Line 636: |
Line 636: |
| ===DIEP. Note 20=== | | ===DIEP. Note 20=== |
| | | |
− | CP 2.418 | + | * CP 2.418 |
| | | |
− | ===DIEP. Work Area=== | + | ==DIEP. De In Esse Predication • Discussion== |
| + | |
| + | ===DIEP. Discussion Note 1=== |
| | | |
| <pre> | | <pre> |
− | 01. 1880, CP 4.12
| |
− | 02. 1880, CP 4.13
| |
− | 03. 1880, CP 4.14
| |
| | | |
− | 04. 1896, CP 3.440
| + | Re: CP 3.441 |
− | 05. 1896, CP 3.441
| + | |
− | 06. 1896, CP 3.442
| + | GR: given that two paragraphs later, Peirce writes: |
− | 07. 1896, CP 3.443
| |
− | 08. 1896, CP 3.444-445
| |
− | 09. 1885, CP 3.374
| |
| | | |
− | 10. 1902, CP 2.323
| + | | if the Devil were elected president of the United States, it would prove |
− | 11. 1895, CP 2.356
| + | | highly conducive to the spiritual welfare of the people (because he will |
| + | | not be elected), yet both Professor Schröder and I prefer to build the |
| + | | algebra of relatives upon this conception of the conditional proposition. |
| | | |
− | 12. 1903, CP 4.517
| + | GR: and given the bizarre situation that the devil HAS been |
| + | elected President of the United States, what does this |
| + | say about Peirce's or Schroder's logic, especially in |
| + | its esthetical and ethical presuppositions? |
| | | |
− | 13. 1903, CP 3.606-608
| + | JA: he means that if the name on the ballot were "The Devil", |
− | 14. 1897, CP 3.526
| + | the people would not thus knowingly elect him. of course, |
− | 15. 1897, CP 3.527
| + | putting his real name on the ballot would be the last thing |
− | 16. 1897, CP 3.527
| + | that the Devil would do. |
− | 17. ????, CP 2.361
| |
− | 18. 1908, CP 3.527 note
| |
− | 19. 1867, 1.559
| |
− | 20.
| |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | JA: but hey, don't read ahead, |
| + | it'll spoil the surprise. |
| | | |
− | 1.559 x
| + | GR: Most interesting interpretation. |
| | | |
− | 2.323 x
| + | GR: Yes, I certainly try not to "spoil the surprise". |
− | 2.347-349
| |
− | 2.356 x
| |
− | 2.361 x
| |
− | 2.382
| |
− | 2.394
| |
− | 2.407-409
| |
− | 2.418
| |
− | 2.546
| |
| | | |
− | 2.
| + | JA: of course, none of this applies in california ... |
− | 323
| |
− | 348
| |
− | 349
| |
− | 546
| |
| | | |
− | 2.
| + | JA: With that last bit (CP 3.442) on the "state of information" (SOI) |
− | 231
| + | in the mix, I guess that I can now follow-up without letting any |
− | 250
| + | more categories out of the bag -- there are only three after all -- |
− | 260
| + | Peirce's simplex faith in the democratic process is conditioned, |
− | 293
| + | simplexly or otherwise, on the evidently inessential contingency |
− | 364
| + | of a "liberally informed electorate" (LIE). |
− | 409
| |
− | 416
| |
− | 418
| |
− | 418n
| |
| | | |
− | 3.374 x
| + | </pre> |
− | 3.375
| |
− | 3.382
| |
− | 3.384 Peirce's Law
| |
− | 3.440-445 x
| |
− | 3.446-448
| |
− | 3.526-527 x
| |
− | 3.606-608 x
| |
| | | |
− | 4.12-14 x
| + | ===DIEP. Discussion Note 2=== |
− | 4.21
| |
− | 4.49
| |
− | 4.372-376
| |
− | 4.401
| |
− | 4.454
| |
− | 4.514-523
| |
− | 4.517 x
| |
− | 4.520
| |
− | 4.564
| |
| | | |
− | 6.450
| + | <pre> |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | CSP = C.S. Peirce |
| + | JA = Jon Awbrey |
| + | BM = Bernard Morand |
| | | |
− | DIEP. Discussion Note 1
| + | CSP: | [A Boolian Algebra With One Constant] (cont.) |
| + | | |
| + | | To express the proposition: "If S then P", |
| + | | first write: |
| + | | |
| + | | A |
| + | | |
| + | | for this proposition. But the proposition |
| + | | is that a certain conceivable state of things |
| + | | is absent from the universe of possibility. |
| + | | Hence instead of A we write: |
| + | | |
| + | | B B |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | BM: All was going right till there for me. |
| | | |
− | Re: CP 3.441
| + | CSP: | Then B expresses the possibility of S being true and P false. |
| | | |
− | GR: given that two paragraphs later, Peirce writes:
| + | BM: Now, I am stopped. May be there is an intermediary |
| + | implicit proposition that I am not seeing? If yes |
| + | which one? This could be of interest to Gary too: |
| + | I guess that for the whole passage the elements |
| + | of the demonstration count more than the |
| + | conclusion in itself. |
| | | |
− | | if the Devil were elected president of the United States, it would prove
| + | CSP: | Since, therefore, SS denies S, it follows |
− | | highly conducive to the spiritual welfare of the people (because he will
| + | | that (SS, P) expresses B. Hence we write: |
− | | not be elected), yet both Professor Schröder and I prefer to build the
| + | | |
− | | algebra of relatives upon this conception of the conditional proposition.
| + | | SS, P; SS, P. |
| + | | |
| + | | C.S. Peirce, CP 4.14, untitled paper circa 1880. |
| | | |
− | GR: and given the bizarre situation that the devil HAS been
| + | Peirce is working analytically here -- I mean that in the good sense of the word -- |
− | elected President of the United States, what does this
| + | in the manner that Bentham calls "paraphrasis", Boole "development", or most math |
− | say about Peirce's or Schroder's logic, especially in
| + | folks "expansion", if I remember right. But he already knows the answer he wants, |
− | its esthetical and ethical presuppositions?
| + | so the whole analysis will have that "pulling a rabbit out of the hat" quality of |
| + | such performances. |
| | | |
− | JA: he means that if the name on the ballot were "The Devil",
| + | The basic operation is unmarked, or you could think of the blank space as a symbol |
− | the people would not thus knowingly elect him. of course,
| + | for the logical operation of "joint denial", that Peirce counted as one of the two |
− | putting his real name on the ballot would be the last thing
| + | possible "amphecks" (cutting both ways), Sheffer called a "stroke", and comp sci |
− | that the Devil would do.
| + | folk call NNOR (neither nor). The punctuation marks are not really operators, |
| + | they just group terms, much like the "puncts" or "dots" of Peano that Russell |
| + | so butchered to the point of unintelligibility, like so much else. |
| | | |
− | JA: but hey, don't read ahead,
| + | In saying "S => P" one is saying "that a certain conceivable state of things |
− | it'll spoil the surprise.
| + | is absent from the universe of possibility" -- sounds awfully "intensional", |
| + | does it not? -- but anyway, the conceivable states of things that one is |
| + | excluding from the universe of possibility are any states of things that |
| + | would form a counterexample to "S => P", namely, those states of things |
| + | that are described by "S and not P". |
| | | |
− | GR: Most interesting interpretation.
| + | That denial would take the form: |
| | | |
− | GR: Yes, I certainly try not to "spoil the surprise".
| + | S and not P. S and not P. |
| | | |
− | JA: of course, none of this applies in california ...
| + | Let's call that the Lady Macbeth denial. |
| | | |
− | JA: With that last bit (CP 3.442) on the "state of information" (SOI)
| + | It remains to analyze the metalanguage phrase "S and not P" |
− | in the mix, I guess that I can now follow-up without letting any
| + | using only "S", "P", and the tacit joint denial connective. |
− | more categories out of the bag -- there are only three after all --
| |
− | Peirce's simplex faith in the democratic process is conditioned,
| |
− | simplexly or otherwise, on the evidently inessential contingency
| |
− | of a "liberally informed electorate" (LIE).
| |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | If I wrote "S P", this would be saying "not S and not P", |
| + | so all I need to do is change the sign on the S part of it, |
| + | which I can do by doubling the S. As we have stipulated, |
| + | doubling is a way of putting things in doubt. Therefore, |
| + | "SS, P" says "S and not P", which is the thing we want |
| + | to deny, and which final denial we can make by writing: |
| | | |
− | DIEP. Discussion Note 2
| + | SS, P; SS, P. |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | Voila! |
| | | |
− | CSP = C.S. Peirce
| + | </pre> |
− | JA = Jon Awbrey
| |
− | BM = Bernard Morand
| |
| | | |
− | CSP: | [A Boolian Algebra With One Constant] (cont.)
| + | ===DIEP. Discussion Note 3=== |
− | |
| |
− | | To express the proposition: "If S then P",
| |
− | | first write:
| |
− | |
| |
− | | A
| |
− | |
| |
− | | for this proposition. But the proposition
| |
− | | is that a certain conceivable state of things
| |
− | | is absent from the universe of possibility.
| |
− | | Hence instead of A we write:
| |
− | |
| |
− | | B B
| |
| | | |
− | BM: All was going right till there for me.
| + | <pre> |
| | | |
− | CSP: | Then B expresses the possibility of S being true and P false.
| + | JA = Jon Awbrey |
| + | TJ = Tom Johnson |
| | | |
− | BM: Now, I am stopped. May be there is an intermediary
| + | Re: CP 4.517 |
− | implicit proposition that I am not seeing? If yes
| |
− | which one? This could be of interest to Gary too:
| |
− | I guess that for the whole passage the elements
| |
− | of the demonstration count more than the
| |
− | conclusion in itself.
| |
| | | |
− | CSP: | Since, therefore, SS denies S, it follows
| + | This started out as an attempt to track down a 30 year old memory, |
− | | that (SS, P) expresses B. Hence we write:
| + | having to do with the phrase "predication (de?) inesse", which |
− | |
| + | I thought I saw first in Peirce, supposed that he got from |
− | | SS, P; SS, P.
| + | Leibniz (who I also read a lot of in those days), and had |
− | |
| + | a "clear and distinct" idea (the worst kind) that it was |
− | | C.S. Peirce, CP 4.14, untitled paper circa 1880.
| + | an "intensional" account of predication. I used to have |
− | | + | access to the microfilm manuscripts of Peirce's nachlass |
− | Peirce is working analytically here -- I mean that in the good sense of the word --
| + | at that time, and if it's there I probably won't get back |
− | in the manner that Bentham calls "paraphrasis", Boole "development", or most math
| + | to it. From what I have uncovered this time around, I seem |
− | folks "expansion", if I remember right. But he already knows the answer he wants,
| + | to be correct about the significance that Leibniz attached to |
− | so the whole analysis will have that "pulling a rabbit out of the hat" quality of
| |
− | such performances.
| |
− | | |
− | The basic operation is unmarked, or you could think of the blank space as a symbol
| |
− | for the logical operation of "joint denial", that Peirce counted as one of the two
| |
− | possible "amphecks" (cutting both ways), Sheffer called a "stroke", and comp sci
| |
− | folk call NNOR (neither nor). The punctuation marks are not really operators,
| |
− | they just group terms, much like the "puncts" or "dots" of Peano that Russell
| |
− | so butchered to the point of unintelligibility, like so much else.
| |
− | | |
− | In saying "S => P" one is saying "that a certain conceivable state of things
| |
− | is absent from the universe of possibility" -- sounds awfully "intensional",
| |
− | does it not? -- but anyway, the conceivable states of things that one is
| |
− | excluding from the universe of possibility are any states of things that
| |
− | would form a counterexample to "S => P", namely, those states of things
| |
− | that are described by "S and not P".
| |
− | | |
− | That denial would take the form:
| |
− | | |
− | S and not P. S and not P.
| |
− | | |
− | Let's call that the Lady Macbeth denial.
| |
− | | |
− | It remains to analyze the metalanguage phrase "S and not P"
| |
− | using only "S", "P", and the tacit joint denial connective.
| |
− | | |
− | If I wrote "S P", this would be saying "not S and not P",
| |
− | so all I need to do is change the sign on the S part of it,
| |
− | which I can do by doubling the S. As we have stipulated,
| |
− | doubling is a way of putting things in doubt. Therefore,
| |
− | "SS, P" says "S and not P", which is the thing we want
| |
− | to deny, and which final denial we can make by writing:
| |
− | | |
− | SS, P; SS, P.
| |
− | | |
− | Voila!
| |
− | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
− | | |
− | DIEP. Discussion Note 3
| |
− | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
− | | |
− | JA = Jon Awbrey
| |
− | TJ = Tom Johnson
| |
− | | |
− | Re: CP 4.517
| |
− | | |
− | This started out as an attempt to track down a 30 year old memory, | |
− | having to do with the phrase "predication (de?) inesse", which | |
− | I thought I saw first in Peirce, supposed that he got from | |
− | Leibniz (who I also read a lot of in those days), and had | |
− | a "clear and distinct" idea (the worst kind) that it was | |
− | an "intensional" account of predication. I used to have | |
− | access to the microfilm manuscripts of Peirce's nachlass | |
− | at that time, and if it's there I probably won't get back | |
− | to it. From what I have uncovered this time around, I seem | |
− | to be correct about the significance that Leibniz attached to | |
| the phrase -- will have to check again -- but all I find so far | | the phrase -- will have to check again -- but all I find so far |
| in the CP is 'conditio/consequentia simplex de inesse' that Peirce | | in the CP is 'conditio/consequentia simplex de inesse' that Peirce |
Line 895: |
Line 814: |
| discover the quantum of truth in the sign "physical causality". | | discover the quantum of truth in the sign "physical causality". |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | </pre> |
| | | |
− | DIEP. Discussion Note 4 | + | ===DIEP. Discussion Note 4=== |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | <pre> |
| | | |
| JA = Jon Awbrey | | JA = Jon Awbrey |
Line 1,014: |
Line 933: |
| http://members.door.net/arisbe/menu/library/bycsp/fixation/fx-frame.htm | | http://members.door.net/arisbe/menu/library/bycsp/fixation/fx-frame.htm |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | </pre> |
| | | |
− | DIEP. Discussion Note 5 | + | ===DIEP. Discussion Note 5=== |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | <pre> |
| | | |
| GR = Gary Richmond | | GR = Gary Richmond |
Line 1,084: |
Line 1,003: |
| That's all I can remember at the moment ... | | That's all I can remember at the moment ... |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | </pre> |
| | | |
− | DIEP. Discussion Note 6 | + | ===DIEP. Discussion Note 6=== |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | <pre> |
| | | |
| JA = Jon Awbrey | | JA = Jon Awbrey |
Line 1,244: |
Line 1,163: |
| I will pick up from there next time. | | I will pick up from there next time. |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | </pre> |
| | | |
− | DIEP. Discussion Note 7 | + | ===DIEP. Discussion Note 7=== |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | <pre> |
| | | |
| BM = Bernard Morand | | BM = Bernard Morand |
Line 1,360: |
Line 1,279: |
| http://www.louvre.fr/img/photos/collec/ager/grande/ma0399.jpg | | http://www.louvre.fr/img/photos/collec/ager/grande/ma0399.jpg |
| | | |
− | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| </pre> | | </pre> |
| | | |
− | ==HAPA. Hypostatic And Prescisive Abstraction== | + | ==DIEP. De In Esse Predication • Work Area== |
− | | |
− | ===HAPA. Note 1===
| |
| | | |
| <pre> | | <pre> |
− | | When we have analyzed a proposition so as to throw into the subject everything
| |
− | | that can be removed from the predicate, all that it remains for the predicate to
| |
− | | represent is the form of connection between the different subjects as expressed in
| |
− | | the propositional 'form'. What I mean by "everything that can be removed from the
| |
− | | predicate" is best explained by giving an example of something not so removable.
