Examples Of Inquiry
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The question arises whether simple programs can emulate the proceedings of scientific inquiries -- that is, to what extent is inquiry algorithmic? I will approach this question through simple examples. Let us first consider John Dewey's "Rainy Day Inquiry" or "Sign of Rain" example, and this time put it under the microscope and look at a few of its finer details. In particular, I can use it to illustrate a couple of important issues: 1. The interpretive aspect of inquiry as a semiotic process. 2. The differential aspect of inquiry as a dynamic process. For ease of reference, I repeat here the original story: | A man is walking on a warm day. | The sky was clear the last time | he observed it; but presently he | notes, while occupied primarily with | other things, that the air is cooler. | It occurs to him that it is probably | going to rain; looking up, he sees | a dark cloud between him and the sun, | and he then quickens his steps. | | What, if anything, in such a situation | can be called thought? Neither the act | of walking nor the noting of the cold is | a thought. Walking is one direction of | activity; looking and noting are other | modes of activity. The likelihood that | it will rain is, however, something | 'suggested'. The pedestrian 'feels' | the cold; he 'thinks of' clouds | and a coming shower. | | John Dewey, 'How We Think', 1910, pp. 6-7 I will let this example soak in a bit before I wring to my present purposes.
Note 2
Susan Awbrey and I discussed Dewey's example of inquiry in our article, "Interpretation as Action: The Risk of Inquiry", that we gave at a Conference on "Hermeneutics and the Human Sciences" in 1992, a revision of which was subsequently published in the journal 'Inquiry: Critical Thinking Across the Disciplines', Volume 15, No. 1, pages 40-52, (Autumn 1995). This paper is available at the Arisbe Web Site or via the following links: http://www.chss.montclair.edu/inquiry/fall95/awbrey.html http://members.door.net/arisbe/menu/library/aboutcsp/aboutcsp.htm Figure 1 indicates the "elementary sign relations" that are involved in this fragment of inquiry. In particular, we have the following two triples of the form <Object, Sign, Interpretant>: 1. <Rain, Cool Air, Thought of Rain> 2. <Rain, Dark Cloud, Thought of Rain> o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `o Sign (Cool Air, Dark Cloud)` ` | | ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | Object (Rain) o------<| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant (Thought of Rain) | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 1. Sign Relation in Dewey's "Rainy Day Inquiry" Here is what we said about the sign-theoretic aspects of the inquiry process that we were able to detect in Dewey's example: | In this narrative we can identify the characters of | the sign relation as follows: 'coolness' is a Sign of | the Object 'rain', and the Interpretant is 'the thought | of the rain's likelihood'. In his 1910 description of | reflective thinking Dewey distinguishes two phases, | "a state of perplexity, hesitation, doubt" and | "an act of search or investigation" (Dewey 1991, 9), | comprehensive stages which are further refined in his | later model of inquiry. In this example, reflection | is the act of the interpreter which establishes a fund | of connections between the sensory shock of coolness | and the objective danger of rain, by way of his | impression that rain is likely. But reflection is | more than irresponsible speculation. In reflection | the interpreter acts to charge or defuse the thought | of rain (the probability of rain in thought) by seeking | other signs which this thought implies and evaluating | the thought according to the results of this search. | | Awbrey & Awbrey, 1992 Next time I will take up the differential aspect of inquiry as a dynamic process of theory change.
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This time I will take up the differential aspect of inquiry as a dynamic process of theory change. Returning to the example in question, let me now draw a more expansive picture of the "Rainy Day" situation, one that augments the account with some consideration of what our peripatetic/precipitate hero was probably doing and thinking, however consciously or other-wise, just slightly before the imaginary events in question. It is clear that our hero did not begin his life with the shock of cool air on his skin, at least, not on this particular, late ambulatory occasion, but probably had a prior distribution of default beliefs about what this day was going to be like. Just to extrapolate in a plausible vein of our imagination, let us play along and say that the initial facts were thus: A_1 = Air warm B_1 = Balmy day C_1 = Clear sky Pulling the "conventional contingency" or "customary connection" trick, let us then relativize the array of this data in the following fashion: C = Current Situation C => A_1, "Currently, the air is warm" C => B_1, "Currently, the day is balmy" C => C_1, "Currently, the sky is clear" For the moment, let this figure of a "current situation" C be one that is allowed to "go with the flow", letting its letter be re-used to anchor whatever the case may become. Now I do not know if it has to be the case that these three features of the current situation had ever been entertained by our ambler in any particular order, but we might suppose their relative consistency as consisting in some such scene as this: The hiker has formed a prior assumption about the case that applies to the current situation, let's say, that the day is balmy, C => B_1, an assumption that he will keep as a default to continue in the same way until there arises a reason to think otherwise. Further, we may imagine quite plausibly that a rule of the form B_1 => A_1 can be applied to the case C => B_1 to deduce the expectation of a certain fact, namely, that the current situation will feature among its phenomena the qualities of the air being warm, C => A_1. So this logical set-up, or the likes of it, is what we may assume, at least, plausibly enough for our currently illustrative purpose, as the logical environ into which our soon to be inquiring ambler strolls one fine and, for the moment, sunny day. The rest you know. The cooler air, A_2, sensually contests and logically contradicts the continuing assumption of the prior condition A_1, demanding a fresh evaluation of the conditioning assumption B_1, altering it into the new hypothesis B_2, boding rain, which abduced case is corroborated to a moderate degree by looking up and spying a cloud in the sky, C_2. Figure 2 manages to sum it all up in a fairly consummate fashion: o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` `A_1` ` ` ` `A_2` ` ` ` ` ` ` ` ` ` `C_1` ` ` ` `C_2` ` | | ` ` o~~~~>>>~~~~o ` ` ` ` ` ` ` ` ` ` ` o~~~~>>>~~~~o ` ` | | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` | | ` ` ` \*` ` ` ` ` `*` ` ` ` ` ` ` ` `*` ` ` ` ` `*/ ` ` ` | | ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` | | ` ` ` ` \ * ` ` ` ` ` * ` ` ` ` ` * ` ` ` ` ` * / ` ` ` ` | | ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` | | ` ` ` ` ` \ `*` ` ` ` ` `*` ` `*` ` ` ` ` `*` / ` ` ` ` ` | | ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` | | ` ` ` ` ` ` \ ` * ` ` ` ` ` * ` ` ` ` ` * ` / ` ` ` ` ` ` | | ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` | | ` ` ` ` ` ` ` \ ` `*` ` `*` ` `*` ` `*` ` / ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ B_1 o~~~~>>>~~~~o B_2 / ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `\` ` `*` ` ` ` `*` ` `/` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` ` * ` ` ` * ` `/` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\` `*` ` `*` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` * ` * `/` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `\ * * /` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` `\*/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | A_1 `=` Air warm` ` ` ` ` ` ` ` ` ` ` A_2 `=` Air cool` ` | | B_1 `=` Balmy day ` ` ` ` ` ` ` ` ` ` B_2 `=` Bodes rain` | | C_1 `=` Clear sky ` ` ` ` ` ` ` ` ` ` C_2 `=` Cloudy sky` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` C `=` Current situation ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 2. Differential Signs of Rain
Note 4
Here is a definition of what Peirce meant by a sign relation: | A sign is something, 'A', which brings something, 'B', | its 'interpretant' sign determined or created by it, | into the same sort of correspondence with something, 'C', | its 'object', as that in which itself stands to 'C'. | | C.S. Peirce, NEM 4, pp. 20-21. | | NEM 4 = 'The New Elements of Mathematics', Vol. 4, | Edited by Carolyn Eisele, Mouton, The Hague, 1976. | | http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm So when I say "coolness is a Sign of the Object rain, and the Interpretant is the thought of the rain's likelihood", it is because I think that the coolness in question brings the thought of the rain's likelihood into the same sort of correspondence with the objective event of rain as that in which the coolness itself stands to the same event of rain.
