me that one of the first useful steps toward a science of <i>semeiotic</i> (<i>σημειωτική</i>), or the cenoscopic science of signs, must be the accurate definition, or logical analysis, of the concepts of the science.</p>
You never know when the future explorer will be yourself.
<p>I define a <i>Sign</i> as anything which on the one hand is so determined by an Object and on the other hand so determines an idea in a person's mind, that this latter determination, which I term the <i>Interpretant</i> of the sign, is thereby mediately determined by that Object.</p>
<p>A sign, therefore, has a triadic relation to its Object and to its Interpretant. But it is necessary to distinguish the <i>Immediate Object</i>, or the Object as the Sign represents it, from the <i>Dynamical Object</i>, or really efficient but not immediately present Object.</p>
<p>It is likewise requisite to distinguish the <i>Immediate Interpretant</i>, i.e. the Interpretant represented or signified in the Sign, from the <i>Dynamic Interpretant</i>, or effect actually produced on the mind by the Sign; and both of these from the <i>Normal Interpretant</i>, or effect that would be produced on the mind by the Sign after sufficient development of thought.</p>
<p>On these considerations I base a recognition of ten respects in which Signs may be divided. I do not say that these divisions are enough. But since every one of them turns out to be a trichotomy, it follows that in order to decide what classes of signs result from them, I have 3<sup>10</sup>, or 59049, difficult questions to carefully consider; and therefore I will not undertake to carry my systematical division of signs any further, but will leave that for future explorers.</p>
<p>(<i>Collected Papers</i>, CP 8.343).</p>
|}
; Jon Awbrey
: You never know when the future explorer will be yourself.
===Discussion Note 16===
===Discussion Note 16===
===Discussion Note 18===
===Discussion Note 18===
; Jon Awbrey
: but now I have to add to my do-list the problems of comparing the whole variorum of letters and drafts of letters to Lady Welby. I only have the CP 8 and Wiener versions here, so I will depend on you for ample excerpts from the Lieb volume.
; Bernard Morand
: I made such a kind of comparison some time ago. I selected the following 3 cases on the criterion of alternate "grounds". Hoping it could save some labor. The first rank expressions come from the MS 339 written in Oct. 1904 and I label them with an (a). I think that it is interesting to note that they were written four years before the letters to Welby and just one or two years after the Syllabus which is the usual reference for the classification in 3 trichotomies and 10 classes. The second (b) is our initial table (from a draft to Lady Welby, Dec. 1908, CP 8.344) and the third (c) comes from a letter sent in Dec. 1908 (CP 8.345–376). A tabular presentation would be better but I can't do it. Comparing (c) against (a) and (b) is informative, I think.
Is this anywhere that it can be linked to from Arisbe?
; Jon Awbrey
I've seen many pretty pictures of these things over the
: Is this anywhere that it can be linked to from Arisbe? I've seen many pretty pictures of these things over the years, but may have to follow my own gnosis for a while.
years, but may have to follow my own gnosis for a while.
Pages I have bookmarked just recently,
: Pages I have bookmarked just recently, but not really had the chance to study:
but not really had the chance to study:
http://www.digitalpeirce.org/hoffmann/p-sighof.htm
: http://www.digitalpeirce.org/hoffmann/p-sighof.htm
http://www.csd.uwo.ca/~merkle/thesis/Introduction.html
: http://www.csd.uwo.ca/~merkle/thesis/Introduction.html
http://members.door.net/arisbe/menu/library/aboutcsp/merkle/hci-abstract.htm
: http://members.door.net/arisbe/menu/library/aboutcsp/merkle/hci-abstract.htm
===Discussion Note 19===
===Discussion Note 19===
===Discussion Note 20===
===Discussion Note 20===
; Howard Callaway
: Though I certainly hesitate to think that we are separated from the world by a veil of signs, it seems clear, too, on Peircean grounds, that no sign can ever capture its object completely.
; Joe Ransdell
: Any case of self-representation is a case of sign-object identity, in some sense of “identity”. I have argued in various places that this is the key to the doctrine of immediate perception as it occurs in Peirce's theory.
To put the phrase back on the lathe:
; Jon Awbrey
: To put the phrase back on the lathe:
: We are not separated from the world by a veil of signs —
: we are the veil of signs.
===Discussion Note 21===
===Discussion Note 21===
===Discussion Note 23===
===Discussion Note 23===
; Jon Awbrey
In trying to answer the rest of your last note,
: In trying to answer the rest of your last note, it seems that we cannot go any further without achieving some concrete clarity as to what is denominated by “standard predicate calculus”, that is, “first order logic”, or whatever.
it seems that we cannot go any further without
achieving some concrete clarity as to what is
denominated by "standard predicate calculus",
that is, "first order logic", or whatever.
There is a "canonical" presentation of the subject, as I remember it, anyway,
: There is a canonical presentation of the subject, as I remember it, anyway, in the following sample of materials from Chang and Keisler's <i>Model Theory</i>. (There's a newer edition of the book but this part of the subject hasn't really changed all that much in ages.)
in the following sample of materials from Chang & Keisler's 'Model Theory'.
(There's a newer edition of the book, but this part of the subject hasn't
really changed all that much in ages.)
Model Theory 01-39
: Model Theory 01-39
===Discussion Note 24===
===Discussion Note 24===
===Discussion Note 26===
===Discussion Note 26===
; Howard Callaway
: But on the other hand, it is not customary to think of “&” as a relation among statements or sentences — as, for instance, logical implication is considered a logical relation between statements or sentences.
Actually, it is the custom in many quarters to treat all of the
; Jon Awbrey
boolean operations, logical connectives, propositional relations,
: Actually, it is the custom in many quarters to treat all of the boolean operations, logical connectives, propositional relations, or whatever you want to call them, as “equal citizens”, having each their “functional” (f : B^k -> B) and their “relational” (L c B^(k+1)) interpretations and applications. From this vantage, the interpretive distinction that is commonly regarded as that between “assertion” and mere “contemplation” is tantamount to a “pragmatic” difference between computing the values of a function on a given domain of arguments and computing the inverse of a function vis-a-vis a prospective true value. This is the logical analogue of the way that our mathematical models of reality have long been working, unsuspected and undisturbed by most philosophers of science, I might add. If only the logical side of the ledger were to be developed rather more fully than it is at present, we might wake one of these days to find our logical accounts of reality, finally, at long last, after an overweaningly longish adolescence, beginning to come of age.
or whatever you want to call them, as "equal citizens", having each
their "functional" (f : B^k -> B) and their "relational" (L c B^(k+1))
interpretations and applications. From this vantage, the interpretive
distinction that is commonly regarded as that between "assertion" and
mere "contemplation" is tantamount to a "pragmatic" difference between
computing the values of a function on a given domain of arguments and
computing the inverse of a function vis-a-vis a prospective true value.
This is the logical analogue of the way that our mathematical models
of reality have long been working, unsuspected and undisturbed by
most philosophers of science, I might add. If only the logical
side of the ledger were to be developed rather more fully than
it is at present, we might wake one of these days to find our
logical accounts of reality, finally, at long last, after an
overweaningly longish adolescence, beginning to come of age.
===Discussion Note 27===
===Discussion Note 27===
===Discussion Note 31===
===Discussion Note 31===
Many illusions of selective reading — like the myth that Peirce did not discover quantification over indices until 1885 — can be dispelled by looking into his 1870 “Logic of Relatives”. I started a web study of this in 2002, reworked again in 2003 and 2004, the current version of which can be found here:
Many illusions of selective reading -- like the myth that Peirce did not
discover quantification over indices until 1885 -- can be dispelled by
looking into his 1870 "Logic of Relatives". I started a web study of
this in 2002, reworked again in 2003 and 2004, the current version
of which can be found here:
* [http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750 LOR Selections]
* [http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1755 LOR Comments]
* [http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1768 LOR Discussion]
I've only gotten as far as the bare infrastructure of Peirce's 1870 LOR,
I've only gotten as far as the bare infrastructure of Peirce's 1870 LOR, but an interesting feature of the study is that, if one draws the pictures that seem almost demanded by his way of linking up indices over expressions, then one can see a prototype of his much later logical graphs developing in the text.
but an interesting feature of the study is that, if one draws the pictures
that seem almost demanded by his way of linking up indices over expressions,
then one can see a prototype of his much later logical graphs developing in
the text.