| |
− | | But first take something removable. "Cain kills Abel." Here the predicate
| |
− | | appears as "--- kills ---." But we can remove killing from the predicate
| |
− | | and make the latter "--- stands in the relation --- to ---." Suppose we
| |
− | | attempt to remove more from the predicate and put the last into the form
| |
− | | "--- exercises the function of relate of the relation --- to ---" and then
| |
− | | putting "the function of relate to the relation" into a another subject leave
| |
− | | as predicate "--- exercises --- in respect to --- to ---." But this "exercises"
| |
− | | expresses "exercises the function". Nay more, it expresses "exercises the function
| |
− | | of relate", so that we find that though we may put this into a separate subject, it
| |
− | | continues in the predicate just the same. Stating this in another form, to say that
| |
− | | "A is in the relation R to B" is to say that A is in a certain relation to R. Let
| |
− | | us separate this out thus: "A is in the relation R^1 (where R^1 is the relation
| |
− | | of a relate to the relation of which it is the relate) to R to B". But A is
| |
− | | here said to be in a certain relation to the relation R^1. So that we can
| |
− | | expresss the same fact by saying, "A is in the relation R^1 to the relation
| |
− | | R^1 to the relation R to B", and so on 'ad infinitum'. A predicate which
| |
− | | can thus be analyzed into parts all homogeneous with the whole I call
| |
− | | a 'continuous predicate'. It is very important in logical analysis,
| |
− | | because a continuous predicate obviously cannot be a 'compound'
| |
− | | except of continuous predicates, and thus when we have carried
| |
− | | analysis so far as to leave only a continuous predicate, we
| |
− | | have carried it to its ultimate elements.
| |
− | |
| |
− | | Peirce, "Letters to Lady Welby", 14 Dec 1908, 'Selected Writings', pp. 396-397.
| |
− | |
| |
− | | Charles S. Peirce, "Letters to Lady Welby", pp. 380-432 in:
| |
− | |'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.
| |
− | </pre>
| |
| | | |
− | ===HAPA. Note 2===
| + | 01. 1880, CP 4.12 |
| + | 02. 1880, CP 4.13 |
| + | 03. 1880, CP 4.14 |
| | | |
− | <pre>
| + | 04. 1896, CP 3.440 |
− | | Another characteristic of mathematical thought is the extraordinary
| + | 05. 1896, CP 3.441 |
− | | use it makes of abstractions. Abstractions have been a favorite
| + | 06. 1896, CP 3.442 |
− | | butt of ridicule in modern times. Now it is very easy to laugh
| + | 07. 1896, CP 3.443 |
− | | at the old physician who is represented as answering the question,
| + | 08. 1896, CP 3.444-445 |
− | | why opium puts people to sleep, by saying that it is because it
| + | 09. 1885, CP 3.374 |
− | | has a dormative virtue. It is an answer that no doubt carries
| + | |
− | | vagueness to its last extreme. Yet, invented as the story was
| + | 10. 1902, CP 2.323 |
− | | to show how little meaning there might be in an abstraction,
| + | 11. 1895, CP 2.356 |
− | | nevertheless the physician's answer does contain a truth
| + | |
− | | that modern philosophy has generally denied: it does
| + | 12. 1903, CP 4.517 |
− | | assert that there really is in opium 'something' which
| |
− | | explains its always putting people to sleep. This has,
| |
− | | I say, been denied by modern philosophers generally.
| |
− | | Not, of course, explicitly; but when they say that
| |
− | | the different events of people going to sleep after
| |
− | | taking opium have really nothing in common, but
| |
− | | only that the mind classes them together -- and
| |
− | | this is what they virtually do say in denying
| |
− | | the reality of generals -- they do implicitly
| |
− | | deny that there is any true explanation of
| |
− | | opium's generally putting people to sleep.
| |
− | |
| |
− | | C.S. Peirce, CP 4.234, "The Simplest Mathematics",
| |
− | | Chapter 3 of the "Minute Logic", Jan-Feb 1902.
| |
− | </pre>
| |
| | | |
− | ===HAPA. Note 3===
| + | 13. 1903, CP 3.606-608 |
| + | 14. 1897, CP 3.526 |
| + | 15. 1897, CP 3.527 |
| + | 16. 1897, CP 3.527 |
| + | 17. ????, CP 2.361 |
| + | 18. 1908, CP 3.527 note |
| + | 19. 1867, 1.559 |
| + | 20. |
| | | |
− | <pre>
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
− | | Look through the modern logical treatises, and you will find that they
| + | |
− | | almost all fall into one or other of two errors, as I hold them to be;
| + | 1.559 x |
− | | that of setting aside the doctrine of abstraction (in the sense in
| |
− | | which an abstract noun marks an abstraction) as a grammatical topic
| |
− | | with which the logician need not particularly concern himself; and
| |
− | | that of confounding abstraction, in this sense, with that operation
| |
− | | of the mind by which we pay attention to one feature of a percept to
| |
− | | the disregard of others. The two things are entirely disconnected.
| |
− | |
| |
− | | The most ordinary fact of perception, such as "it is light", involves
| |
− | | 'precisive' abstraction, or 'prescission'. But 'hypostatic' abstraction,
| |
− | | the abstraction which transforms "it is light" into "there is light here",
| |
− | | which is the sense which I shall commonly attach to the word abstraction
| |
− | | (since 'prescission' will do for precisive abstraction) is a very special
| |
− | | mode of thought. It consists in taking a feature of a percept or percepts
| |
− | | (after it has already been prescinded from the other elements of the percept),
| |
− | | so as to take propositional form in a judgment (indeed, it may operate upon
| |
− | | any judgment whatsoever), and in conceiving this fact to consist in the
| |
− | | relation between the subject of that judgment and another subject, which
| |
− | | has a mode of being that merely consists in the truth of propositions of
| |
− | | which the corresponding concrete term is the predicate.
| |
− | |
| |
− | | Thus, we transform the proposition, "honey is sweet",
| |
− | | into "honey possesses sweetness". "Sweetness" might be
| |
− | | called a fictitious thing, in one sense. But since the
| |
− | | mode of being attributed to it 'consists' in no more than
| |
− | | the fact that some things are sweet, and it is not pretended,
| |
− | | or imagined, that it has any other mode of being, there is,
| |
− | | after all, no fiction. The only profession made is that we
| |
− | | consider the fact of honey being sweet under the form of a
| |
− | | relation; and so we really can. I have selected sweetness
| |
− | | as an instance of one of the least useful of abstractions.
| |
− | | Yet even this is convenient. It facilitates such thoughts
| |
− | | as that the sweetness of honey is particularly cloying;
| |
− | | that the sweetness of honey is something like the
| |
− | | sweetness of a honeymoon; etc.
| |
− | |
| |
− | | C.S. Peirce, CP 4.235, "The Simplest Mathematics",
| |
− | | Chapter 3 of the "Minute Logic", Jan-Feb 1902.
| |
− | </pre>
| |
| | | |
− | ===HAPA. Note 4===
| + | 2.323 x |
| + | 2.347-349 |
| + | 2.356 x |
| + | 2.361 x |
| + | 2.382 |
| + | 2.394 |
| + | 2.407-409 |
| + | 2.418 |
| + | 2.546 |
| | | |
− | <pre>
| + | 2. |
− | | Abstractions are particularly congenial to mathematics. Everyday life
| + | 323 |
− | | first, for example, found the need of that class of abstractions which
| + | 348 |
− | | we call 'collections'. Instead of saying that some human beings are
| + | 349 |
− | | males and all the rest females, it was found convenient to say that
| + | 546 |
− | | 'mankind' consists of the male 'part' and the female 'part'. The
| |
− | | same thought makes classes of collections, such as pairs, leashes,
| |
− | | quatrains, hands, weeks, dozens, baker's dozens, sonnets, scores,
| |
− | | quires, hundreds, long hundreds, gross, reams, thousands, myriads,
| |
− | | lacs, millions, milliards, milliasses, etc. These have suggested
| |
− | | a great branch of mathematics.*
| |
− | |
| |
− | | Again, a point moves: it is by abstraction that the geometer says that
| |
− | | it "describes a line". This line, though an abstraction, itself moves;
| |
− | | and this is regarded as generating a surface; and so on.
| |
− | |
| |
− | | So likewise, when the analyst treats operations as themselves subjects of
| |
− | | operations, a method whose utility will not be denied, this is another
| |
− | | instance of abstraction. Maxwell's notion of a tension exercised upon
| |
− | | lines of electrical force, transverse to them, is somewhat similar.
| |
− | |
| |
− | | These examples exhibit the great rolling billows of abstraction in the ocean
| |
− | | of mathematical thought; but when we come to a minute examination of it,
| |
− | | we shall find, in every department, incessant ripples of the same form
| |
− | | of thought, of which the examples I have mentioned give no hint.
| |
− | |
| |
− | |* Of course, the moment a collection is recognized as an abstraction we have
| |
− | | to admit that even a percept is an abstraction or represents an abstraction,
| |
− | | if matter has parts. It therefore becomes difficult to maintain that all
| |
− | | abstractions are fictions.
| |
− | |
| |
− | | C.S. Peirce, CP 4.235, "The Simplest Mathematics",
| |
− | | Chapter 3 of the "Minute Logic", Jan-Feb 1902.
| |
− | </pre>
| |
| | | |
− | ===HAPA. Note 5===
| + | 2. |
| + | 231 |
| + | 250 |
| + | 260 |
| + | 293 |
| + | 364 |
| + | 409 |
| + | 416 |
| + | 418 |
| + | 418n |
| | | |
− | <pre>
| + | 3.374 x |
− | | Hypostasis. Literally the Greek word signifies that which stands under
| + | 3.375 |
− | | and serves as a support. In philosophy it means a singular substance,
| + | 3.382 |
− | | also called a supposite, 'suppositum', by the Scholastics, especially
| + | 3.384 Peirce's Law |
− | | if the substance is a completely subsisting one, whether non-living
| + | 3.440-445 x |
− | | or living, irrational or rational. However, a rational hypostasis
| + | 3.446-448 |
− | | has the same meaning as the term, 'person'.
| + | 3.526-527 x |
− | |
| + | 3.606-608 x |
− | | J.J.R. [= J.J. Rolbiecki] in:
| |
− | |
| |
− | | Dagobert D. Runes (ed.), 'Dictionary of Philosophy',
| |
− | | Littlefield, Adams, & Company, Totowa, NJ, 1972.
| |
− | </pre>
| |
| | | |
− | ===HAPA. Note 6===
| + | 4.12-14 x |
| + | 4.21 |
| + | 4.49 |
| + | 4.372-376 |
| + | 4.401 |
| + | 4.454 |
| + | 4.514-523 |
| + | 4.517 x |
| + | 4.520 |
| + | 4.564 |
| + | |
| + | 6.450 |
| | | |
− | <pre>
| |
− | | But the highest kind of synthesis is what the mind is compelled to make neither
| |
− | | by the inward attractions of the feelings or representations themselves, nor by
| |
− | | a transcendental force of necessity, but in the interest of intelligibility,
| |
− | | that is, in the interest of the synthesizing "I think" itself; and this
| |
− | | it does by introducing an idea not contained in the data, which gives
| |
− | | connections which they would not otherwise have had. This kind of
| |
− | | synthesis has not been sufficiently studied, and especially the
| |
− | | intimate relationship of its different varieties has not been
| |
− | | duly considered. The work of the poet or novelist is not so
| |
− | | utterly different from that of the scientific man. The artist
| |
− | | introduces a fiction; but it is not an arbitrary one; it exhibits
| |
− | | affinities to which the mind accords a certain approval in pronouncing
| |
− | | them beautiful, which if it is not exactly the same as saying that the
| |
− | | synthesis is true, is something of the same general kind. The geometer
| |
− | | draws a diagram, which if not exactly a fiction, is at least a creation,
| |
− | | and by means of observation of that diagram he is able to synthesize and
| |
− | | show relations between elements which before seemed to have no necessary
| |
− | | connection. The realities compel us to put some things into very close
| |
− | | relation and others less so, in a highly complicated, and in the [true?]
| |
− | | sense itself unintelligible manner; but it is the genius of the mind,
| |
− | | that takes up all these hints of sense, adds immensely to them, makes
| |
− | | them precise, and shows them in intelligible form in the intuitions
| |
− | | of space and time. Intuition is the regarding of the abstract in
| |
− | | a concrete form, by the realistic hypostatization of relations;
| |
− | | that is the one sole method of valuable thought. Very shallow
| |
− | | is the prevalent notion that this is something to be avoided.
| |
− | | You might as well say at once that reasoning is to be avoided
| |
− | | because it has led to so much error; quite in the same philistine
| |
− | | line of thought would that be; and so well in accord with the spirit
| |
− | | of nominalism that I wonder some one does not put it forward. The true
| |
− | | precept is not to abstain from hypostatization, but to do it intelligently ...