Note 5
For future reference -- if I may in fact refer to a reference in the future -- here is a further explanation of what Peirce meant by a sign relation: | A 'Sign', or 'Representamen', is a First which stands | in such a genuine triadic relation to a Second, called | its 'Object', as to be capable of determining a Third, | called its 'Interpretant', to assume the same triadic | relation to its Object in which it stands itself to | the same Object. | | The triadic relation is 'genuine', that is, its three members | are bound together by it in a way that does not consist in any | complexus of dyadic relations. That is the reason the Interpretant, | or Third, cannot stand in a mere dyadic relation to the Object, but | must stand in such a relation to it as the Representamen itself does. | | Nor can the triadic relation in which the Third stands be merely | similar to that in which the First stands, for this would make the | relation of the Third to the First a degenerate Secondness merely. | The Third must indeed stand in such a relation, and thus must be | capable of determining a Third of its own; but besides that, it | must have a second triadic relation in which the Representamen, | or rather the relation thereof to its Object, shall be its own | (the Third's) Object, and must be capable of determining a Third | to this relation. All this must equally be true of the Third's | Third and so on endlessly; and this, and more, is involved in | the familiar idea of a Sign; and as the term Representamen is | here used, nothing more is implied. | | A 'Sign' is a Representamen with a mental Interpretant. | | Possibly there may be Representamens that are not Signs. | | Thus, if a sunflower, in turning towards the sun, | becomes by that very act fully capable, without | further condition, of reproducing a sunflower | which turns in precisely corresponding ways | toward the sun, and of doing so with the | same reproductive power, the sunflower | would become a Representamen of the sun. | | But 'thought' is the chief, if not | the only, mode of representation. | | C.S. Peirce, "Syllabus" (c. 1902), 'Collected Papers', CP 2.274
Note 6
With this much background penciled in, let's revisit again the contextualized picture or differential figure that we derived from Dewey's "Sign of Rain" example: o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | `Air Warm ` `Air Cool ` ` ` ` ` ` `Clear Sky` Cloudy Sky` | | ` `A_1` ` ` ` `A_2` ` ` ` ` ` ` ` ` ` `C_1` ` ` ` `C_2` ` | | ` ` o~~~~>>>~~~~o ` ` ` ` ` ` ` ` ` ` ` o~~~~>>>~~~~o ` ` | | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` | | ` ` ` \*` ` ` ` ` `*` ` ` ` ` ` ` ` `*` ` ` ` ` `*/ ` ` ` | | ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` | | ` ` ` ` \ * ` ` ` ` ` * ` ` ` ` ` * ` ` ` ` ` * / ` ` ` ` | | ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` | | ` ` ` ` ` \ `*` ` ` ` ` `*` ` `*` ` ` ` ` `*` / ` ` ` ` ` | | ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` | | ` ` ` ` ` ` \ ` * ` ` ` ` ` * ` ` ` ` ` * ` / ` ` ` ` ` ` | | ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` | | ` ` ` ` ` ` ` \ ` `*` ` `*` ` `*` ` `*` ` / ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` `\`Balmy` ` ` ` ` ` Boding`/` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ B_1 o~~~~>>>~~~~o B_2 / ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `\` ` `*` ` ` ` `*` ` `/` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` ` * ` ` ` * ` `/` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\` `*` ` `*` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` * ` * `/` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `\ * * /` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` `\*/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` Current Situation ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | A_1 `=` Air warm` ` ` ` ` ` ` ` ` ` ` A_2 `=` Air cool` ` | | B_1 `=` Balmy day ` ` ` ` ` ` ` ` ` ` B_2 `=` Bodes rain` | | C_1 `=` Clear sky ` ` ` ` ` ` ` ` ` ` C_2 `=` Cloudy sky` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 3. Signs of Rain Viewed in Their Natural Context The question lingers: What justifies our calling by the name of inquiry Dewey's sample of a semiotic process, namely, the sign relational transit from the fact of cool air, C => A_2, to the case of rain, C => B_2, and from the thought of that case to the ruly act of looking up for any further signs of rain that might be in the sky? Let's try to focus for a while on what we may see as the "differential" or the "distributional" aspect of inquiry. If you follow the idea that inquiry begins with a state of tension in the affected agent of the process, then you are likely to recognize the legion of diverse names for this annoyingly irritating mode of being -- doubt, problem, surprise, uncertainty -- as forming variable manifestations of a differential theme, for example, that a difference exists between what an agent observes or accepts as actual and what that agent either expects or intends to be the case. Here, the agent has an initial expectation of fair weather, due most likely to his initial observations of a clear sky, but then discrepant sensations of significantly cooler air cause him to pause, to reflect, and to update his forecast of the imminent weather conditions to a foreboding of rain.
Note 7
The question that drives me to examine these examples of inquiry is the relationship among signs, information, inference, and the typical trajectories of inquiry. At this point in the discussion, we need a bit of background information about the pragmatic theory of inquiry. I am presenting the long version of that on a another thread, stemming from either one of these alternative urlocations: INTRO. http://forum.wolframscience.com/showthread.php?threadid=598 INTRO. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1720 To keep from holding up this more concrete discussion of examples, here is a short introduction to the principal ideas, as I see them: It is frequently useful to approach the concept of an inquiry process as a specialization of a sign relation, in the following three phases: 1. Sign Relation A "sign relation" simpliciter, L c O x S x I, could be just about any 3-adic relation on the arbitrary domains O, S, I, so long as it satisfies one of the adequate definitions of a sign relation. 2. Sign Process A "sign process" is a sign relation plus a significant sense of transition. This means that there is a definite, non-trivial sense in which a sign determines its interpretant signs with respect to its objects. We often find ourselves writing "<o, s, i>" as "<o, s, s'>" in such cases, where the semiotic transition s ~> s' takes place in respect of the object o. 3. Inquiry Process An "inquiry process" is a sign process that has value-directed transitions. This means that there is a property, a quality, or a scalar value that can be associated with a sign in relation to its objects, and that the transit from a sign to an interpretant in regard to an object occurs in such a way that the value is increased in the process. For example, semiotic actions like inquiry and computation are directed in such a way as to increase the "aptness", "brevity", or "clarity" of the signs on which they operate.
Note 8
Here's the "New List" text about the relations between the types of signs and the types of inference, that is, the morphological and temporal constituents of inquiry: | In an argument, the premisses form a representation of | the conclusion, because they indicate the interpretant | of the argument, or representation representing it to | represent its object. The premisses may afford a | likeness, index, or symbol of the conclusion. | | [Deduction of a Fact] | | In deductive argument, the conclusion is represented | by the premisses as by a general sign under which it | is contained. | | [Abduction of a Case] | | In hypotheses, something 'like' the conclusion is proved, | that is, the premisses form a likeness of the conclusion. | Take, for example, the following argument:-- | | M is, for instance, P_1, P_2, P_3, and P_4; | | S is P_1, P_2, P_3, and P_4: | | [Therefore], S is M. | | Here the first premiss amounts to this, that | "P_1, P_2, P_3, and P_4" is a likeness of M, | and thus the premisses are or represent | a likeness of the conclusion. | | [Induction of a Rule] | | That it is different with induction another example will show. | | S_1, S_2, S_3, and S_4 are taken as samples of the collection M; | | S_1, S_2, S_3, and S_4 are P: | | [Therefore], All M is P. | | Hence the first premiss amounts to saying that "S_1, S_2, S_3, and S_4" | is an index of M. Hence the premisses are an index of the conclusion. | | C.S. Peirce, 'Collected Papers' CP 1.559, 'Chronological Edition' CE 2, p. 58. Let the expression "P_1 & P_2 & P_3 & P_4" denote the proposition Q = Conjunction (P_1, P_2, P_3, P_4). Then we may draw the following Figure of Abduction: o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` P_1 ` P_2 ` ` ` ` P_3 ` P_4 ` ` ` ` ` | | ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` | | ` ` ` ` ` ` \*` ` \ ` ` ` ` / ` `*/|` ` ` ` ` ` | | ` ` ` ` ` ` `\`*` `\` ` ` `/` `*`/`|` ` ` ` ` ` | | ` ` ` ` ` ` ` \ `*` \ ` ` / `*` / `|` ` ` ` ` ` | | ` ` ` ` ` ` ` `\` `* \` `/`*` `/` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ ` `*\ /*` ` / ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `Q` ` `.` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` `|` ` / ` `*` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` `|` `/` `*` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ `|` / `*`Case ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\`|`/`*` `S=>M ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \|/*` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `S` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Figure 4. Abduction of the Case S => M Let the expression "S_1 v S_2 v S_3 v S_4" denote the proposition L = Disjunction (S_1, S_2, S_3, S_4). Then we may draw the following Figure of Induction: o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `P` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` /|\*` ` Rule` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `/`|`\`*` M=>P` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` / `|` \ `*` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `/` `|` `\` `*` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` / ` `|` ` \ ` `*` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `L` ` `.` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` / ` `*/ \*` ` \ ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` `/` `*`/` `\`*` `\` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` / `*` / ` ` \ `*` \ `|` ` ` ` ` ` | | ` ` ` ` ` ` `/`*` `/` ` ` `\` `*`\`|` ` ` ` ` ` | | ` ` ` ` ` ` /*` ` / ` ` ` ` \ ` `*\|` ` ` ` ` ` | | ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` | | ` ` ` ` ` S_1 ` S_2 ` ` ` ` S_3 ` S_4 ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Figure 5. Induction to the Rule M => P Reference: | C.S. Peirce, "New List", CP 1.559, CE 2, p. 58. | | Charles Sanders Peirce, "On a New List of Categories" (1867), |'Collected Papers' CP 1.545-567, 'Chronological Edition' CE 2, pp. 49-59. | | http://www.peirce.org/writings/p32.html | http://members.door.net/arisbe/menu/library/bycsp/newlist/nl-frame.htm
Note 9
Given the above background, concepts, and data, what is the proper way of seeing the relationship between the two trios that we have drawn for Dewey's example of inquiry, specifically, the sign-theoretic 3-tuple and the syllogistic 3-angle? (See Figures 6 and 7). o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `o Sign (Cool Air)` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | Object (Rain) o------<| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant (Thought of Rain) | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 6. Sign Relation in Dewey's "Rainy Day Inquiry" o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `Air Cool ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` A ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ^^` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` |A` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | b ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | `d` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` Fact` | ` u ` ` o Before Rain ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` `c` `^` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` e / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` `/ `Case` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` `Current Situation` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 7. Abducing a Case from a Fact and a Rule An immediately obvious difference between the two Figures is that the sign triple has the "Thought of Rain" whereas the syllogistic triple has the object state "Before Rain". Is this a significant difference between the two diagrams? I will think on it ...
