| Line 4,673: |
Line 4,673: |
| | That is, a lover of every woman in the universe of discourse | | That is, a lover of every woman in the universe of discourse |
| | would be a lover of W_1 and a lover of W_2 and lover of W_3. | | would be a lover of W_1 and a lover of W_2 and lover of W_3. |
| − | </pre>
| |
| − |
| |
| − | ==Work Area==
| |
| − |
| |
| − | <pre>
| |
| − | Up to this point in the discussion, we have observed that
| |
| − | the "number of" map 'v' : S -> R such that 'v's = [s] has
| |
| − | the following morphic properties:
| |
| − |
| |
| − | 0. [0] = 0
| |
| − |
| |
| − | 1. 'v'
| |
| − |
| |
| − | 2. x -< y => [x] =< [y]
| |
| − |
| |
| − | 3. [x +, y] =< [x] + [y]
| |
| − |
| |
| − | contingent:
| |
| − |
| |
| − | 4. [xy] = [x][y]
| |
| − |
| |
| − | view relation P c X x Y x Z as related to three functions:
| |
| − |
| |
| − | `p_1` c
| |
| − | `p_3` c X x Y x Pow(Z)
| |
| − |
| |
| − |
| |
| − | f(x)
| |
| − |
| |
| − | f(x+y) = f(x) + f(y)
| |
| − |
| |
| − | f(p(x, y)) = q(f(x), f(y))
| |
| − |
| |
| − | P(x, y, z)
| |
| − |
| |
| − | (f^-1)(y)
| |
| − |
| |
| − | f(z(x, y)) = z'(f(x), f(y))
| |
| − |
| |
| − | Definition. f(x:y:z) = (fx:fy:fz).
| |
| − |
| |
| − | f(x:y:z) = (fx:fy:
| |
| − |
| |
| − | x:y:z in R => fx:fy:fz in fR
| |
| − |
| |
| − | R(x, y, z) => (fR)(fx, fy, fz)
| |
| − |
| |
| − | (L, x, y, z) => (fL, fx, fy, fz)
| |
| − |
| |
| − | (x, y, z, L) => (xf, yf, zf, Lf)
| |
| − |
| |
| − | (x, y, z, b) => (xf, yf, zf, bf)
| |
| − |
| |
| − |
| |
| − | fzxy = z'(fx)(fy)
| |
| − |
| |
| − |
| |
| − | F
| |
| − | o
| |
| − | |
| |
| − | o
| |
| − | / \
| |
| − | o o
| |
| − | o
| |
| − | . | .
| |
| − | . | .
| |
| − | . | .
| |
| − | . o .
| |
| − | . / \ .
| |
| − | . / \ .
| |
| − | . / \ .
| |
| − | . o o .
| |
| − | . . .
| |
| − | . . .
| |
| − | .
| |
| − |
| |
| − |
| |
| − | C o . / \ . o
| |
| − | | . / \ . | CF
| |
| − | | . o o . |
| |
| − | f o . . . o fF
| |
| − | / \ . . . / \
| |
| − | / . \ . o o
| |
| − | X o o Y XF YF
| |
| − |
| |
| − | <u, v, w> in P ->
| |
| − |
| |
| − | o---------o---------o---------o---------o
| |
| − | | # h | h | f |
| |
| − | o=========o=========o=========o=========o
| |
| − | | P # X | Y | Z |
| |
| − | o---------o---------o---------o---------o
| |
| − | | Q # U | V | W |
| |
| − | o---------o---------o---------o---------o
| |
| − |
| |
| − | Products of diagonal extensions:
| |
| − |
| |
| − | 1,1, = !1!!1!
| |
| − |
| |
| − | = "anything that is anything that is ---"
| |
| − |
| |
| − | = "anything that is ---"
| |
| − |
| |
| − | = !1!
| |
| − |
| |
| − | m,n = "man that is noble"
| |
| − |
| |
| − | = (C:C +, I:I +, J:J +, O:O)(C +, D +, O)
| |
| − |
| |
| − | = C +, O
| |
| − |
| |
| − | n,m = "noble that is man"
| |
| − |
| |
| − | = (C:C +, D:D +, O:O)(C +, I +, J +, O)
| |
| − |
| |
| − | = C +, O
| |
| − |
| |
| − | n,w = "noble that is woman"
| |
| − |
| |
| − | = (C:C +, D:D +, O:O)(B +, D +, E)
| |
| − |
| |
| − | = D
| |
| − |
| |
| − | w,n = "woman that is noble"
| |
| − |
| |
| − | = (B:B +, D:D +, E:E)(C +, D +, O)
| |
| − |
| |
| − | = D
| |
| − |
| |
| − | Given a set X and a subset M c X, define e_M,
| |
| − | the "idempotent representation" of M over X,
| |
| − | as the 2-adic relation e_M c X x X which is
| |
| − | the identity relation on M. In other words,
| |
| − | e_M = {<x, x> : x in M}.
| |
| − |
| |
| − | Transposing this by steps into Peirce's notation:
| |
| − |
| |
| − | e_M = {<x, x> : x in M}
| |
| − |
| |
| − | = {x:x : x in M}
| |
| − |
| |
| − | = Sum_X |x in M| x:x
| |
| − |
| |
| − | 'l' = "lover of ---"
| |
| − |
| |
| − | 's' = "servant of ---"
| |
| − |
| |
| − | 'l', = "lover that is --- of ---"
| |
| − |
| |
| − | 's', = "servant that is --- of ---"
| |
| − |
| |
| − | | But not only may any absolute term be thus regarded as a relative term,
| |
| − | | but any relative term may in the same way be regarded as a relative with
| |
| − | | one correlate more. It is convenient to take this additional correlate
| |
| − | | as the first one.
| |
| − | |
| |
| − | | Then:
| |
| − | |
| |
| − | | 'l','s'w
| |
| − | |
| |
| − | | will denote a lover of a woman that is a servant of that woman.
| |
| − | |
| |
| − | | C.S. Peirce, CP 3.73
| |
| − |
| |
| − | o---------o----+----o---------o---------o----+----o---------o
| |
| − | o-----------------------------o-----------------------------o
| |
| − | | Objective Framework (OF) | Interpretive Framework (IF) |
| |
| − | o-----------------------------o-----------------------------o
| |
| − | | Objects | Signs |
| |
| − | o-----------------------------o-----------------------------o
| |
| − | | |
| |
| − | | C o--------------- |
| |
| − | | |
| |
| − | | F o--------------- |
| |
| − | | |
| |
| − | | I o--------------- |
| |
| − | | |
| |
| − | | O o--------------- |
| |
| − | | |
| |
| − | | B o--------------- |
| |
| − | | |
| |
| − | | D o--------------- |
| |
| − | | |
| |
| − | | E o--------------- |
| |
| − | | o "m" |
| |
| − | | / |
| |
| − | | / |
| |
| − | | / |
| |
| − | | o o o-----------@ |
| |
| − | | \ |
| |
| − | | \ |
| |
| − | | \ |
| |
| − | | o |
| |
| − | | |
| |
| − | o-----------------------------o-----------------------------o
| |
| − |
| |
| − | †‡||§¶
| |
| − | @#||$%
| |
| − |
| |
| − | quality, reflection, synecdoche
| |
| − |
| |
| − | 1. neglect of
| |
| − | 2. neglect of
| |
| − | 3. neglect of nil?
| |
| − |
| |
| − | Now, it's not the end of the story, of course, but it's a start.
| |
| − | The significant thing is what is usually the significant thing
| |
| − | in mathematics, at least, that two distinct descriptions refer
| |
| − | to the same things. Incidentally, Peirce is not really being
| |
| − | as indifferent to the distinctions between signs and things
| |
| − | as this ascii text makes him look, but uses a host of other
| |
| − | type-faces to distinguish the types and the uses of signs.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 1==
| |
| − |
| |
| − | <pre>
| |
| − | GR = Gary Richmond
| |
| − |
| |
| − | GR: I wonder if the necessary "elementary triad" spoken of
| |
| − | below isn't somehow implicated in those discussions
| |
| − | "invoking a 'closure principle'".
| |
| − |
| |
| − | GR, quoting CSP:
| |
| − |
| |
| − | | 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.
| |
| − |
| |
| − | GR: (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
| |
| − | 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.
| |
| − |
| |
| − | GR: PS. I came upon the above passage last night reading through
| |
| − | the Peirce selections in John J. Stuhr's 'Classical American
| |
| − | Philosophy: Essential Readings and Interpretive Essays',
| |
| − | Oxford University, 1987 (the passage above is found on
| |
| − | pp 61-62), readily available in paperback in a new
| |
| − | edition, I believe.
| |
| − |
| |
| − | GR: 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 2==
| |
| − |
| |
| − | <pre>
| |
| − | BU = Ben Udell
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | BU: 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:
| |
| − |
| |
| − | JA: 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.
| |
| − |
| |
| − | BU: "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.
| |
| − |
| |
| − | 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:
| |
| − |
| |
| − | | Zeroth Law Of Semantics
| |
| − | |
| |
| − | | Meaning is a privilege not a right.
| |
| − | | Not all pictures depict.
| |
| − | | Not all signs denote.
| |
| − | |
| |
| − | | Never confuse a property of a sign,
| |
| − | | for instance, existence,
| |
| − | | with a sign of a property,
| |
| − | | for instance, existence.
| |
| − | |
| |
| − | | Taking a property of a sign,
| |
| − | | for a sign of a property,
| |
| − | | is the zeroth sign of
| |
| − | | nominal thinking,
| |
| − | | and the first
| |
| − | | mistake.
| |
| − | |
| |
| − | | Also Sprach Zero*
| |
| − |
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 3==
| |
| − |
| |
| − | <pre>
| |
| − | JR = Joe Ransdell
| |
| − |
| |
| − | JR: 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.
| |
| − |
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 4==
| |
| − |
| |
| − | <pre>
| |
| − | BU = Benjamin Udell
| |
| − |
| |
| − | BU: 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,
| |
| − | 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.
| |
| − |
| |
| − | 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 '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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 5==
| |
| − |
| |
| − | <pre>
| |
| − | CG = Clark Goble
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | JA, quoting CSP:
| |
| − |
| |
| − | | For example,
| |
| − | |
| |
| − | | f + u
| |
| − | |
| |
| − | | means all Frenchmen besides all violinists, and,
| |
| − | | therefore, considered as a logical term, implies
| |
| − | | that all French violinists are 'besides themselves'.
| |
| − |
| |
| − | CG: Could you clarify your use of "besides"?
| |
| − |
| |
| − | CG: 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
| |
| − | 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 "+,"
| |
| − | 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 A |_| B = C does
| |
| − | not allow one to say determinately that A = C - B.
| |
| − | I can't recall if Boole uses this 'besides' idiom,
| |
| − | but will check later.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 6==
| |
| − |
| |
| − | <pre>
| |
| − | CG = Clark Goble
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | JA: 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.
| |
| − |
| |
| − | CG: Is that essay related to any of the essays
| |
| − | in the two volume 'Essential Peirce'? I'm
| |
| − | rather interested in how he speaks there.
| |
| − |
| |
| − | No, the EP volumes are extremely weak on logical selections.
| |
| − | I see nothing there that deals with the logic of relatives.
| |
| − |
| |
| − | JA: But Peirce is saying that he prefers to use the sign "+,"
| |
| − | for inclusive disjunction, corresponding to the union of
| |
| − | the associated classes.
| |
| − |
| |
| − | CG: 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 'beside themselves'".
| |
| − |
| |
| − | CG: Did Peirce have anything to say about
| |
| − | what we'd call non-commuting operators?
| |
| − |
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 7==
| |
| − |
| |
| − | <pre>
| |
| − | GR = Gary Richmond
| |
| − |
| |
| − | GR: I am very much enjoying, which is to say,
| |
| − | learning from your interlacing commentary
| |
| − | on Peirce's 1870 "Logic of Relatives" paper.
| |
| − |
| |
| − | GR: What an extraordinary paper the 1870 "LOG" 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"
| |
| − | but nowhere near mined in depth yet. The whole quiver of arrows between
| |
| − | 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
| |
| − | 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 --
| |
| − | 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.
| |
| − |
| |
| − | GR: 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 --
| |
| − | I am guessing that things will probably "descalate" a bit over the next week,
| |
| − | but then, so will our attention spans ...
| |
| − |
| |
| − | Speaking of which, I will have to break here, and pick up the rest later ...