==Discussion Work Areas==
==Discussion Work Areas==
<pre>
<pre>
It's been that way for about as long as anybody can remember, and
It's been that way for about as long as anybody can remember, and
it will remain so, in spite of the spate of history rewriting and
it will remain so, in spite of the spate of history rewriting and
image re-engineering that has become the new rage in self-styled
image re-engineering that has become the new rage in self-styled
"analytic" circles.
"analytic" circles.
</pre>
</pre>
<pre>
<pre>
The brands of objection that you continue to make, with no evidence
The brands of objection that you continue to make, with no evidence
of reflection on the many explanations that I and others have taken
of reflection on the many explanations that I and others have taken
other matter of culture suddenly turn into just
other matter of culture suddenly turn into just
that in matters of simple mathematical fact.
that in matters of simple mathematical fact.
</pre>
</pre>
==Document History==
==Work Area==
===Ontology List (Dec 2002 – Feb 2003)===
===Figure 51===
====Version 1====
{| align="center" cellspacing ="6" width="90%"
|
<pre>
t_1 t_32 t_33 t_64 t_65 t_96 ... ...
o ... o o ... o o ... o o ... o U
\ | / \ | / \ | / \ | /
\ | / \ | / \ | / \ | / T
\|/ \|/ \|/ \|/
o o o o V
m_1 m_2 m_3 ...
</pre>
|}
====Version 2====
{| align="center" cellspacing ="6" width="90%"
|
<pre>
T_1 T_32 T_33 T_64 T_65 T_96 ... ...
o ... o o ... o o ... o o ... o t
\ | / \ | / \ | / \ | /
\ | / \ | / \ | / \ | / 't'
\|/ \|/ \|/ \|/
o o o o m
M_1 M_2 M_3 ...
</pre>
|}
====Version 3====
{| align="center" cellspacing ="6" width="90%"
|
<pre>
# http://suo.ieee.org/ontology/msg04457.html
M_1 M_2 M_3 ...
o o o o m
# http://suo.ieee.org/ontology/msg04459.html
/|\ /|\ /|\ /|\
# http://suo.ieee.org/ontology/msg04462.html
/ | \ / | \ / | \ / | \ 't'
/ | \ / | \ / | \ / | \
o ... o o ... o o ... o o ... o t
T_1 T_32 T_33 T_64 T_65 T_96 ... ...
</pre>
|}
==Mathematical Demonstration and the Doctrine of Individuals==
# http://suo.ieee.org/ontology/msg04498.html
===CP 3.92===
# http://suo.ieee.org/ontology/msg04500.html
<h4>Selection from C.S. Peirce, “Logic Of Relatives” (1870), CP 3.45–149</h4>
# http://suo.ieee.org/ontology/msg04502.html
<div style="margin-left:25px;">
# http://suo.ieee.org/ontology/msg04504.html
92. Demonstration of the sort called mathematical is founded on suppositions of particular cases. The geometrician draws a figure; the algebraist assumes a letter to signify a single quantity fulfilling the required conditions. But while the mathematician supposes an individual case, his hypothesis is yet perfectly general, because he considers no characters of the individual case but those which must belong to every such case. The advantage of his procedure lies in the fact that the logical laws of individual terms are simpler than those which relate to general terms, because individuals are either identical or mutually exclusive, and cannot intersect or be subordinated to one another as classes can. Mathematical demonstration is not, therefore, more restricted to matters of intuition than any other kind of reasoning. Indeed, logical algebra conclusively proves that mathematics extends over the whole realm of formal logic; and any theory of cognition which cannot be adjusted to this fact must be abandoned. We may reap all the advantages which the mathematician is supposed to derive from intuition by simply making general suppositions of individual cases.
# http://suo.ieee.org/ontology/msg04508.html
</div>
# http://suo.ieee.org/ontology/msg04510.html
<h4>References</h4>
# http://suo.ieee.org/ontology/msg04512.html
<ul>
<li>Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”, <i>Memoirs of the American Academy of Arts and Sciences</i> 9, 317–378, 26 January 1870. Reprinted, <i>Collected Papers</i> 3.45–149, <i>Chronological Edition</i> 2, 359–429. Online <a href="http://www.jstor.org/stable/25058006" target="_blank">(1)</a> <a href="https://archive.org/details/jstor-25058006" target="_blank">(2)</a> <a href="http://books.google.com/books?id=fFnWmf5oLaoC" target="_blank">(3)</a>.</li>
# http://suo.ieee.org/ontology/msg04516.html
<li>Peirce, C.S., <i>Collected Papers of Charles Sanders Peirce</i>, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958.</li>
# http://suo.ieee.org/ontology/msg04518.html
# http://suo.ieee.org/ontology/msg04521.html
<li>Peirce, C.S., <i>Writings of Charles S. Peirce : A Chronological Edition</i>, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.</li>
</ul>
<h4>Resources</h4>
# http://suo.ieee.org/ontology/msg04543.html
<ul><li><a href="http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives" target="_blank" title="Peirce's 1870 Logic Of Relatives">Peirce's 1870 Logic Of Relatives</a></li></ul>
===CP 3.93===
{| align="center" cellpadding="0" cellspacing="0" width="90%"
|
<p>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 <math>\mathrm{A}\!</math> be such a term. Then, if it is neither true that all <math>\mathrm{A}\!</math> is <math>\mathrm{X}\!</math> nor that no <math>\mathrm{A}\!</math> is <math>\mathrm{X},\!</math> it must be true that some <math>\mathrm{A}\!</math> is <math>\mathrm{X}\!</math> and some <math>\mathrm{A}\!</math> is not <math>\mathrm{X};\!</math> and therefore <math>\mathrm{A}\!</math> may be divided into <math>\mathrm{A}\!</math> that is <math>\mathrm{X}\!</math> and <math>\mathrm{A}\!</math> that is not <math>\mathrm{X},\!</math> which is contrary to its nature as a logical atom.</p>
<p>Such a term can be realized neither in thought nor in sense.</p>
<p>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 sweetness 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 no facts which prove that there is never the least vagueness in the immediate sensation.</p>
<p>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.</p>
<p>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 <i>absolutely</i> 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 <math>I\!</math> be a term which in consequence of such neglect becomes indivisible in that discourse, we have in that discourse,</p>
<p align="center"><math>[I] = 1.\!</math></p>
<p>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 <i>individual</i> (τὸ ἄτομον) and <i>singular</i> (τὸ καθ᾿ ἕκαστον); but as those who have used the word <i>individual</i> have not been aware that absolute individuality is merely ideal, it has come to be used in a more general sense.</p>
<p>(CP 3.93, CE 2, 389–390).</p>
<p>Charles Sanders Peirce, “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”, <i>Memoirs of the American Academy</i>, Volume 9, pp. 317–378, 26 January 1870, <i>Collected Papers</i> (CP 3.45–149), <i>Chronological Edition</i> (CE 2, 359–429).</p>
|}
<b>Note.</b> On the square bracket notation used above: Peirce explains this notation at [http://inquiryintoinquiry.com/2014/01/29/peirces-1870-logic-of-relatives-%E2%80%A2-selection-2/ CP 3.65].
{| align="center" cellpadding="0" cellspacing="0" width="90%"
| <p>I propose to denote the number of a logical term by enclosing the term in square brackets, thus, <math>[t].\!</math></p>
|}
The <i>number</i> of an absolute term, as in the case of <math>I,\!</math> is defined as the number of individuals it denotes.