Note 10
Cathy Legg's "Missing The Bus" Example Here is another remarkably instructive example that can be tackled moderately well by blocking it out as a "zeroth order theory (ZOT): | I'm waiting for my morning bus and it doesn't arrive: surprise. | I then think -- in the past sometimes my bus hasn't arrived when | it's a public holiday I've forgotten about: this case should be | the same (induction), I then form the hypothesis that it is | a public holiday (abduction). | | Cathy Legg, "Missing the Bus", as posted to the Peirce List: | | Subj: Re: Chomsky on Peirce on Abduction | Date: Fri, 28 Apr 2000, 15:39:25 +1000 (EST) | From: Cathy Legg <...> | To: Peirce Discussion Forum <...>
Note 11
Cathy Legg's "Missing The Bus" Example (cont.) Here is my analysis of Cathy Legg's "Missing the Bus" problem, to the extent that it can be represented within the constraints of propositional models, sentential logic, or zeroth order logic. Let "C" represent the Current situation, that is, the intinerant inquirer's current situation under the circumstances of the problem in question, also depicted by a "circle" in a venn diagram. This is just a cheap propositional gimmick for covering to some extent the "indexical" characterisitics of the situation in question, but without having to resort to the use of variables that range over domains of "individual situations". Next, let us contemplate the alternative possibilities, formulated here as Proposition X versus Proposition Y. X = [C => A] = [In the Current situation, the bus Arrives] Y = [C => ~A] = [In the Current situation, the bus does Not Arrive] As it happens, X is one's expectation, while Y is one's observation. This difference between one's expectation and one's observation is what one affectively experience as a surprise. Let me stress this. The observed fact is Y, but what renders it surprising is its difference from X, and this occurs on the point of detaching the alternative consequents, A versus ~A. Incidentally, it is this "differential" aspect of inquiry that led me, starting about a decade ago, to begin to develop a "differential logic", extending "propositional calculus" in almost precisely the same way that differential calculus extends analytic geometry. But let us get back to the situation at the bus stop. The way that induction enters this situation is as a component of previous cycles of inquiry that led to the formation of a Rule, even if it is only a "probable approximate rule", more or less as formulated in Proposition K: K = [B => A] = [In the Best case scenario, the bus Arrives] It does not affect the analysis at all if you have in mind another sort of descriptor than "best", say, "normal", "ordinary", or so on, so long as you acknowledge the conducive function or the mediating role of any middle term like B. When our traveller gets to the bus stop, it is most likely that she is in a slightly confused, indeterminate, uncertain, or vague state of mind, in the sense that she has probably not even stopped to ask herself the question we'll call Question Q: Q = [Is it really true that J?], where: J = [C => B] = [The Current situation is a Best case scenario] Consequently, she has walked, or ran, as is frequently the case, right into the current situation, operating under the influence of something like the following train of an automatic deduction: Case J: C => B Rule K: B => A ----------------- Fact X: C => A And this is just where we came in, with the discrepancy between the expected fact X : C => A and the observed fact Y : C => ~A. The surprise that one meets with, instead of the bus, might lead one to question all sorts of things. Any number of speculations might come to mind. Among the more rational possibilities, the surprise might cause one to inquire into any and all of the premisses that fed into the above deduction, if not the axioms of the logic that one happens to be implementing at the moment. But let's suppose that one lights on the Case C => B, as it is most frequently the Case that is the cause of the problem, and therefore, in accord with a higher order induction of the inquiry into inquiry, it is most frequently the Case that empirical people consider first. And so, after reflecting on the situation, and eliciting certain features of how one's habitual reasoning processes fed into it, quasi modo intuitio, one decides to vary the description of the Case, in this case, from saying that C => B to asking whether it might not be true that C => ~B, that is, asking oneself, "Can it be that the current situation is not actually the best (modal, normal, ordinary, usual, ...) case, and that this may be the cause of my expectation being disappointed?"
Note 12
Cathy Legg's "Missing The Bus" Example (cont.) Let us now illustrate the particulars that we find in "The Case of the Missing Bus" by using the sort of "propositional logic in a lattice" diagram that I used to articulate the basic brands of inference, in what now must seem like so many long notes past. Let me recap the story as we know it so far in the syllogistic or "propositional constraint reasoning" (PCR) style of picture. Figure 8 sketchily summarizes the first phase of the reconstruction. o---------------------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` `A` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (A) ` | | ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` | | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` | | ` ` ` \ * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * / ` ` ` | | ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` | | ` ` ` ` \ ` * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * ` / ` ` ` ` | | ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` | | ` ` ` ` ` \ ` ` * ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` * ` ` / ` ` ` ` ` | | ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` | | ` ` ` ` ` ` \ ` ` ` * ` ` ` ` ` ` ` ` ` ` ` ` * ` ` ` / ` ` ` ` ` ` | | ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` | | ` ` ` ` ` ` ` \ ` ` ` B o ` ` ` ` ` ` ` ` o (B) ` ` / ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ ` ` ` `*` ` ` ` ` ` ` `*` ` ` ` / ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` ` ` * ` ` ` ` ` ` * ` ` ` / ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ ` ` `*` ` ` ` ` `*` ` ` / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \ ` ` * ` ` ` ` * ` ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` `*` ` ` `*` ` / ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` * ` ` * ` / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` \ `*` `* `/ ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` \ * * / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | A `=` Arriving bus situations ` \*/ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | B `=` Best case situations` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | C `=` Current situation ` ` ` ` `C` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o---------------------------------------------------------------------o Figure 8. Cathy Legg's "Missing the Bus" Example The point elements in these diagrams represent the "propositions" that one is contemplating with respect to a domain of objects, persons, situations, and so on. Another option is to treat them as the "terms" of the description: Major term, Middle term, Minor term, and so on. The line elements in these diagrams represent the "logical relations" that are being considered between certain pairs of propositions, or else the "premisses" that are being contemplated between various pairs of terms, where roughly vertical lines indicate "implications", the antecedent lower and the consequent higher, and where roughly horizontal placements indicate relationship of "alteration" (change) or "alternation" (diversity), that is, the situation among a number of alternatives, exclusive or inclusive, that are available for one to change or to choose among. It is my guess that something like this style of geometric figure was used by Aristotle, and may have been a common sort of picture at the time, at least, this is the impression that I get from the way that he uses two different styles of language for indicating the various sorts of logical relationships that are relevant to the fundamental types of reasoning situation that he discusses. For instance, Aristotle often uses the geometric label of the line segment AB to indicate the premiss B => A. Of course, this may just be a fluke of Greek grammar, or of its later transcription. There a convenient technical nomenclature that was added at a later date, in which the various line elements depicting the premisses and relations are customarily labeled as "Cases", "Facts", and "Rules", and I will use this style of language rather freely to talk about the different roles that different premisses may enjoy in the various forms of reasoning. One other thing: I often use the following equivalent notations: "(A)" = "~A" = "A'" = "Not A". Among other things, this gives the following notational equality: "(A (B))" = "A => B" = "Not A without B". I hope that will be enough of a set-up to get this show on the road. Data of the Situation: Alternative Facts: (C (A)) versus ( C ((A))), that is, (C A). Alternative Cases: (C (B)) versus ( C ((B))), that is, (C B). Alternative Rules: (B (A)) versus ((B)((A))), that is, (A (B)). We meet the surprising Fact : C => (A), depicted by the line segment (A)C. The reason that this Fact is surprising is that we automatically expected a different Fact, namely, C => A. And, assuming the current situation C, which we always do -- since this whole intervention of C is just a gimmick for supplying a pivot to our thought -- we were led moreover to expect A, the arrival of the bus. If we stop to think about it, we come to realize that there is a middle term that we have been taking for granted, say "B", the "benign" situation, the "best case" scenario (assuming that the best case means catching the bus), or maybe just the modal, normal, ordinary, or usual case, if you like those terms better. The name "reflection" seems to fit the process by which we can become aware of the previously automatic, implicit, and probably unconscious deduction that led to a current expectation, the one that is subject to conflict with a current observation, thereby generating a dilemma, a problem, or a surprise. Nota Bene. Actually, I use the word "problem" more specifically to refer to a difference between an intention and an observation, but that is another, yet related story. In the process of reflecting on the "program" of a habitual deduction, we become able to identify the intermediate and the middle terms that go "into it", and at this point we become able to contemplate their deliberate variation. In this way, we become able to pass from the class of propositions that are schematized by "B" to one or two in the class of propositions that are summarized by "~B", and thereby guessing a new Case, for example, that the current situation has the marks of a public holiday, C => H, where H => ~B, and so is not beneficial for our immediate purposes, tedious as they are.