| |
− | |
| |
− | | C.S. Peirce, CP 1.383, "A Guess at the Riddle",
| |
− | | circa 1890, 'Collected Papers', CP 1.354-416.
| |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Note 7=== | + | ==HAPA. Hypostatic And Prescisive Abstraction== |
| + | |
| + | ===HAPA. Note 1=== |
| | | |
| <pre> | | <pre> |
− | | Exceedingly important are the relatives signifying "-- is a quality of --" | + | | When we have analyzed a proposition so as to throw into the subject everything |
− | | and "-- is a relation of -- to --". It may be said that mathematical | + | | that can be removed from the predicate, all that it remains for the predicate to |
− | | reasoning (which is the only deductive reasoning, if not absolutely, | + | | represent is the form of connection between the different subjects as expressed in |
− | | at least eminently) almost entirely turns on the consideration of | + | | the propositional 'form'. What I mean by "everything that can be removed from the |
− | | abstractions as if they were objects. The protest of nominalism | + | | predicate" is best explained by giving an example of something not so removable. |
− | | against such hypostatisation, although, if it knew how to formulate | + | | But first take something removable. "Cain kills Abel." Here the predicate |
− | | itself, it would be justified as against much of the empty disputation | + | | appears as "--- kills ---." But we can remove killing from the predicate |
− | | of the medieval Dunces, yet, as it was and is formulated, is simply a | + | | and make the latter "--- stands in the relation --- to ---." Suppose we |
− | | protest against the only kind of thinking that has ever advanced human | + | | attempt to remove more from the predicate and put the last into the form |
− | | culture. Nobody will work long with the logic of relatives -- unless | + | | "--- exercises the function of relate of the relation --- to ---" and then |
− | | he restricts the problems of his studies very much -- without seeing | + | | putting "the function of relate to the relation" into a another subject leave |
− | | that this is true. | + | | as predicate "--- exercises --- in respect to --- to ---." But this "exercises" |
| + | | expresses "exercises the function". Nay more, it expresses "exercises the function |
| + | | of relate", so that we find that though we may put this into a separate subject, it |
| + | | continues in the predicate just the same. Stating this in another form, to say that |
| + | | "A is in the relation R to B" is to say that A is in a certain relation to R. Let |
| + | | us separate this out thus: "A is in the relation R^1 (where R^1 is the relation |
| + | | of a relate to the relation of which it is the relate) to R to B". But A is |
| + | | here said to be in a certain relation to the relation R^1. So that we can |
| + | | expresss the same fact by saying, "A is in the relation R^1 to the relation |
| + | | R^1 to the relation R to B", and so on 'ad infinitum'. A predicate which |
| + | | can thus be analyzed into parts all homogeneous with the whole I call |
| + | | a 'continuous predicate'. It is very important in logical analysis, |
| + | | because a continuous predicate obviously cannot be a 'compound' |
| + | | except of continuous predicates, and thus when we have carried |
| + | | analysis so far as to leave only a continuous predicate, we |
| + | | have carried it to its ultimate elements. |
| + | | |
| + | | Peirce, "Letters to Lady Welby", 14 Dec 1908, 'Selected Writings', pp. 396-397. |
| | | | | |
− | | C.S. Peirce, CP 3.509, "The Logic of Relatives", | + | | Charles S. Peirce, "Letters to Lady Welby", pp. 380-432 in: |
− | |'The Monist', vol. 7, pp. 161-217, 1897. | + | |'Charles S. Peirce: Selected Writings (Values in a Universe |
− | |'Collected Papers', CP 3.456-552.
| + | | of Chance)', Edited with an Introduction and Notes by |
| + | | Philip P. Wiener, Dover, New York, NY, 1966. |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Note 8=== | + | ===HAPA. Note 2=== |
| | | |
| <pre> | | <pre> |
− | | The logical term 'subjectal abstraction' here requires a | + | | Another characteristic of mathematical thought is the extraordinary |
− | | word of explanation; for there are few treatises on logic | + | | use it makes of abstractions. Abstractions have been a favorite |
− | | which notice subjectal abstraction under any name, except so | + | | butt of ridicule in modern times. Now it is very easy to laugh |
− | | far as to confuse it with precisive abstraction which is an | + | | at the old physician who is represented as answering the question, |
− | | entirely different logical function. When we say that the | + | | why opium puts people to sleep, by saying that it is because it |
− | | Columbia library building is 'large', this remark is a result | + | | has a dormative virtue. It is an answer that no doubt carries |
− | | of precisive abstraction by which the man who makes the remark | + | | vagueness to its last extreme. Yet, invented as the story was |
− | | leaves out of account all the other features of his image of | + | | to show how little meaning there might be in an abstraction, |
− | | the building, and takes the word "large" which is entirely | + | | nevertheless the physician's answer does contain a truth |
− | | unlike that image -- and when I say the word is unlike the | + | | that modern philosophy has generally denied: it does |
− | | image, I mean that the general signification of the word is | + | | assert that there really is in opium 'something' which |
− | | utterly disparate from the image, which involves no predicates | + | | explains its always putting people to sleep. This has, |
− | | at all. Such is 'precisive abstraction'. But now if this man | + | | I say, been denied by modern philosophers generally. |
− | | goes on to remark that the largeness of the building is very | + | | Not, of course, explicitly; but when they say that |
− | | impressive, he converts the applicability of that predicate | + | | the different events of people going to sleep after |
− | | from being a way of thinking about the building to being | + | | taking opium have really nothing in common, but |
− | | itself a subject of thought, and that operation is | + | | only that the mind classes them together -- and |
− | | 'subjectal abstraction'. | + | | this is what they virtually do say in denying |
| + | | the reality of generals -- they do implicitly |
| + | | deny that there is any true explanation of |
| + | | opium's generally putting people to sleep. |
| | | | | |
− | | C.S. Peirce, CP 4.332, "Ordinals", circa 1905. | + | | C.S. Peirce, CP 4.234, "The Simplest Mathematics", |
| + | | Chapter 3 of the "Minute Logic", Jan-Feb 1902. |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Note 9=== | + | ===HAPA. Note 3=== |
| | | |
| <pre> | | <pre> |
− | | Predicate. | + | | Look through the modern logical treatises, and you will find that they |
| + | | almost all fall into one or other of two errors, as I hold them to be; |
| + | | that of setting aside the doctrine of abstraction (in the sense in |
| + | | which an abstract noun marks an abstraction) as a grammatical topic |
| + | | with which the logician need not particularly concern himself; and |
| + | | that of confounding abstraction, in this sense, with that operation |
| + | | of the mind by which we pay attention to one feature of a percept to |
| + | | the disregard of others. The two things are entirely disconnected. |
| | | | | |
− | | The view which pragmatic logic takes of the predicate, in consequence of | + | | The most ordinary fact of perception, such as "it is light", involves |
− | | its assuming that the entire purpose of deductive logic is to ascertain | + | | 'precisive' abstraction, or 'prescission'. But 'hypostatic' abstraction, |
− | | the necessary conditions of the truth of signs, without any regard to | + | | the abstraction which transforms "it is light" into "there is light here", |
− | | the accidents of Indo-European grammar, will be here briefly stated. | + | | which is the sense which I shall commonly attach to the word abstraction |
− | | Cf. Negation [CP 2.378-380]. | + | | (since 'prescission' will do for precisive abstraction) is a very special |
| + | | mode of thought. It consists in taking a feature of a percept or percepts |
| + | | (after it has already been prescinded from the other elements of the percept), |
| + | | so as to take propositional form in a judgment (indeed, it may operate upon |
| + | | any judgment whatsoever), and in conceiving this fact to consist in the |
| + | | relation between the subject of that judgment and another subject, which |
| + | | has a mode of being that merely consists in the truth of propositions of |
| + | | which the corresponding concrete term is the predicate. |
| | | | | |
− | | In any proposition, i.e., any statement which must be true or false, | + | | Thus, we transform the proposition, "honey is sweet", |
− | | let some parts be struck out so that the remnant is not a proposition, | + | | into "honey possesses sweetness". "Sweetness" might be |
− | | but is such that it becomes a proposition when each blank is filled by | + | | called a fictitious thing, in one sense. But since the |
− | | a proper name. The erasures are not to be made in a mechanical way, but | + | | mode of being attributed to it 'consists' in no more than |
− | | with such modifications as may be necessary to preserve the partial sense | + | | the fact that some things are sweet, and it is not pretended, |
− | | of the fragment. Such a residue is a 'predicate'. The same proposition | + | | or imagined, that it has any other mode of being, there is, |
− | | may be mutilated in various ways so that different fragments will appear | + | | after all, no fiction. The only profession made is that we |
− | | as predicates. Thus, take the proposition "Every man reveres some woman." | + | | consider the fact of honey being sweet under the form of a |
− | | This contains the following predicates, among others: | + | | relation; and so we really can. I have selected sweetness |
| + | | as an instance of one of the least useful of abstractions. |
| + | | Yet even this is convenient. It facilitates such thoughts |
| + | | as that the sweetness of honey is particularly cloying; |
| + | | that the sweetness of honey is something like the |
| + | | sweetness of a honeymoon; etc. |
| | | | | |
− | | ". . . reveres some woman."
| + | | C.S. Peirce, CP 4.235, "The Simplest Mathematics", |
− | |
| + | | Chapter 3 of the "Minute Logic", Jan-Feb 1902. |
− | | ". . . is either not a man or reveres some woman."
| |
− | |
| |
− | | "Any previously selected man reveres . . ."
| |
− | |
| |
− | | "Any previously selected man is . . ."
| |
− | |
| |
− | | C.S. Peirce, 'Collected Papers', CP 2.358, in dictionary entry for "Predicate", | |
− | | J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 325-326. | |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Note 10=== | + | ===HAPA. Note 4=== |
| | | |
| <pre> | | <pre> |
− | | Relatives Of Second Intention | + | | Abstractions are particularly congenial to mathematics. Everyday life |
| + | | first, for example, found the need of that class of abstractions which |
| + | | we call 'collections'. Instead of saying that some human beings are |
| + | | males and all the rest females, it was found convenient to say that |
| + | | 'mankind' consists of the male 'part' and the female 'part'. The |
| + | | same thought makes classes of collections, such as pairs, leashes, |
| + | | quatrains, hands, weeks, dozens, baker's dozens, sonnets, scores, |
| + | | quires, hundreds, long hundreds, gross, reams, thousands, myriads, |
| + | | lacs, millions, milliards, milliasses, etc. These have suggested |
| + | | a great branch of mathematics.* |
| + | | |
| + | | Again, a point moves: it is by abstraction that the geometer says that |
| + | | it "describes a line". This line, though an abstraction, itself moves; |
| + | | and this is regarded as generating a surface; and so on. |
| | | | | |
− | | The general method of graphical representation of propositions has now | + | | So likewise, when the analyst treats operations as themselves subjects of |
− | | been given in all its essential elements, except, of course, that we | + | | operations, a method whose utility will not be denied, this is another |
− | | have not, as yet, studied any truths concerning special relatives; | + | | instance of abstraction. Maxwell's notion of a tension exercised upon |
− | | for to do so would seem, at first, to be "extralogical". Logic in
| + | | lines of electrical force, transverse to them, is somewhat similar. |
− | | this stage of its development may be called 'paradisaical logic', | + | | |
− | | because it represents the state of Man's cognition before the | + | | These examples exhibit the great rolling billows of abstraction in the ocean |
− | | Fall. For although, with this apparatus, it easy to write | + | | of mathematical thought; but when we come to a minute examination of it, |
− | | propositions necessarily true, it is absolutely impossible
| + | | we shall find, in every department, incessant ripples of the same form |
− | | to write any which is necessarily false, or, in any way | + | | of thought, of which the examples I have mentioned give no hint. |
− | | which that stage of logic affords, to find out that | |
− | | anything is false. The mind has not as yet eaten
| |
− | | of the fruit of the Tree of Knowledge of Truth
| |
− | | and Falsity.
| |
| | | | | |
− | | Probably it will not be doubted that every child in | + | |* Of course, the moment a collection is recognized as an abstraction we have |
− | | its mental development necessarily passes through
| + | | to admit that even a percept is an abstraction or represents an abstraction, |
− | | a stage in which he has some ideas, but yet has
| + | | if matter has parts. It therefore becomes difficult to maintain that all |
− | | never recognised that an idea may be erroneous; | + | | abstractions are fictions. |
− | | and a stage that every child necessarily passes | |
− | | through must have been formerly passed through
| |
− | | by the race in its adult development. It may
| |
− | | be doubted whether many of the lower animals
| |
− | | have any clear and steady conception of
| |
− | | falsehood; for their instincts work | |
− | | so unerringly that there is little
| |
− | | to force it upon their attention.
| |
− | | Yet plainly without a knowledge
| |
− | | of falsehood no development
| |
− | | of discursive reason can
| |
− | | take place.
| |
| | | | | |
− | | C.S. Peirce, 'Collected Papers', CP 3.488, | + | | C.S. Peirce, CP 4.235, "The Simplest Mathematics", |
− | |"The Logic of Relatives", 'Monist', vol. 7, | + | | Chapter 3 of the "Minute Logic", Jan-Feb 1902. |
− | | pp. 161-217, 1897.
| |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Note 11=== | + | ===HAPA. Note 5=== |
| | | |
| <pre> | | <pre> |
− | | Relatives Of Second Intention (cont.) | + | | Hypostasis. Literally the Greek word signifies that which stands under |
| + | | and serves as a support. In philosophy it means a singular substance, |
| + | | also called a supposite, 'suppositum', by the Scholastics, especially |
| + | | if the substance is a completely subsisting one, whether non-living |
| + | | or living, irrational or rational. However, a rational hypostasis |
| + | | has the same meaning as the term, 'person'. |
| | | | | |
− | | This paradisaical logic appears in the study of non-relative formal logic. | + | | J.J.R. [= J.J. Rolbiecki] in: |
− | | But 'there' no possible avenue appears by which the knowledge of falsehood
| |
− | | could be brought into this Garden of Eden except by the arbitrary and
| |
− | | inexplicable introduction of the Serpent in the guise of a proposition
| |
− | | necessarily false. The logic of relatives affords such an avenue,
| |
− | | and 'that', the very avenue by which in actual development,
| |
− | | this stage of logic supervenes. It is the avenue of
| |
− | | experience and logical reflexion.