==Document History==
===2002 • Peirce List===
# http://www.cspeirce.com/peirce-l/12-14-02.htm
# http://www.cspeirce.com/peirce-l/12-15-02.htm
===2002–2003 • Ontology List===
* http://web.archive.org/web/20070302144532/http://suo.ieee.org/ontology/thrd20.html#04416
* http://web.archive.org/web/20070304201457/http://suo.ieee.org/ontology/thrd21.html#04425
* http://web.archive.org/web/20070302144532/http://suo.ieee.org/ontology/thrd20.html#04455
* http://web.archive.org/web/20070225053324/http://suo.ieee.org/ontology/thrd22.html#04515
# http://web.archive.org/web/20070302152249/http://suo.ieee.org/ontology/msg04416.html
# http://web.archive.org/web/20070304003617/http://suo.ieee.org/ontology/msg04417.html
# http://web.archive.org/web/20070303180330/http://suo.ieee.org/ontology/msg04418.html
# http://web.archive.org/web/20070304003631/http://suo.ieee.org/ontology/msg04419.html
# http://web.archive.org/web/20070304003523/http://suo.ieee.org/ontology/msg04421.html
# http://web.archive.org/web/20070304003534/http://suo.ieee.org/ontology/msg04422.html
# http://web.archive.org/web/20070304003546/http://suo.ieee.org/ontology/msg04423.html
# http://web.archive.org/web/20070303180343/http://suo.ieee.org/ontology/msg04424.html
# http://web.archive.org/web/20070304003512/http://suo.ieee.org/ontology/msg04425.html
# http://web.archive.org/web/20070304003646/http://suo.ieee.org/ontology/msg04426.html
# http://web.archive.org/web/20070304003657/http://suo.ieee.org/ontology/msg04427.html
# http://web.archive.org/web/20070303180353/http://suo.ieee.org/ontology/msg04431.html
# http://web.archive.org/web/20070304003707/http://suo.ieee.org/ontology/msg04432.html
# http://web.archive.org/web/20070304003718/http://suo.ieee.org/ontology/msg04435.html
# http://web.archive.org/web/20070304003452/http://suo.ieee.org/ontology/msg04436.html
# http://web.archive.org/web/20070303180403/http://suo.ieee.org/ontology/msg04437.html
# http://web.archive.org/web/20070304003728/http://suo.ieee.org/ontology/msg04438.html
# http://web.archive.org/web/20070303180414/http://suo.ieee.org/ontology/msg04439.html
# http://web.archive.org/web/20070304003423/http://suo.ieee.org/ontology/msg04440.html
# http://web.archive.org/web/20070304003502/http://suo.ieee.org/ontology/msg04441.html
# http://web.archive.org/web/20070304003738/http://suo.ieee.org/ontology/msg04442.html
# http://web.archive.org/web/20070304003748/http://suo.ieee.org/ontology/msg04443.html
# http://web.archive.org/web/20070304003432/http://suo.ieee.org/ontology/msg04444.html
# http://web.archive.org/web/20070303180423/http://suo.ieee.org/ontology/msg04445.html
# http://web.archive.org/web/20070304003758/http://suo.ieee.org/ontology/msg04446.html
# http://web.archive.org/web/20070304003809/http://suo.ieee.org/ontology/msg04447.html
# http://web.archive.org/web/20070304003818/http://suo.ieee.org/ontology/msg04448.html
# http://web.archive.org/web/20070304003829/http://suo.ieee.org/ontology/msg04449.html
# http://web.archive.org/web/20070304003842/http://suo.ieee.org/ontology/msg04450.html
# http://web.archive.org/web/20070304003853/http://suo.ieee.org/ontology/msg04451.html
# http://web.archive.org/web/20070304003903/http://suo.ieee.org/ontology/msg04452.html
# http://web.archive.org/web/20070304003913/http://suo.ieee.org/ontology/msg04453.html
# http://web.archive.org/web/20070304003923/http://suo.ieee.org/ontology/msg04454.html
# http://web.archive.org/web/20070303180434/http://suo.ieee.org/ontology/msg04456.html
# http://web.archive.org/web/20070304003933/http://suo.ieee.org/ontology/msg04457.html
# http://web.archive.org/web/20070304003943/http://suo.ieee.org/ontology/msg04458.html
# http://web.archive.org/web/20070304003954/http://suo.ieee.org/ontology/msg04459.html
# http://web.archive.org/web/20070304004004/http://suo.ieee.org/ontology/msg04462.html
# http://web.archive.org/web/20070304004014/http://suo.ieee.org/ontology/msg04464.html
# http://web.archive.org/web/20070304004024/http://suo.ieee.org/ontology/msg04473.html
# http://web.archive.org/web/20070304004034/http://suo.ieee.org/ontology/msg04478.html
# http://web.archive.org/web/20070303180444/http://suo.ieee.org/ontology/msg04484.html
# http://web.archive.org/web/20070304004044/http://suo.ieee.org/ontology/msg04487.html
# http://web.archive.org/web/20070303180454/http://suo.ieee.org/ontology/msg04488.html
# http://web.archive.org/web/20070304004054/http://suo.ieee.org/ontology/msg04492.html
# http://web.archive.org/web/20070303180504/http://suo.ieee.org/ontology/msg04497.html
# http://web.archive.org/web/20070303180514/http://suo.ieee.org/ontology/msg04498.html
# http://web.archive.org/web/20070304004104/http://suo.ieee.org/ontology/msg04499.html
# http://web.archive.org/web/20070304004114/http://suo.ieee.org/ontology/msg04500.html
# http://web.archive.org/web/20070304004126/http://suo.ieee.org/ontology/msg04501.html
# http://web.archive.org/web/20070304004137/http://suo.ieee.org/ontology/msg04502.html
# http://web.archive.org/web/20070304004147/http://suo.ieee.org/ontology/msg04503.html
# http://web.archive.org/web/20070304004158/http://suo.ieee.org/ontology/msg04504.html
# http://web.archive.org/web/20070303180524/http://suo.ieee.org/ontology/msg04506.html
# http://web.archive.org/web/20070302152300/http://suo.ieee.org/ontology/msg04508.html
# http://web.archive.org/web/20070302152309/http://suo.ieee.org/ontology/msg04509.html
# http://web.archive.org/web/20070302152319/http://suo.ieee.org/ontology/msg04510.html
# http://web.archive.org/web/20070302152329/http://suo.ieee.org/ontology/msg04511.html
# http://web.archive.org/web/20070228081319/http://suo.ieee.org/ontology/msg04512.html
# http://web.archive.org/web/20070228081328/http://suo.ieee.org/ontology/msg04513.html
# http://web.archive.org/web/20070228081356/http://suo.ieee.org/ontology/msg04516.html
# http://web.archive.org/web/20070228081406/http://suo.ieee.org/ontology/msg04517.html
# http://web.archive.org/web/20070228081419/http://suo.ieee.org/ontology/msg04518.html
# http://web.archive.org/web/20070228081429/http://suo.ieee.org/ontology/msg04521.html
# http://web.archive.org/web/20070228081440/http://suo.ieee.org/ontology/msg04539.html
# http://web.archive.org/web/20070228081449/http://suo.ieee.org/ontology/msg04541.html
# http://web.archive.org/web/20070228081501/http://suo.ieee.org/ontology/msg04542.html
# http://web.archive.org/web/20070228081512/http://suo.ieee.org/ontology/msg04543.html
# http://web.archive.org/web/20070228081347/http://suo.ieee.org/ontology/msg04515.html
===2003 • Ontology List • Discussion===
* http://web.archive.org/web/20070302144532/http://suo.ieee.org/ontology/thrd20.html#04460
<ol start="10">
<ol start="10">
<li>http://suo.ieee.org/ontology/msg04460.html</li>
<li>http://web.archive.org/web/20070305104636/http://suo.ieee.org/ontology/msg04460.html</li>
<li>http://suo.ieee.org/ontology/msg04461.html</li>
<li>http://web.archive.org/web/20070305123739/http://suo.ieee.org/ontology/msg04461.html</li>
<li>http://suo.ieee.org/ontology/msg04471.html</li>