Note 13
Cathy Legg's "Missing The Bus" Example (concl.) I left off last time at the point where you were just beginning to contemplate the possibility that your current situation might fall under the case description of a public holiday, thereby explaining the absence of the expected bus, and a hypothesis which, if true, would reduce your affective sense of surprise at the accustomed bus not being there at the place-time that you were accustomed to observe it. Now, if you're like me, you might eventually think to look up, and then to look around your surrounding neighborhood, to see if you can observe any further evidence or any other naturally occurring signs that might bear on your new hypothesis one way or another. This, of course, brings us to the deductive phase of our present inquiry. And, equally of course, our immedately present phase of deduction must be distinguished from all of those previous deductions, not to mention their Promethean and Epimethean (fore and aft) bracketings by all of those previous bits of abductive and inductive reasoning that went into making up what were no doubt many previous cycles, and a vast host of parallel cycles, and a countless array of epicycles on our deference to an inquiry that may be indefinitely deferred. Well, after that importunate word from our spontaneity, I think that it is due time to get back to our story. We have all been waiting for this bus long enough! [This essay was written just after Easter 2000.] If I had been walking on a residential street hereabouts, through most of last week, when this "missing of the bus" caper was alleged to have happened, I could have looked up and looked around and seen all the gaily colored balloons, the flapping ribbons, and the many other festive decorations that were decked out on many of the houses and the trees by all of the neighborhood parents who were throwing together to treat their collective broods to an Easter Egg Hunt. So that would have served to confirm the hypothesis of a holiday, and perhaps it may have even altered my sense of what was "best", "benign", "beneficial" -- trudging off on my accustomed way, in pursuit of my habitual goals, or stopping to enjoy the signs of another custom, and even to follow them -- but that's another story altogether! Anyway, it behooves me to try and size up the present moment of inquiry. Let me unfold the map again and make a few additional notations upon it. o---------------------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` `A` ` ` ` ` ` ` ` ` ` ` ` `D` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (A) ` | | ` ` o ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` | | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` | | ` ` ` \ * ` ` ` ` ` ` ` ` ` ` * ` ` ` ` ` ` ` ` ` ` ` ` ` * / ` ` ` | | ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` | | ` ` ` ` \ ` * ` ` ` ` ` ` ` ` `*` ` ` ` ` ` ` ` ` ` ` * ` / ` ` ` ` | | ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` | | ` ` ` ` ` \ ` ` * ` ` ` ` ` ` ` * ` ` ` ` ` ` ` ` * ` ` / ` ` ` ` ` | | ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` | | ` ` ` ` ` ` \ ` ` ` * ` ` ` ` ` `*` ` ` ` ` ` * ` ` ` / ` ` ` ` ` ` | | ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` | | ` ` ` ` ` ` ` \ ` ` ` B o ` ` ` ` * ` ` ` o (B) ` ` / ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ ` ` ` `*` ` ` ` `*` ` `*` ` ` ` / ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` ` ` * ` ` ` ` * ` * ` ` ` / ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ ` ` `*` ` ` ` `*`*` ` ` / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \ ` ` * ` ` ` ` o H ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` `*` ` ` `*` ` / ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` * ` ` * ` / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` \ `*` `* `/ ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` \ * * / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | A `=` Arriving bus situations ` \*/ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | B `=` Best case situations` ` ` `o` ` ` D `=` Decorative situations | | C `=` Current situation ` ` ` ` `C` ` ` H `=` Holiday situations` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o---------------------------------------------------------------------o Figure 9. Cathy Legg's "Busman's Holiday" Example I think that this pretty graphically says what I've been striving to say in the last thousand words or so, and I am tempted to leave it at that, but temptations to desist, you will have observed, are the sorts of temptations I can easily resist! So let me attempt to sum it up all over again, this time once again in schematic symbols and in rather more verbose but slightly more descriptive phrases. Abduction of a Case: Fact: C => (A), In the current situation, the bus is not arriving. Rule: H => (A), If it is a holiday, the bus would not be arriving. ---------------------------------------------------------------------- Case: C => H , Perhaps the current situation is a holiday. The validity of this abduction as a form of reasoning, in the only way that its particular form of non-demonstrative inference can be said to be valid, depends on the validity of the corresponding deduction, from the Case : C => H and the Rule : H => ~A to the Fact : C => ~A. So it needs to be remembered that the utility of this deduction, which only concludes what has already been observed, is that it succeeds in its aim to reduce the surprise of that observation. Deduction of a Fact: Case: C => H , In the current situation, it is a holiday. Rule: H => D , If it is a holiday, there will be decorations. ----------------------------------------------------------------------- Fact: C => D , In the current situation, there will be decorations. The inductive phase, in this situation, consists of looking up and testing whether the prediction comes true. I have been studying for few years now, and still remain a bit puzzled, as to how exactly this sense of induction fits in logically, if it does at all, with the other meaning of induction, namely, of a non-demonstrative inference from a Case and a Fact to a Rule.
Note 14
Let's return to the question that I asked in EOI Note 9, that had to do with the relationship between the semiotic or sign-theoretic triad and the logical syzygy, for example: o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `o Sign (Cool Air)` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | Object (Rain) o------<| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant (Thought of Rain) | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 14.1 Sign Relation in Dewey's "Rainy Day Inquiry" o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `Air Cool ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` A ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ^^` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` |A` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | b ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | `d` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` Fact` | ` u ` ` o Before Rain ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` `c` `^` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` e / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` `/ `Case` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` `Current Situation` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 14.2 Abducing a Case from a Fact and a Rule We need a word to cover all three uses of the later type of figure -- abductive, deductive, inductive -- since "syllogism" refers to the deductive use alone, and so I will experiment with using the word "syzygy" to cover all three ways of reading the same configuration. Last time we looked at this situation I reflected as follows: | An immediately obvious difference between the two Figures | is that the sign triple has the "Thought of Rain" whereas | the syllogistic triple has the object state "Before Rain". | Is this a significant difference between the two diagrams? For the sake of the NKS readers, there was some discussion of this point on the Inquiry and Peirce Lists that they may find beneficial, and that may yet come to fruition, but I will plod ahead on my own recognizance. Here are the links to what record I was able to make of those discussions: Peirce List: http://lyris.acs.ttu.edu/cgi-bin/lyris.pl?visit=peirce-l Inquiry List: http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
Note 15
In reviewing some of my previous writing on the issues in this area,
I came across the following collection of thoughts that seem of use.
For my part in this investigation, I have been
trying to resolve a couple of related problems:
1. What is the proper articulation of the inquiry process in terms
of the various kinds of inference, apodictic and approximate,
that various thinkers have identified as being relevant to it?
2. What is the proper placement of inquiry within a theory of signs?
My approach to this problem area has been to track back to the authors
of some of our initial ideas about signs and inquiry, to see if I could
work out for myself what they were thinking and how they moved from one
stage of their thought to the next, and maybe along the way to see if
I can see anything that they may have missed, or omitted to discuss
clearly enough. I am especially interested in the transition that
C.S. Peirce made from syllogistic to relational forms of thinking
about signs and inquiry, as that corresponds to an important task
in what might be called "computational architectronics", that of
building adequate logical systems on a solid propositional layer.