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 8==
| |
| − |
| |
| − | <pre>
| |
| − | GR = Gary Richmond
| |
| − |
| |
| − | GR: 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".
| |
| − |
| |
| − | 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.
| |
| − |
| |
| − | GR: But what interested me even more in LOR, Note 5, was the sign < ("less than"
| |
| − | joined to the sign of identity = to yield P's famous sign -< (or more clearly,
| |
| − | =<) of inference, which combines the two (so that -< (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".
| |
| − |
| |
| − | Then let us draw a picture.
| |
| − |
| |
| − | "(F (G))", read "not F without G", means that F (G), that is, F and not G,
| |
| − | is the only region exempted from the occupation of being in this universe:
| |
| − |
| |
| − | o-----------------------------------------------------------o
| |
| − | |`X`````````````````````````````````````````````````````````|
| |
| − | |```````````````````````````````````````````````````````````|
| |
| − | |`````````````o-------------o```o-------------o`````````````|
| |
| − | |````````````/ \`/```````````````\````````````|
| |
| − | |```````````/ o`````````````````\```````````|
| |
| − | |``````````/ /`\`````````````````\``````````|
| |
| − | |`````````/ /```\`````````````````\`````````|
| |
| − | |````````/ /`````\`````````````````\````````|
| |
| − | |```````o o```````o`````````````````o```````|
| |
| − | |```````| |```````|`````````````````|```````|
| |
| − | |```````| |```````|`````````````````|```````|
| |
| − | |```````| F |```````|````````G````````|```````|
| |
| − | |```````| |```````|`````````````````|```````|
| |
| − | |```````| |```````|`````````````````|```````|
| |
| − | |```````o o```````o`````````````````o```````|
| |
| − | |````````\ \`````/`````````````````/````````|
| |
| − | |`````````\ \```/`````````````````/`````````|
| |
| − | |``````````\ \`/`````````````````/``````````|
| |
| − | |```````````\ o`````````````````/```````````|
| |
| − | |````````````\ /`\```````````````/````````````|
| |
| − | |`````````````o-------------o```o-------------o`````````````|
| |
| − | |```````````````````````````````````````````````````````````|
| |
| − | |```````````````````````````````````````````````````````````|
| |
| − | o-----------------------------------------------------------o
| |
| − |
| |
| − | Collapsing the vacuous region like soapfilm popping on a wire frame,
| |
| − | we draw the constraint (F (G)) in the following alternative fashion:
| |
| − |
| |
| − | o-----------------------------------------------------------o
| |
| − | |`X`````````````````````````````````````````````````````````|
| |
| − | |```````````````````````````````````````````````````````````|
| |
| − | |```````````````````````````````o-------------o`````````````|
| |
| − | |``````````````````````````````/```````````````\````````````|
| |
| − | |`````````````````````````````o`````````````````\```````````|
| |
| − | |````````````````````````````/`\`````````````````\``````````|
| |
| − | |```````````````````````````/```\`````````````````\`````````|
| |
| − | |``````````````````````````/`````\`````````````````\````````|
| |
| − | |`````````````````````````o```````o`````````````````o```````|
| |
| − | |`````````````````````````|```````|`````````````````|```````|
| |
| − | |`````````````````````````|```````|`````````````````|```````|
| |
| − | |`````````````````````````|```F```|````````G````````|```````|
| |
| − | |`````````````````````````|```````|`````````````````|```````|
| |
| − | |`````````````````````````|```````|`````````````````|```````|
| |
| − | |`````````````````````````o```````o`````````````````o```````|
| |
| − | |``````````````````````````\`````/`````````````````/````````|
| |
| − | |```````````````````````````\```/`````````````````/`````````|
| |
| − | |````````````````````````````\`/`````````````````/``````````|
| |
| − | |`````````````````````````````o`````````````````/```````````|
| |
| − | |``````````````````````````````\```````````````/````````````|
| |
| − | |```````````````````````````````o-------------o`````````````|
| |
| − | |```````````````````````````````````````````````````````````|
| |
| − | |```````````````````````````````````````````````````````````|
| |
| − | o-----------------------------------------------------------o
| |
| − |
| |
| − | So, "(F (G))", "F => G", "F =< G", "F -< G", "F c G",
| |
| − | under suitable mutations of interpretation, are just
| |
| − | so many ways of saying that the denotation of "F" is
| |
| − | contained within the denotation of "G".
| |
| − |
| |
| − | Now, let us look to the "characteristic functions" or "indicator functions"
| |
| − | of the various regions of being. It is frequently convenient to ab-use the
| |
| − | same letters for them and merely keep a variant interpretation "en thy meme",
| |
| − | but let us be more meticulous here, and reserve the corresponding lower case
| |
| − | letters "f" and "g" to denote the indicator functions of the regions F and G,
| |
| − | respectively.
| |
| − |
| |
| − | Taking B = {0, 1} as the boolean domain, we have:
| |
| − |
| |
| − | f, g : X -> B
| |
| − |
| |
| − | (f^(-1))(1) = F
| |
| − |
| |
| − | (g^(-1))(1) = G
| |
| − |
| |
| − | In general, for h : X -> B, an expression like "(h^(-1))(1)"
| |
| − | can be read as "the inverse of h evaluated at 1", in effect,
| |
| − | denoting the set of points in X where h evaluates to "true".
| |
| − | This is called the "fiber of truth" in h, and I have gotten
| |
| − | where I like to abbreviate it as "[|h|]".
| |
| − |
| |
| − | Accordingly, we have:
| |
| − |
| |
| − | F = [|f|] = (f^(-1))(1) c X
| |
| − |
| |
| − | G = [|g|] = (g^(-1))(1) c X
| |
| − |
| |
| − | This brings us to the question, what sort
| |
| − | of "functional equation" between f and g
| |
| − | goes with the regional constraint (F (G))?
| |
| − |
| |
| − | Just this, that f(x) =< g(x) for all x in X,
| |
| − | where the '=<' relation on the values in B
| |
| − | has the following operational table for
| |
| − | the pairing "row head =< column head".
| |
| − |
| |
| − | o---------o---------o---------o
| |
| − | | =< # 0 | 1 |
| |
| − | o=========o=========o=========o
| |
| − | | 0 # 1 | 1 |
| |
| − | o---------o---------o---------o
| |
| − | | 1 # 0 | 1 |
| |
| − | o---------o---------o---------o
| |
| − |
| |
| − | And this, of course, is the same thing as the truth table
| |
| − | for the conditional connective or the implication relation.
| |
| − |
| |
| − | GR: By the way, in the semiosis implied by the modal gamma graphs,
| |
| − | could -< (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,
| |
| − | 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 '-<' 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 ...
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 9==
| |
| − |
| |
| − | <pre>
| |
| − | GR = Gary Richmond
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | JA: 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.
| |
| − |
| |
| − | GR: I cannot agree with you regarding modal logic. Personally
| |
| − | I feel that the gamma part of the EG's 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!
| |
| − | 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.
| |
| − |
| |
| − | Speeching Of Which ---
| |
| − | Best Of The Season ...
| |
| − | And Happy Trailing ...
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 10==
| |
| − |
| |
| − | <pre>
| |
| − | BM = Bernard Morand
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | BM: Thanks for your very informative talk. There
| |
| − | is a point that I did not understand in note 35:
| |
| − |
| |
| − | JA: If we operate in accordance with Peirce's example of `g`'o'h
| |
| − | 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:
| |
| − |
| |
| − | JA: 'l','s'w = 'l','s'(B +, D +, E) = 'l','s'B +, 'l','s'D +, 'l','s'E
| |
| − |
| |
| − | BM: 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"?
| |
| − |
| |
| − | 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, xy = yx, as soon as we extend to 2-adic relations,
| |
| − | but keep the associative law, x(yz) = (xy)z, as the multiplication of 2-adics
| |
| − | is the logical analogue of ordinary matrix multiplication, and Peirce like
| |
| − | most mathematicians treats the double distributive law, x(y + z) = xy + xz
| |
| − | and (x + y)z = xz + yz, 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 (J:J:D)(J:D)(D) = J.
| |
| − | If it were strictly associative, then we would have the following:
| |
| − |
| |
| − | 1. (J:J:D)((J:D)(D)) = (J:J:D)(J) = 0?
| |
| − |
| |
| − | 2. ((J:J:D)(J:D))(D) = (J)(D) = 0?
| |
| − |
| |
| − | 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 MS's
| |
| − | that I read it.
| |
| − |
| |
| − | 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 '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.
| |
| − |
| |
| − | BM: 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
| |
| − | than I am able to make right now, but maybe
| |
| − | I'll get back to it later today or tomorrow.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 11==
| |
| − |
| |
| − | <pre>
| |
| − | BM = Bernard Morand
| |
| − |
| |
| − | BM: 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
| |
| − | 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.
| |
| − |
| |
| − | 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.
| |
| − |
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 12==
| |
| − |
| |
| − | <pre>
| |
| − | BM = Bernard Morand
| |
| − |
| |
| − | BM: 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,
| |
| − | 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!
| |
| − |
| |
| − | 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.
| |
| − |
| |
| − | It may appear that one has side-stepped the issue of empiricism
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 13==
| |
| − |
| |
| − | <pre>
| |
| − | BM = Bernard Morand
| |
| − |
| |
| − | BM: 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.
| |
| − |
| |
| − | BM: So we get:
| |
| − |
| |
| − | I - According to the Mode of Apprehension of the Sign itself - S
| |
| − | II - According to the Mode of Presentation of the Immediate Object - Oi
| |
| − | III - According to the Mode of Being of the Dynamical Object - Od
| |
| − | IV - According to the Relation of the Sign to its Dynamical Object - S-Od
| |
| − | V - According to the Mode of Presentation of the Immediate Interpretant - Ii
| |
| − | VI - According to the Mode of Being of the Dynamical Interpretant - Id
| |
| − | VII - According to the relation of the Sign to the Dynamical Interpretant - S-Id
| |
| − | VIII - According to the Nature of the Normal Interpretant - If
| |
| − | IX - According to the the relation of the Sign to the Normal Interpretant - S-If
| |
| − | X - According to the Triadic Relation of the Sign to its Dynamical Object
| |
| − | and to its Normal Interpretant - S-Od-If
| |
| − |
| |
| − | 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.
| |
| − |
| |
| − | 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
| |
| − |
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 14==
| |
| − |
| |
| − | <pre>
| |
| − | BM = Bernard Morand
| |
| − |
| |
| − | [Table. Ten Divisions of Signs (Peirce, Morand)]
| |
| − |
| |
| − | BM: Yes this is clearer (in particular in expressing relations with :)
| |
| − |
| |
| − | This is what Peirce used to form elementary relatives, for example,
| |
| − | o:s:i = <o, s, i>, and I find it utterly ubertous in a wide variety
| |
| − | of syntactic circumstances.
| |
| − |
| |
| − | BM: I suggest making a correction to myself if
| |
| − | the table is destinate to become canonic.
| |
| − |
| |
| − | Hah! Good one!
| |
| − |
| |
| − | BM: 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 I_n in place of I_f for now.
| |
| − |
| |
| − | 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:
| |
| − |
| |
| − | 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_n |
| |
| − | | 9 | Relation | Sign | Normal Interp | S : I_n |
| |
| − | o---o---------------o------------------o------------------o---------------o
| |
| − | | A | Tri. Relation | Sign | Dynamical Object | |
| |
| − | | | | | & Normal Interp | S : O_d : I_n |
| |
| − | o---o---------------o------------------o------------------o---------------o
| |
| − |
| |
| − | BM: Peirce gives the following definition (CP 8.343):
| |
| − |
| |
| − | BM, quoting CSP:
| |
| − |
| |
| − | | It is likewise requisite to distinguish
| |
| − | | the 'Immediate Interpretant', i.e. the
| |
| − | | Interpretant represented or signified in
| |
| − | | the Sign, from the 'Dynamic Interpretant',
| |
| − | | or effect actually produced on the mind
| |
| − | | by the Sign; and both of these from
| |
| − | | the 'Normal Interpretant', or effect
| |
| − | | that would be produced on the mind by
| |
| − | | the Sign after sufficient development
| |
| − | | of thought.
| |
| − | |
| |
| − | | C.S. Peirce, 'Collected Papers', CP 8.343.
| |
| − |
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 15==
| |
| − |
| |
| − | <pre>
| |
| − | 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.
| |
| − |
| |
| − | | It seems to me that one of the first useful steps toward a science
| |
| − | | of 'semeiotic' ([Greek 'semeiootike']), or the cenoscopic science
| |
| − | | of signs, must be the accurate definition, or logical analysis,
| |
| − | | of the concepts of the science.
| |
| − | |
| |
| − | | I define a 'Sign' 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 'Interpretant'
| |
| − | | of the sign, is thereby mediately determined by that
| |
| − | | Object.