| |
| | | | | |
− | | By 'logical' reflexion, I mean the observation of thoughts | + | | Dagobert D. Runes (ed.), 'Dictionary of Philosophy', |
− | | in their expressions. Aquinas remarked that this sort of | + | | Littlefield, Adams, & Company, Totowa, NJ, 1972. |
− | | reflexion is requisite to furnish us with those ideas | + | </pre> |
− | | which, from lack of contrast, ordinary external | + | |
− | | experience fails to bring into prominence. | + | ===HAPA. Note 6=== |
− | | He called such ideas 'second intentions'. | + | |
| + | <pre> |
| + | | But the highest kind of synthesis is what the mind is compelled to make neither |
| + | | by the inward attractions of the feelings or representations themselves, nor by |
| + | | a transcendental force of necessity, but in the interest of intelligibility, |
| + | | that is, in the interest of the synthesizing "I think" itself; and this |
| + | | it does by introducing an idea not contained in the data, which gives |
| + | | connections which they would not otherwise have had. This kind of |
| + | | synthesis has not been sufficiently studied, and especially the |
| + | | intimate relationship of its different varieties has not been |
| + | | duly considered. The work of the poet or novelist is not so |
| + | | utterly different from that of the scientific man. The artist |
| + | | introduces a fiction; but it is not an arbitrary one; it exhibits |
| + | | affinities to which the mind accords a certain approval in pronouncing |
| + | | them beautiful, which if it is not exactly the same as saying that the |
| + | | synthesis is true, is something of the same general kind. The geometer |
| + | | draws a diagram, which if not exactly a fiction, is at least a creation, |
| + | | and by means of observation of that diagram he is able to synthesize and |
| + | | show relations between elements which before seemed to have no necessary |
| + | | connection. The realities compel us to put some things into very close |
| + | | relation and others less so, in a highly complicated, and in the [true?] |
| + | | sense itself unintelligible manner; but it is the genius of the mind, |
| + | | that takes up all these hints of sense, adds immensely to them, makes |
| + | | them precise, and shows them in intelligible form in the intuitions |
| + | | of space and time. Intuition is the regarding of the abstract in |
| + | | a concrete form, by the realistic hypostatization of relations; |
| + | | that is the one sole method of valuable thought. Very shallow |
| + | | is the prevalent notion that this is something to be avoided. |
| + | | You might as well say at once that reasoning is to be avoided |
| + | | because it has led to so much error; quite in the same philistine |
| + | | line of thought would that be; and so well in accord with the spirit |
| + | | of nominalism that I wonder some one does not put it forward. The true |
| + | | precept is not to abstain from hypostatization, but to do it intelligently ... |
| | | | | |
− | | It is by means of 'relatives of second intention'
| + | | C.S. Peirce, CP 1.383, "A Guess at the Riddle", |
− | | that the general method of logical representation
| + | | circa 1890, 'Collected Papers', CP 1.354-416. |
− | | is to find completion.
| |
− | |
| |
− | | C.S. Peirce, 'Collected Papers', CP 3.489-490, | |
− | |"The Logic of Relatives", 'The Monist', vol. 7, | |
− | | pp. 161-217, 1897.
| |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Note 12=== | + | ===HAPA. Note 7=== |
| | | |
| <pre> | | <pre> |
− | | One branch of deductive logic, of which from the nature of | + | | Exceedingly important are the relatives signifying "-- is a quality of --" |
− | | things ordinary logic could give no satisfactory account,
| + | | and "-- is a relation of -- to --". It may be said that mathematical |
− | | relates to the vitally important matter of abstraction. | + | | reasoning (which is the only deductive reasoning, if not absolutely, |
− | | | + | | at least eminently) almost entirely turns on the consideration of |
− | | Indeed, the student of ordinary logic naturally regards abstraction, | + | | abstractions as if they were objects. The protest of nominalism |
− | | or the passage from "the rose smells sweet" to "the rose has perfume", | + | | against such hypostatisation, although, if it knew how to formulate |
− | | to be a quasi-grammatical matter, calling for little or no notice from | + | | itself, it would be justified as against much of the empty disputation |
− | | the logician. The fact is, however, that almost every great step in | + | | of the medieval Dunces, yet, as it was and is formulated, is simply a |
− | | mathematical reasoning derives its importance from the fact that it | + | | protest against the only kind of thinking that has ever advanced human |
− | | involves an abstraction.
| + | | culture. Nobody will work long with the logic of relatives -- unless |
| + | | he restricts the problems of his studies very much -- without seeing |
| + | | that this is true. |
| | | | | |
− | | For by means of abstraction, the transitory elements of thought, | + | | C.S. Peirce, CP 3.509, "The Logic of Relatives", |
− | | the 'epea pteroenta' [winged words], are made substantive elements,
| + | |'The Monist', vol. 7, pp. 161-217, 1897. |
− | | as James terms them, 'epea apteroenta' [plucked words].* It thus
| + | |'Collected Papers', CP 3.456-552. |
− | | becomes possible to study their relations and to apply to these
| + | </pre> |
− | | relations discoveries already made respecting analogous relations.
| |
− | | In this way, for example, operations become themselves the subjects
| |
− | | of operations.
| |
− | |
| |
− | |* William James, 'Principles of Psychology', vol. 1, p. 243. | |
− | | | |
− | | C.S. Peirce, 'Collected Papers', CP 3.642, in dictionary entry for "Relatives",
| |
− | | J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 447-450.
| |
| | | |
− | Incidental Musement:
| + | ===HAPA. Note 8=== |
| | | |
− | http://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Hom.+Il.+1.172
| + | <pre> |
| + | | The logical term 'subjectal abstraction' here requires a |
| + | | word of explanation; for there are few treatises on logic |
| + | | which notice subjectal abstraction under any name, except so |
| + | | far as to confuse it with precisive abstraction which is an |
| + | | entirely different logical function. When we say that the |
| + | | Columbia library building is 'large', this remark is a result |
| + | | of precisive abstraction by which the man who makes the remark |
| + | | leaves out of account all the other features of his image of |
| + | | the building, and takes the word "large" which is entirely |
| + | | unlike that image -- and when I say the word is unlike the |
| + | | image, I mean that the general signification of the word is |
| + | | utterly disparate from the image, which involves no predicates |
| + | | at all. Such is 'precisive abstraction'. But now if this man |
| + | | goes on to remark that the largeness of the building is very |
| + | | impressive, he converts the applicability of that predicate |
| + | | from being a way of thinking about the building to being |
| + | | itself a subject of thought, and that operation is |
| + | | 'subjectal abstraction'. |
| + | | |
| + | | C.S. Peirce, CP 4.332, "Ordinals", circa 1905. |
| </pre> | | </pre> |
| | | |
− | ==HAPA. Hypostatic And Prescisive Abstraction • Discussion== | + | ===HAPA. Note 9=== |
| | | |
− | ===HAPA. Discussion Note 1=== | + | <pre> |
| + | | Predicate. |
| + | | |
| + | | The view which pragmatic logic takes of the predicate, in consequence of |
| + | | its assuming that the entire purpose of deductive logic is to ascertain |
| + | | the necessary conditions of the truth of signs, without any regard to |
| + | | the accidents of Indo-European grammar, will be here briefly stated. |
| + | | Cf. Negation [CP 2.378-380]. |
| + | | |
| + | | In any proposition, i.e., any statement which must be true or false, |
| + | | let some parts be struck out so that the remnant is not a proposition, |
| + | | but is such that it becomes a proposition when each blank is filled by |
| + | | a proper name. The erasures are not to be made in a mechanical way, but |
| + | | with such modifications as may be necessary to preserve the partial sense |
| + | | of the fragment. Such a residue is a 'predicate'. The same proposition |
| + | | may be mutilated in various ways so that different fragments will appear |
| + | | as predicates. Thus, take the proposition "Every man reveres some woman." |
| + | | This contains the following predicates, among others: |
| + | | |
| + | | ". . . reveres some woman." |
| + | | |
| + | | ". . . is either not a man or reveres some woman." |
| + | | |
| + | | "Any previously selected man reveres . . ." |
| + | | |
| + | | "Any previously selected man is . . ." |
| + | | |
| + | | C.S. Peirce, 'Collected Papers', CP 2.358, in dictionary entry for "Predicate", |
| + | | J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 325-326. |
| + | </pre> |
| + | |
| + | ===HAPA. Note 10=== |
| | | |
| <pre> | | <pre> |
− | Referring to a few of Peirce's standard discussions
| + | | Relatives Of Second Intention |
− | of "hypostatic abstraction" (HA), the main thing | + | | |
− | about HA is that it turns an adjective or some
| + | | The general method of graphical representation of propositions has now |
− | part of a predicate into an extra subject,
| + | | been given in all its essential elements, except, of course, that we |
− | upping the arity of the main predicate
| + | | have not, as yet, studied any truths concerning special relatives; |
− | in the process.
| + | | for to do so would seem, at first, to be "extralogical". Logic in |
− | | + | | this stage of its development may be called 'paradisaical logic', |
− | For example, a typical case of HA occurs in the transformation | + | | because it represents the state of Man's cognition before the |
− | from "honey is sweet" to "honey possesses sweetness", which we
| + | | Fall. For although, with this apparatus, it easy to write |
− | could choose to represent in several different ways as follows:
| + | | propositions necessarily true, it is absolutely impossible |
− | | + | | to write any which is necessarily false, or, in any way |
− | Sweet(honey) ~~~> Possesses(honey, sweetness)
| + | | which that stage of logic affords, to find out that |
− | | + | | anything is false. The mind has not as yet eaten |
− | S(h) ~~~> P(h, s)
| + | | of the fruit of the Tree of Knowledge of Truth |
− | | + | | and Falsity. |
− | S P
| + | | |
− | o o
| + | | Probably it will not be doubted that every child in |
− | | ~~~> |
| + | | its mental development necessarily passes through |
− | o o | + | | a stage in which he has some ideas, but yet has |
− | h <h,s>
| + | | never recognised that an idea may be erroneous; |
− | | + | | and a stage that every child necessarily passes |
− | ^
| + | | through must have been formerly passed through |
− | [S] ~~~> /P\
| + | | by the race in its adult development. It may |
− | | o->-o
| + | | be doubted whether many of the lower animals |
− | | | |
| + | | have any clear and steady conception of |
− | o o o
| + | | falsehood; for their instincts work |
− | h h s
| + | | so unerringly that there is little |
− | | + | | to force it upon their attention. |
− | The chief thing about this form of grammatical transformation is that we | + | | Yet plainly without a knowledge |
− | abstract the adjective "sweet" from the main predicate, thus arriving at
| + | | of falsehood no development |
− | a new, increased-arity predicate "possesses", and as a by-product of the
| + | | of discursive reason can |
− | reaction, as it were, precipitating out the substantive "sweetness" as a
| + | | take place. |
− | new subject of the new predicate.
| + | | |
| + | | C.S. Peirce, 'Collected Papers', CP 3.488, |
| + | |"The Logic of Relatives", 'Monist', vol. 7, |
| + | | pp. 161-217, 1897. |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Discussion Note 2=== | + | ===HAPA. Note 11=== |
| | | |
| <pre> | | <pre> |
− | Abstractions And Their Deciduation Problems
| + | | Relatives Of Second Intention (cont.) |
− | | + | | |
− | I have studied mathematics one way or another most of my life,
| + | | This paradisaical logic appears in the study of non-relative formal logic. |
− | and mathematics is nothing if not the study of abstract objects,
| + | | But 'there' no possible avenue appears by which the knowledge of falsehood |
− | yet I do not believe that I am ready to venture my own definition
| + | | could be brought into this Garden of Eden except by the arbitrary and |
− | of "abstract object", not just yet, and I honestly do not know if | + | | inexplicable introduction of the Serpent in the guise of a proposition |
− | I ever will be, but what I have been attempting intermittently to
| + | | necessarily false. The logic of relatives affords such an avenue, |
− | do all this while is to transmit the sort of information that the
| + | | and 'that', the very avenue by which in actual development, |
− | typical backwoodsman in the wild wold of logic and mathematics
| + | | this stage of logic supervenes. It is the avenue of |
− | might regard as being analogous to a botanical key, useful in
| + | | experience and logical reflexion. |
− | recognizing various species of abstract objects, with which
| + | | |
− | I can genuinely say that I have some acquaintance, although
| + | | By 'logical' reflexion, I mean the observation of thoughts |
− | I would prefer to defer, in my reference, in my reverence,
| + | | in their expressions. Aquinas remarked that this sort of |
− | to ones who I know know vastly more. So forgive a quote:
| + | | reflexion is requisite to furnish us with those ideas |
− | | + | | which, from lack of contrast, ordinary external |
− | | To most otherwise "forest-minded" folk, the approach of autumn | + | | experience fails to bring into prominence. |
− | | with its showers of many-colored leaves, spells the end of the | + | | He called such ideas 'second intentions'. |
− | | season's activities in the indentification [sic] of deciduous | + | | |
− | | trees and shrubs. Without leaves, the members of the forest
| + | | It is by means of 'relatives of second intention' |
− | | community, unless they be relatively large, seem to lose | + | | that the general method of logical representation |
− | | much of their summer's identity and may even descend to | + | | is to find completion. |
− | | the level of "brush". This is in reality not the case, | |
− | | as may be easily discovered by examining any leafless | |
− | | twig with a 10-x pocket lens, or even with the naked | |
− | | eye. A casual glance at Plate 1 will also serve to | |
− | | show that woody plants in winter are anything but | |
− | | featureless. | |
| | | | | |
− | | Harlow, William M., | + | | C.S. Peirce, 'Collected Papers', CP 3.489-490, |
− | |"Twig Key to the Deciduous Woody Plants of Eastern North America", | + | |"The Logic of Relatives", 'The Monist', vol. 7, |
− | | 4th ed., reprinted in 'Fruit Key and Twig Key to Trees and Shrubs',
| + | | pp. 161-217, 1897. |
− | | Dover, New York, NY, 1959. Originally published by the author 1954. | |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Discussion Note 3=== | + | ===HAPA. Note 12=== |
| | | |
| <pre> | | <pre> |
− | I think that it would be useful at this time to run back through
| + | | One branch of deductive logic, of which from the nature of |
− | one of Peirce's best descriptions of the two kinds of abstraction,
| + | | things ordinary logic could give no satisfactory account, |
− | and try to tackle it line by line.