I have spent a fair amount of time staring at the likes
of the following two structures and trying to figure out
how they fit together, figuratively speaking, of course:
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `o Sign ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` Object o---------O` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 15.1 Elementary Sign Relation
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` Z ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | Ab` > \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\ /` `\` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` Fact` | <-o-De` o Y ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/ \` `/` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | In` > / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 15.2 Three Kinds of Inference
After I had stared at the second picture a very long time,
I came to see that the two approximate forms of inference,
Abduction and Induction, have in common the property that
they bring a middle term into the immediate configuration.
Then I remembered that Aristotle is supposed to have said:
The essence of quick wit lies in grasping the middle term.
But where do these middle terms come from, anyway? It is
conventional to say that they come in with the abductions
of the cases that first evidence any need to call on them,
and that this is what puts them in the pot for inductions
and deductions to bid for them on any subsequent occasion.
But maybe it would make sense to recognize an independent
process, solely dedicated to finding or making mediations.
Conceived in this way, this process would be a duction in
the opposite direction from Deduction, dub it "Adduction".
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` Z ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` `\` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` Fact` | Ad ---> o Y ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` `/` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 15.3 Adduction of a Middle Term
I'm not too committed to this name for the action,
and it has been used on one or two rare occasions
as yet another name for abduction, but I will use
it until I come up with a name that I like better.
Note 16
medium = a set of middle terms o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` `o Sign ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` Object o---------O` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Figure 15.1 Elementary Sign Relation o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` Z ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | Ab` > \ ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | `\ /` `\` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` Fact` | <-o-De` o Y ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | `/ \` `/` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | In` > / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Figure 15.2 Three Kinds of Inference o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` Z ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` ` \ ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` ` `\` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` Fact` | Ad ---> o Y ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` ` `/` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` ` / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Figure 15.3 Adduction of a Middle Term o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` P_1 ` P_2 ` ` ` ` P_3 ` P_4 ` ` ` ` ` | | ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` | | ` ` ` ` ` ` \*` ` \ ` ` ` ` / ` `*/|` ` ` ` ` ` | | ` ` ` ` ` ` `\`*` `\` ` ` `/` `*`/`|` ` ` ` ` ` | | ` ` ` ` ` ` ` \ `*` \ ` ` / `*` / `|` ` ` ` ` ` | | ` ` ` ` ` ` ` `\` `* \` `/`*` `/` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ ` `*\ /*` ` / ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `Q` ` `.` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `B` Before Rain` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` `|` ` / ` `*` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` `|` `/` `*` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ `|` / `*`Case ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\`|`/`*` `S=>M ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \|/*` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `S` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` P_1 ` A ` ` ` ` D ` P_4 ` ` ` ` ` | | ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` | | ` ` ` ` ` ` \*` ` \ ` ` ` ` / ` `*/|` ` ` ` ` ` | | ` ` ` ` ` ` `\`*` `\` ` ` `/` `*`/`|` ` ` ` ` ` | | ` ` ` ` ` ` ` \ `*` \ ` ` / `*` / `|` ` ` ` ` ` | | ` ` ` ` ` ` ` `\` `* \` `/`*` `/` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ ` `*\ /*` ` / ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `Q` ` `.` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` `|` ` / ` `*` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` `|` `/` `*` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ `|` / `*`Case ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\`|`/`*` `S=>M ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \|/*` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `S` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o
Work Area
o-----------------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | `Air Warm ` `Air Cool ` ` ` ` ` ` `Clear Sky` Cloudy Sky` | | ` `A_1` ` ` ` `A_2` ` ` ` ` ` ` ` ` ` `C_1` ` ` ` `C_2` ` | | ` ` o~~~~>>>~~~~o ` ` ` ` ` ` ` ` ` ` ` o~~~~>>>~~~~o ` ` | | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` | | ` ` ` \*` ` ` ` ` `*` ` ` ` ` ` ` ` `*` ` ` ` ` `*/ ` ` ` | | ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` | | ` ` ` ` \ * ` ` ` ` ` * ` ` ` ` ` * ` ` ` ` ` * / ` ` ` ` | | ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` | | ` ` ` ` ` \ `*` ` ` ` ` `*` ` `*` ` ` ` ` `*` / ` ` ` ` ` | | ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` | | ` ` ` ` ` ` \ ` * ` ` ` ` ` * ` ` ` ` ` * ` / ` ` ` ` ` ` | | ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` | | ` ` ` ` ` ` ` \ ` `*` ` `*` ` `*` ` `*` ` / ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` `\`Balmy` ` ` ` ` ` Boding`/` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ B_1 o~~~~>>>~~~~o B_2 / ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `\` ` `*` ` ` ` `*` ` `/` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` ` * ` ` ` * ` `/` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\` `*` ` `*` `/` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `\` * ` * `/` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` `\ * * /` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` / ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` `\*/` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` Current Situation ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | A_1 `=` Air warm` ` ` ` ` ` ` ` ` ` ` A_2 `=` Air cool` ` | | B_1 `=` Balmy day ` ` ` ` ` ` ` ` ` ` B_2 `=` Bodes rain` | | C_1 `=` Clear sky ` ` ` ` ` ` ` ` ` ` C_2 `=` Cloudy sky` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-----------------------------------------------------------o Figure 3. Signs of Rain Viewed in Their Natural Context
Discussion Note 1
JA = Jon Awbrey
TG = Tom Gollier
Re: EOI 2. http://stderr.org/pipermail/inquiry/2004-November/001705.html
In: EOI. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1704
The reason that I've returned to Dewey's "Rainy Day Inquiry",
for what seems like the umpteenth time, is that it marks one
of the many limits of my understanding with respect to the
relationship between signs and inquiry in Peirce's thought,
and especially as it developed, differentially or radically,
as the case may be, over his lifetime and on into our times.
So everything I say here is still very tentative in my mind.
TG: Why wouldn't your diagram look like this?
o---------------------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Sign (Sensory Cool Air, Dark Cloud)` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| Object o-----<| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Interpretant (Mental Cool Air, Dark Cloud = Rain)|
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o---------------------------------------------------------------------o
Figure 1'. Sign Relation in Dewey's "Rainy Day Inquiry"
Before I answer I need to know what you have in mind for the object.
I took it to be the "future contingent" immanent/imminent rainstorm,
an objective state of affairs when it eventually comes to be actual.
Let's see if we can clear that up first.
P.S. According to my custom, I will archive these
notes, queries, and replies at the Inquiry List, so
that I can remember what I've said in the contingent
future, so anybody who objects to my copying their
remarks there should please say so, and I won't.
TG: That is to say the "cool air and dark cloud"
is indeed a sign just as the interpretant is
also a sign including the same elements and
relationships plus a conlusion formally drawn
from them. If nothing else, "rain" can't be
the object because it hasn't rained yet in the
example. Actually, I would propose it as the
"ground", the characteristic by which the elements
and relations both the sign and the interpretant
are linked to the object. The object, however,
would seem to me to be all the elements and/or
relationships that might go into producing signs
and interpretants about the weather, the walk
home, or whatever context we choose.
TG: Anyway, Jon, I'm glad to see you "flooding the bandwidth" for a
change, although I'm sure there have been limits imposed. How did
that old song go? "We'll have fun 'til daddy takes the T-Bird away"?
Discussion Note 2
JA = Jon Awbrey
TG = Tom Gollier
Someday I'll tell you the story of how I came to have
such tunnel vision this week, but now that I've read
your whole note carefully enough I will try to make
a better reply.
TG: Why wouldn't you diagram look like this?
o---------------------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Sign (Sensory Cool Air, Dark Cloud)` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| Object o-----<| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Interpretant (Mental Cool Air, Dark Cloud = Rain)|
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o---------------------------------------------------------------------o
Figure 1'. Sign Relation in Dewey's "Rainy Day Inquiry"
TG: That is to say the "cool air and dark cloud"
is indeed a sign just as the interpretant is
also a sign including the same elements and
relationships plus a conlusion formally drawn
from them. If nothing else, "rain" can't be
the object because it hasn't rained yet in the
example. Actually, I would propose it as the
"ground", the characteristic by which the elements
and relations both the sign and the interpretant
are linked to the object. The object, however,
would seem to me to be all the elements and/or
relationships that might go into producing signs
and interpretants about the weather, the walk
home, or whatever context we choose.
I don't think that there's a unique way of assigning elements
to sign relational roles, in this example or any other, so I'd
only hope to argue that my choices are allowed by the definition
of a sign relation and that they explain some important aspects
of what is going on with regard to the inquiry in play.
The question that we come to once again is (1) whether
a sign relation necessarily involves causal components,
in the sense of 2-adic cause/effect relations between
some of its domains, or (2) whether it is essentially
a logical or information-theoretic relation among
three domains of elements.