| |
| − | |
| |
| − | | A sign, therefore, has a triadic relation to
| |
| − | | its Object and to its Interpretant. But it is
| |
| − | | necessary to distinguish the 'Immediate Object',
| |
| − | | or the Object as the Sign represents it, from
| |
| − | | the 'Dynamical Object', or really efficient
| |
| − | | but not immediately present Object.
| |
| − | |
| |
| − | | It is likewise requisite to distinguish
| |
| − | | the 'Immediate Interpretant', i.e. the
| |
| − | | Interpretant represented or signified in
| |
| − | | the Sign, from the 'Dynamic Interpretant',
| |
| − | | or effect actually produced on the mind
| |
| − | | by the Sign; and both of these from
| |
| − | | the 'Normal Interpretant', or effect
| |
| − | | that would be produced on the mind by
| |
| − | | the Sign after sufficient development
| |
| − | | of thought.
| |
| − | |
| |
| − | | 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 3^10, 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.
| |
| − | |
| |
| − | | C.S. Peirce, 'Collected Papers', CP 8.343.
| |
| − |
| |
| − | You never know when the future explorer will be yourself.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 16==
| |
| − |
| |
| − | <pre>
| |
| − | Burks, the editor of CP 8, attaches this footnote
| |
| − | to CP 8.342-379, "On the Classification of Signs":
| |
| − |
| |
| − | | From a partial draft of a letter to Lady Welby, bearing
| |
| − | | the dates of 24, 25, and 28 December 1908, Widener IB3a,
| |
| − | | with an added quotation in 368n23. ...
| |
| − |
| |
| − | There is a passage roughly comparable to CP 8.343 in a letter
| |
| − | to Lady Welby dated 23 December 1908, pages 397-409 in Wiener,
| |
| − | which is incidentally the notorious "sop to Cerberus" letter:
| |
| − |
| |
| − | | It is usual and proper to distinguish two Objects of a Sign,
| |
| − | | the Mediate without, and the Immediate within the Sign. Its
| |
| − | | Interpretant is all that the Sign conveys: acquaintance with
| |
| − | | its Object must be gained by collateral experience.
| |
| − | |
| |
| − | | The Mediate Object is the Object outside of the Sign; I call
| |
| − | | it the 'Dynamoid' Object. The Sign must indicate it by a hint;
| |
| − | | and this hint, or its substance, is the 'Immediate' Object.
| |
| − | |
| |
| − | | Each of these two Objects may be said to be capable of either of
| |
| − | | the three Modalities, though in the case of the Immediate Object,
| |
| − | | this is not quite literally true.
| |
| − | |
| |
| − | | Accordingly, the Dynamoid Object may be a Possible; when I term
| |
| − | | the Sign an 'Abstractive'; such as the word Beauty; and it will be
| |
| − | | none the less an Abstractive if I speak of "the Beautiful", since it is
| |
| − | | the ultimate reference, and not the grammatical form, that makes the sign
| |
| − | | an 'Abstractive'.
| |
| − | |
| |
| − | | When the Dynamoid Object is an Occurrence (Existent thing or Actual fact
| |
| − | | of past or future), I term the Sign a 'Concretive'; any one barometer
| |
| − | | is an example; and so is a written narrative of any series of events.
| |
| − | |
| |
| − | | For a 'Sign' whose Dynamoid Object is a Necessitant, I have at present
| |
| − | | no better designation than a 'Collective', which is not quite so bad a
| |
| − | | name as it sounds to be until one studies the matter: but for a person,
| |
| − | | like me, who thinks in quite a different system of symbols to words, it
| |
| − | | is so awkward and often puzzling to translate one's thought into words!
| |
| − | |
| |
| − | | If the Immediate Object is a "Possible", that is, if the Dynamoid Object
| |
| − | | is indicated (always more or less vaguely) by means of its Qualities, etc.,
| |
| − | | I call the Sign a 'Descriptive';
| |
| − | |
| |
| − | | if the Immediate is an Occurrence, I call the Sign a 'Designative';
| |
| − | |
| |
| − | | and if the Immediate Object is a Necessitant, I call the Sign a
| |
| − | | 'Copulant'; for in that case the Object has to be so identified
| |
| − | | by the Interpreter that the Sign may represent a necessitation.
| |
| − | | My name is certainly a temporary expedient.
| |
| − | |
| |
| − | | It is evident that a possible can determine nothing but a Possible,
| |
| − | | it is equally so that a Necessitant can be determined by nothing but
| |
| − | | a Necessitant. Hence it follows from the Definition of a Sign that
| |
| − | | since the Dynamoid Object determines the Immediate Object,
| |
| − | |
| |
| − | | Which determines the Sign itself,
| |
| − | | which determines the Destinate Interpretant
| |
| − | | which determines the Effective Interpretant
| |
| − | | which determines the Explicit Interpretant
| |
| − | |
| |
| − | | the six trichotomies, instead of determining 729 classes of signs,
| |
| − | | as they would if they were independent, only yield 28 classes;
| |
| − | | and if, as I strongly opine (not to say almost prove), there
| |
| − | | are four other trichotomies of signs of the same order of
| |
| − | | importance, instead of making 59,049 classes, these will
| |
| − | | only come to 66.
| |
| − | |
| |
| − | | The additional 4 trichotomies are undoubtedly, first:
| |
| − | |
| |
| − | | Icons*, Symbols, Indices,
| |
| − | |
| |
| − | |*(or Simulacra, Aristotle's 'homoiomata'), caught from Plato, who I guess took it
| |
| − | | from the Mathematical school of logic, for it earliest appears in the 'Phaedrus'
| |
| − | | which marks the beginning of Plato's being decisively influenced by that school.
| |
| − | | Lutoslowski is right in saying that the 'Phaedrus' is later than the 'Republic'
| |
| − | | but his date 379 B.C. is about eight years too early.
| |
| − | |
| |
| − | | and then 3 referring to the Interpretants. One of these I am pretty confident
| |
| − | | is into: 'Suggestives', 'Imperatives', 'Indicatives', where the Imperatives
| |
| − | | include the Interrogatives. Of the other two I 'think' that one must be
| |
| − | | into Signs assuring their Interpretants by:
| |
| − | |
| |
| − | | Instinct, Experience, Form.
| |
| − | |
| |
| − | | The other I suppose to be what, in my 'Monist'
| |
| − | | exposition of Existential Graphs, I called:
| |
| − | |
| |
| − | | Semes, Phemes, Delomes.
| |
| − | |
| |
| − | | CSP, 'Selected Writings', pp. 406-408.
| |
| − | |
| |
| − | |'Charles S. Peirce: Selected Writings (Values in a Universe of Chance)',
| |
| − | | edited with an introduction and notes by Philip P. Wiener, Dover,
| |
| − | | New York, NY, 1966. Originally published under the subtitle
| |
| − | | in parentheses above, Doubleday & Company, 1958.
| |
| − |
| |
| − | But see CP 4.549-550 for a significant distinction between
| |
| − | the categories (or modalities) and the orders of intention.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 17==
| |
| − |
| |
| − | <pre>
| |
| − | HC = Howard Callaway
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | JA: In closing, observe that the teridentity relation has turned up again
| |
| − | in this context, as the second comma-ing of the universal term itself:
| |
| − |
| |
| − | 1,, = B:B:B +, C:C:C +, D:D:D +, E:E:E +, I:I:I +, J:J:J +, O:O:O.
| |
| − |
| |
| − | HC: I see that you've come around to a mention of teridentity again, Jon.
| |
| − | Still, if I recall the prior discussions, then no one doubts that we
| |
| − | can have a system of notation in which teridentity appears (I don't
| |
| − | actually see it here).
| |
| − |
| |
| − | Perhaps we could get at the root of the misunderstanding
| |
| − | if you tell me why you don't actually see the concept of
| |
| − | teridentity being exemplified here.
| |
| − |
| |
| − | If it's only a matter of having lost the context of the
| |
| − | present discussion over the break, then you may find the
| |
| − | previous notes archived at the distal ends of the ur-links
| |
| − | that I append below (except for the first nine discussion
| |
| − | notes that got lost in a disk crash at the Arisbe Dev site).
| |
| − |
| |
| − | HC: Also, I think we can have a system of notation in which
| |
| − | teridentity is needed. Those points seem reasonably clear.
| |
| − |
| |
| − | The advantage of a concept is the integration of a species of manifold.
| |
| − | The necessity of a concept is the incapacity to integrate it otherwise.
| |
| − |
| |
| − | Of course, no one should be too impressed with a concept that
| |
| − | is only the artifact of a particular system of representation.
| |
| − | So before we accord a concept the status of addressing reality,
| |
| − | and declare it a term of some tenured office in our intellects,
| |
| − | we would want to see some evidence that it helps us to manage
| |
| − | a reality that we cannot see a way to manage any other way.
| |
| − |
| |
| − | Granted.
| |
| − |
| |
| − | Now how in general do we go about an investiture of this sort?
| |
| − | That is the big question that would serve us well to consider
| |
| − | in the process of the more limited investigation of identity.
| |
| − | Indeed, I do not see how it is possible to answer the small
| |
| − | question if no understanding is reached on the big question.
| |
| − |
| |
| − | HC: What remains relatively unclear is why we should need a system of notation
| |
| − | in which teridentity appears or is needed as against one in which it seems
| |
| − | not to be needed -- since assertion of identity can be made for any number
| |
| − | of terms in the standard predicate calculus.
| |
| − |
| |
| − | This sort of statement totally non-plusses me.
| |
| − | It seems like a complete non-sequitur or even
| |
| − | a contradiction in terms to me.
| |
| − |
| |
| − | The question is about the minimal adequate resource base for
| |
| − | defining, deriving, or generating all of the concepts that we
| |
| − | need for a given but very general type of application that we
| |
| − | conventionally but equivocally refer to as "logic". You seem
| |
| − | to be saying something like this: We don't need 3-identity
| |
| − | because we have 4-identity, 5-identity, 6-identity, ..., in
| |
| − | the "standard predicate calculus". The question is not what
| |
| − | concepts are generated in all the generations that follow the
| |
| − | establishment of the conceptual resource base (axiom system),
| |
| − | but what is the minimal set of concepts that we can use to
| |
| − | generate the needed collection of concepts. And there the
| |
| − | answer is, in a way that is subject to the usual sorts of
| |
| − | mathematical proof, that 3-identity is the minimum while
| |
| − | 2-identity is not big enough to do the job we want to do.
| |
| − |
| |
| − | Logic Of Relatives 01-41, LOR Discussion Notes 10-17.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 18==
| |
| − |
| |
| − | <pre>
| |
| − | BM = Bernard Morand
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | JA: 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.
| |
| − |
| |
| − | BM: I made such a kind of comparison some time ago. I selected
| |
| − | the following 3 cases on the criterium 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 8.345-8.376).
| |
| − | 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?
| |
| − | I've seen many pretty pictures of these things over the
| |
| − | years, but may have to follow my own gnosis for a while.
| |
| − |
| |
| − | Pages I have bookmarked just recently,
| |
| − | but not really had the chance to study:
| |
| − |
| |
| − | http://www.digitalpeirce.org/hoffmann/p-sighof.htm
| |
| − | http://www.csd.uwo.ca/~merkle/thesis/Introduction.html
| |
| − | http://members.door.net/arisbe/menu/library/aboutcsp/merkle/hci-abstract.htm
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 19==
| |
| − |
| |
| − | <pre>
| |
| − | BM = Bernard Morand
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | I now have three partially answered messages on the table,
| |
| − | so I will just grab this fragment off the top of the deck.
| |
| − |
| |
| − | BM: Peirce gives the following definition (CP 8.343):
| |
| − |
| |
| − | BM, quoting CSP:
| |
| − |
| |
| − | | It is likewise requisite to distinguish
| |
| − | | the 'Immediate Interpretant', i.e. the
| |
| − | | Interpretant represented or signified in
| |
| − | | the Sign, from the 'Dynamic Interpretant',
| |
| − | | or effect actually produced on the mind
| |
| − | | by the Sign; and both of these from
| |
| − | | the 'Normal Interpretant', or effect
| |
| − | | that would be produced on the mind by
| |
| − | | the Sign after sufficient development
| |
| − | | of thought.
| |
| − | |
| |
| − | | C.S. Peirce, 'Collected Papers', CP 8.343.
| |
| − |
| |
| − | JA: Well, you've really tossed me in the middle of the briar patch now!
| |
| − | I must continue with my reading from the 1870 LOR, ...