<li>http://web.archive.org/web/20070305103313/http://suo.ieee.org/ontology/msg04471.html</li>
<li>http://suo.ieee.org/ontology/msg04472.html</li>
<li>http://web.archive.org/web/20070305104646/http://suo.ieee.org/ontology/msg04472.html</li>
<li>http://suo.ieee.org/ontology/msg04475.html</li>
<li>http://web.archive.org/web/20070305201820/http://suo.ieee.org/ontology/msg04475.html</li>
<li>http://suo.ieee.org/ontology/msg04476.html</li>
<li>http://web.archive.org/web/20070305104656/http://suo.ieee.org/ontology/msg04476.html</li>
<li>http://suo.ieee.org/ontology/msg04477.html</li>
<li>http://web.archive.org/web/20070305104706/http://suo.ieee.org/ontology/msg04477.html</li>
<li>http://suo.ieee.org/ontology/msg04479.html</li>
<li>http://web.archive.org/web/20070305104716/http://suo.ieee.org/ontology/msg04479.html</li>
<li>http://suo.ieee.org/ontology/msg04480.html</li>
<li>http://web.archive.org/web/20070305104727/http://suo.ieee.org/ontology/msg04480.html</li>
<li>http://suo.ieee.org/ontology/msg04481.html</li>
<li>http://web.archive.org/web/20070305104746/http://suo.ieee.org/ontology/msg04481.html</li>
<li>http://suo.ieee.org/ontology/msg04482.html</li>
<li>http://web.archive.org/web/20070307071521/http://suo.ieee.org/ontology/msg04482.html</li>
<li>http://suo.ieee.org/ontology/msg04483.html</li>
<li>http://web.archive.org/web/20040730203244/http://suo.ieee.org/ontology/msg04483.html</li>
<li>http://suo.ieee.org/ontology/msg04485.html</li>
<li>http://web.archive.org/web/20070305104801/http://suo.ieee.org/ontology/msg04485.html</li>
<li>http://suo.ieee.org/ontology/msg04486.html</li>
<li>http://web.archive.org/web/20040729135710/http://suo.ieee.org/ontology/msg04486.html</li>
<li>http://suo.ieee.org/ontology/msg04493.html</li>
<li>http://web.archive.org/web/20070305104812/http://suo.ieee.org/ontology/msg04493.html</li>
<li>http://suo.ieee.org/ontology/msg04494.html</li>
<li>http://web.archive.org/web/20070305104822/http://suo.ieee.org/ontology/msg04494.html</li>
<li>http://suo.ieee.org/ontology/msg04495.html</li>
<li>http://web.archive.org/web/20070305104832/http://suo.ieee.org/ontology/msg04495.html</li>
<li>http://suo.ieee.org/ontology/msg04496.html</li>
<li>http://web.archive.org/web/20070305104842/http://suo.ieee.org/ontology/msg04496.html</li>
</ol>
</ol>
===Arisbe List (Jan–Feb 2003)===
===2003 • Arisbe List===
* http://web.archive.org/web/20140617201402/http://stderr.org/pipermail/arisbe/2003-January/thread.html#1453
* http://web.archive.org/web/20140617201402/http://stderr.org/pipermail/arisbe/2003-January/thread.html#1485
* http://web.archive.org/web/20140617201402/http://stderr.org/pipermail/arisbe/2003-January/thread.html#1505
* http://web.archive.org/web/20140619114718/http://stderr.org/pipermail/arisbe/2003-February/thread.html#1520
<ol start="38">
<li>http://web.archive.org/web/20140617201423/http://stderr.org/pipermail/arisbe/2003-January/001453.html</li>
<li>http://web.archive.org/web/20050506011725/http://stderr.org/pipermail/arisbe/2003-January/001454.html</li>
<li>http://web.archive.org/web/20050506011629/http://stderr.org/pipermail/arisbe/2003-January/001457.html</li>
<li>http://web.archive.org/web/20050506011625/http://stderr.org/pipermail/arisbe/2003-January/001461.html</li>
<li>http://web.archive.org/web/20050506011649/http://stderr.org/pipermail/arisbe/2003-January/001467.html</li>
<li>http://web.archive.org/web/20050506011653/http://stderr.org/pipermail/arisbe/2003-January/001470.html</li>
<li>http://web.archive.org/web/20051202053753/http://stderr.org/pipermail/arisbe/2003-January/001471.html</li>
<li>http://web.archive.org/web/20050824084910/http://stderr.org/pipermail/arisbe/2003-January/001475.html</li>
<li>http://web.archive.org/web/20051202075602/http://stderr.org/pipermail/arisbe/2003-January/001480.html</li>
<li>http://web.archive.org/web/20050826203125/http://stderr.org/pipermail/arisbe/2003-January/001481.html</li>
<li>http://web.archive.org/web/20051202045453/http://stderr.org/pipermail/arisbe/2003-January/001482.html</li>
<li>http://web.archive.org/web/20051202035157/http://stderr.org/pipermail/arisbe/2003-January/001483.html</li>
<li>http://web.archive.org/web/20051202053307/http://stderr.org/pipermail/arisbe/2003-January/001484.html</li>
<li>http://web.archive.org/web/20051202042621/http://stderr.org/pipermail/arisbe/2003-January/001485.html</li>
<li>http://web.archive.org/web/20051202070136/http://stderr.org/pipermail/arisbe/2003-January/001486.html</li>
<li>http://web.archive.org/web/20051202011212/http://stderr.org/pipermail/arisbe/2003-January/001488.html</li>
<li>http://web.archive.org/web/20050506090030/http://stderr.org/pipermail/arisbe/2003-January/001489.html</li>
<li>http://web.archive.org/web/20050506090129/http://stderr.org/pipermail/arisbe/2003-January/001503.html</li>
<li>http://web.archive.org/web/20050506090050/http://stderr.org/pipermail/arisbe/2003-January/001505.html</li>
<li>http://web.archive.org/web/20050506090219/http://stderr.org/pipermail/arisbe/2003-January/001507.html</li>
<li>http://web.archive.org/web/20050506090106/http://stderr.org/pipermail/arisbe/2003-January/001513.html</li>
<li>http://web.archive.org/web/20050506090223/http://stderr.org/pipermail/arisbe/2003-January/001514.html</li>
<li>http://web.archive.org/web/20050506090154/http://stderr.org/pipermail/arisbe/2003-January/001515.html</li>
<li>http://web.archive.org/web/20070315211932/http://stderr.org/pipermail/arisbe/2003-February/001520.html</li>
<li>http://web.archive.org/web/20070315211952/http://stderr.org/pipermail/arisbe/2003-February/001525.html</li>
<li>http://web.archive.org/web/20070315212032/http://stderr.org/pipermail/arisbe/2003-February/001529.html</li>
<li>http://web.archive.org/web/20070315212112/http://stderr.org/pipermail/arisbe/2003-February/001534.html</li>
<li>http://web.archive.org/web/20070315163838/http://stderr.org/pipermail/arisbe/2003-February/001567.html</li>
<li>http://web.archive.org/web/20070315212724/http://stderr.org/pipermail/arisbe/2003-February/001578.html</li>
<li>http://web.archive.org/web/20070315212733/http://stderr.org/pipermail/arisbe/2003-February/001579.html</li>
<li>http://web.archive.org/web/20070315212814/http://stderr.org/pipermail/arisbe/2003-February/001587.html</li>
</ol>
===2003 • Arisbe List • Discussion===
* http://web.archive.org/web/20140617201402/http://stderr.org/pipermail/arisbe/2003-January/thread.html#1455
<ol start="12">
<ol start="12">
<li>http://stderr.org/pipermail/arisbe/2003-January/001455.html</li>
<li>http://web.archive.org/web/20051202040453/http://stderr.org/pipermail/arisbe/2003-January/001455.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001456.html</li>
<li>http://web.archive.org/web/20050826052233/http://stderr.org/pipermail/arisbe/2003-January/001456.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001458.html</li>
<li>http://web.archive.org/web/20050506011705/http://stderr.org/pipermail/arisbe/2003-January/001458.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001459.html</li>