If I read your above remark correctly, you seem to rule out
the possibility that a sign can come before its object in time,
perhaps on the basis that the denotative component is causal in
nature and directed from objects to their signs.
Let me know if I have read you right so far.
TG: Anyway, Jon, I'm glad to see you "flooding the bandwidth" for a
change, although I'm sure there have been limits imposed. How did
that old song go? "We'll have fun 'til daddy takes the T-Bird away"?
It's fun^3, of course.
Discussion Note 3
JA = Jon Awbrey
TG = Tom Gollier
TG: I'm looking at the sign and interpretant
as "diagrams" such as are described at
CP 2.227-228.
| The faculty which I call abstractive observation
| is one which ordinary people perfectly recognize,
| but for which the theories of philosophers sometimes
| hardly leave room. It is a familiar experience to
| every human being to wish for something quite beyond
| his present means, and to follow that wish by the
| question, 'Should I wish for that thing just the same,
| if I had ample means to gratify it?' To answer that
| question, he searches his heart, and in doing so makes
| what I term an abstractive observation. He makes in his
| imagination a sort of skeleton diagram, or outline sketch,
| of himself, considers what modifications the hypothetical
| state of things would require to be made in that picture,
| and then examines it, that is, 'observes' what he has
| imagined, to see whether the same ardent desire is
| there to be discerned (CP 2.227).
| A sign, or 'representamen', is something which stands to somebody for
| something in some respect or capacity. It addresses somebody, that is,
| creates in the mind of that person an equivalent sign, or perhaps a more
| developed sign. That sign which it creates I call the 'interpretant' of
| the first sign. The sign stands for something, its 'object'. It stands
| for that object, not in all respects, but in reference to a sort of idea,
| which I have sometimes called the 'ground' of the representamen (CP 2.228).
You adduce a couple of very important passages, to which we two
and others have returned many times. For future reference, let
me just connect to another context where they came up, and which
formed a critical turning point in my own understanding of them,
as I think that this whole question may rate another visitation:
Inquiry Into Inquiry:
III. http://suo.ieee.org/ontology/msg03077.html
Logic As Semiotic:
LAS. http://stderr.org/pipermail/arisbe/2001-August/thread.html#844
TG: Thus, in the diagram:
o---------------------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Sign (Sensory Cool Air, Dark Cloud)` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| Object o-----<| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Interpretant (Mental Cool Air, Dark Cloud = Rain)|
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o---------------------------------------------------------------------o
Figure 1'. Sign Relation in Dewey's "Rainy Day Inquiry"
TG: both sign and interpretant are taken as diagrams with certain elements
and relations between them based on the "ground" of, say, rain or the
possibility of rain as the basis for abstractively observing the sign
or imagining the interpretant. If we ask, abstracted from what, or
what is the object, that can only be the context or situation.
If we try to specify the object in any more detail or exactness,
we don't have an object at all but rather another sign.
I detect a certain ambiguity in your use of the word "diagram" here.
Figures 1 and 1' are diagrammatic representations of sign relational
triples. I would call them higher order signs of a particular type,
and have classified these sorts of HO signs elsewhere on the web.
Let me pause here, and see if we have an understanding on that point.
Discussion Note 4
JA = Jon Awbrey
TG = Tom Gollier
Assuming that we'll eventually be able to sort out
the different senses of the word "diagram" as Peirce
uses it, let me take up your comments piece by piece.
TG: I'm looking at the sign and interpretant
as "diagrams" such as are described at
CP 2.227-228.
Here is the whole of CP 2.227, in two pieces:
| Logic, in its general sense, is, as I believe I have shown,
| only another name for 'semiotic' ([Greek: semeiotike]), the
| quasi-necessary, or formal, doctrine of signs. By describing
| the doctrine as "quasi-necessary", or formal, I mean that we
| observe the characters of such signs as we know, and from such
| an observation, by a process which I will not object to naming
| Abstraction, we are led to statements, eminently fallible, and
| therefore in one sense by no means necessary, as to what 'must be'
| the characters of all signs used by a "scientific" intelligence,
| that is to say, by an intelligence capable of learning by experience.
|
| As to that process of abstraction, it is itself a sort of observation.
| The faculty which I call abstractive observation is one which ordinary
| people perfectly recognize, but for which the theories of philosophers
| sometimes hardly leave room. It is a familiar experience to every human
| being to wish for something quite beyond his present means, and to follow
| that wish by the question, "Should I wish for that thing just the same,
| if I had ample means to gratify it?" To answer that question, he searches
| his heart, and in doing so makes what I term an abstractive observation.
| He makes in his imagination a sort of skeleton diagram, or outline sketch,
| of himself, considers what modifications the hypothetical state of things
| would require to be made in that picture, and then examines it, that is,
| 'observes' what he has imagined, to see whether the same ardent desire
| is there to be discerned. By such a process, which is at bottom very
| much like mathematical reasoning, we can reach conclusions as to what
| 'would be' true of signs in all cases, so long as the intelligence
| using them was scientific. (CP 2.227).
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.227,
| Editors' Note: From an unidentified fragment, c. 1897.
I read this as a characterization of logic, which is
a critical reflection on signs, and thus a normative,
"quasi-necessary", or "formal" science, as Peirce
uses the words. So there's a lot more going on
here at a reflective level than what we need
merely to define the sign relation itself.
| A sign, or 'representamen', is something which stands to somebody
| for something in some respect or capacity. It addresses somebody,
| that is, creates in the mind of that person an equivalent sign, or
| perhaps a more developed sign. That sign which it creates I call
| the 'interpretant' of the first sign. The sign stands for something,
| its 'object'. It stands for that object, not in all respects, but in
| reference to a sort of idea, which I have sometimes called the 'ground'
| of the representamen. (CP 2.228).
This is another perfectly good definition of a sign relation,
provided that we take it with the necessary grain of salt that
is called for to season the sop of a psychologistic misreading.
I will tell you my personal way of understanding the "ground"
of a sign relation, perhaps on account of the fact that field
and gestalt theories were among my first loves in physics and
psychology. The elements of all possible sign relations float
like dust motes in the air, or like iron filings on a plate of
glass, and the ground is that beam of sunlight or magnetic field
that constellates the patterned figures in the medium that we see.
Formally speaking, then, shorn of all metaphor as much as possible,
the ground is just that constraint which picks out certain triples
and chaffs the rest. In short, it is but an alias for the entire
sign relation as a subset of a cartesian product, L c O x S x I.
Discussion Note 5
JA = Jon Awbrey
TG = Tom Gollier
Continuing from where I left off last time ...
TG: Thus, in the diagram:
o---------------------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Sign (Sensory Cool Air, Dark Cloud)` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| Object o-----<| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `o Interpretant (Mental Cool Air, Dark Cloud = Rain)|
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o---------------------------------------------------------------------o
Figure 1'. Sign Relation in Dewey's "Rainy Day Inquiry"
TG: both sign and interpretant are taken as diagrams with certain elements
and relations between them based on the "ground" of, say, rain or the
possibility of rain as the basis for abstractively observing the sign
or imagining the interpretant. If we ask, abstracted from what, or
what is the object, that can only be the context or situation.
If we try to specify the object in any more detail or exactness,
we don't have an object at all but rather another sign.
I don't have any argument against taking the
sensation of coolness and the conception of
coolness as a sign/interpretant pair, but it
wasn't what Dewey highlighted in his example,
to which line of thinking I was trying to hew.
I cannot follow the identification of espied
dark clouds with the future contingent rain,
however.
As a general issue, it seems that Peirce's theory of signs
is robbed of much of its significance if we cannot take it
to speak of any conceivable objects of speech and thought,
including abstract, conjectural, contingent, hypothetical,
intentional, and potential objects.
Discussion Note 6
JA = Jon Awbrey
TG = Tom Gollier
Al fine ...
TG: Of course, this is where I always get hit with that
"sign, sign, everything's a sign" refrain, and it's
true the object can be represented by a sign. That's
what we're doing here. If we represent it with another
sign, it's own sign apart from the sign and interpretant
of this diagram, then we just play the same game we're
playing now with a different sign and its interpretant
and its object. That's not what seems to be going on
with the "ordinary" guy in Dewey's example. With him
there's just the abstractive observation (sign) resulting
in an imagined diagram (interpretant) from which he infers
"rain". The object, the context or situation, is indeed the
third element, the one we are in fact making explicit only
in this one respect with this sign and this interpretant.
I refrain from that refrain, as it seems beside the point to me.