| |
| − |
| |
| − | BM: Yes indeed! I am irritated by having not the necessary
| |
| − | turn of mind to fully grasp it. But it seems to be a
| |
| − | prerequisite in order to understand the very meaning
| |
| − | of the above table. It could be the same for:
| |
| − |
| |
| − | BM, quoting CSP:
| |
| − |
| |
| − | | I define a 'Sign' 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 'Interpretant'
| |
| − | | of the sign, is thereby mediately determined by that
| |
| − | | Object.
| |
| − |
| |
| − | BM: The so-called "latter determination" would make the 'Interpretant'
| |
| − | a tri-relative term into a teridentity involving Sign and Object.
| |
| − | Isn't it?
| |
| − |
| |
| − | BM: I thought previously that the Peirce's phrasing was just applying the
| |
| − | principle of transitivity. From O determines S and S determines I,
| |
| − | it follows: O determines I. But this is not the same as teridentity.
| |
| − | Do you think so or otherwise?
| |
| − |
| |
| − | My answers are "No" and "Otherwise".
| |
| − |
| |
| − | Continuing to discourse about definite universes thereof,
| |
| − | the 3-identity term over the universe 1 = {A, B, C, D, ...} --
| |
| − | I only said it was definite, I didn't say it wasn't vague! --
| |
| − | designates, roughly speaking, the 3-adic relation that may
| |
| − | be hinted at by way of the following series:
| |
| − |
| |
| − | 1,, = A:A:A +, B:B:B +, C:C:C +, D:D:D +, ...
| |
| − |
| |
| − | I did a study on Peirce's notion of "determination".
| |
| − | As I understand it so far, we need to keep in mind
| |
| − | that it is more fundamental than causation, can be
| |
| − | a form of "partial determination", and is roughly
| |
| − | formal, mathematical, or "information-theoretic",
| |
| − | not of necessity invoking any temporal order.
| |
| − |
| |
| − | For example, when we say "The points A and B determine the line AB",
| |
| − | this invokes the concept of a 3-adic relation of determination that
| |
| − | does not identify A, B, AB, is not transitive, as transitivity has
| |
| − | to do with the composition of 2-adic relations and would amount to
| |
| − | the consideration of a degenerate 3-adic relation in this context.
| |
| − |
| |
| − | Now, it is possible to have a sign relation q whose sum enlists
| |
| − | an elementary sign relation O:S:I where O = S = I. For example,
| |
| − | it makes perfect sense to me to say that the whole universe may
| |
| − | be a sign of itself to itself, so the conception is admissable.
| |
| − | But this amounts to a very special case, by no means general.
| |
| − | More generally, we are contemplating sums like the following:
| |
| − |
| |
| − | q = O1:S1:I1 +, O2:S2:I2 +, O3:S3:I3 +, ...
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 20==
| |
| − |
| |
| − | <pre>
| |
| − | HC = Howard Callaway
| |
| − | JR = Joe Ransdell
| |
| − |
| |
| − | HC: 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.
| |
| − |
| |
| − | JR: 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:
| |
| − |
| |
| − | | We are not separated from the world by a veil of signs --
| |
| − | | we are the veil of signs.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 21==
| |
| − |
| |
| − | <pre>
| |
| − | AS = Armando Sercovich
| |
| − |
| |
| − | AS: We are not separated from the world by a veil of signs nor we are a veil of signs.
| |
| − | Simply we are signs.
| |
| − |
| |
| − | AS, quoting CSP:
| |
| − |
| |
| − | | The *man-sign* acquires information, and comes to mean more than he did before.
| |
| − | | But so do words. Does not electricity mean more now than it did in the days
| |
| − | | of Franklin? Man makes the word, and the word means nothing which the man
| |
| − | | has not made it mean, and that only to some man. But since man can think
| |
| − | | only by means of words or other external symbols, these might turn round
| |
| − | | and say: "You mean nothing which we have not taught you, and then only
| |
| − | | so far as you address some word as the interpretant of your thought".
| |
| − | | In fact, therefore, men and words reciprocally educate each other;
| |
| − | | each increase of a man's information involves, and is involved by,
| |
| − | | a corresponding increase of a word's information.
| |
| − | |
| |
| − | | Without fatiguing the reader by stretching this parallelism too far, it is
| |
| − | | sufficient to say that there is no element whatever of man's consciousness
| |
| − | | which has not something corresponding to it in the word; and the reason is
| |
| − | | obvious. It is that the word or sign which man uses *is* the man itself.
| |
| − | | For, as the fact that every thought is a sign, taken in conjunction with
| |
| − | | the fact that life is a train of thought, proves that man is a sign; so,
| |
| − | | that every thought is an *external* sign proves that man is an external
| |
| − | | sign. That is to say, the man and the external sign are identical, in
| |
| − | | the same sense in which the words 'homo' and 'man' are identical. Thus
| |
| − | | my language is the sum total of myself; for the man is the thought ...
| |
| − | |
| |
| − | |'Charles S. Peirce: Selected Writings (Values in a Universe of Chance)',
| |
| − | | edited with an introduction and notes by Philip P. Wiener, Dover,
| |
| − | | New York, NY, 1966. Originally published under the subtitle
| |
| − | | in parentheses above, Doubleday & Company, 1958.
| |
| − |
| |
| − | I read you loud and clear.
| |
| − | Every manifold must have
| |
| − | its catalytic converter.
| |
| − |
| |
| − | <Innumerate Continuation:>
| |
| − |
| |
| − | TUC = The Usual CISPEC
| |
| − |
| |
| − | TUC Alert:
| |
| − |
| |
| − | | E.P.A. Says Catalytic Converter Is
| |
| − | | Growing Cause of Global Warming
| |
| − | | By Matthew L. Wald
| |
| − | | Copyright 1998 The New York Times
| |
| − | | May 29, 1998
| |
| − | | -----------------------------------------------------------------------
| |
| − | | WASHINGTON -- The catalytic converter, an invention that has sharply
| |
| − | | reduced smog from cars, has now become a significant and growing cause
| |
| − | | of global warming, according to the Environmental Protection Agency
| |
| − |
| |
| − | Much as I would like to speculate ad libitum on these exciting new prospects for the
| |
| − | application of Peirce's chemico-algebraic theory of logic to the theorem-o-dynamics
| |
| − | of auto-semeiosis, I must get back to "business as usual" (BAU) ...
| |
| − |
| |
| − | And now a word from our sponsor ...
| |
| − |
| |
| − | http://www2.naias.com/
| |
| − |
| |
| − | Reporting from Motown ---
| |
| − |
| |
| − | Jon Awbrey
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 22==
| |
| − |
| |
| − | <pre>
| |
| − | HC = Howard Callaway
| |
| − |
| |
| − | HC: You quote the following passage from a prior posting of mine:
| |
| − |
| |
| − | HC: What remains relatively unclear is why we should need a system of notation
| |
| − | in which teridentity appears or is needed as against one in which it seems
| |
| − | not to be needed -- since assertion of identity can be made for any number
| |
| − | of terms in the standard predicate calculus.
| |
| − |
| |
| − | HC: You comment as follows:
| |
| − |
| |
| − | JA: This sort of statement totally non-plusses me.
| |
| − | It seems like a complete non-sequitur or even
| |
| − | a contradiction in terms to me.
| |
| − |
| |
| − | JA: The question is about the minimal adequate resource base for
| |
| − | defining, deriving, or generating all of the concepts that we
| |
| − | need for a given but very general type of application that we
| |
| − | conventionally but equivocally refer to as "logic". You seem
| |
| − | to be saying something like this: We don't need 3-identity
| |
| − | because we have 4-identity, 5-identity, 6-identity, ..., in
| |
| − | the "standard predicate calculus". The question is not what
| |
| − | concepts are generated in all the generations that follow the
| |
| − | establishment of the conceptual resource base (axiom system),
| |
| − | but what is the minimal set of concepts that we can use to
| |
| − | generate the needed collection of concepts. And there the
| |
| − | answer is, in a way that is subject to the usual sorts of
| |
| − | mathematical proof, that 3-identity is the minimum while
| |
| − | 2-identity is not big enough to do the job we want to do.
| |
| − |
| |
| − | HC: I have fallen a bit behind on this thread while attending to some other
| |
| − | matters, but in this reply, you do seem to me to be coming around to an
| |
| − | understanding of the issues involved, as I see them. You put the matter
| |
| − | this way, "We don't need 3-identity because we have 4-identity, 5-identity,
| |
| − | 6-identity, ..., in the 'standard predicate calculus'". Actually, as I think
| |
| − | you must know, there is no such thing as "4-identity", "5-identity", etc., in
| |
| − | the standard predicate calculus. It is more that such concepts are not needed,
| |
| − | just as teridentity is not needed, since the general apparatus of the predicate
| |
| − | calculus allows us to express identity among any number of terms without special
| |
| − | provision beyond "=".
| |
| − |
| |
| − | No, that is not the case. Standard predicate calculus allows the expression
| |
| − | of predicates I_k, for k = 2, 3, 4, ..., such that I_k (x_1, ..., x_k) holds
| |
| − | if and only if all x_j, for j = 1 to k, are identical. So predicate calculus
| |
| − | contains a k-identity predicate for all such k. So whether "they're in there"
| |
| − | is not an issue. The question is whether these or any other predicates can be
| |
| − | constructed or defined in terms of 2-adic relations alone. And the answer is
| |
| − | no, they cannot. The vector of the misconception counterwise appears to be
| |
| − | as various a virus as the common cold, and every bit as resistant to cure.
| |
| − | I have taken the trouble to enumerate some of the more prevalent strains,
| |
| − | but most of them appear to go back to the 'Principia Mathematica', and
| |
| − | the variety of nominalism called "syntacticism" -- Ges-und-heit! --
| |
| − | that was spread by it, however unwittedly by some of its carriers.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 23==
| |
| − |
| |
| − | <pre>
| |
| − | 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.
| |
| − |
| |
| − | There is a "canonical" presentation of the subject, as I remember it, anyway,
| |
| − | 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
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 24==
| |
| − |
| |
| − | <pre>
| |
| − | HC = Howard Callaway
| |
| − |
| |
| − | HC: I might object that "teridentity" seems to come
| |
| − | to a matter of "a=b & b=c", so that a specific
| |
| − | predicate of teridentity seems unnecessary.
| |
| − |
| |
| − | I am presently concerned with expositing and interpreting
| |
| − | the logical system that Peirce laid out in the LOR of 1870.
| |
| − | It is my considered opinion after thirty years of study that
| |
| − | there are untapped resources remaining in this work that have
| |
| − | yet to make it through the filters of that ilk of syntacticism
| |
| − | that was all the rage in the late great 1900's. I find there
| |
| − | to be an appreciably different point of view on logic that is
| |
| − | embodied in Peirce's work, and until we have made the minimal
| |
| − | effort to read what he wrote it is just plain futile to keep
| |
| − | on pretending that we have already assimilated it, or that
| |
| − | we are qualified to evaluate its cogency.
| |
| − |
| |
| − | The symbol "&" that you employ above denotes a mathematical object that
| |
| − | qualifies as a 3-adic relation. Independently of my own views, there
| |
| − | is an abundance of statements in evidence that mathematical thinkers
| |
| − | from Peirce to Goedel consider the appreciation of facts like this
| |
| − | to mark the boundary between realism and nominalism in regard to
| |
| − | mathematical objects.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 25==
| |
| − |
| |
| − | <pre>
| |
| − | HC = Howard Callaway
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | HC: I might object that "teridentity" seems to come
| |
| − | to a matter of "a=b & b=c", so that a specific
| |
| − | predicate of teridentity seems unnecessary.
| |
| − |
| |
| − | JA: I am presently concerned with expositing and interpreting
| |
| − | the logical system that Peirce laid out in the LOR of 1870.
| |
| − | It is my considered opinion after thirty years of study that
| |
| − | there are untapped resources remaining in this work that have
| |
| − | yet to make it through the filters of that ilk of syntacticism
| |
| − | that was all the rage in the late great 1900's. I find there
| |
| − | to be an appreciably different point of view on logic that is
| |
| − | embodied in Peirce's work, and until we have made the minimal
| |
| − | effort to read what he wrote it is just plain futile to keep
| |
| − | on pretending that we have already assimilated it, or that
| |
| − | we are qualified to evaluate its cogency.
| |
| − |
| |
| − | JA: The symbol "&" that you employ above denotes a mathematical object that
| |
| − | qualifies as a 3-adic relation. Independently of my own views, there
| |
| − | is an abundance of statements in evidence that mathematical thinkers
| |
| − | from Peirce to Goedel consider the appreciation of facts like this
| |
| − | to mark the boundary between realism and nominalism in regard to
| |
| − | mathematical objects.