| + | | relates to the vitally important matter of abstraction. |
− | | + | | |
− | The first and simpler type of abstraction is "prescisive abstraction" --
| + | | Indeed, the student of ordinary logic naturally regards abstraction, |
− | where here I have taken something like the running average of several
| + | | or the passage from "the rose smells sweet" to "the rose has perfume", |
− | different spellings of the term -- that merely extracts or selectively
| + | | to be a quasi-grammatical matter, calling for little or no notice from |
− | attends to a feature or a property of a more concrete object. In this
| + | | the logician. The fact is, however, that almost every great step in |
− | case one passes from an object to one of its properties, very analogous
| + | | mathematical reasoning derives its importance from the fact that it |
− | to the sort of mathematical operation that is usually called "projection".
| + | | involves an abstraction. |
− | Here, one speaks of "prescinding" the property in question from the object,
| + | | |
− | whereby prescisive abstraction acquires the equivalent name of "prescission".
| + | | For by means of abstraction, the transitory elements of thought, |
| + | | the 'epea pteroenta' [winged words], are made substantive elements, |
| + | | as James terms them, 'epea apteroenta' [plucked words].* It thus |
| + | | becomes possible to study their relations and to apply to these |
| + | | relations discoveries already made respecting analogous relations. |
| + | | In this way, for example, operations become themselves the subjects |
| + | | of operations. |
| + | | |
| + | |* William James, 'Principles of Psychology', vol. 1, p. 243. |
| + | | |
| + | | C.S. Peirce, 'Collected Papers', CP 3.642, in dictionary entry for "Relatives", |
| + | | J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 447-450. |
| | | |
− | The second, more substantial type of abstraction is "hypostatic abstraction".
| + | Incidental Musement: |
− | This is the operation that we regard as bringing the abstract object proper
| |
− | into being, or into the sphere of human thought, or at least into the frame
| |
− | of a particular discussion. In this case one passes from a concrete object
| |
− | or situation, via a selection of properties, to end with an abstract object.
| |
| | | |
− | | Look through the modern logical treatises, and you will find that they
| + | http://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Hom.+Il.+1.172 |
− | | almost all fall into one or other of two errors, as I hold them to be;
| + | </pre> |
− | | that of setting aside the doctrine of abstraction (in the sense in
| |
− | | which an abstract noun marks an abstraction) as a grammatical topic
| |
− | | with which the logician need not particularly concern himself; and
| |
− | | that of confounding abstraction, in this sense, with that operation
| |
− | | of the mind by which we pay attention to one feature of a percept to
| |
− | | the disregard of others. The two things are entirely disconnected.
| |
| | | |
− | Here Peirce gives a first description of the two types of abstraction
| + | ==HAPA. Hypostatic And Prescisive Abstraction • Discussion== |
− | and emphasizes the importance of distinguishing them one from another.
| |
| | | |
− | | The most ordinary fact of perception, such as "it is light",
| + | ===HAPA. Discussion Note 1=== |
− | | involves 'precisive' abstraction, or 'prescission'.
| |
| | | |
− | In other words, all attention is selective to some degree,
| + | <pre> |
− | so any perception, such as that which we typically express
| + | Referring to a few of Peirce's standard discussions |
− | by means of the sentence "It is light" involves prescission,
| + | of "hypostatic abstraction" (HA), the main thing |
− | a trimming of the whole experience to crop an observed fact.
| + | about HA is that it turns an adjective or some |
| + | part of a predicate into an extra subject, |
| + | upping the arity of the main predicate |
| + | in the process. |
| | | |
− | | But 'hypostatic' abstraction, the abstraction which transforms
| + | For example, a typical case of HA occurs in the transformation |
− | | "it is light" into "there is light here", which is the sense
| + | from "honey is sweet" to "honey possesses sweetness", which we |
− | | which I shall commonly attach to the word abstraction (since
| + | could choose to represent in several different ways as follows: |
− | | 'prescission' will do for precisive abstraction) is a very
| |
− | | special mode of thought.
| |
| | | |
− | In the transformation from "It is light" to "There is light here",
| + | Sweet(honey) ~~~> Possesses(honey, sweetness) |
− | the spelling "light" is transformed from an adjective into a noun.
| |
− | This is the typical grammatical clue that an underlying operation
| |
− | of "hypostatic" or "subjectal" abstraction has been accomplished.
| |
| | | |
− | | It consists in taking a feature of a percept or percepts (after it has
| + | S(h) ~~~> P(h, s) |
− | | already been prescinded from the other elements of the percept), so as
| |
− | | to take propositional form in a judgment (indeed, it may operate upon
| |
− | | any judgment whatsoever), and in conceiving this fact to consist in the
| |
− | | relation between the subject of that judgment and another subject, which
| |
− | | has a mode of being that merely consists in the truth of propositions of
| |
− | | which the corresponding concrete term is the predicate.
| |
| | | |
− | This is very significant. It marks not just a grammatical
| + | S P |
− | transformation that happens to be taking place in a given
| + | o o |
− | example of hypostatic abstraction, but describes the very
| + | | ~~~> | |
− | form of a certain transformation that took place all along
| + | o o |
− | the frontiers of thought in the formal sciences beginning
| + | h <h,s> |
− | toward the middle of the Nineteenth Century, a development
| |
− | in which C.S. Peirce was a major force and prime expositor.
| |
| | | |
− | But I'll need to save the rest of that story for tomorrow.
| + | ^ |
| + | [S] ~~~> /P\ |
| + | | o->-o |
| + | | | | |
| + | o o o |
| + | h h s |
| | | |
− | Reference:
| + | The chief thing about this form of grammatical transformation is that we |
− | | + | abstract the adjective "sweet" from the main predicate, thus arriving at |
− | | C.S. Peirce, CP 4.235, "The Simplest Mathematics",
| + | a new, increased-arity predicate "possesses", and as a by-product of the |
− | | Chapter 3 of the "Minute Logic", Jan-Feb 1902.
| + | reaction, as it were, precipitating out the substantive "sweetness" as a |
− | |
| + | new subject of the new predicate. |
− | | http://suo.ieee.org/ontology/msg05091.html
| |
| </pre> | | </pre> |
| | | |
− | ===HAPA. Discussion Note 4=== | + | ===HAPA. Discussion Note 2=== |
| | | |
| <pre> | | <pre> |
− | By way of starting to compile a "key to abstractions and relatives"
| + | Abstractions And Their Deciduation Problems |
− | in the spirit of an old-fashioned field study key, I have gone back
| |
− | through our neck of the woulds and gathered these initial specimens:
| |
| | | |
− | 1. HIROTUFIA. Handy Indexical Rules Of Thumb Used For Identifying Abstractions
| + | I have studied mathematics one way or another most of my life, |
− | | + | and mathematics is nothing if not the study of abstract objects, |
− | 1.1. One of the features that points to an abstract object or
| + | yet I do not believe that I am ready to venture my own definition |
− | a hypostatic abstraction is its being known by description,
| + | of "abstract object", not just yet, and I honestly do not know if |
− | in other words, by the predicates that are attributed to it
| + | I ever will be, but what I have been attempting intermittently to |
− | in remote reports of some variety, or in the various stories
| + | do all this while is to transmit the sort of information that the |
− | and theories that are spun about it, instead of being known
| + | typical backwoodsman in the wild wold of logic and mathematics |
− | more concretely and directly by acquaintance. That is one
| + | might regard as being analogous to a botanical key, useful in |
− | of the marks of all of the things that I mentioned before:
| + | recognizing various species of abstract objects, with which |
− | dormitive virtues, egos, numbers, quarks, sweetness, the
| + | I can genuinely say that I have some acquaintance, although |
− | Starship Enterprise, and last not not least, unicorns.
| + | I would prefer to defer, in my reference, in my reverence, |
| + | to ones who I know know vastly more. So forgive a quote: |
| | | |
− | 1.2. CSP on HA: "It consists in taking a feature of a percept
| + | | To most otherwise "forest-minded" folk, the approach of autumn |
− | or percepts (after it has already been prescinded from the
| + | | with its showers of many-colored leaves, spells the end of the |
− | other elements of the percept), so as to take propositional
| + | | season's activities in the indentification [sic] of deciduous |
− | form in a judgment (indeed, it may operate upon any judgment
| + | | trees and shrubs. Without leaves, the members of the forest |
− | whatsoever), and in conceiving this fact to consist in the
| + | | community, unless they be relatively large, seem to lose |
− | relation between the subject of that judgment and another
| + | | much of their summer's identity and may even descend to |
− | subject, which has a mode of being that merely consists
| + | | the level of "brush". This is in reality not the case, |
− | in the truth of propositions of which the corresponding
| + | | as may be easily discovered by examining any leafless |
− | concrete term is the predicate."
| + | | twig with a 10-x pocket lens, or even with the naked |
| + | | eye. A casual glance at Plate 1 will also serve to |
| + | | show that woody plants in winter are anything but |
| + | | featureless. |
| + | | |
| + | | Harlow, William M., |
| + | |"Twig Key to the Deciduous Woody Plants of Eastern North America", |
| + | | 4th ed., reprinted in 'Fruit Key and Twig Key to Trees and Shrubs', |
| + | | Dover, New York, NY, 1959. Originally published by the author 1954. |
| + | </pre> |
| | | |
− | 2. HIROTUFIR. Handy Indexical Rules Of Thumb Used For Identifying Relatives
| + | ===HAPA. Discussion Note 3=== |
| | | |
− | 2.1. A practical test of whether a property of a thing
| + | <pre> |
− | is a relative property of a thing is that one needs
| + | I think that it would be useful at this time to run back through |
− | additional information, beyond that which identifies
| + | one of Peirce's best descriptions of the two kinds of abstraction, |
− | the thing, in order to make a decision about whether
| + | and try to tackle it line by line. |
− | the thing in question has the property in question.
| |
| | | |
− | 2.2. Let me just throw out this thought: Words and phrases like
| + | The first and simpler type of abstraction is "prescisive abstraction" -- |
− | "ego", "number", "quark", "unicorn", "Starship Enterprise",
| + | where here I have taken something like the running average of several |
− | along with all of the rest of the words and phrases that
| + | different spellings of the term -- that merely extracts or selectively |
− | we use, have no meaning at all outside of some community,
| + | attends to a feature or a property of a more concrete object. In this |
− | context, or framework of interpretation, so all of their
| + | case one passes from an object to one of its properties, very analogous |
− | meanings and all of their specifications on any semantic
| + | to the sort of mathematical operation that is usually called "projection". |
− | or semiotic feature, like "abstract" or "concrete", are
| + | Here, one speaks of "prescinding" the property in question from the object, |
− | relative to the given community, context, or framework
| + | whereby prescisive abstraction acquires the equivalent name of "prescission". |
− | of interpretation that gives them those meanings and
| + | |
− | those specifications.
| + | The second, more substantial type of abstraction is "hypostatic abstraction". |
− | </pre>
| + | This is the operation that we regard as bringing the abstract object proper |
| + | into being, or into the sphere of human thought, or at least into the frame |
| + | of a particular discussion. In this case one passes from a concrete object |
| + | or situation, via a selection of properties, to end with an abstract object. |
| | | |
− | ===HAPA. Discussion Note 5===
| + | | Look through the modern logical treatises, and you will find that they |
| + | | almost all fall into one or other of two errors, as I hold them to be; |
| + | | that of setting aside the doctrine of abstraction (in the sense in |
| + | | which an abstract noun marks an abstraction) as a grammatical topic |
| + | | with which the logician need not particularly concern himself; and |
| + | | that of confounding abstraction, in this sense, with that operation |
| + | | of the mind by which we pay attention to one feature of a percept to |
| + | | the disregard of others. The two things are entirely disconnected. |
| | | |
− | <pre>
| + | Here Peirce gives a first description of the two types of abstraction |
− | BM = Bernard Morand
| + | and emphasizes the importance of distinguishing them one from another. |
| | | |
− | | CSP on HA: "It consists in taking a feature of a percept | + | | The most ordinary fact of perception, such as "it is light", |
− | | or percepts (after it has already been prescinded from the
| + | | involves 'precisive' abstraction, or 'prescission'. |
− | | other elements of the percept), so as to take propositional
| |
− | | form in a judgment (indeed, it may operate upon any judgment
| |
− | | whatsoever), and in conceiving this fact to consist in the
| |
− | | relation between the subject of that judgment and another
| |
− | | subject, which has a mode of being that merely consists | |
− | | in the truth of propositions of which the corresponding
| |
− | | concrete term is the predicate."
| |
| | | |
− | BM: Could you give the source of this passage?