<li>http://web.archive.org/web/20050506011657/http://stderr.org/pipermail/arisbe/2003-January/001459.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001460.html</li>
<li>http://web.archive.org/web/20050506011857/http://stderr.org/pipermail/arisbe/2003-January/001460.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001462.html</li>
<li>http://web.archive.org/web/20050506011701/http://stderr.org/pipermail/arisbe/2003-January/001462.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001463.html</li>
<li>http://web.archive.org/web/20050826112404/http://stderr.org/pipermail/arisbe/2003-January/001463.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001464.html</li>
<li>http://web.archive.org/web/20051202065741/http://stderr.org/pipermail/arisbe/2003-January/001464.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001465.html</li>
<li>http://web.archive.org/web/20050827050454/http://stderr.org/pipermail/arisbe/2003-January/001465.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001466.html</li>
<li>http://web.archive.org/web/20051202100823/http://stderr.org/pipermail/arisbe/2003-January/001466.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001468.html</li>
<li>http://web.archive.org/web/20050506011801/http://stderr.org/pipermail/arisbe/2003-January/001468.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001469.html</li>
<li>http://web.archive.org/web/20050824223011/http://stderr.org/pipermail/arisbe/2003-January/001469.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001476.html</li>
<li>http://web.archive.org/web/20050506011633/http://stderr.org/pipermail/arisbe/2003-January/001476.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001477.html</li>
<li>http://web.archive.org/web/20050506011849/http://stderr.org/pipermail/arisbe/2003-January/001477.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001478.html</li>
<li>http://web.archive.org/web/20050826141451/http://stderr.org/pipermail/arisbe/2003-January/001478.html</li>
<li>http://stderr.org/pipermail/arisbe/2003-January/001479.html</li>
<li>http://web.archive.org/web/20050506011845/http://stderr.org/pipermail/arisbe/2003-January/001479.html</li>
</ol>
</ol>
===Inquiry List (Mar–Apr 2003)===
===2003 • Inquiry List===
* http://stderr.org/pipermail/inquiry/2003-March/thread.html#186
* http://web.archive.org/web/20150224210000/http://stderr.org/pipermail/inquiry/2003-March/thread.html#186
* http://stderr.org/pipermail/inquiry/2003-April/thread.html#245
* http://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#245
# http://stderr.org/pipermail/inquiry/2003-March/000186.html
# http://web.archive.org/web/20081120062116/http://stderr.org/pipermail/inquiry/2003-March/000186.html
# http://web.archive.org/web/20061013222246/http://stderr.org/pipermail/inquiry/2003-March/000187.html
# http://stderr.org/pipermail/inquiry/2003-March/000188.html
# http://web.archive.org/web/20061013221536/http://stderr.org/pipermail/inquiry/2003-March/000188.html
# http://web.archive.org/web/20061013222728/http://stderr.org/pipermail/inquiry/2003-March/000189.html
# http://stderr.org/pipermail/inquiry/2003-March/000190.html
# http://web.archive.org/web/20061013222333/http://stderr.org/pipermail/inquiry/2003-March/000190.html
# http://web.archive.org/web/20061013221823/http://stderr.org/pipermail/inquiry/2003-March/000191.html
# http://stderr.org/pipermail/inquiry/2003-March/000194.html
# http://web.archive.org/web/20070305235828/http://stderr.org/pipermail/inquiry/2003-March/000194.html
# http://web.archive.org/web/20070302055237/http://stderr.org/pipermail/inquiry/2003-March/000195.html
# http://stderr.org/pipermail/inquiry/2003-April/000245.html
# http://web.archive.org/web/20070303020850/http://stderr.org/pipermail/inquiry/2003-April/000245.html
# http://web.archive.org/web/20070306225534/http://stderr.org/pipermail/inquiry/2003-April/000246.html
# http://stderr.org/pipermail/inquiry/2003-April/000247.html
# http://web.archive.org/web/20070315063236/http://stderr.org/pipermail/inquiry/2003-April/000247.html
# http://stderr.org/pipermail/inquiry/2003-April/000248.html
# http://web.archive.org/web/20070310205044/http://stderr.org/pipermail/inquiry/2003-April/000248.html
# http://web.archive.org/web/20070310205014/http://stderr.org/pipermail/inquiry/2003-April/000249.html
# http://stderr.org/pipermail/inquiry/2003-April/000250.html
# http://web.archive.org/web/20061013223819/http://stderr.org/pipermail/inquiry/2003-April/000250.html
# http://web.archive.org/web/20070310204954/http://stderr.org/pipermail/inquiry/2003-April/000251.html
# http://stderr.org/pipermail/inquiry/2003-April/000252.html
# http://web.archive.org/web/20070309174344/http://stderr.org/pipermail/inquiry/2003-April/000252.html
# http://stderr.org/pipermail/inquiry/2003-April/000253.html
# http://web.archive.org/web/20070310205054/http://stderr.org/pipermail/inquiry/2003-April/000253.html
# http://stderr.org/pipermail/inquiry/2003-April/000254.html
# http://web.archive.org/web/20070310205024/http://stderr.org/pipermail/inquiry/2003-April/000254.html
# http://web.archive.org/web/20070310205034/http://stderr.org/pipermail/inquiry/2003-April/000255.html
# http://stderr.org/pipermail/inquiry/2003-April/000256.html
# http://web.archive.org/web/20070310205105/http://stderr.org/pipermail/inquiry/2003-April/000256.html
# http://web.archive.org/web/20070310205116/http://stderr.org/pipermail/inquiry/2003-April/000257.html
# http://stderr.org/pipermail/inquiry/2003-April/000258.html
# http://web.archive.org/web/20070309174424/http://stderr.org/pipermail/inquiry/2003-April/000258.html
# http://stderr.org/pipermail/inquiry/2003-April/000259.html
# http://web.archive.org/web/20070311141543/http://stderr.org/pipermail/inquiry/2003-April/000259.html
# http://web.archive.org/web/20070309202630/http://stderr.org/pipermail/inquiry/2003-April/000260.html
# http://stderr.org/pipermail/inquiry/2003-April/000261.html
# http://web.archive.org/web/20070309202751/http://stderr.org/pipermail/inquiry/2003-April/000261.html
# http://web.archive.org/web/20070309174451/http://stderr.org/pipermail/inquiry/2003-April/000262.html
# http://stderr.org/pipermail/inquiry/2003-April/000263.html
# http://web.archive.org/web/20070309202431/http://stderr.org/pipermail/inquiry/2003-April/000263.html
# http://web.archive.org/web/20070310204947/http://stderr.org/pipermail/inquiry/2003-April/000264.html
# http://stderr.org/pipermail/inquiry/2003-April/000265.html
# http://web.archive.org/web/20070309202640/http://stderr.org/pipermail/inquiry/2003-April/000265.html
# http://web.archive.org/web/20070309202441/http://stderr.org/pipermail/inquiry/2003-April/000267.html
# http://stderr.org/pipermail/inquiry/2003-April/000268.html
# http://web.archive.org/web/20070310205004/http://stderr.org/pipermail/inquiry/2003-April/000268.html
# http://web.archive.org/web/20061013223536/http://stderr.org/pipermail/inquiry/2003-April/000269.html
# http://stderr.org/pipermail/inquiry/2003-April/000270.html
# http://web.archive.org/web/20070309202731/http://stderr.org/pipermail/inquiry/2003-April/000270.html
# http://stderr.org/pipermail/inquiry/2003-April/000271.html