| |
| − |
| |
| − | HC: I would agree, I think, that "&" may be thought of
| |
| − | as a function mapping pairs of statements onto the
| |
| − | conjunction of that pair.
| |
| − |
| |
| − | Yes, indeed, in the immortal words of my very first college algebra book:
| |
| − | "A binary operation is a ternary relation". As it happens, the symbol "&"
| |
| − | is equivocal in its interpretation -- computerese today steals a Freudian
| |
| − | line and dubs it "polymorphous" -- it can be regarded in various contexts
| |
| − | as a 3-adic relation on syntactic elements called "sentences", on logical
| |
| − | elements called "propositions", or on truth values collated in the boolean
| |
| − | domain B = {false, true} = {0, 1}. But the mappings and relations between
| |
| − | all of these interpretive choices are moderately well understood. Still,
| |
| − | no matter how many ways you enumerate for looking at a B-bird, the "&" is
| |
| − | always 3-adic. And that is sufficient to meet your objection, so I think
| |
| − | I will just leave it there until next time.
| |
| − |
| |
| − | On a related note, that I must postpone until later:
| |
| − | We seem to congrue that there is a skewness between
| |
| − | the way that most mathematicians use logic and some
| |
| − | philosophers talk about logic, but I may not be the
| |
| − | one to set it adjoint, much as I am inclined to try.
| |
| − | At the moment I have this long-post-poned exponency
| |
| − | to carry out. I will simply recommend for your due
| |
| − | consideration Peirce's 1870 Logic Of Relatives, and
| |
| − | leave it at that. There's a cornucopiousness to it
| |
| − | that's yet to be dreamt of in the philosophy of the
| |
| − | 1900's. I am doing what I can to infotain you with
| |
| − | the Gardens of Mathematical Recreations that I find
| |
| − | within Peirce's work, and that's in direct response
| |
| − | to many, okay, a couple of requests. Perhaps I can
| |
| − | not hope to attain the degree of horticultural arts
| |
| − | that Gardners before me have exhibited in this work,
| |
| − | but then again, who could? Everybody's a critic --
| |
| − | but the better ones read first, and criticize later.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 26==
| |
| − |
| |
| − | <pre>
| |
| − | HC = Howard Callaway
| |
| − |
| |
| − | HC: 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
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 27==
| |
| − |
| |
| − | <pre>
| |
| − | HC = Howard Callaway
| |
| − |
| |
| − | HC: For, if I make an assertion A&B, then I am not asserting
| |
| − | that the statement A stands in a relation to a statement B.
| |
| − | Instead, I am asserting the conjunction A&B (which logically
| |
| − | implies both the conjuncts in view of the definition of "&").
| |
| − |
| |
| − | Please try to remember where we came in. This whole play of
| |
| − | animadversions about 3-adicity and 3-identity is set against
| |
| − | the backdrop of a single point, over the issue as to whether
| |
| − | 3-adic relations are wholly dispensable or somehow essential
| |
| − | to logic, mathematics, and indeed to argument, communication,
| |
| − | and reasoning in general. Some folks clamor "Off with their
| |
| − | unnecessary heads!" -- other people, who are forced by their
| |
| − | occupations to pay close attention to the ongoing complexity
| |
| − | of the processes at stake, know that, far from finding 3-ads
| |
| − | in this or that isolated corner of the realm, one can hardly
| |
| − | do anything at all in the ways of logging or mathing without
| |
| − | running smack dab into veritable hosts of them.
| |
| − |
| |
| − | I have just shown that "a=b & b=c" involves a 3-adic relation.
| |
| − | Some people would consider this particular 3-adic relation to
| |
| − | be more complex than the 3-identity relation, but that may be
| |
| − | a question of taste. At any rate, the 3-adic aspect persists.
| |
| − |
| |
| − | HC: If "&" counts as a triadic relation, simply because it serves
| |
| − | to conjoin two statements into a third, then it would seem that
| |
| − | any binary relation 'R' will count as triadic, simply because
| |
| − | it places two things into a relation, which is a "third" thing.
| |
| − | By the same kind of reasoning a triadic relation, as ordinarily
| |
| − | understood would be really 4-adic.
| |
| − |
| |
| − | The rest of your comments are just confused,
| |
| − | and do not use the terms as they are defined.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 28==
| |
| − |
| |
| − | <pre>
| |
| − | JA = Jon Awbrey
| |
| − | JR = Joseph Ransdell
| |
| − |
| |
| − | JA: 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.
| |
| − |
| |
| − | JR: Yes, I take this as underscoring and explicating the import of
| |
| − | making logic prior to rather than dependent upon metaphysics.
| |
| − |
| |
| − | I think that Peirce, and of course many math folks, would take math
| |
| − | as prior, on a par, or even identical with logic. Myself I've been
| |
| − | of many minds about this over the years. The succinctest picture
| |
| − | that I get from Peirce is always this one:
| |
| − |
| |
| − | | [Riddle of the Sphynx]
| |
| − | |
| |
| − | | Normative science rests largely on phenomenology and on mathematics;
| |
| − | | Metaphysics on phenomenology and on normative science.
| |
| − | |
| |
| − | | C.S. Peirce, CP 1.186 (1903)
| |
| − | |
| |
| − | |
| |
| − | | o Metaphysics
| |
| − | | /|
| |
| − | | / |
| |
| − | | / |
| |
| − | | Normative Science o |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | / \|
| |
| − | | Mathematics o o Phenomenology
| |
| − | |
| |
| − | |
| |
| − | | ROTS. http://stderr.org/pipermail/inquiry/2004-March/001262.html
| |
| − |
| |
| − | Logic being a normative science must depend on math and phenomenology.
| |
| − |
| |
| − | Of course, it all depends on what a person means by "logic" ...
| |
| − |
| |
| − | JA: I also observe that Peirce takes the individual objects of
| |
| − | a particular universe of discourse in a "generative" way,
| |
| − | not a "totalizing" way, and thus they afford us with the
| |
| − | basis for talking freely about collections, constructions,
| |
| − | properties, qualities, subsets, and "higher types", as
| |
| − | the phrase is mint.
| |
| − |
| |
| − | JR: Would this be essentially the same as regarding quantification as
| |
| − | distributive rather than collective, i.e. we take the individuals
| |
| − | of a class one-by-one as selectable rather than as somehow given
| |
| − | all at once, collectively?
| |
| − |
| |
| − | Gosh, that's a harder question. Your suggestion reminds me
| |
| − | of the way that some intuitionist and even some finitist
| |
| − | mathematicians talk when they reflect on math practice.
| |
| − | I have leanings that way, but when I have tried to
| |
| − | give up the classical logic axioms, I have found
| |
| − | them too built in to my way of thinking to quit.
| |
| − | Still, a healthy circumspection about about our
| |
| − | often-wrongly vaunted capacties to conceive of
| |
| − | totalities is a habitual part of current math.
| |
| − | Again, I think individuals are made not born,
| |
| − | that is, to some degree factitious and mere
| |
| − | compromises of this or that conveniency.
| |
| − | This is one of the reasons that I have
| |
| − | been trying to work out the details
| |
| − | of a functional approach to logic,
| |
| − | propostional, quantificational,
| |
| − | and relational.
| |
| − |
| |
| − | Cf: INTRO 30. http://stderr.org/pipermail/inquiry/2004-November/001765.html
| |
| − | In: INTRO. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1720
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 29==
| |
| − |
| |
| − | <pre>
| |
| − | JA = Jon Awbrey
| |
| − | GR = Gary Richmond
| |
| − |
| |
| − | Re: LOR.COM 11.24. http://stderr.org/pipermail/inquiry/2004-November/001836.html
| |
| − | In: LOR.COM. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1755
| |
| − |
| |
| − | JA: The manner in which these arrows and qualified arrows help us
| |
| − | to construct a suspension bridge that unifies logic, semiotics,
| |
| − | statistics, stochastics, and information theory will be one of
| |
| − | the main themes that I aim to elaborate throughout the rest of
| |
| − | this inquiry.
| |
| − |
| |
| − | GR: Pretty ambitious, Jon. I'm sure you're up to it.
| |
| − |
| |
| − | GR: I'd like to anticipate 3 versions: The mathematical (cactus diagrams, etc.),
| |
| − | the poetic, and the commonsensical -- ordinary language for those who are
| |
| − | NEITHER logicians NOR poets.
| |
| − |
| |
| − | GR: Are you up to THAT?
| |
| − |
| |
| − | Riddle A Body: "Time Enough, And Space, Excalibrate Co-Arthurs Should Apply"
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 30==
| |
| − |
| |
| − | <pre>
| |
| − | JA = Jon Awbrey
| |
| − | GR = Gary Richmond
| |
| − |
| |
| − | Re: LOR.DIS 29. http://stderr.org/pipermail/inquiry/2004-November/001838.html
| |
| − | In: LOR.DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1768
| |
| − |
| |
| − | JA: Riddle A Body: "Time Enough, And Space, Excalibrate Co-Arthurs Should Apply"
| |
| − |
| |
| − | GR: Well said, and truly!
| |
| − |
| |
| − | Body A Riddle: TEASE CASA = Fun House.
| |
| − | </pre>
| |
| − |
| |
| − | ==Discussion Note 31==
| |
| − |
| |
| − | <pre>
| |
| − | 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:
| |
| − |
| |
| − | LOR. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750
| |
| − | LOR-COM. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1755
| |
| − | LOR-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1768
| |
| − |
| |
| − | 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.
| |
| − | </pre>
| |
| − |
| |
| − | ==Work Area 1==
| |
| − | <pre>
| |
| − | BM: Several discussions could take place there,
| |
| − | as to the reasons for the number of divisions,
| |
| − | the reasons of the titles themselves. Another
| |
| − | one is my translation from "normal interpretant"
| |
| − | into "final interpretant" (which one is called
| |
| − | elsewhere "Eventual Interpretant" or "Destinate
| |
| − | Interpretant" by CSP). I let all this aside
| |
| − | to focus on the following remark:
| |
| − |
| |
| − | BM: 6 divisions correspond to individual correlates:
| |
| − |
| |
| − | (S, O_i, O_d, I_i, I_d, I_n),
| |
| − |
| |
| − | 3 divisions correspond to dyads:
| |
| − |
| |
| − | (S : O_d, S : I_d, S : I_n),
| |
| − |
| |
| − | and the tenth to a triad:
| |
| − |
| |
| − | (S : O_d : I_n).
| |
| − |
| |
| − | This remark would itself deserve
| |
| − | a lot of explanations but one
| |
| − | more time I let this aside.
| |
| − |
| |
| − | BM: Then we have the following very clear statement from Peirce:
| |
| − |
| |
| − | | It follows from the Definition of a Sign
| |
| − | | that since the Dynamoid Object determines
| |
| − | | the Immediate Object,
| |
| − | | which determines the Sign,
| |
| − | | which determines the Destinate Interpretant
| |
| − | | which determines the Effective Interpretant
| |
| − | | which determines the Explicit Interpretant
| |
| − | |
| |
| − | | the six trichotomies, instead of determining 729 classes of signs,
| |
| − | | as they would if they were independent, only yield 28 classes; and
| |
| − | | if, as I strongly opine (not to say almost prove) there are four other
| |
| − | | trichotomies of signs of the same order of importance, instead of making
| |
| − | | 59049 classes, these will only come to 66.
| |
| − | |
| |
| − | | CSP, "Letter to Lady Welby", 14 Dec 1908, LW, p. 84.
| |
| − |
| |
| − | BM: The separation made by CSP between 6 divisions and four others
| |
| − | seems to rely upon the suggested difference between individual
| |
| − | correlates and relations. We get the idea that the 10 divisions
| |
| − | are ordered on the whole and will end into 66 classes (by means of
| |
| − | three ordered modal values on each division: maybe, canbe, wouldbe).
| |
| − | Finally we have too the ordering for the divisions relative to the
| |
| − | correlates that I write in my notation:
| |
| − |
| |
| − | Od -> Oi -> S -> If -> Id -> Ii.
| |
| − |
| |
| − | BM: This order of "determinations" has bothered many people
| |
| − | but if we think of it as operative in semiosis, it seems
| |
| − | to be correct (at least to my eyes). Thus the question is:
| |
| − | where, how, and why the "four other trichotomies" fit in this
| |
| − | schema to obtain a linear ordering on the whole 10 divisions?
| |
| − | May be the question can be rephrased as: how intensional
| |
| − | relationships fit into an extensional one? Possibly the
| |
| − | question could be asked the other way. R. Marty responds
| |
| − | that in a certain sense the four trichotomies give nothing
| |
| − | more than the previous six ones but I strongly doubt of this.