| + | In other words, all attention is selective to some degree, |
| + | so any perception, such as that which we typically express |
| + | by means of the sentence "It is light" involves prescission, |
| + | a trimming of the whole experience to crop an observed fact. |
| | | |
− | This came up in the context of several different threads on the SUO and
| + | | But 'hypostatic' abstraction, the abstraction which transforms |
− | Ontology Lists that involved different people's ideas about abstraction:
| + | | "it is light" into "there is light here", which is the sense |
− | Cathy Legg mentioned HA a la Cyc and/or Davidson that piqued my interest,
| + | | which I shall commonly attach to the word abstraction (since |
− | but I am still waiting for clarification of its relation to Peirce's HA;
| + | | 'prescission' will do for precisive abstraction) is a very |
− | Matthew West has a distinction between the categories of <abstract_object>
| + | | special mode of thought. |
− | and <possible_individual> in his Lifecycle Integration Schema, a datamodel
| |
− | and/or ontology that is currently being considered by the SUO working group;
| |
− | John Sowa dreams of a divine apportionment of every thing between the domain
| |
− | of Physical Earth and the realm of Abstract Heaven in his Philosophy, Horatio. | |
| | | |
− | Here is the stem cell of the LIS filiation:
| + | In the transformation from "It is light" to "There is light here", |
| + | the spelling "light" is transformed from an adjective into a noun. |
| + | This is the typical grammatical clue that an underlying operation |
| + | of "hypostatic" or "subjectal" abstraction has been accomplished. |
| | | |
− | LIS. Lifecycle Integration Schema -- Matthew West
| + | | It consists in taking a feature of a percept or percepts (after it has |
| + | | already been prescinded from the other elements of the percept), so as |
| + | | to take propositional form in a judgment (indeed, it may operate upon |
| + | | any judgment whatsoever), and in conceiving this fact to consist in the |
| + | | relation between the subject of that judgment and another subject, which |
| + | | has a mode of being that merely consists in the truth of propositions of |
| + | | which the corresponding concrete term is the predicate. |
| | | |
− | 01. http://suo.ieee.org/email/msg10712.html
| + | This is very significant. It marks not just a grammatical |
| + | transformation that happens to be taking place in a given |
| + | example of hypostatic abstraction, but describes the very |
| + | form of a certain transformation that took place all along |
| + | the frontiers of thought in the formal sciences beginning |
| + | toward the middle of the Nineteenth Century, a development |
| + | in which C.S. Peirce was a major force and prime expositor. |
| | | |
− | Here are the links to the source materials
| + | But I'll need to save the rest of that story for tomorrow. |
− | and discussion notes that have accumulated
| |
− | up to this point on HA and PA:
| |
| | | |
− | HAPA. Hypostatic And Prescisive Abstraction
| + | Reference: |
| | | |
− | 01. http://suo.ieee.org/ontology/msg05089.html -- Cain and Abel
| + | | C.S. Peirce, CP 4.235, "The Simplest Mathematics", |
− | 02. http://suo.ieee.org/ontology/msg05090.html -- Dormative Virtue
| + | | Chapter 3 of the "Minute Logic", Jan-Feb 1902. |
− | 03. http://suo.ieee.org/ontology/msg05091.html -- Honey is Sweet
| + | | |
− | 04. http://suo.ieee.org/ontology/msg05093.html -- Math Abstraction
| + | | http://suo.ieee.org/ontology/msg05091.html |
− | 05. http://suo.ieee.org/ontology/msg05100.html -- Reading Runes
| + | </pre> |
− | 06. http://suo.ieee.org/ontology/msg05101.html -- Hypostatization
| |
− | 07. http://suo.ieee.org/ontology/msg05105.html -- Abstract Objects
| |
− | 08. http://suo.ieee.org/ontology/msg05108.html -- Subjectal Abstraction
| |
| | | |
− | D1. http://suo.ieee.org/ontology/msg05092.html -- Metaphormazes
| + | ===HAPA. Discussion Note 4=== |
− | D2. http://suo.ieee.org/ontology/msg05110.html -- Deciduation Problems
| |
− | D3. http://suo.ieee.org/ontology/msg05111.html -- Recapitulation
| |
− | D4. http://suo.ieee.org/ontology/msg05112.html -- Key To Abstraction
| |
− | D5. http://suo.ieee.org/ontology/msg05113.html -- Self Reference?
| |
| | | |
− | The passage that you mention is quoted initially at No. 3, and
| + | <pre> |
− | it is discussed further at D1, D3, D4, and prospectively at D5.
| + | By way of starting to compile a "key to abstractions and relatives" |
| + | in the spirit of an old-fashioned field study key, I have gone back |
| + | through our neck of the woulds and gathered these initial specimens: |
| | | |
− | Have to break fast for breakfast as I am still semi-asleep ...
| + | 1. HIROTUFIA. Handy Indexical Rules Of Thumb Used For Identifying Abstractions |
| | | |
− | BM = Bernard Morand
| + | 1.1. One of the features that points to an abstract object or |
| + | a hypostatic abstraction is its being known by description, |
| + | in other words, by the predicates that are attributed to it |
| + | in remote reports of some variety, or in the various stories |
| + | and theories that are spun about it, instead of being known |
| + | more concretely and directly by acquaintance. That is one |
| + | of the marks of all of the things that I mentioned before: |
| + | dormitive virtues, egos, numbers, quarks, sweetness, the |
| + | Starship Enterprise, and last not not least, unicorns. |
| | | |
− | BM: I wonder whether Peirce is refering here to second
| + | 1.2. CSP on HA: "It consists in taking a feature of a percept |
− | intention or namely to hypostatic abstraction (HA).
| + | or percepts (after it has already been prescinded from the |
| + | other elements of the percept), so as to take propositional |
| + | form in a judgment (indeed, it may operate upon any judgment |
| + | whatsoever), and in conceiving this fact to consist in the |
| + | relation between the subject of that judgment and another |
| + | subject, which has a mode of being that merely consists |
| + | in the truth of propositions of which the corresponding |
| + | concrete term is the predicate." |
| | | |
− | BM: If we take as a starting case:
| + | 2. HIROTUFIR. Handy Indexical Rules Of Thumb Used For Identifying Relatives |
| | | |
− | (1) "Opium puts to sleep",
| + | 2.1. A practical test of whether a property of a thing |
| + | is a relative property of a thing is that one needs |
| + | additional information, beyond that which identifies |
| + | the thing, in order to make a decision about whether |
| + | the thing in question has the property in question. |
| | | |
− | in order to transform it by HA, we get:
| + | 2.2. Let me just throw out this thought: Words and phrases like |
| + | "ego", "number", "quark", "unicorn", "Starship Enterprise", |
| + | along with all of the rest of the words and phrases that |
| + | we use, have no meaning at all outside of some community, |
| + | context, or framework of interpretation, so all of their |
| + | meanings and all of their specifications on any semantic |
| + | or semiotic feature, like "abstract" or "concrete", are |
| + | relative to the given community, context, or framework |
| + | of interpretation that gives them those meanings and |
| + | those specifications. |
| + | </pre> |
| | | |
− | (2) "Opium has a dormitive virtue".
| + | ===HAPA. Discussion Note 5=== |
| | | |
− | BM: I see it as the transformation of a fact into | + | <pre> |
− | a more abstract concept, or say something like
| + | BM = Bernard Morand |
− | "opium has the general property of putting to sleep".
| |
− | It is hypostatic in the sense that it requires no further
| |
− | proposition than (1) and that the transformation relies on
| |
− | an "ens rationis". But from (2) we can also get for example:
| |
| | | |
− | (3) "this discourse has a dormitive virtue",
| + | | CSP on HA: "It consists in taking a feature of a percept |
| + | | or percepts (after it has already been prescinded from the |
| + | | other elements of the percept), so as to take propositional |
| + | | form in a judgment (indeed, it may operate upon any judgment |
| + | | whatsoever), and in conceiving this fact to consist in the |
| + | | relation between the subject of that judgment and another |
| + | | subject, which has a mode of being that merely consists |
| + | | in the truth of propositions of which the corresponding |
| + | | concrete term is the predicate." |
| | | |
− | which requires a second subject (a fact about discourse).
| + | BM: Could you give the source of this passage? |
− | I would be tempted to call this latter transformation
| |
− | second intention, and it seems to fit with your quote
| |
− | before. But going from (2) to (3) doesn't seem to be
| |
− | an hypostatic abstraction stricly speaking.
| |
| | | |
− | BM: Thanks for throwing some light on this if possible.
| + | This came up in the context of several different threads on the SUO and |
− | </pre> | + | Ontology Lists that involved different people's ideas about abstraction: |
| + | Cathy Legg mentioned HA a la Cyc and/or Davidson that piqued my interest, |
| + | but I am still waiting for clarification of its relation to Peirce's HA; |
| + | Matthew West has a distinction between the categories of <abstract_object> |
| + | and <possible_individual> in his Lifecycle Integration Schema, a datamodel |
| + | and/or ontology that is currently being considered by the SUO working group; |
| + | John Sowa dreams of a divine apportionment of every thing between the domain |
| + | of Physical Earth and the realm of Abstract Heaven in his Philosophy, Horatio. |
| | | |
− | ===HAPA. Discussion Note 6===
| + | Here is the stem cell of the LIS filiation: |
| | | |
− | <pre>
| + | LIS. Lifecycle Integration Schema -- Matthew West |
− | BM = Bernard Morand
| |
| | | |
− | The genealogy of this circle of thoughts goes a bit like this:
| + | 01. http://suo.ieee.org/email/msg10712.html |
| | | |
− | | Bentham's "Theory of Fictions" begat (paraphrastically)
| + | Here are the links to the source materials |
− | | Schönfinkel's "Bausteine" and this begat (independently)
| + | and discussion notes that have accumulated |
− | | Church's "Lambda Calculus" and this begat (in good time)
| + | up to this point on HA and PA: |
− | | McCarthy's "Lisp" and all the rest is AI and IEEE ...
| |
| | | |
− | It is no accident, at least not from the right "state of information" (SOI),
| + | HAPA. Hypostatic And Prescisive Abstraction |
− | how lambda abstraction got its tale, as it is truly most pertinently tagged.
| |
− | It is said that the lambda came from Russell('s) and Whitehead's employment
| |
− | of a caret (^) to mark a cousin operation of relational conversion, but let
| |
− | me try to look that up later. At any rate, the main idea has been stock in
| |
− | trade of mathematics for as long as anybody can remember, and in philosophy
| |
− | more generally (or vaguely, I can never remember which) the laurel is often
| |
− | placed on Bentham for his idea of paraphrasis. Here's a general/vague link:
| |
| | | |
− | http://www.utm.edu/research/iep/b/bentham.htm | + | 01. http://suo.ieee.org/ontology/msg05089.html -- Cain and Abel |
| + | 02. http://suo.ieee.org/ontology/msg05090.html -- Dormative Virtue |
| + | 03. http://suo.ieee.org/ontology/msg05091.html -- Honey is Sweet |
| + | 04. http://suo.ieee.org/ontology/msg05093.html -- Math Abstraction |
| + | 05. http://suo.ieee.org/ontology/msg05100.html -- Reading Runes |
| + | 06. http://suo.ieee.org/ontology/msg05101.html -- Hypostatization |
| + | 07. http://suo.ieee.org/ontology/msg05105.html -- Abstract Objects |
| + | 08. http://suo.ieee.org/ontology/msg05108.html -- Subjectal Abstraction |
| | | |
− | What we see here is the very same thing going on
| + | D1. http://suo.ieee.org/ontology/msg05092.html -- Metaphormazes |
− | in the colloquial homilies that Peirce attempted
| + | D2. http://suo.ieee.org/ontology/msg05110.html -- Deciduation Problems |
− | to use to adumbrate the spirit of abstraction in | + | D3. http://suo.ieee.org/ontology/msg05111.html -- Recapitulation |
− | the formal sciences.
| + | D4. http://suo.ieee.org/ontology/msg05112.html -- Key To Abstraction |
| + | D5. http://suo.ieee.org/ontology/msg05113.html -- Self Reference? |
| + | |
| + | The passage that you mention is quoted initially at No. 3, and |
| + | it is discussed further at D1, D3, D4, and prospectively at D5. |
| + | |
| + | Have to break fast for breakfast as I am still semi-asleep ... |
| + | |
| + | BM = Bernard Morand |
| | | |
| BM: I wonder whether Peirce is refering here to second | | BM: I wonder whether Peirce is refering here to second |
Line 2,085: |
Line 2,030: |
| (2) "Opium has a dormitive virtue". | | (2) "Opium has a dormitive virtue". |
| | | |
− | Here is the diagram that I drew for the analogous case
| + | BM: I see it as the transformation of a fact into |
− | of "virtus dulcitiva", in lay terminology, "sweetness". | + | a more abstract concept, or say something like |
| + | "opium has the general property of putting to sleep". |
| + | It is hypostatic in the sense that it requires no further |
| + | proposition than (1) and that the transformation relies on |
| + | an "ens rationis". But from (2) we can also get for example: |
| | | |
− | Referring to a few of Peirce's standard discussions
| + | (3) "this discourse has a dormitive virtue", |
− | of "hypostatic abstraction" (HA), the main thing
| |
− | about HA is that it turns an adjective or some
| |
− | part of a predicate into an extra subject,
| |
− | upping the arity of the main predicate
| |
− | in the process.
| |
| | | |
− | For example, a typical case of HA occurs in the transformation
| + | which requires a second subject (a fact about discourse). |
− | from "honey is sweet" to "honey possesses sweetness", which we | + | I would be tempted to call this latter transformation |
− | could choose to represent in several different ways as follows:
| + | second intention, and it seems to fit with your quote |
| + | before. But going from (2) to (3) doesn't seem to be |
| + | an hypostatic abstraction stricly speaking. |
| | | |
− | Sweet(honey) ~~~> Possesses(honey, sweetness)
| + | BM: Thanks for throwing some light on this if possible. |
| + | </pre> |
| | | |
− | S(h) ~~~> P(h, s)
| + | ===HAPA. Discussion Note 6=== |
| | | |
− | S P
| + | <pre> |
− | o o
| + | BM = Bernard Morand |
− | | ~~~> |
| |
− | o o
| |
− | h <h,s>
| |
| | | |
− | ^
| + | The genealogy of this circle of thoughts goes a bit like this: |
− | [S] ~~~> /P\
| |
− | | o->-o
| |
− | | | |
| |
− | o o o
| |
− | h h s
| |
| | | |
− | Figs. Are Sweet. If served in season. At just the right temps.
| + | | Bentham's "Theory of Fictions" begat (paraphrastically) |
| + | | Schönfinkel's "Bausteine" and this begat (independently) |
| + | | Church's "Lambda Calculus" and this begat (in good time) |
| + | | McCarthy's "Lisp" and all the rest is AI and IEEE ... |
| | | |
− | The chief thing about this form of grammatical transformation is that we
| + | It is no accident, at least not from the right "state of information" (SOI), |
− | abstract the adjective "sweet" from the main predicate, thus arriving at
| + | how lambda abstraction got its tale, as it is truly most pertinently tagged. |
− | a new, increased-arity predicate "possesses", and as a by-product of the
| + | It is said that the lambda came from Russell('s) and Whitehead's employment |
− | reaction, as it were, precipitating out the substantive "sweetness" as a
| + | of a caret (^) to mark a cousin operation of relational conversion, but let |
− | new subject of the new predicate.
| + | me try to look that up later. At any rate, the main idea has been stock in |
| + | trade of mathematics for as long as anybody can remember, and in philosophy |
| + | more generally (or vaguely, I can never remember which) the laurel is often |
| + | placed on Bentham for his idea of paraphrasis. Here's a general/vague link: |
| | | |
− | BM: I see it as the transformation of a fact into a more abstract concept, or
| + | http://www.utm.edu/research/iep/b/bentham.htm |
− | say something like "opium has the general property of putting to sleep".
| |
| | | |
− | Sticking, sweetly, if you will, to the notion that a concept is a mental symbol,
| + | What we see here is the very same thing going on |
− | some might say that a sufficently "precise" abstract concept is already present
| + | in the colloquial homilies that Peirce attempted |
− | in the predicate "is_sweet", but HA takes a step beyond that, as some would say, | + | to use to adumbrate the spirit of abstraction in |
− | onto the flypaper of "abstract but substantial objects" like 'virtus dulcitiva'.