# http://web.archive.org/web/20061013223302/http://stderr.org/pipermail/inquiry/2003-April/000271.html
# http://web.archive.org/web/20070310205134/http://stderr.org/pipermail/inquiry/2003-April/000273.html
# http://stderr.org/pipermail/inquiry/2003-April/000274.html
# http://web.archive.org/web/20070310205146/http://stderr.org/pipermail/inquiry/2003-April/000274.html
# http://web.archive.org/web/20070310075558/http://stderr.org/pipermail/inquiry/2003-April/000275.html
# http://stderr.org/pipermail/inquiry/2003-April/000276.html
# http://web.archive.org/web/20070309174501/http://stderr.org/pipermail/inquiry/2003-April/000276.html
# http://web.archive.org/web/20070311141604/http://stderr.org/pipermail/inquiry/2003-April/000277.html
# http://stderr.org/pipermail/inquiry/2003-April/000278.html
# http://web.archive.org/web/20070309202651/http://stderr.org/pipermail/inquiry/2003-April/000278.html
# http://web.archive.org/web/20070311141625/http://stderr.org/pipermail/inquiry/2003-April/000279.html
# http://stderr.org/pipermail/inquiry/2003-April/000280.html
# http://web.archive.org/web/20070310205157/http://stderr.org/pipermail/inquiry/2003-April/000280.html
# http://web.archive.org/web/20070310205207/http://stderr.org/pipermail/inquiry/2003-April/000281.html
# http://stderr.org/pipermail/inquiry/2003-April/000282.html
# http://web.archive.org/web/20070309174530/http://stderr.org/pipermail/inquiry/2003-April/000282.html
# http://stderr.org/pipermail/inquiry/2003-April/000283.html
# http://web.archive.org/web/20070310205217/http://stderr.org/pipermail/inquiry/2003-April/000283.html
# http://web.archive.org/web/20070310205228/http://stderr.org/pipermail/inquiry/2003-April/000284.html
# http://stderr.org/pipermail/inquiry/2003-April/000285.html
# http://web.archive.org/web/20070309202710/http://stderr.org/pipermail/inquiry/2003-April/000285.html
# http://web.archive.org/web/20070310205237/http://stderr.org/pipermail/inquiry/2003-April/000286.html
# http://stderr.org/pipermail/inquiry/2003-April/000287.html
# http://web.archive.org/web/20070310205247/http://stderr.org/pipermail/inquiry/2003-April/000287.html
# http://web.archive.org/web/20070309202720/http://stderr.org/pipermail/inquiry/2003-April/000288.html
# http://stderr.org/pipermail/inquiry/2003-April/000289.html
# http://web.archive.org/web/20061013223711/http://stderr.org/pipermail/inquiry/2003-April/000289.html
# http://web.archive.org/web/20070310205257/http://stderr.org/pipermail/inquiry/2003-April/000290.html
# http://stderr.org/pipermail/inquiry/2003-April/000291.html
# http://web.archive.org/web/20061013223830/http://stderr.org/pipermail/inquiry/2003-April/000291.html
# http://web.archive.org/web/20070310205307/http://stderr.org/pipermail/inquiry/2003-April/000294.html
# http://stderr.org/pipermail/inquiry/2003-April/000295.html
# http://web.archive.org/web/20061013224103/http://stderr.org/pipermail/inquiry/2003-April/000295.html
# http://stderr.org/pipermail/inquiry/2003-April/000296.html
# http://web.archive.org/web/20070310205317/http://stderr.org/pipermail/inquiry/2003-April/000296.html
# http://web.archive.org/web/20070310095852/http://stderr.org/pipermail/inquiry/2003-April/000297.html
# http://stderr.org/pipermail/inquiry/2003-April/000298.html
# http://web.archive.org/web/20061013223138/http://stderr.org/pipermail/inquiry/2003-April/000298.html
# http://web.archive.org/web/20070310205328/http://stderr.org/pipermail/inquiry/2003-April/000299.html
# http://stderr.org/pipermail/inquiry/2003-April/000300.html
# http://web.archive.org/web/20061013223241/http://stderr.org/pipermail/inquiry/2003-April/000300.html
# http://web.archive.org/web/20081120085752/http://stderr.org/pipermail/inquiry/2003-April/000301.html
# http://stderr.org/pipermail/inquiry/2003-April/000302.html
# http://web.archive.org/web/20070310205349/http://stderr.org/pipermail/inquiry/2003-April/000302.html
# http://web.archive.org/web/20070311141532/http://stderr.org/pipermail/inquiry/2003-April/000303.html
# http://stderr.org/pipermail/inquiry/2003-April/000305.html
# http://web.archive.org/web/20070309203110/http://stderr.org/pipermail/inquiry/2003-April/000305.html
# http://web.archive.org/web/20070310205359/http://stderr.org/pipermail/inquiry/2003-April/000306.html
# http://stderr.org/pipermail/inquiry/2003-April/000307.html
# http://web.archive.org/web/20070310205409/http://stderr.org/pipermail/inquiry/2003-April/000307.html
# http://stderr.org/pipermail/inquiry/2003-April/000308.html
# http://web.archive.org/web/20070310204919/http://stderr.org/pipermail/inquiry/2003-April/000308.html
# http://stderr.org/pipermail/inquiry/2003-April/000309.html
# http://web.archive.org/web/20070310205420/http://stderr.org/pipermail/inquiry/2003-April/000309.html
===Inquiry List : Selections (Nov 2004)===
===2004 • Inquiry List • Selections===
* http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750
* http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750
# http://stderr.org/pipermail/inquiry/2004-November/001750.html
# http://web.archive.org/web/20060217232934/http://stderr.org/pipermail/inquiry/2004-November/001750.html
# http://stderr.org/pipermail/inquiry/2004-November/001751.html
# http://web.archive.org/web/20081120211119/http://stderr.org/pipermail/inquiry/2004-November/001751.html
# http://stderr.org/pipermail/inquiry/2004-November/001752.html
# http://web.archive.org/web/20081120205154/http://stderr.org/pipermail/inquiry/2004-November/001752.html
# http://stderr.org/pipermail/inquiry/2004-November/001753.html
# http://web.archive.org/web/20060217232947/http://stderr.org/pipermail/inquiry/2004-November/001753.html
# http://stderr.org/pipermail/inquiry/2004-November/001754.html
# http://web.archive.org/web/20081120202444/http://stderr.org/pipermail/inquiry/2004-November/001754.html
# http://stderr.org/pipermail/inquiry/2004-November/001760.html
# http://web.archive.org/web/20081120202147/http://stderr.org/pipermail/inquiry/2004-November/001760.html
# http://stderr.org/pipermail/inquiry/2004-November/001769.html
# http://web.archive.org/web/20081120191806/http://stderr.org/pipermail/inquiry/2004-November/001769.html
# http://stderr.org/pipermail/inquiry/2004-November/001774.html
# http://web.archive.org/web/20081120212429/http://stderr.org/pipermail/inquiry/2004-November/001774.html
# http://stderr.org/pipermail/inquiry/2004-November/001783.html
# http://web.archive.org/web/20120222231523/http://stderr.org/pipermail/inquiry/2004-November/001783.html
# http://stderr.org/pipermail/inquiry/2004-November/001794.html
# http://web.archive.org/web/20120222231525/http://stderr.org/pipermail/inquiry/2004-November/001794.html
# http://stderr.org/pipermail/inquiry/2004-November/001812.html
# http://web.archive.org/web/20060217233454/http://stderr.org/pipermail/inquiry/2004-November/001812.html
# http://stderr.org/pipermail/inquiry/2004-November/001842.html
# http://web.archive.org/web/20060217233731/http://stderr.org/pipermail/inquiry/2004-November/001842.html
===Inquiry List : Commentary (Nov 2004)===