| |
| − |
| |
| − | BM: I put the problem in graphical form in an attached file
| |
| − | because my message editor will probably make some mistakes.
| |
| − | I make a distinction between arrow types drawing because I am
| |
| − | not sure that the sequence of correlates determinations is of
| |
| − | the same nature than correlates determination inside relations.
| |
| − |
| |
| − | BM: It looks as if the problem amounts to some kind of projection
| |
| − | of relations on the horizontal axis made of correlates.
| |
| − |
| |
| − | BM: If we consider some kind of equivalence (and this seems necessary to
| |
| − | obtain a linear ordering), by means of Agent -> Patient reductions on
| |
| − | relations, then erasing transitive determinations leads to:
| |
| − |
| |
| − | Od -> Oi -> S -> S-Od -> If -> S-If -> S-Od-If -> Id -> S-Id -> Ii
| |
| − |
| |
| − | BM: While it is interesting to compare the subsequence
| |
| − | S-Od -> If -> S-If -> S-Od-If with the pragmatic maxim,
| |
| − | I have no clear idea of the (in-) validity of such a result.
| |
| − | But I am convinced that the clarity has to come from the
| |
| − | Logic Of Relatives.
| |
| − |
| |
| − | BM: I will be very grateful if you can make something with all that stuff.
| |
| − |
| |
| − |
| |
| − |
| |
| − | LOR. Work 2
| |
| − |
| |
| − |
| |
| − |
| |
| − | BM: I also found this passage which may be of some interest
| |
| − | (CP 4.540, Prolegomena to an Apology of Pragmatism):
| |
| − |
| |
| − | | But though an Interpretant is not necessarily a Conclusion, yet a
| |
| − | | Conclusion is necessarily an Interpretant. So that if an Interpretant is
| |
| − | | not subject to the rules of Conclusions there is nothing monstrous in my
| |
| − | | thinking it is subject to some generalization of such rules. For any
| |
| − | | evolution of thought, whether it leads to a Conclusion or not, there is a
| |
| − | | certain normal course, which is to be determined by considerations not in
| |
| − | | the least psychological, and which I wish to expound in my next
| |
| − | | article;†1 and while I entirely agree, in opposition to distinguished
| |
| − | | logicians, that normality can be no criterion for what I call
| |
| − | | rationalistic reasoning, such as alone is admissible in science, yet it
| |
| − | | is precisely the criterion of instinctive or common-sense reasoning,
| |
| − | | which, within its own field, is much more trustworthy than rationalistic
| |
| − | | reasoning. In my opinion, it is self-control which makes any other than
| |
| − | | the normal course of thought possible, just as nothing else makes any
| |
| − | | other than the normal course of action possible; and just as it is
| |
| − | | precisely that that gives room for an ought-to-be of conduct, I mean
| |
| − | | Morality, so it equally gives room for an ought-to-be of thought, which
| |
| − | | is Right Reason; and where there is no self-control, nothing but the
| |
| − | | normal is possible. If your reflections have led you to a different
| |
| − | | conclusion from mine, I can still hope that when you come to read my next
| |
| − | | article, in which I shall endeavor to show what the forms of thought are,
| |
| − | | in general and in some detail, you may yet find that I have not missed
| |
| − | | the truth.
| |
| − |
| |
| − | JA: 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.
| |
| − |
| |
| − | BM: I think that I understand your reticence. I wonder if:
| |
| − |
| |
| − | a. the fact that the letters to Lady Welby have been published as such,
| |
| − | has not lead to approach the matter in a certain way.
| |
| − |
| |
| − | b. other sources, eventually unpublished, would give another lighting on
| |
| − | the subject, namely a logical one. I think of MS 339 for example that
| |
| − | seems to be part of the Logic Notebook. I have had access to some pages
| |
| − | of it, but not to the whole MS.
| |
| − |
| |
| − | BM: A last remark. I don't think that classification is a mania for CSP but I
| |
| − | know that you know that! It is an instrument of thought and I think that
| |
| − | it is in this case much more a plan for experimenting than the exposition
| |
| − | of a conclusion. Experimenting what ? There is a strange statement in a
| |
| − | letter to W. James where CSP says that what is in question in his "second
| |
| − | way of dividing signs" is the logical theory of numbers. I give this from
| |
| − | memory. I have not the quote at hand now but I will search for it if needed.
| |
| − |
| |
| − |
| |
| − |
| |
| − | LOR. Work 3
| |
| − |
| |
| − |
| |
| − |
| |
| − | BM = Bernard Morand
| |
| − | JA = Jon Awbrey
| |
| − |
| |
| − | JA: ... 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.
| |
| − |
| |
| − | BM: I made such a kind of comparison some time ago. I selected the following
| |
| − | 3 cases on the criterium 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 8.345-8.376). A
| |
| − | tabular presentation would be better but I can't do it. Comparing (c)
| |
| − | against (a) and (b) is informative, I think.
| |
| − |
| |
| − | Division 1
| |
| − |
| |
| − | (a) According to the matter of the Sign
| |
| − |
| |
| − | (b) According to the Mode of Apprehension of the Sign itself
| |
| − |
| |
| − | (c) Signs in respect to their Modes of possible Presentation
| |
| − |
| |
| − | Division 2
| |
| − |
| |
| − | (a) According to the Immediate Object
| |
| − |
| |
| − | (b) According to the Mode of Presentation of the Immediate Object
| |
| − |
| |
| − | (c) Objects, as they may be presented
| |
| − |
| |
| − | Division 3
| |
| − |
| |
| − | (a) According to the Matter of the Dynamic Object
| |
| − |
| |
| − | (b) According to the Mode of Being of the Dynamical Object
| |
| − |
| |
| − | (c) In respect to the Nature of the Dynamical Objects of Signs
| |
| − |
| |
| − | Division 4
| |
| − |
| |
| − | (a) According to the mode of representing object by the Dynamic Object
| |
| − |
| |
| − | (b) According to the Relation of the Sign to its Dynamical Object
| |
| − |
| |
| − | (c) The fourth Trichotomy
| |
| − |
| |
| − | Division 5
| |
| − |
| |
| − | (a) According to the Immédiate Interpretant
| |
| − |
| |
| − | (b) According to the Mode of Presentation of the Immediate Interpretant
| |
| − |
| |
| − | (c) As to the nature of the Immediate (or Felt ?) Interpretant
| |
| − |
| |
| − | Division 6
| |
| − |
| |
| − | (a) According to the Matter of Dynamic Interpretant
| |
| − |
| |
| − | (b) According to the Mode of Being of the Dynamical Interpretant
| |
| − |
| |
| − | (c) As to the Nature of the Dynamical Interpretant
| |
| − |
| |
| − | Division 7
| |
| − |
| |
| − | (a) According to the Mode of Affecting Dynamic Interpretant
| |
| − |
| |
| − | (b) According to the relation of the Sign to the Dynamical Interpretant
| |
| − |
| |
| − | (c) As to the Manner of Appeal to the Dynamic Interpretant
| |
| − |
| |
| − | Division 8
| |
| − |
| |
| − | (a) According to the Matter of Representative Interpretant
| |
| − |
| |
| − | (b) According to the Nature of the Normal Interpretant
| |
| − |
| |
| − | (c) According to the Purpose of the Eventual Interpretant
| |
| − |
| |
| − | Division 9
| |
| − |
| |
| − | (a) According to the Mode of being represented by Representative Interpretant
| |
| − |
| |
| − | (b) According to the the relation of the Sign to the Normal Interpretant
| |
| − |
| |
| − | (c) As to the Nature of the Influence of the Sign
| |
| − |
| |
| − | Division 10
| |
| − |
| |
| − | (a) According to the Mode of being represented to represent object by Sign, Truly
| |
| − |
| |
| − | (b) According to the Triadic Relation of the Sign to its Dynamical Object and to
| |
| − | its Normal Interpretant
| |
| − |
| |
| − | (c) As to the Nature of the Assurance of the Utterance
| |
| − |
| |
| − |
| |
| − |
| |
| − | LOR. Work 4
| |
| − |
| |
| − |
| |
| − |
| |
| − | JA: It may appear that one has side-stepped the issue of empiricism
| |
| − | 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 ...
| |
| − |
| |
| − | HC: In contrast with this it strikes me that not all meanings of "analytic"
| |
| − | and "synthetic" have much, if anything, to do with the "analytic and the
| |
| − | synthetic", say, as in Quine's criticism of the "dualism" of empiricism.
| |
| − | Surely no one thinks that a plausible analysis must be analytic or that
| |
| − | synthetic materials tell us much about epistemology. So, it is not
| |
| − | clear that anything connected with analyticity or a priori knowledge
| |
| − | will plausibly or immediately arise from a discussion of analytical
| |
| − | geometry. Prevalent mathematical assumptions or postulates, yes --
| |
| − | but who says these are a prior? Can't non-Euclidean geometry also
| |
| − | be treated in the style of analytic geometry?
| |
| − |
| |
| − | HC: I can imagine the a discussion might be forced in
| |
| − | that direction, but the connections don't strike me
| |
| − | as at all obvious or pressing. Perhaps Jon would just
| |
| − | like to bring up the notion of the synthetic apriori?
| |
| − | But why?
| |
| − |
| |
| − |
| |
| − |
| |
| − | LOR. Work 5
| |
| − |
| |
| − |
| |
| − |
| |
| − | HC = Howard Callaway
| |
| − |
| |
| − | HC: But I see you as closer to my theme or challenge, when you say
| |
| − | "The question is about the minimal adequate resource base for
| |
| − | defining, deriving, or generating all of the concepts that we
| |
| − | need for a given but very general type of application that we
| |
| − | conventinally but equivocally refer to as 'logic'".
| |
| − |
| |
| − | HC: I think it is accepted on all sides of the discussion that there
| |
| − | is some sort of "equivalence" between the standard predicate logic
| |
| − | and Peirce's graphs.
| |
| − |
| |
| − | There you would be mistaken, except perhaps for the fact that
| |
| − | "some sort of equivalence" is vague to the depths of vacuity.
| |
| − | It most particularly does not mean "all sorts of equivalence"
| |
| − | or even "all important sorts of equivalence". It is usually
| |
| − | interpreted to mean an extremely abstract type of syntactic
| |
| − | equivalence, and that is undoubtedly one important type of
| |
| − | equivalence that it is worth examining whether two formal
| |
| − | systems have or not. But it precisely here that we find
| |
| − | another symptom of syntacticism, namely, the deprecation
| |
| − | of all other important qualities of formal systems, most
| |
| − | pointedly their "analystic, "semantic", and "pragmatic"
| |
| − | qualities, which make all the difference in how well the
| |
| − | system actually serves its users in a real world practice.
| |
| − | You can almost hear the whining and poohing coming from the
| |
| − | syntactic day camp, but those are the hard facts of the case.
| |
| − |
| |
| − | HC: But we find this difference in relation to the vocabulary used to express
| |
| − | identity. From the point of view of starting with the predicate calculus,
| |
| − | we don't need "teridentity". So, this seems to suggest there is something
| |
| − | of interesting contrast in Peirce's logic, which brings in this concept.
| |
| − | The obvious question may be expressed by asking why we need teridentity
| |
| − | in Peirce's system and how Peirce's system may recommend itself in contrast
| |
| − | to the standard way with related concepts. This does seem to call for
| |
| − | a comparative evaluation of distinctive systems. That is not an easy task,
| |
| − | as I think we all understand. But I do think that if it is a goal to have
| |
| − | Peirce's system better appreciated, then that kind of question must be
| |
| − | addressed. If "=" is sufficient in the standard predicate calculus,
| |
| − | to say whatever we may need to say about the identity of terms, then
| |
| − | what is the advantage of an alternative system which insists on always
| |
| − | expressing identity of triples?
| |
| − |
| |
| − | HC: The questions may look quite different, depending on where we start.
| |
| − | But in any case, I thought I saw some better appreciation of the
| |
| − | questions in your comments above.
| |
| − |
| |
| − |
| |
| − |
| |
| − | LOR. Work 6
| |
| − |
| |
| − |
| |
| − |
| |
| − | 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
| |
| − | image re-engineering that has become the new rage in self-styled
| |
| − | "analytic" circles.
| |
| − |
| |
| − |
| |
| − |
| |
| − | LOR. Work 7
| |
| − |
| |
| − |
| |
| − |
| |
| − | The brands of objection that you continue to make, with no evidence
| |
| − | of reflection on the many explanations that I and others have taken
| |
| − | the time to write out for you, lead me to believe that you are just
| |
| − | not interested in making that effort. That's okay, life is short,
| |
| − | the arts are long and many, there is always something else to do.