| + | the formal sciences. |
| | | |
− | BM: It is hypostatic in the sense that it requires no further | + | BM: I wonder whether Peirce is refering here to second |
− | proposition than (1) and that the transformation relies on | + | intention or namely to hypostatic abstraction (HA). |
− | an "ens rationis".
| |
| | | |
− | Yes, this is the critical observation.
| + | BM: If we take as a starting case: |
| | | |
− | BM: But from (2) we can also get for example:
| + | (1) "Opium puts to sleep", |
| | | |
− | (3) "this discourse has a dormitive virtue", | + | in order to transform it by HA, we get: |
| | | |
− | which requires a second subject (a fact about discourse). | + | (2) "Opium has a dormitive virtue". |
| | | |
− | This is known as "application of the abstraction to another argument",
| + | Here is the diagram that I drew for the analogous case |
− | and it is analogous to the other half of the lambda calculus paradigm.
| + | of "virtus dulcitiva", in lay terminology, "sweetness". |
| | | |
− | BM: I would be tempted to call this latter transformation
| + | Referring to a few of Peirce's standard discussions |
− | second intention, and it seems to fit with your quote
| + | of "hypostatic abstraction" (HA), the main thing |
− | before. But going from (2) to (3) doesn't seem to be
| + | about HA is that it turns an adjective or some |
− | an hypostatic abstraction stricly speaking.
| + | part of a predicate into an extra subject, |
| + | upping the arity of the main predicate |
| + | in the process. |
| | | |
− | As for the matter of intentional orders, I foggily peirceive | + | For example, a typical case of HA occurs in the transformation |
− | but the clue that it has something to do with the operations | + | from "honey is sweet" to "honey possesses sweetness", which we |
| + | could choose to represent in several different ways as follows: |
| + | |
| + | Sweet(honey) ~~~> Possesses(honey, sweetness) |
| + | |
| + | S(h) ~~~> P(h, s) |
| + | |
| + | S P |
| + | o o |
| + | | ~~~> | |
| + | o o |
| + | h <h,s> |
| + | |
| + | ^ |
| + | [S] ~~~> /P\ |
| + | | o->-o |
| + | | | | |
| + | o o o |
| + | h h s |
| + | |
| + | Figs. Are Sweet. If served in season. At just the right temps. |
| + | |
| + | The chief thing about this form of grammatical transformation is that we |
| + | abstract the adjective "sweet" from the main predicate, thus arriving at |
| + | a new, increased-arity predicate "possesses", and as a by-product of the |
| + | reaction, as it were, precipitating out the substantive "sweetness" as a |
| + | new subject of the new predicate. |
| + | |
| + | BM: I see it as the transformation of a fact into a more abstract concept, or |
| + | say something like "opium has the general property of putting to sleep". |
| + | |
| + | Sticking, sweetly, if you will, to the notion that a concept is a mental symbol, |
| + | some might say that a sufficently "precise" abstract concept is already present |
| + | in the predicate "is_sweet", but HA takes a step beyond that, as some would say, |
| + | onto the flypaper of "abstract but substantial objects" like 'virtus dulcitiva'. |
| + | |
| + | BM: It is hypostatic in the sense that it requires no further |
| + | proposition than (1) and that the transformation relies on |
| + | an "ens rationis". |
| + | |
| + | Yes, this is the critical observation. |
| + | |
| + | BM: But from (2) we can also get for example: |
| + | |
| + | (3) "this discourse has a dormitive virtue", |
| + | |
| + | which requires a second subject (a fact about discourse). |
| + | |
| + | This is known as "application of the abstraction to another argument", |
| + | and it is analogous to the other half of the lambda calculus paradigm. |
| + | |
| + | BM: I would be tempted to call this latter transformation |
| + | second intention, and it seems to fit with your quote |
| + | before. But going from (2) to (3) doesn't seem to be |
| + | an hypostatic abstraction stricly speaking. |
| + | |
| + | As for the matter of intentional orders, I foggily peirceive |
| + | but the clue that it has something to do with the operations |
| that I throw together under the name of "reflection", and by | | that I throw together under the name of "reflection", and by |
| this plurality of reflection to say I abstract some fraction | | this plurality of reflection to say I abstract some fraction |
Line 8,859: |
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| '''Ontology List (Sep 2003)''' | | '''Ontology List (Sep 2003)''' |
| | | |
− | * http://suo.ieee.org/ontology/thrd10.html#05026 | + | * http://web.archive.org/web/20070305021905/http://suo.ieee.org/ontology/thrd10.html#05026 |
− | # http://suo.ieee.org/ontology/msg05026.html | + | # http://web.archive.org/web/20070313230956/http://suo.ieee.org/ontology/msg05026.html |
− | # http://suo.ieee.org/ontology/msg05027.html | + | # http://web.archive.org/web/20070316003847/http://suo.ieee.org/ontology/msg05027.html |
− | # http://suo.ieee.org/ontology/msg05028.html | + | # http://web.archive.org/web/20070317131614/http://suo.ieee.org/ontology/msg05028.html |
− | # http://suo.ieee.org/ontology/msg05029.html | + | # http://web.archive.org/web/20070320020154/http://suo.ieee.org/ontology/msg05029.html |
− | # http://suo.ieee.org/ontology/msg05030.html | + | # http://web.archive.org/web/20070323144756/http://suo.ieee.org/ontology/msg05030.html |
− | # http://suo.ieee.org/ontology/msg05031.html | + | # http://web.archive.org/web/20070328013010/http://suo.ieee.org/ontology/msg05031.html |
− | # http://suo.ieee.org/ontology/msg05033.html | + | # http://web.archive.org/web/20050826220928/http://suo.ieee.org/ontology/msg05033.html |
− | # http://suo.ieee.org/ontology/msg05034.html | + | # http://web.archive.org/web/20070316003856/http://suo.ieee.org/ontology/msg05034.html |
− | # http://suo.ieee.org/ontology/msg05035.html | + | # http://web.archive.org/web/20070313231006/http://suo.ieee.org/ontology/msg05035.html |
− | # http://suo.ieee.org/ontology/msg05038.html | + | # http://web.archive.org/web/20070313231017/http://suo.ieee.org/ontology/msg05038.html |
− | # http://suo.ieee.org/ontology/msg05039.html | + | # http://web.archive.org/web/20070313231027/http://suo.ieee.org/ontology/msg05039.html |
− | # http://suo.ieee.org/ontology/msg05040.html | + | # http://web.archive.org/web/20070313231037/http://suo.ieee.org/ontology/msg05040.html |
− | # http://suo.ieee.org/ontology/msg05041.html | + | # http://web.archive.org/web/20070313231048/http://suo.ieee.org/ontology/msg05041.html |
− | # http://suo.ieee.org/ontology/msg05048.html | + | # http://web.archive.org/web/20070313231058/http://suo.ieee.org/ontology/msg05048.html |
− | # http://suo.ieee.org/ontology/msg05049.html | + | # http://web.archive.org/web/20070310113354/http://suo.ieee.org/ontology/msg05049.html |
− | # http://suo.ieee.org/ontology/msg05050.html | + | # http://web.archive.org/web/20070313231108/http://suo.ieee.org/ontology/msg05050.html |
− | # http://suo.ieee.org/ontology/msg05052.html | + | # http://web.archive.org/web/20070310113519/http://suo.ieee.org/ontology/msg05052.html |
− | # http://suo.ieee.org/ontology/msg05053.html | + | # http://web.archive.org/web/20070222033549/http://suo.ieee.org/ontology/msg05053.html |
− | # http://suo.ieee.org/ontology/msg05082.html | + | # http://web.archive.org/web/20070219035929/http://suo.ieee.org/ontology/msg05082.html |
| | | |
| ===DIEP. De In Esse Predication • Discussion History=== | | ===DIEP. De In Esse Predication • Discussion History=== |
Line 8,884: |
Line 8,886: |
| '''Inquiry List (Sep 2003)''' | | '''Inquiry List (Sep 2003)''' |
| | | |
− | * http://stderr.org/pipermail/inquiry/2003-September/thread.html#786 | + | * http://web.archive.org/web/20120505135759/http://stderr.org/pipermail/inquiry/2003-September/thread.html#786 |
− | # http://stderr.org/pipermail/inquiry/2003-September/000786.html | + | # http://web.archive.org/web/20061014001032/http://stderr.org/pipermail/inquiry/2003-September/000786.html |
− | # http://stderr.org/pipermail/inquiry/2003-September/000790.html | + | # http://web.archive.org/web/20061014001019/http://stderr.org/pipermail/inquiry/2003-September/000790.html |
− | # http://stderr.org/pipermail/inquiry/2003-September/000796.html | + | # http://web.archive.org/web/20061014000906/http://stderr.org/pipermail/inquiry/2003-September/000796.html |
− | # http://stderr.org/pipermail/inquiry/2003-September/000797.html | + | # http://web.archive.org/web/20061014001045/http://stderr.org/pipermail/inquiry/2003-September/000797.html |
− | # http://stderr.org/pipermail/inquiry/2003-September/000799.html | + | # http://web.archive.org/web/20061014000930/http://stderr.org/pipermail/inquiry/2003-September/000799.html |
− | # http://stderr.org/pipermail/inquiry/2003-September/000803.html | + | # http://web.archive.org/web/20061014001253/http://stderr.org/pipermail/inquiry/2003-September/000803.html |
− | # http://stderr.org/pipermail/inquiry/2003-September/000806.html | + | # http://web.archive.org/web/20061014001212/http://stderr.org/pipermail/inquiry/2003-September/000806.html |
| + | # http://web.archive.org/web/20061014000859/http://stderr.org/pipermail/inquiry/2003-September/000798.html |
| | | |
| '''Ontology List (Sep 2003)''' | | '''Ontology List (Sep 2003)''' |
| | | |
− | * http://suo.ieee.org/ontology/thrd10.html#05032 | + | * http://web.archive.org/web/20070305021905/http://suo.ieee.org/ontology/thrd10.html#05032 |
− | # http://suo.ieee.org/ontology/msg05032.html | + | # http://web.archive.org/web/20070317221422/http://suo.ieee.org/ontology/msg05032.html |
− | # http://suo.ieee.org/ontology/msg05036.html | + | # http://web.archive.org/web/20070316003906/http://suo.ieee.org/ontology/msg05036.html |
− | # http://suo.ieee.org/ontology/msg05043.html | + | # http://web.archive.org/web/20121010204912/http://suo.ieee.org/ontology/msg05043.html |
− | # http://suo.ieee.org/ontology/msg05045.html | + | # http://web.archive.org/web/20070222033717/http://suo.ieee.org/ontology/msg05045.html |
− | # http://suo.ieee.org/ontology/msg05047.html | + | # http://web.archive.org/web/20070222033504/http://suo.ieee.org/ontology/msg05047.html |
− | # http://suo.ieee.org/ontology/msg05051.html | + | # http://web.archive.org/web/20070222033848/http://suo.ieee.org/ontology/msg05051.html |
− | # http://suo.ieee.org/ontology/msg05054.html | + | # http://web.archive.org/web/20070219072137/http://suo.ieee.org/ontology/msg05054.html |
| + | # http://web.archive.org/web/20070222033828/http://suo.ieee.org/ontology/msg05046.html |
| | | |
− | ===HAPA. Hypostatic And Prescisive Abstraction 1=== | + | ===HAPA. Hypostatic And Prescisive Abstraction 1 • Document History=== |
| | | |
− | ====SUO List====
| + | '''Ontology List (Sep–Oct 2003)''' |
| + | |
| + | # http://suo.ieee.org/ontology/msg05089.html -- Continuous Predicate |
| + | # http://suo.ieee.org/ontology/msg05090.html -- Dormitive Virtue |
| + | # http://suo.ieee.org/ontology/msg05091.html -- Dulcitive Virtue |
| + | # http://suo.ieee.org/ontology/msg05093.html -- Math Abstraction |
| + | # http://suo.ieee.org/ontology/msg05100.html -- Reading Runes |
| + | # http://suo.ieee.org/ontology/msg05101.html -- Hypostatization |
| + | # http://suo.ieee.org/ontology/msg05105.html -- Abstract Objects |
| + | # http://suo.ieee.org/ontology/msg05108.html -- Subjectal Abstraction |
| + | # http://suo.ieee.org/ontology/msg05118.html -- Definition of Predicate |
| + | # http://suo.ieee.org/ontology/msg05121.html -- Second Intentions |
| + | # http://suo.ieee.org/ontology/msg05122.html -- Logical Reflexion |
| + | # http://suo.ieee.org/ontology/msg05125.html -- Epea Apteroenta |
| + | |
| + | '''SUO List (Sep–Oct 2003)''' |
| | | |
| # http://suo.ieee.org/email/msg10964.html -- Continuous Predicate | | # http://suo.ieee.org/email/msg10964.html -- Continuous Predicate |
Line 8,921: |
Line 8,940: |
| # http://suo.ieee.org/email/msg11290.html -- Epea Apteroenta | | # http://suo.ieee.org/email/msg11290.html -- Epea Apteroenta |
| | | |
− | ====Ontology List==== | + | ===HAPA. Hypostatic And Prescisive Abstraction 1 • Discussion History=== |
| | | |
− | # http://suo.ieee.org/ontology/msg05089.html -- Continuous Predicate
| + | '''Ontology List (Sep–Oct 2003)''' |
− | # http://suo.ieee.org/ontology/msg05090.html -- Dormitive Virtue
| |
− | # http://suo.ieee.org/ontology/msg05091.html -- Dulcitive Virtue
| |
− | # http://suo.ieee.org/ontology/msg05093.html -- Math Abstraction
| |
− | # http://suo.ieee.org/ontology/msg05100.html -- Reading Runes
| |
− | # http://suo.ieee.org/ontology/msg05101.html -- Hypostatization
| |
− | # http://suo.ieee.org/ontology/msg05105.html -- Abstract Objects
| |
− | # http://suo.ieee.org/ontology/msg05108.html -- Subjectal Abstraction
| |
− | # http://suo.ieee.org/ontology/msg05118.html -- Definition of Predicate
| |
− | # http://suo.ieee.org/ontology/msg05121.html -- Second Intentions
| |
− | # http://suo.ieee.org/ontology/msg05122.html -- Logical Reflexion
| |
− | # http://suo.ieee.org/ontology/msg05125.html -- Epea Apteroenta
| |
| | | |
− | ===HAPA. Hypostatic And Prescisive Abstraction 1 : Discussion===
| + | # http://suo.ieee.org/ontology/msg05092.html -- Metaphormazes |
| + | # http://suo.ieee.org/ontology/msg05110.html -- Deciduation Problems |
| + | # http://suo.ieee.org/ontology/msg05111.html -- Thematic Recapitulation |
| + | # http://suo.ieee.org/ontology/msg05112.html -- Field Key, Kitchen Recipe |