===2004 • Inquiry List • Comments===
* http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1755
{|
{|
|-
|-
| align=right | 1. || http://stderr.org/pipermail/inquiry/2004-November/001755.html
| align=right | 1. || http://web.archive.org/web/20060217233003/http://stderr.org/pipermail/inquiry/2004-November/001755.html
|-
|-
| align=right | 2. ||http://stderr.org/pipermail/inquiry/2004-November/001756.html
| align=right | 2. || http://web.archive.org/web/20060217233011/http://stderr.org/pipermail/inquiry/2004-November/001756.html
|-
|-
| align=right | 3. || http://stderr.org/pipermail/inquiry/2004-November/001757.html
| align=right | 3. || http://web.archive.org/web/20081120200505/http://stderr.org/pipermail/inquiry/2004-November/001757.html
|-
|-
| align=right | 4. || http://stderr.org/pipermail/inquiry/2004-November/001758.html
| align=right | 4. || http://web.archive.org/web/20081120200000/http://stderr.org/pipermail/inquiry/2004-November/001758.html
|-
|-
| align=right | 5. || http://stderr.org/pipermail/inquiry/2004-November/001759.html
| align=right | 5. || http://web.archive.org/web/20060217233024/http://stderr.org/pipermail/inquiry/2004-November/001759.html
|-
|-
| align=right | 6. || http://stderr.org/pipermail/inquiry/2004-November/001761.html
| align=right | 6. || http://web.archive.org/web/20120222231542/http://stderr.org/pipermail/inquiry/2004-November/001761.html
|-
|-
| align=right | 7. || http://stderr.org/pipermail/inquiry/2004-November/001770.html
| align=right | 7. || http://web.archive.org/web/20120222231543/http://stderr.org/pipermail/inquiry/2004-November/001770.html
|-
|-
| align=right | 8.1. || http://stderr.org/pipermail/inquiry/2004-November/001775.html
| align=right | 8.1. || http://web.archive.org/web/20120222231545/http://stderr.org/pipermail/inquiry/2004-November/001775.html
|-
|-
| align=right | 8.2. || http://stderr.org/pipermail/inquiry/2004-November/001776.html
| align=right | 8.2. || http://web.archive.org/web/20120222231547/http://stderr.org/pipermail/inquiry/2004-November/001776.html
|-
|-
| align=right | 8.3. || http://stderr.org/pipermail/inquiry/2004-November/001777.html
| align=right | 8.3. || http://web.archive.org/web/20120222231549/http://stderr.org/pipermail/inquiry/2004-November/001777.html
|-
|-
| align=right | 8.4. || http://stderr.org/pipermail/inquiry/2004-November/001778.html
| align=right | 8.4. || http://web.archive.org/web/20120222231551/http://stderr.org/pipermail/inquiry/2004-November/001778.html
|-
|-
| align=right | 8.5. || http://stderr.org/pipermail/inquiry/2004-November/001781.html
| align=right | 8.5. || http://web.archive.org/web/20120222231553/http://stderr.org/pipermail/inquiry/2004-November/001781.html
|-
|-
| align=right | 8.6. || http://stderr.org/pipermail/inquiry/2004-November/001782.html
| align=right | 8.6. || http://web.archive.org/web/20120222231555/http://stderr.org/pipermail/inquiry/2004-November/001782.html
|-
|-
| align=right | 9.1. || http://stderr.org/pipermail/inquiry/2004-November/001787.html
| align=right | 9.1. || http://web.archive.org/web/20120222231557/http://stderr.org/pipermail/inquiry/2004-November/001787.html
|-
|-
| align=right | 9.2. || http://stderr.org/pipermail/inquiry/2004-November/001788.html
| align=right | 9.2. || http://web.archive.org/web/20120222231559/http://stderr.org/pipermail/inquiry/2004-November/001788.html
|-
|-
| align=right | 9.3. || http://stderr.org/pipermail/inquiry/2004-November/001789.html
| align=right | 9.3. || http://web.archive.org/web/20120222231601/http://stderr.org/pipermail/inquiry/2004-November/001789.html
|-
|-
| align=right | 9.4. || http://stderr.org/pipermail/inquiry/2004-November/001790.html
| align=right | 9.4. || http://web.archive.org/web/20120222231604/http://stderr.org/pipermail/inquiry/2004-November/001790.html
|-
|-
| align=right | 9.5. || http://stderr.org/pipermail/inquiry/2004-November/001791.html
| align=right | 9.5. || http://web.archive.org/web/20120222231606/http://stderr.org/pipermail/inquiry/2004-November/001791.html
|-
|-
| align=right | 9.6. || http://stderr.org/pipermail/inquiry/2004-November/001792.html
| align=right | 9.6. || http://web.archive.org/web/20120222231608/http://stderr.org/pipermail/inquiry/2004-November/001792.html
|-
|-
| align=right | 9.7. || http://stderr.org/pipermail/inquiry/2004-November/001793.html
| align=right | 9.7. || http://web.archive.org/web/20120222231610/http://stderr.org/pipermail/inquiry/2004-November/001793.html
|-
|-
| align=right | 10.01. || http://stderr.org/pipermail/inquiry/2004-November/001795.html
| align=right | 10.01. || http://web.archive.org/web/20120222231611/http://stderr.org/pipermail/inquiry/2004-November/001795.html
|-
|-
| align=right | 10.02. || http://stderr.org/pipermail/inquiry/2004-November/001796.html
| align=right | 10.02. || http://web.archive.org/web/20120222231613/http://stderr.org/pipermail/inquiry/2004-November/001796.html
|-
|-
| align=right | 10.03. || http://stderr.org/pipermail/inquiry/2004-November/001797.html
| align=right | 10.03. || http://web.archive.org/web/20120222231615/http://stderr.org/pipermail/inquiry/2004-November/001797.html
|-
|-
| align=right | 10.04. || http://stderr.org/pipermail/inquiry/2004-November/001798.html
| align=right | 10.04. || http://web.archive.org/web/20120222231617/http://stderr.org/pipermail/inquiry/2004-November/001798.html
|-
|-
| align=right | 10.05. || http://stderr.org/pipermail/inquiry/2004-November/001799.html
| align=right | 10.05. || http://web.archive.org/web/20120222231619/http://stderr.org/pipermail/inquiry/2004-November/001799.html
|-
|-
| align=right | 10.06. || http://stderr.org/pipermail/inquiry/2004-November/001800.html
| align=right | 10.06. || http://web.archive.org/web/20120222231621/http://stderr.org/pipermail/inquiry/2004-November/001800.html
|-
|-
| align=right | 10.07. || http://stderr.org/pipermail/inquiry/2004-November/001801.html
| align=right | 10.07. || http://web.archive.org/web/20120222231623/http://stderr.org/pipermail/inquiry/2004-November/001801.html
|-
|-
| align=right | 10.08. || http://stderr.org/pipermail/inquiry/2004-November/001802.html
| align=right | 10.08. || http://web.archive.org/web/20120222231625/http://stderr.org/pipermail/inquiry/2004-November/001802.html
|-
|-
| align=right | 10.09. || http://stderr.org/pipermail/inquiry/2004-November/001803.html
| align=right | 10.09. || http://web.archive.org/web/20120222231627/http://stderr.org/pipermail/inquiry/2004-November/001803.html
|-
|-
| align=right | 10.10. || http://stderr.org/pipermail/inquiry/2004-November/001804.html
| align=right | 10.10. || http://web.archive.org/web/20120222231629/http://stderr.org/pipermail/inquiry/2004-November/001804.html
|-
|-
| align=right | 10.11. || http://stderr.org/pipermail/inquiry/2004-November/001805.html
| align=right | 10.11. || http://web.archive.org/web/20120222231829/http://stderr.org/pipermail/inquiry/2004-November/001805.html
|-
|-
| align=right | 11.01. || http://stderr.org/pipermail/inquiry/2004-November/001813.html