| |
| − |
| |
| − | HC: For, if I make an assertion A&B, then I am not asserting
| |
| − | that the statement A stands in a relation to a statement B.
| |
| − | Instead, I am asserting the conjunction A&B (which logically
| |
| − | implies both the conjuncts in view of the definition of "&").
| |
| − | If "&" counts as a triadic relation, simply because it serves
| |
| − | to conjoin two statements into a third, then it would seem that
| |
| − | any binary relation 'R' will count as triadic, simply because
| |
| − | it places two things into a relation, which is a "third" thing.
| |
| − | By the same kind of reasoning a triadic relation, as ordinarily
| |
| − | understood would be really 4-adic.
| |
| − |
| |
| − | HC: Now, I think this is the kind of argument you are making, ...
| |
| − |
| |
| − | No, it's the kind of argument that you are making.
| |
| − | I am not making that kind of argument, and Peirce
| |
| − | did not make that kind of argument. Peirce used
| |
| − | his terms subject to definitions that would have
| |
| − | been understandable, and remain understandable,
| |
| − | to those of his readers who understand these
| |
| − | elementary definitions, either though their
| |
| − | prior acquaintance with standard concepts
| |
| − | or through their basic capacity to read
| |
| − | a well-formed, if novel definition.
| |
| − |
| |
| − | Peirce made certain observations about the structure of logical concepts
| |
| − | and the structure of their referents. Those observations are accurate
| |
| − | and important. He expressed those observations in a form that is clear
| |
| − | to anybody who knows the meanings of the technical terms that he used,
| |
| − | and he is not responsible for the interpretations of those who don't.
| |
| − |
| |
| − | HC: ... and it seems to both trivialize the claimed argument
| |
| − | for teridentity, by trivializing the conception of what
| |
| − | is to count as a triadic, as contrasted with a binary
| |
| − | relation, and it also seems to introduce a confusion
| |
| − | about what is is count as a binary, vs. a triadic
| |
| − | relation.
| |
| − |
| |
| − | Yes, the argument that you are making trivializes
| |
| − | just about everything in sight, but that is the
| |
| − | common and well-known property of any argument
| |
| − | that fails to base itself on a grasp of the
| |
| − | first elements of the subject matter.
| |
| − |
| |
| − | HC: If this is mathematical realism, then so much the worse for
| |
| − | mathematical realism. I am content to think that we do not
| |
| − | have a free hand in making up mathematical truth.
| |
| − |
| |
| − | No, it's not mathematical realism. It is your reasoning,
| |
| − | and it exhibits all of the symptoms of syntacticism that
| |
| − | I have already diagnosed. It's a whole other culture
| |
| − | from what is pandemic in the practice of mathematics,
| |
| − | and it never fails to surprise me that people who
| |
| − | would never call themselves "relativists" in any
| |
| − | other matter of culture suddenly turn into just
| |
| − | that in matters of simple mathematical fact.
| |
| − | </pre>
| |
| − |
| |
| − | ==Logic Of Relatives : Old Series==
| |
| − |
| |
| − | <pre>
| |
| − | 00. http://suo.ieee.org/ontology/thrd20.html#04416
| |
| − | 01. http://suo.ieee.org/ontology/msg04416.html
| |
| − | 02. http://suo.ieee.org/ontology/msg04417.html
| |
| − | 03. http://suo.ieee.org/ontology/msg04418.html
| |
| − | 04. http://suo.ieee.org/ontology/msg04419.html
| |
| − | 05. http://suo.ieee.org/ontology/msg04421.html
| |
| − | 06. http://suo.ieee.org/ontology/msg04422.html
| |
| − | 07. http://suo.ieee.org/ontology/msg04423.html
| |
| − | 08. http://suo.ieee.org/ontology/msg04424.html
| |
| − | 09. http://suo.ieee.org/ontology/msg04425.html
| |
| − | 10. http://suo.ieee.org/ontology/msg04426.html
| |
| − | 11. http://suo.ieee.org/ontology/msg04427.html
| |
| − | 12. http://suo.ieee.org/ontology/msg04431.html
| |
| − | 13. http://suo.ieee.org/ontology/msg04432.html
| |
| − | 14. http://suo.ieee.org/ontology/msg04435.html
| |
| − | 15. http://suo.ieee.org/ontology/msg04436.html
| |
| − | 16. http://suo.ieee.org/ontology/msg04437.html
| |
| − | 17. http://suo.ieee.org/ontology/msg04438.html
| |
| − | 18. http://suo.ieee.org/ontology/msg04439.html
| |
| − | 19. http://suo.ieee.org/ontology/msg04440.html
| |
| − | 20. http://suo.ieee.org/ontology/msg04441.html
| |
| − | 21. http://suo.ieee.org/ontology/msg04442.html
| |
| − | 22. http://suo.ieee.org/ontology/msg04443.html
| |
| − | 23. http://suo.ieee.org/ontology/msg04444.html
| |
| − | 24. http://suo.ieee.org/ontology/msg04445.html
| |
| − | 25. http://suo.ieee.org/ontology/msg04446.html
| |
| − | 26. http://suo.ieee.org/ontology/msg04447.html
| |
| − | 27. http://suo.ieee.org/ontology/msg04448.html
| |
| − | 28. http://suo.ieee.org/ontology/msg04449.html
| |
| − | 29. http://suo.ieee.org/ontology/msg04450.html
| |
| − | 30. http://suo.ieee.org/ontology/msg04451.html
| |
| − | 31. http://suo.ieee.org/ontology/msg04452.html
| |
| − | 32. http://suo.ieee.org/ontology/msg04453.html
| |
| − | 33. http://suo.ieee.org/ontology/msg04454.html
| |
| − | 34. http://suo.ieee.org/ontology/msg04456.html
| |
| − | 35. http://suo.ieee.org/ontology/msg04457.html
| |
| − | 36. http://suo.ieee.org/ontology/msg04458.html
| |
| − | 37. http://suo.ieee.org/ontology/msg04459.html
| |
| − | 38. http://suo.ieee.org/ontology/msg04462.html
| |
| − | 39. http://suo.ieee.org/ontology/msg04464.html
| |
| − | 40. http://suo.ieee.org/ontology/msg04473.html
| |
| − | 41. http://suo.ieee.org/ontology/msg04478.html
| |
| − | 42. http://suo.ieee.org/ontology/msg04484.html
| |
| − | 43. http://suo.ieee.org/ontology/msg04487.html
| |
| − | 44. http://suo.ieee.org/ontology/msg04488.html
| |
| − | 45. http://suo.ieee.org/ontology/msg04492.html
| |
| − | 46. http://suo.ieee.org/ontology/msg04497.html
| |
| − | 47. http://suo.ieee.org/ontology/msg04498.html
| |
| − | 48. http://suo.ieee.org/ontology/msg04499.html
| |
| − | 49. http://suo.ieee.org/ontology/msg04500.html
| |
| − | 50. http://suo.ieee.org/ontology/msg04501.html
| |
| − | 51. http://suo.ieee.org/ontology/msg04502.html
| |
| − | 52. http://suo.ieee.org/ontology/msg04503.html
| |
| − | 53. http://suo.ieee.org/ontology/msg04504.html
| |
| − | 54. http://suo.ieee.org/ontology/msg04506.html
| |
| − | 55. http://suo.ieee.org/ontology/msg04508.html
| |
| − | 56. http://suo.ieee.org/ontology/msg04509.html
| |
| − | 57. http://suo.ieee.org/ontology/msg04510.html
| |
| − | 58. http://suo.ieee.org/ontology/msg04511.html
| |
| − | 59. http://suo.ieee.org/ontology/msg04512.html
| |
| − | 60. http://suo.ieee.org/ontology/msg04513.html
| |
| − | 61. http://suo.ieee.org/ontology/msg04516.html
| |
| − | 62. http://suo.ieee.org/ontology/msg04517.html
| |
| − | 63. http://suo.ieee.org/ontology/msg04518.html
| |
| − | 64. http://suo.ieee.org/ontology/msg04521.html
| |
| − | 65. http://suo.ieee.org/ontology/msg04539.html
| |
| − | 66. http://suo.ieee.org/ontology/msg04541.html
| |
| − | 67. http://suo.ieee.org/ontology/msg04542.html
| |
| − | 68. http://suo.ieee.org/ontology/msg04543.html
| |
| − | </pre>
| |
| − |
| |
| − | ==Logic of Relatives : Discussion==
| |
| − |
| |
| − | <pre>
| |
| − | 00. http://suo.ieee.org/ontology/thrd19.html#04460
| |
| − | 10. http://suo.ieee.org/ontology/msg04460.html
| |
| − | 11. http://suo.ieee.org/ontology/msg04461.html
| |
| − | 12. http://suo.ieee.org/ontology/msg04471.html
| |
| − | 13. http://suo.ieee.org/ontology/msg04472.html
| |
| − | 14. http://suo.ieee.org/ontology/msg04475.html
| |
| − | 15. http://suo.ieee.org/ontology/msg04476.html
| |
| − | 16. http://suo.ieee.org/ontology/msg04477.html
| |
| − | 17. http://suo.ieee.org/ontology/msg04479.html
| |
| − | 18. http://suo.ieee.org/ontology/msg04480.html
| |
| − | 19. http://suo.ieee.org/ontology/msg04481.html
| |
| − | 20. http://suo.ieee.org/ontology/msg04482.html
| |
| − | 21. http://suo.ieee.org/ontology/msg04483.html
| |
| − | 22. http://suo.ieee.org/ontology/msg04485.html
| |
| − | 23. http://suo.ieee.org/ontology/msg04486.html
| |
| − | 24. http://suo.ieee.org/ontology/msg04493.html
| |
| − | 25. http://suo.ieee.org/ontology/msg04494.html
| |
| − | 26. http://suo.ieee.org/ontology/msg04495.html
| |
| − | 27. http://suo.ieee.org/ontology/msg04496.html
| |
| − | </pre>
| |
| − |
| |
| − | ==Logic Of Relatives : 2003==
| |
| − |
| |
| − | <pre>
| |
| − | LOR. http://stderr.org/pipermail/inquiry/2003-March/thread.html#186
| |
| − | LOR. http://stderr.org/pipermail/inquiry/2003-April/thread.html#245
| |
| − |
| |
| − | 01. http://stderr.org/pipermail/inquiry/2003-March/000186.html
| |
| − | 02. http://stderr.org/pipermail/inquiry/2003-March/000187.html
| |
| − | 03. http://stderr.org/pipermail/inquiry/2003-March/000188.html
| |
| − | 04. http://stderr.org/pipermail/inquiry/2003-March/000189.html
| |
| − | 05. http://stderr.org/pipermail/inquiry/2003-March/000190.html
| |
| − | 06. http://stderr.org/pipermail/inquiry/2003-March/000191.html
| |
| − | 07. http://stderr.org/pipermail/inquiry/2003-March/000194.html
| |
| − | 08. http://stderr.org/pipermail/inquiry/2003-March/000195.html
| |
| − | 09. http://stderr.org/pipermail/inquiry/2003-April/000245.html
| |
| − | 10. http://stderr.org/pipermail/inquiry/2003-April/000246.html
| |
| − | 11. http://stderr.org/pipermail/inquiry/2003-April/000247.html
| |
| − | 12. http://stderr.org/pipermail/inquiry/2003-April/000248.html
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| − | 13. http://stderr.org/pipermail/inquiry/2003-April/000249.html
| |
| − | 14. http://stderr.org/pipermail/inquiry/2003-April/000250.html
| |
| − | 15. http://stderr.org/pipermail/inquiry/2003-April/000251.html
| |
| − | 16. http://stderr.org/pipermail/inquiry/2003-April/000252.html
| |
| − | 17. http://stderr.org/pipermail/inquiry/2003-April/000253.html
| |
| − | 18. http://stderr.org/pipermail/inquiry/2003-April/000254.html
| |
| − | 19. http://stderr.org/pipermail/inquiry/2003-April/000255.html
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| − | 20. http://stderr.org/pipermail/inquiry/2003-April/000256.html
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| − | 21. http://stderr.org/pipermail/inquiry/2003-April/000257.html
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| − | 22. http://stderr.org/pipermail/inquiry/2003-April/000258.html
| |
| − | 23. http://stderr.org/pipermail/inquiry/2003-April/000259.html
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| − | 24. http://stderr.org/pipermail/inquiry/2003-April/000260.html
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| − | 25. http://stderr.org/pipermail/inquiry/2003-April/000261.html
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| − | 26. http://stderr.org/pipermail/inquiry/2003-April/000262.html
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| − | 27. http://stderr.org/pipermail/inquiry/2003-April/000263.html
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| − | 28. http://stderr.org/pipermail/inquiry/2003-April/000264.html
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| − | 29. http://stderr.org/pipermail/inquiry/2003-April/000265.html
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| − | 30. http://stderr.org/pipermail/inquiry/2003-April/000267.html
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| − | 31. http://stderr.org/pipermail/inquiry/2003-April/000268.html
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| − | 32. http://stderr.org/pipermail/inquiry/2003-April/000269.html
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| − | 33. http://stderr.org/pipermail/inquiry/2003-April/000270.html