| + | # http://suo.ieee.org/ontology/msg05113.html -- Indirect Self Reference |
| + | # http://suo.ieee.org/ontology/msg05114.html -- Genealogy & Paraphrasis |
| + | # http://suo.ieee.org/ontology/msg05115.html -- Intention & Reflection |
| + | # http://suo.ieee.org/ontology/msg05116.html -- Rhematic Saturation |
| + | # http://suo.ieee.org/ontology/msg05117.html -- Relational Turn |
| + | # http://suo.ieee.org/ontology/msg05119.html -- Tabula Erasa |
| + | # http://suo.ieee.org/ontology/msg05120.html -- Directions |
| | | |
− | ====SUO List====
| + | '''SUO List (Sep–Oct 2003)''' |
| | | |
| # http://suo.ieee.org/email/msg10967.html -- Metaphormazes | | # http://suo.ieee.org/email/msg10967.html -- Metaphormazes |
Line 8,952: |
Line 8,970: |
| # http://suo.ieee.org/email/msg11267.html -- Directions | | # http://suo.ieee.org/email/msg11267.html -- Directions |
| | | |
− | ====Ontology List==== | + | ===HAPA. Hypostatic And Prescisive Abstraction 2 • Document History=== |
| | | |
− | # http://suo.ieee.org/ontology/msg05092.html -- Metaphormazes
| + | '''Inquiry List (Sep–Oct 2003)''' |
− | # http://suo.ieee.org/ontology/msg05110.html -- Deciduation Problems
| |
− | # http://suo.ieee.org/ontology/msg05111.html -- Thematic Recapitulation
| |
− | # http://suo.ieee.org/ontology/msg05112.html -- Field Key, Kitchen Recipe
| |
− | # http://suo.ieee.org/ontology/msg05113.html -- Indirect Self Reference
| |
− | # http://suo.ieee.org/ontology/msg05114.html -- Genealogy & Paraphrasis
| |
− | # http://suo.ieee.org/ontology/msg05115.html -- Intention & Reflection
| |
− | # http://suo.ieee.org/ontology/msg05116.html -- Rhematic Saturation
| |
− | # http://suo.ieee.org/ontology/msg05117.html -- Relational Turn
| |
− | # http://suo.ieee.org/ontology/msg05119.html -- Tabula Erasa
| |
− | # http://suo.ieee.org/ontology/msg05120.html -- Directions
| |
| | | |
− | ===HAPA. Hypostatic And Prescisive Abstraction 2===
| + | * http://stderr.org/pipermail/inquiry/2003-September/thread.html#841 |
− | | + | * http://stderr.org/pipermail/inquiry/2003-October/thread.html#899 |
− | ====SUO List====
| + | # http://stderr.org/pipermail/inquiry/2003-September/000841.html |
− | | + | # http://stderr.org/pipermail/inquiry/2003-September/000842.html |
− | # http://suo.ieee.org/email/msg10964.html | + | # http://stderr.org/pipermail/inquiry/2003-September/000843.html |
− | # http://suo.ieee.org/email/msg10965.html | + | # http://stderr.org/pipermail/inquiry/2003-September/000851.html |
− | # http://suo.ieee.org/email/msg10966.html | + | # http://stderr.org/pipermail/inquiry/2003-September/000858.html |
− | # http://suo.ieee.org/email/msg10991.html | + | # http://stderr.org/pipermail/inquiry/2003-September/000859.html |
− | # http://suo.ieee.org/email/msg11022.html | + | # http://stderr.org/pipermail/inquiry/2003-September/000863.html |
− | # http://suo.ieee.org/email/msg11025.html | + | # http://stderr.org/pipermail/inquiry/2003-September/000866.html |
− | # http://suo.ieee.org/email/msg11028.html | + | # http://stderr.org/pipermail/inquiry/2003-October/000899.html |
− | # http://suo.ieee.org/email/msg11079.html | + | # http://stderr.org/pipermail/inquiry/2003-October/000902.html |
− | # http://suo.ieee.org/email/msg11239.html | + | # http://stderr.org/pipermail/inquiry/2003-October/000903.html |
− | # http://suo.ieee.org/email/msg11271.html | + | # http://stderr.org/pipermail/inquiry/2003-October/000906.html |
− | # http://suo.ieee.org/email/msg11277.html | |
− | # http://suo.ieee.org/email/msg11290.html | |
| | | |
− | ====Ontology List====
| + | '''Ontology List (Sep–Oct 2003)''' |
| | | |
| # http://suo.ieee.org/ontology/msg05089.html | | # http://suo.ieee.org/ontology/msg05089.html |
Line 8,998: |
Line 9,004: |
| # http://suo.ieee.org/ontology/msg05125.html | | # http://suo.ieee.org/ontology/msg05125.html |
| | | |
− | ====Inquiry List====
| + | '''SUO List (Sep–Oct 2003)''' |
| | | |
− | * http://stderr.org/pipermail/inquiry/2003-September/thread.html#841 | + | # http://suo.ieee.org/email/msg10964.html |
− | * http://stderr.org/pipermail/inquiry/2003-October/thread.html#899 | + | # http://suo.ieee.org/email/msg10965.html |
| + | # http://suo.ieee.org/email/msg10966.html |
| + | # http://suo.ieee.org/email/msg10991.html |
| + | # http://suo.ieee.org/email/msg11022.html |
| + | # http://suo.ieee.org/email/msg11025.html |
| + | # http://suo.ieee.org/email/msg11028.html |
| + | # http://suo.ieee.org/email/msg11079.html |
| + | # http://suo.ieee.org/email/msg11239.html |
| + | # http://suo.ieee.org/email/msg11271.html |
| + | # http://suo.ieee.org/email/msg11277.html |
| + | # http://suo.ieee.org/email/msg11290.html |
| + | |
| + | ===HAPA. Hypostatic And Prescisive Abstraction 2 • Discussion History=== |
| + | |
| + | '''Inquiry List (Sep–Oct 2003)''' |
| + | |
| + | * http://stderr.org/pipermail/inquiry/2003-September/thread.html#844 |
| + | * http://stderr.org/pipermail/inquiry/2003-October/thread.html#891 |
| + | * http://stderr.org/pipermail/inquiry/2003-October/thread.html#900 |
| + | # http://stderr.org/pipermail/inquiry/2003-September/000844.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000891.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000892.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000893.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000894.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000895.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000896.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000897.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000898.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000900.html |
| + | # http://stderr.org/pipermail/inquiry/2003-October/000901.html |
| | | |
− | # http://stderr.org/pipermail/inquiry/2003-September/000841.html
| + | '''Ontology List (Sep–Oct 2003)''' |
− | # http://stderr.org/pipermail/inquiry/2003-September/000842.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-September/000843.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-September/000851.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-September/000858.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-September/000859.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-September/000863.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-September/000866.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-October/000899.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-October/000902.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-October/000903.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-October/000906.html
| |
| | | |
− | ===HAPA. Hypostatic And Prescisive Abstraction 2 : Discussion===
| + | # http://suo.ieee.org/ontology/msg05092.html |
| + | # http://suo.ieee.org/ontology/msg05110.html |
| + | # http://suo.ieee.org/ontology/msg05111.html |
| + | # http://suo.ieee.org/ontology/msg05112.html |
| + | # http://suo.ieee.org/ontology/msg05113.html |
| + | # http://suo.ieee.org/ontology/msg05114.html |
| + | # http://suo.ieee.org/ontology/msg05115.html |
| + | # http://suo.ieee.org/ontology/msg05116.html |
| + | # http://suo.ieee.org/ontology/msg05117.html |
| + | # http://suo.ieee.org/ontology/msg05119.html |
| + | # http://suo.ieee.org/ontology/msg05120.html |
| | | |
− | ====SUO List====
| + | '''SUO List (Sep–Oct 2003)''' |
| | | |
| # http://suo.ieee.org/email/msg10967.html | | # http://suo.ieee.org/email/msg10967.html |
Line 9,027: |
Line 9,061: |
| # http://suo.ieee.org/email/msg11232.html | | # http://suo.ieee.org/email/msg11232.html |
| # http://suo.ieee.org/email/msg11234.html | | # http://suo.ieee.org/email/msg11234.html |
− | # http://suo.ieee.org/email/msg11236.html | + | # http://suo.ieee.org/email/msg11236.html |
− | # http://suo.ieee.org/email/msg11237.html | + | # http://suo.ieee.org/email/msg11237.html |
− | # http://suo.ieee.org/email/msg11240.html | + | # http://suo.ieee.org/email/msg11240.html |
− | # http://suo.ieee.org/email/msg11267.html | + | # http://suo.ieee.org/email/msg11267.html |
− | | + | |
− | ====Ontology List==== | + | ===JITL. Just In Time Logic • Document History=== |
− | | + | |
− | # http://suo.ieee.org/ontology/msg05092.html
| + | '''Inquiry List (Aug 2003 – Apr 2005)''' |
− | # http://suo.ieee.org/ontology/msg05110.html
| + | |
− | # http://suo.ieee.org/ontology/msg05111.html
| + | * http://stderr.org/pipermail/inquiry/2003-August/thread.html#712 |
− | # http://suo.ieee.org/ontology/msg05112.html | + | * http://stderr.org/pipermail/inquiry/2005-April/thread.html#2542 |
− | # http://suo.ieee.org/ontology/msg05113.html
| + | # http://stderr.org/pipermail/inquiry/2003-August/000712.html |
− | # http://suo.ieee.org/ontology/msg05114.html | + | # http://stderr.org/pipermail/inquiry/2003-August/000714.html |
− | # http://suo.ieee.org/ontology/msg05115.html
| + | # http://stderr.org/pipermail/inquiry/2003-August/000717.html |
− | # http://suo.ieee.org/ontology/msg05116.html | + | # http://stderr.org/pipermail/inquiry/2003-August/000719.html |
− | # http://suo.ieee.org/ontology/msg05117.html
| + | # http://stderr.org/pipermail/inquiry/2003-August/000722.html |
− | # http://suo.ieee.org/ontology/msg05119.html | + | # http://stderr.org/pipermail/inquiry/2003-August/000723.html |
− | # http://suo.ieee.org/ontology/msg05120.html
| + | # http://stderr.org/pipermail/inquiry/2003-August/000724.html |
− | | + | # http://stderr.org/pipermail/inquiry/2003-August/000725.html |
− | ====Inquiry List====
| + | # http://stderr.org/pipermail/inquiry/2003-August/000726.html |
− | | + | # http://stderr.org/pipermail/inquiry/2003-August/000727.html |
− | * http://stderr.org/pipermail/inquiry/2003-September/thread.html#844
| + | # http://stderr.org/pipermail/inquiry/2003-August/000728.html |
− | * http://stderr.org/pipermail/inquiry/2003-October/thread.html#891
| + | # http://stderr.org/pipermail/inquiry/2003-August/000729.html |
− | * http://stderr.org/pipermail/inquiry/2003-October/thread.html#900
| + | # http://stderr.org/pipermail/inquiry/2003-August/000730.html |
− | | + | # http://stderr.org/pipermail/inquiry/2003-August/000731.html |
− | # http://stderr.org/pipermail/inquiry/2003-September/000844.html | + | # http://stderr.org/pipermail/inquiry/2003-August/000732.html |
− | # http://stderr.org/pipermail/inquiry/2003-October/000891.html | + | # http://stderr.org/pipermail/inquiry/2005-April/002542.html |
− | # http://stderr.org/pipermail/inquiry/2003-October/000892.html | + | # http://stderr.org/pipermail/inquiry/2005-April/002543.html |
− | # http://stderr.org/pipermail/inquiry/2003-October/000893.html | + | # http://stderr.org/pipermail/inquiry/2005-April/002544.html |
− | # http://stderr.org/pipermail/inquiry/2003-October/000894.html | |
− | # http://stderr.org/pipermail/inquiry/2003-October/000895.html | |
− | # http://stderr.org/pipermail/inquiry/2003-October/000896.html | |
− | # http://stderr.org/pipermail/inquiry/2003-October/000897.html | |
− | # http://stderr.org/pipermail/inquiry/2003-October/000898.html | |
− | # http://stderr.org/pipermail/inquiry/2003-October/000900.html | |
− | # http://stderr.org/pipermail/inquiry/2003-October/000901.html | |
− | | |
− | ===JITL. Just In Time Logic===
| |
| | | |
− | ====Ontology List====
| + | '''Ontology List (Aug 2003)''' |
| | | |
| * http://suo.ieee.org/ontology/thrd11.html#04961 | | * http://suo.ieee.org/ontology/thrd11.html#04961 |
Line 9,085: |
Line 9,110: |
| # http://suo.ieee.org/ontology/msg04979.html | | # http://suo.ieee.org/ontology/msg04979.html |
| # http://suo.ieee.org/ontology/msg04980.html | | # http://suo.ieee.org/ontology/msg04980.html |
− |
| |
− | ====Inquiry List====
| |
− |
| |
− | * http://stderr.org/pipermail/inquiry/2003-August/thread.html#712
| |
− | * http://stderr.org/pipermail/inquiry/2005-April/thread.html#2542
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000712.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000714.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000717.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000719.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000722.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000723.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000724.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000725.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000726.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000727.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000728.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000729.html
| |
− | # http://stderr.org/pipermail/inquiry/2003-August/000730.html
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− | # http://stderr.org/pipermail/inquiry/2003-August/000731.html
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− | # http://stderr.org/pipermail/inquiry/2003-August/000732.html
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− | # http://stderr.org/pipermail/inquiry/2005-April/002542.html
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− | # http://stderr.org/pipermail/inquiry/2005-April/002543.html
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− | # http://stderr.org/pipermail/inquiry/2005-April/002544.html
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− | ==Work Area==
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| | | |
| ===OLOD. Quine On The Limits Of Decision • Document History=== | | ===OLOD. Quine On The Limits Of Decision • Document History=== |