| align=right | 11.01. || http://web.archive.org/web/20060217233458/http://stderr.org/pipermail/inquiry/2004-November/001813.html
|-
|-
| align=right | 11.02. || http://stderr.org/pipermail/inquiry/2004-November/001814.html
| align=right | 11.02. || http://web.archive.org/web/20051215103907/http://stderr.org/pipermail/inquiry/2004-November/001814.html
|-
|-
| align=right | 11.03. || http://stderr.org/pipermail/inquiry/2004-November/001815.html
| align=right | 11.03. || http://web.archive.org/web/20120222231842/http://stderr.org/pipermail/inquiry/2004-November/001815.html
|-
|-
| align=right | 11.04. || http://stderr.org/pipermail/inquiry/2004-November/001816.html
| align=right | 11.04. || http://web.archive.org/web/20120222231853/http://stderr.org/pipermail/inquiry/2004-November/001816.html
|-
|-
| align=right | 11.05. || http://stderr.org/pipermail/inquiry/2004-November/001817.html
| align=right | 11.05. || http://web.archive.org/web/20060217233520/http://stderr.org/pipermail/inquiry/2004-November/001817.html
|-
|-
| align=right | 11.06. || http://stderr.org/pipermail/inquiry/2004-November/001818.html
| align=right | 11.06. || http://web.archive.org/web/20060217233527/http://stderr.org/pipermail/inquiry/2004-November/001818.html
|-
|-
| align=right | 11.07. || http://stderr.org/pipermail/inquiry/2004-November/001819.html
| align=right | 11.07. || http://web.archive.org/web/20120222231859/http://stderr.org/pipermail/inquiry/2004-November/001819.html
|-
|-
| align=right | 11.08. || http://stderr.org/pipermail/inquiry/2004-November/001820.html
| align=right | 11.08. || http://web.archive.org/web/20120222231901/http://stderr.org/pipermail/inquiry/2004-November/001820.html
|-
|-
| align=right | 11.09. || http://stderr.org/pipermail/inquiry/2004-November/001821.html
| align=right | 11.09. || http://web.archive.org/web/20120222231903/http://stderr.org/pipermail/inquiry/2004-November/001821.html
|-
|-
| align=right | 11.10. || http://stderr.org/pipermail/inquiry/2004-November/001822.html
| align=right | 11.10. || http://web.archive.org/web/20120222231905/http://stderr.org/pipermail/inquiry/2004-November/001822.html
|-
|-
| align=right | 11.11. || http://stderr.org/pipermail/inquiry/2004-November/001823.html
| align=right | 11.11. || http://web.archive.org/web/20120222231907/http://stderr.org/pipermail/inquiry/2004-November/001823.html
|-
|-
| align=right | 11.12. || http://stderr.org/pipermail/inquiry/2004-November/001824.html
| align=right | 11.12. || http://web.archive.org/web/20120222231909/http://stderr.org/pipermail/inquiry/2004-November/001824.html
|-
|-
| align=right | 11.13. || http://stderr.org/pipermail/inquiry/2004-November/001825.html
| align=right | 11.13. || http://web.archive.org/web/20120222232025/http://stderr.org/pipermail/inquiry/2004-November/001825.html
|-
|-
| align=right | 11.14. || http://stderr.org/pipermail/inquiry/2004-November/001826.html
| align=right | 11.14. || http://web.archive.org/web/20120222232029/http://stderr.org/pipermail/inquiry/2004-November/001826.html
|-
|-
| align=right | 11.15. || http://stderr.org/pipermail/inquiry/2004-November/001827.html
| align=right | 11.15. || http://web.archive.org/web/20120222232030/http://stderr.org/pipermail/inquiry/2004-November/001827.html
|-
|-
| align=right | 11.16. || http://stderr.org/pipermail/inquiry/2004-November/001828.html
| align=right | 11.16. || http://web.archive.org/web/20120222232032/http://stderr.org/pipermail/inquiry/2004-November/001828.html
|-
|-
| align=right | 11.17. || http://stderr.org/pipermail/inquiry/2004-November/001829.html
| align=right | 11.17. || http://web.archive.org/web/20120222232035/http://stderr.org/pipermail/inquiry/2004-November/001829.html
|-
|-
| align=right | 11.18. || http://stderr.org/pipermail/inquiry/2004-November/001830.html
| align=right | 11.18. || http://web.archive.org/web/20120222232037/http://stderr.org/pipermail/inquiry/2004-November/001830.html
|-
|-
| align=right | 11.19. || http://stderr.org/pipermail/inquiry/2004-November/001831.html
| align=right | 11.19. || http://web.archive.org/web/20120222232041/http://stderr.org/pipermail/inquiry/2004-November/001831.html
|-
|-
| align=right | 11.20. || http://stderr.org/pipermail/inquiry/2004-November/001832.html
| align=right | 11.20. || http://web.archive.org/web/20120222232043/http://stderr.org/pipermail/inquiry/2004-November/001832.html
|-
|-
| align=right | 11.21. || http://stderr.org/pipermail/inquiry/2004-November/001833.html
| align=right | 11.21. || http://web.archive.org/web/20120222232044/http://stderr.org/pipermail/inquiry/2004-November/001833.html
|-
|-
| align=right | 11.22. || http://stderr.org/pipermail/inquiry/2004-November/001834.html
| align=right | 11.22. || http://web.archive.org/web/20120222232046/http://stderr.org/pipermail/inquiry/2004-November/001834.html
|-
|-
| align=right | 11.23. || http://stderr.org/pipermail/inquiry/2004-November/001835.html
| align=right | 11.23. || http://web.archive.org/web/20120222232048/http://stderr.org/pipermail/inquiry/2004-November/001835.html
|-
|-
| align=right | 11.24. || http://stderr.org/pipermail/inquiry/2004-November/001836.html
| align=right | 11.24. || http://web.archive.org/web/20120222232049/http://stderr.org/pipermail/inquiry/2004-November/001836.html
|-
|-
| align=right | 12. || http://stderr.org/pipermail/inquiry/2004-November/001843.html
| align=right | 12. || http://web.archive.org/web/20060217233738/http://stderr.org/pipermail/inquiry/2004-November/001843.html
|}
|}
===Inquiry List : Discussion (Nov 2004, Jan 2005, Apr 2009)===
===2004–2009 • Inquiry List • Discussion===
* http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1768
* http://web.archive.org/web/20061013215458/http://stderr.org/pipermail/inquiry/2005-January/thread.html#2301
* http://web.archive.org/web/20120428203121/http://stderr.org/pipermail/inquiry/2009-April/thread.html#3548
<ol start="28">
<ol start="28">
<li>http://stderr.org/pipermail/inquiry/2004-November/001768.html</li>
<li>http://web.archive.org/web/20120222232055/http://stderr.org/pipermail/inquiry/2004-November/001768.html</li>
<li>http://stderr.org/pipermail/inquiry/2004-November/001838.html</li>
<li>http://web.archive.org/web/20120222232057/http://stderr.org/pipermail/inquiry/2004-November/001838.html</li>
<li>http://stderr.org/pipermail/inquiry/2004-November/001840.html</li>
<li>http://web.archive.org/web/20120222232101/http://stderr.org/pipermail/inquiry/2004-November/001840.html</li>
<li>http://stderr.org/pipermail/inquiry/2005-January/002301.html</li>
<li>http://web.archive.org/web/20061014002508/http://stderr.org/pipermail/inquiry/2005-January/002301.html</li>
<li>http://stderr.org/pipermail/inquiry/2009-April/003548.html</li>
<li>http://web.archive.org/web/20120206222034/http://stderr.org/pipermail/inquiry/2009-April/003548.html</li>
</ol>
</ol>
…
===2007 • MyWikiBiz Copy===
* [http://mywikibiz.com/User:Jon_Awbrey Jon Awbrey] • [http://mywikibiz.com/index.php?title=Directory_talk:Jon_Awbrey/Papers/Peirce%27s_1870_Logic_Of_Relatives&oldid=51117 Peirce's 1870 Logic Of Relatives • 10 October 2007]