But I think that you might be misled by CP 2.227 into thinking
that AO is involved in every sign process, instead of being
the peculiar feature of logical reflection. Just my very
rough and chancey guess at this point, though.
TG: In short, I've always felt it's a cheap trick to pretend to solve
the problems posed by the Kantian thing-in-itself by the citing the
fact we do invent signs to represent it. Geez, no problem there.
And, I think when Peirce said objects are signs he had in mind more
the way a diagram, such as our modern scientific view of the solar
system, can come to take the place of the object itself. If the
guy in the example were abstracting the elements and relationships
of this sign and interpretant from a fully developed scientific
conception of weather, it elements and interactions, that had
stood the inductive tests of time such that he would take that
diagram for the object itself, then we might say that is the
sign-object in the above diagram. But that would be a different,
more sophisticated example; one that Peirce got to in the omitted
part of 2.227, but one I don't think we should jump to too quickly.
Yes, at least, so far as I think I understand
some of what you are saying here. Our hero's
observations are figured in relief against
the ground of his prior expectations.
Discussion Note 7
JA = Jon Awbrey
TG = Tom Gollier
TG: I am indeed being led, or misled as the case may be, into
"thinking that AO [or a diagram] is involved in every sign
process". But first, Peirce says: "All necessary reasoning
without exception is diagrammatic" [CP 5.162]. And, more
broadly this would appear to apply to any kind of deductive
reasoning or inferences, including the inference of "rain"
in this example. So it does seem to be a properly logical
orientation for the analysis of this particular example.
The way I read them, the passages at CP 2.227-228 and NEM 4 pp. 20-21
are variations on the very same theme, to explain the relationship of
logic to semiotic, the differentia being that logic is formal semiotic,
by which Peirce means quasi-necessary or normative. This leaves room
for a portion of semiotic to be contingent, empirical, or descriptive.
Also, the inference from coolness to rain is abductive not deductive.
TG: But if we're going to talk about the sign process in general, rather
than just this example, it does seem to me that the "sign", as Peirce
construes it, occupies that transitive ground of a middle term in what
can be broadly considered "deductions". And if that's correct, then
what Peirce has to say about diagrams and necessary or mathematical
reasoning would give us an internal view of the actual mechanics
within a sign by which it applies to objects on the one side and
produces interpretants on the other.
TG: It's just an hypothesis though, so am I being "misled" by it?
Too close to the whiching hour -- will have to save the rest for tomorrow.
Discussion Note 8
JA = Jon Awbrey
TG = Tom Gollier
Starting from where I left off ...
TG: But if we're going to talk about the sign process in general, rather
than just this example, it does seem to me that the "sign", as Peirce
construes it, occupies that transitive ground of a middle term in what
can be broadly considered "deductions". And if that's correct, then
what Peirce has to say about diagrams and necessary or mathematical
reasoning would give us an internal view of the actual mechanics
within a sign by which it applies to objects on the one side and
produces interpretants on the other.
TG: It's just an hypothesis though, so am I being "misled" by it?
In Peirce's early work, at least, the different kinds of signs were
associated with the different kinds of inferences, respectively.
Re: ICE 3ff. http://stderr.org/pipermail/inquiry/2003-March/000198.html
In: ICE. http://stderr.org/pipermail/inquiry/2003-March/thread.html#196
To what extent this survives in his later work would take some
additional study. Also, I'm not sure that all deductions are
apodictic, as there may be types of probable reasoning that
follow the deductive pattern, only less certainly.
Discussion Note 9
Here's the "New List" text about the relations between the types of signs and the types of inference, that is, the morphological and temporal constituents of inquiry: | In an argument, the premisses form a representation of | the conclusion, because they indicate the interpretant | of the argument, or representation representing it to | represent its object. The premisses may afford a | likeness, index, or symbol of the conclusion. | | [Deduction of a Fact] | | In deductive argument, the conclusion is represented | by the premisses as by a general sign under which it | is contained. | | [Abduction of a Case] | | In hypotheses, something 'like' the conclusion is proved, | that is, the premisses form a likeness of the conclusion. | Take, for example, the following argument:-- | | M is, for instance, P_1, P_2, P_3, and P_4; | | S is P_1, P_2, P_3, and P_4: | | [Therefore], S is M. | | Here the first premiss amounts to this, that | "P_1, P_2, P_3, and P_4" is a likeness of M, | and thus the premisses are or represent | a likeness of the conclusion. | | [Induction of a Rule] | | That it is different with induction another example will show. | | S_1, S_2, S_3, and S_4 are taken as samples of the collection M; | | S_1, S_2, S_3, and S_4 are P: | | [Therefore], All M is P. | | Hence the first premiss amounts to saying that "S_1, S_2, S_3, and S_4" | is an index of M. Hence the premisses are an index of the conclusion. | | Peirce, 'Collected Papers' CP 1.559, 'Chronological Edition' CE 2, p. 58. Let the expression "P_1 & P_2 & P_3 & P_4" denote the proposition Q = Conjunction (P_1, P_2, P_3, P_4). Then we may draw the following Figure of Abduction: o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` P_1 ` P_2 ` ` ` ` P_3 ` P_4 ` ` ` ` ` | | ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` | | ` ` ` ` ` ` \*` ` \ ` ` ` ` / ` `*/|` ` ` ` ` ` | | ` ` ` ` ` ` `\`*` `\` ` ` `/` `*`/`|` ` ` ` ` ` | | ` ` ` ` ` ` ` \ `*` \ ` ` / `*` / `|` ` ` ` ` ` | | ` ` ` ` ` ` ` `\` `* \` `/`*` `/` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` \ ` `*\ /*` ` / ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `Q` ` `.` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` \ ` `|` ` / ` `*` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `\` `|` `/` `*` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` \ `|` / `*`Case ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `\`|`/`*` `S=>M ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` \|/*` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `S` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Figure A. Abduction of the Case S => M Let the expression "S_1 v S_2 v S_3 v S_4" denote the proposition L = Disjunction (S_1, S_2, S_3, S_4). Then we may draw the following Figure of Induction: o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `P` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` /|\*` ` Rule` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` `/`|`\`*` M=>P` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` / `|` \ `*` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` `/` `|` `\` `*` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` / ` `|` ` \ ` `*` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` `.` ` `L` ` `.` ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` ` / ` `*/ \*` ` \ ` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` `/` `*`/` `\`*` `\` `|` ` ` ` ` ` | | ` ` ` ` ` ` ` / `*` / ` ` \ `*` \ `|` ` ` ` ` ` | | ` ` ` ` ` ` `/`*` `/` ` ` `\` `*`\`|` ` ` ` ` ` | | ` ` ` ` ` ` /*` ` / ` ` ` ` \ ` `*\|` ` ` ` ` ` | | ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` | | ` ` ` ` ` S_1 ` S_2 ` ` ` ` S_3 ` S_4 ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Figure B. Induction to the Rule M => P Reference: | C.S. Peirce, "New List", CP 1.559, CE 2, p. 58. | | Charles Sanders Peirce, "On a New List of Categories" (1867), |'Collected Papers' CP 1.545-567, 'Chronological Edition' CE 2, pp. 49-59. | | http://www.peirce.org/writings/p32.html | http://members.door.net/arisbe/menu/library/bycsp/newlist/nl-frame.htm
Discussion Note 10
JA = Jon Awbrey
JD = John Dewey
TG = Tom Gollier
Re: EOI-DIS 7. http://stderr.org/pipermail/inquiry/2004-November/001717.html
In: EOI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
TG: In Discussion Note 7 you write:
JA: Also, the inference from coolness to rain is abductive not deductive.
TG: This is rather hard for me to envision in terms of either your drawing
or mine. How is "rain" something that explains anything in either of
our diagrams? If we redo your drawing:
o------------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
| ` ` ` ` ` ` ` ` ` ` ` ` `o Sign (Thought of Rain) ` ` ` ` `|
| ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
| ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
| Object (Rain) o-------O ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
| ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
| ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
| ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant (Quicken his pace)`|
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
o------------------------------------------------------------o
Figure 1". Sign Relation in Dewey's "Rainy Day Inquiry"
TG: then "rain" would make sense as an abductive inference, for we would be
abductively inferring that "rain" is the explanation of the man quickening
his pace. This obviously changes the example, but I'm wondering if this
is what you have in mind in saying "rain" is the product of an abductive
inference?
This where the viscosity of the wicket has been bedeviling me
for the last 15 years or so, and I have this deja vu feeling
that we had this same discussion on the Peirce List 2 or 3
years ago, so I'll look up the notes of that time around
and see whether I've got any new ideas about it ...