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| − | 34. http://stderr.org/pipermail/inquiry/2003-April/000271.html
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| − | 35. http://stderr.org/pipermail/inquiry/2003-April/000273.html
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| − | 36. http://stderr.org/pipermail/inquiry/2003-April/000274.html
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| − | 37. http://stderr.org/pipermail/inquiry/2003-April/000275.html
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| − | 38. http://stderr.org/pipermail/inquiry/2003-April/000276.html
| |
| − | 39. http://stderr.org/pipermail/inquiry/2003-April/000277.html
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| − | 40. http://stderr.org/pipermail/inquiry/2003-April/000278.html
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| − | 41. http://stderr.org/pipermail/inquiry/2003-April/000279.html
| |
| − | 42. http://stderr.org/pipermail/inquiry/2003-April/000280.html
| |
| − | 43. http://stderr.org/pipermail/inquiry/2003-April/000281.html
| |
| − | 44. http://stderr.org/pipermail/inquiry/2003-April/000282.html
| |
| − | 45. http://stderr.org/pipermail/inquiry/2003-April/000283.html
| |
| − | 46. http://stderr.org/pipermail/inquiry/2003-April/000284.html
| |
| − | 47. http://stderr.org/pipermail/inquiry/2003-April/000285.html
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| − | 48. http://stderr.org/pipermail/inquiry/2003-April/000286.html
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| − | 49. http://stderr.org/pipermail/inquiry/2003-April/000287.html
| |
| − | 50. http://stderr.org/pipermail/inquiry/2003-April/000288.html
| |
| − | 51. http://stderr.org/pipermail/inquiry/2003-April/000289.html
| |
| − | 52. http://stderr.org/pipermail/inquiry/2003-April/000290.html
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| − | 53. http://stderr.org/pipermail/inquiry/2003-April/000291.html
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| − | 54. http://stderr.org/pipermail/inquiry/2003-April/000294.html
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| − | 55. http://stderr.org/pipermail/inquiry/2003-April/000295.html
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| − | 56. http://stderr.org/pipermail/inquiry/2003-April/000296.html
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| − | 57. http://stderr.org/pipermail/inquiry/2003-April/000297.html
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| − | 58. http://stderr.org/pipermail/inquiry/2003-April/000298.html
| |
| − | 59. http://stderr.org/pipermail/inquiry/2003-April/000299.html
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| − | 60. http://stderr.org/pipermail/inquiry/2003-April/000300.html
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| − | 61. http://stderr.org/pipermail/inquiry/2003-April/000301.html
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| − | 62. http://stderr.org/pipermail/inquiry/2003-April/000302.html
| |
| − | 63. http://stderr.org/pipermail/inquiry/2003-April/000303.html
| |
| − | 64. http://stderr.org/pipermail/inquiry/2003-April/000305.html
| |
| − | 65. http://stderr.org/pipermail/inquiry/2003-April/000306.html
| |
| − | 66. http://stderr.org/pipermail/inquiry/2003-April/000307.html
| |
| − | 67. http://stderr.org/pipermail/inquiry/2003-April/000308.html
| |
| − | 68. http://stderr.org/pipermail/inquiry/2003-April/000309.html
| |
| − | </pre>
| |
| − |
| |
| − | ==Logic Of Relatives : 2004==
| |
| − |
| |
| − | <pre>
| |
| − | 00. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750
| |
| − | 01. http://stderr.org/pipermail/inquiry/2004-November/001750.html
| |
| − | 02. http://stderr.org/pipermail/inquiry/2004-November/001751.html
| |
| − | 03. http://stderr.org/pipermail/inquiry/2004-November/001752.html
| |
| − | 04. http://stderr.org/pipermail/inquiry/2004-November/001753.html
| |
| − | 05. http://stderr.org/pipermail/inquiry/2004-November/001754.html
| |
| − | 06. http://stderr.org/pipermail/inquiry/2004-November/001760.html
| |
| − | 07. http://stderr.org/pipermail/inquiry/2004-November/001769.html
| |
| − | 08. http://stderr.org/pipermail/inquiry/2004-November/001774.html
| |
| − | 09. http://stderr.org/pipermail/inquiry/2004-November/001783.html
| |
| − | 10. http://stderr.org/pipermail/inquiry/2004-November/001794.html
| |
| − | 11. http://stderr.org/pipermail/inquiry/2004-November/001812.html
| |
| − | 12. http://stderr.org/pipermail/inquiry/2004-November/001842.html
| |
| − | </pre>
| |
| − |
| |
| − | ==Logic Of Relatives : Commentary==
| |
| − |
| |
| − | <pre>
| |
| − | 00. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1755
| |
| − | 01. http://stderr.org/pipermail/inquiry/2004-November/001755.html
| |
| − | 02. http://stderr.org/pipermail/inquiry/2004-November/001756.html
| |
| − | 03. http://stderr.org/pipermail/inquiry/2004-November/001757.html
| |
| − | 04. http://stderr.org/pipermail/inquiry/2004-November/001758.html
| |
| − | 05. http://stderr.org/pipermail/inquiry/2004-November/001759.html
| |
| − | 06. http://stderr.org/pipermail/inquiry/2004-November/001761.html
| |
| − | 07. http://stderr.org/pipermail/inquiry/2004-November/001770.html
| |
| − | 08.1. http://stderr.org/pipermail/inquiry/2004-November/001775.html
| |
| − | 08.2. http://stderr.org/pipermail/inquiry/2004-November/001776.html
| |
| − | 08.3. http://stderr.org/pipermail/inquiry/2004-November/001777.html
| |
| − | 08.4. http://stderr.org/pipermail/inquiry/2004-November/001778.html
| |
| − | 08.5. http://stderr.org/pipermail/inquiry/2004-November/001781.html
| |
| − | 08.6. http://stderr.org/pipermail/inquiry/2004-November/001782.html
| |
| − | 09.1. http://stderr.org/pipermail/inquiry/2004-November/001787.html
| |
| − | 09.2. http://stderr.org/pipermail/inquiry/2004-November/001788.html
| |
| − | 09.3. http://stderr.org/pipermail/inquiry/2004-November/001789.html
| |
| − | 09.4. http://stderr.org/pipermail/inquiry/2004-November/001790.html
| |
| − | 09.5. http://stderr.org/pipermail/inquiry/2004-November/001791.html
| |
| − | 09.6. http://stderr.org/pipermail/inquiry/2004-November/001792.html
| |
| − | 09.7. http://stderr.org/pipermail/inquiry/2004-November/001793.html
| |
| − | 10.01. http://stderr.org/pipermail/inquiry/2004-November/001795.html
| |
| − | 10.02. http://stderr.org/pipermail/inquiry/2004-November/001796.html
| |
| − | 10.03. http://stderr.org/pipermail/inquiry/2004-November/001797.html
| |
| − | 10.04. http://stderr.org/pipermail/inquiry/2004-November/001798.html
| |
| − | 10.05. http://stderr.org/pipermail/inquiry/2004-November/001799.html
| |
| − | 10.06. http://stderr.org/pipermail/inquiry/2004-November/001800.html
| |
| − | 10.07. http://stderr.org/pipermail/inquiry/2004-November/001801.html
| |
| − | 10.08. http://stderr.org/pipermail/inquiry/2004-November/001802.html
| |
| − | 10.09. http://stderr.org/pipermail/inquiry/2004-November/001803.html
| |
| − | 10.10. http://stderr.org/pipermail/inquiry/2004-November/001804.html
| |
| − | 10.11. http://stderr.org/pipermail/inquiry/2004-November/001805.html
| |
| − | 11.01. http://stderr.org/pipermail/inquiry/2004-November/001813.html
| |
| − | 11.02. http://stderr.org/pipermail/inquiry/2004-November/001814.html
| |
| − | 11.03. http://stderr.org/pipermail/inquiry/2004-November/001815.html
| |
| − | 11.04. http://stderr.org/pipermail/inquiry/2004-November/001816.html
| |
| − | 11.05. http://stderr.org/pipermail/inquiry/2004-November/001817.html
| |
| − | 11.06. http://stderr.org/pipermail/inquiry/2004-November/001818.html
| |
| − | 11.07. http://stderr.org/pipermail/inquiry/2004-November/001819.html
| |
| − | 11.08. http://stderr.org/pipermail/inquiry/2004-November/001820.html
| |
| − | 11.09. http://stderr.org/pipermail/inquiry/2004-November/001821.html
| |
| − | 11.10. http://stderr.org/pipermail/inquiry/2004-November/001822.html
| |
| − | 11.11. http://stderr.org/pipermail/inquiry/2004-November/001823.html
| |
| − | 11.12. http://stderr.org/pipermail/inquiry/2004-November/001824.html
| |
| − | 11.13. http://stderr.org/pipermail/inquiry/2004-November/001825.html
| |
| − | 11.14. http://stderr.org/pipermail/inquiry/2004-November/001826.html
| |
| − | 11.15. http://stderr.org/pipermail/inquiry/2004-November/001827.html
| |
| − | 11.16. http://stderr.org/pipermail/inquiry/2004-November/001828.html
| |
| − | 11.17. http://stderr.org/pipermail/inquiry/2004-November/001829.html
| |
| − | 11.18. http://stderr.org/pipermail/inquiry/2004-November/001830.html
| |
| − | 11.19. http://stderr.org/pipermail/inquiry/2004-November/001831.html
| |
| − | 11.20. http://stderr.org/pipermail/inquiry/2004-November/001832.html
| |
| − | 11.21. http://stderr.org/pipermail/inquiry/2004-November/001833.html
| |
| − | 11.22. http://stderr.org/pipermail/inquiry/2004-November/001834.html
| |
| − | 11.23. http://stderr.org/pipermail/inquiry/2004-November/001835.html
| |
| − | 11.24. http://stderr.org/pipermail/inquiry/2004-November/001836.html
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| − | 12. http://stderr.org/pipermail/inquiry/2004-November/001843.html
| |
| − | </pre>
| |
| − |
| |
| − | ==Logic Of Relatives : Discussion==
| |
| − |
| |
| − | <pre>
| |
| − | 00. http://suo.ieee.org/ontology/thrd20.html#04460
| |
| − | 00. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1768
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| − | 00. http://stderr.org/pipermail/inquiry/2005-January/thread.html#2301
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| − |
| |
| − | 10. http://suo.ieee.org/ontology/msg04460.html
| |
| − | 11. http://suo.ieee.org/ontology/msg04461.html
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| − | 12. http://suo.ieee.org/ontology/msg04471.html
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| − | 13. http://suo.ieee.org/ontology/msg04472.html
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| − | 14. http://suo.ieee.org/ontology/msg04475.html
| |
| − | 15. http://suo.ieee.org/ontology/msg04476.html
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| − | 16. http://suo.ieee.org/ontology/msg04477.html
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| − | 17. http://suo.ieee.org/ontology/msg04479.html
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| − | 18. http://suo.ieee.org/ontology/msg04480.html
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| − | 19. http://suo.ieee.org/ontology/msg04481.html
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| − | 20. http://suo.ieee.org/ontology/msg04482.html
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| − | 21. http://suo.ieee.org/ontology/msg04483.html
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| − | 22. http://suo.ieee.org/ontology/msg04485.html
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| − | 23. http://suo.ieee.org/ontology/msg04486.html
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| − | 24. http://suo.ieee.org/ontology/msg04493.html
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| − | 25. http://suo.ieee.org/ontology/msg04494.html
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| − | 26. http://suo.ieee.org/ontology/msg04495.html
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| − | 27. http://suo.ieee.org/ontology/msg04496.html
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| − | 28. http://stderr.org/pipermail/inquiry/2004-November/001768.html
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| − | 29. http://stderr.org/pipermail/inquiry/2004-November/001838.html
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| − | 30. http://stderr.org/pipermail/inquiry/2004-November/001840.html
| |
| − | 31. http://stderr.org/pipermail/inquiry/2005-January/002301.html
| |
| | </pre> | | </pre> |