The problem is that we have two styles of diagrams,
the sign relational and the syllogistic triagrams:
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `o Sign ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` Object o---------O` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 10.1 Elementary Sign Relation
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` Z ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | Ab` > \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\ /` `\` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` Fact` | <-o-De` o Y ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/ \` `/` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | In` > / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 10.2 Three Kinds of Inference
The diagram that makes the abductive character of the
inference clear is the following syllogistic figure,
where the case that it's about to rain is abduced
from the fact that the air is cooler and the
rule that cooler air implies that it's
about to rain.
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `Air Cool ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` A ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ^^` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |A` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | b ` ` \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `d` ` `\` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` Fact` | ` u ` ` o 'Bout To Rain ` ` |
| ` ` ` ` ` ` ` ` ` | ` `c` `^` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` e / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` `Current Situation` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 10.3 Abduction of Case from Fact and Rule
TG: Dewey seems to exhibit the same aversion to looking at the
original example as a form of deduction despite the fact he
does what to distinguish it from just seeing the image of
something in the clouds. He writes in a footnote after
listing "points to, tells of, betokens, prognosticates,
represents, stands for, implies" as synonyms for what
has occurred in the example example of inferring the
possibility of rain.
JD: "*Implies* is more often used when a principle or general truth brings
about belief in some other truth; the other phrases are more frequently
used to denote the cases in which one fact or event leads us to believe
in something else." [Fn 2, MW 6.187]
But our peripatetic protagonist is not certain it will rain,
neither on the data of cool air, nor on the evidence of
dark clouds, nor even on the cumulation of both facts,
so any notion of exact deductive inference would be
precipitous at best. To say that we deduce the
possibility of rain is fudging the issue,
since the mere possibility of rain is
always present, in any case, dataful
or dataless.
TG: But, (1) I don't think Peirce would limit implication or deduction
in that formalistic kind of way and (2) even inferring facts from
facts to facts we still employ a diagrammatic representation
transitively as a sign. Thus, smoke "points to, tells of,
betokens, prognosticates, represents, stands for" fire
because we use a diagrammatic conjunction of those
two facts, smoke and fire, to infer the one from
the other. This may not be the stuff of
"general truths", but it does seem to
be generally "deductive" rather than
abductive or inductive?
Dewey is invoking "implication" very loosely here,
more-ally or less-ally equivalent to "inference",
with respect to which we admit demonstrative
and non-demonstrative varieties, all tolled,
but the inferences to rain or fire are not
certain in these cases, so not deductive.
Discussion Note 11
AB = Auke van Breemen
JA = Jon Awbrey
Re: EOI 9. http://stderr.org/pipermail/inquiry/2004-November/001762.html
In: EOI. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1704
JA: An immediately obvious difference between the two Figures
is that the sign triple has the "Thought of Rain" whereas
the syllogistic triple has the object state "Before Rain".
Is this a significant difference between the two diagrams?
AB: I am just reading 'Real Knowledge', by Jan Sleutels, 1994, Diss.
It is about internalist and externalist accounts of knowledge in
neural epistemics. At first glance a difference between the sign
triple and the syllogistic one is that the syllogistic one prohibits
an internalist account whereas the sign triple diagram may or may not
be externalistic. (Just the Figures, without its Peircean or syllogistic
context that is. We know that it is externalistic.)
I confess that I've never quite understood this talk of
externalist versus internalist perspectives, much less
its application to Peirce. Maybe this is my chance to
try again. Could you lay out your reasoning here in
more detail for me?
Discussion Note 12
JA = Jon Awbrey
TG = Tom Gollier
Re: EOI 9. http://stderr.org/pipermail/inquiry/2004-November/001762.html
In: EOI. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1704
TG: Even if we look at abduction as inferring this is a case of
some rule rather than of an explanation (although those are
just two ways of saying the same thing anyway), I don't see
where "rain" is what is being adduced. For the abduction
according the way I would look at it would be that:
TG: - This is a case of air getting cool
As "Case", "Fact", "Rule" are used in this context, this is a Fact,
in effect, the deductive conclusion "C => A", paraphrased something
like "the current situation is one in which the air is cooler".
You can tell it's a Fact because it is taken as 100% certain,
a done deal, that the air is cooler. If the ambler doubts
his senses, that is a horse of another cooler, and not
at all the situation that we are discussing here.
TG: And that this abduction, when combined with the rule that:
TG: - Cool air is an indication of rain
For this to be a Rule in the deductive sense, you would have to delete
the expletive fudge factor "indication" and state simply that A => B,
in other words, "If the Air is cooler then it's Bound to rain".
TG: allows our hero to deduce rain may very well be in the offing.
But the deductive inference is apodictic, bound, certain,
demonstrative, exact, and does not allow of the modality
that you admit as "may very well be" in your conclusion.
TG: But, then, looking at your diagram:
o-----------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `Air Cool ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` A ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ^^` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` |A` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | b ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | `d` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` Fact` | ` u ` ` o Before Rain ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` `c` `^` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` e / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` `/ `Case` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `Current Situation` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-----------------------------------------------------------o
Figure 7. Abducing a Case from a Fact and a Rule
TG: while it does have the "current situation" in the place of "rain"
as the object, it strangely reverses the "case" and the "fact".
It would seem the case (or minor premise) should tie the current
situation to the antecedent of the rule, or "cool air" in this
case, while the fact (or conclusion) should link the current
situation to the consequent, rain or "before rain"?
The rule of thumb for telling a fact from a case
is that the fact is evident on the face of things,
while the case tends to be a more inobvious cause.
TG: I hope you're not tiring of this exercise,
and remaining stuck on Notes 1 or 2 as it were,
but I think it's important to take examples as
concretely analyzable in their own right rather
than abstract exemplifications of principles more
abstract still. To me it's the difference Dewey
makes between inferring rain from the clouds
and seeing faces in them.
No, the hike has been healthy exercise so far.
I think that a satisfactory analysis of this
humble excursion would go a long way toward
understanding the true relationship between
signs and inquiry, and also the development
that Peirce and much later Dewey underwent.
Discussion Note 13
AB = Auke van Breemen
JA = Jon Awbrey
Re: EOI-DIS 11. http://stderr.org/pipermail/inquiry/2004-November/001767.html
In: EOI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
[NB. I use links like the above to avoid long quotations of previous discussions.]
JA: I confess that I've never quite understood this talk of
externalist versus internalist perspectives, much less
its application to Peirce. Maybe this is my chance to
try again. Could you lay out your reasoning here
in more detail for me?
AB: With regard to application it may be wise to apply Peirce to the
internal-external perspectives instead of the other way around.
I think I can agree with that.
AB: I saw myself confronted with neural epistemic while trying
to decide whether a detailed analysis of a sign must take
care of the processes that occur in the brain or whether
we can do without it. This is part of an exchange of
thought with Francis about sign processes. So I am
not primarily interested in the opposition between
internal and external itself.
This may sound like an overly free association,
but have you read Freud's 1895 'Project'?
Here are some excerpts from the last time
that I happened to return to it:
PSY. http://stderr.org/pipermail/arisbe/2003-February/thread.html#1633
PSY. http://stderr.org/pipermail/arisbe/2003-February/thread.html#1661
PSY. http://stderr.org/pipermail/arisbe/2003-March/thread.html#1720
AB: At bottom it seems that the distinction arises as a consequences of
making an opposition between subject and world. Probably your remark
about individuals being made, not born is relevant here.
AB: (The pages refer to Sleutels work. I do not give his position
but some remarks concerning his picture of the opposition.
The language is definitely not Peircean.)
AB: [Sleutels, p. 205]
Internalist thinking: "Mental symbols served a clear purpose.
They were needed to go proxy for states of affairs in the external
world: the world as such is inaccessible to the subject, but its
mental symbols are immediately present to consciousness, affording
to the subject mediate (inferential access to the world)."
AB: Externalist thinking: "the primary relation is not between subject
and symbol, but between subject and world. Hence it would seem that
the world is immediately 'given' to the subject. Therefore mental
representations are no longer needed: they do not ass [?] to our
understanding of cognition."
I guess I consider that a false dilemma,
the very sort of aporia that the theory
of 3-adic sign relations is designed to
bypass. A very similar sort of thing
happens with the animadversions of
coherentists versus objectivists.
AB: Sleutels wants to have best of both worlds. (p. 204).
The present externalist account takes the exact opposite stance
[regarding the superfluous character of mental representations]:
its project is to understand internal computational structure from
differences in content, defined in terms of the subject's different
relations to external states of events.
AB: Much more can be said of course. But in regard to your diagrams.
The mental 'thought of rain' vs the object state 'before rain'
differ in that the former is more easily appropriated by
internalist thinking, than the object state.
AB: Of course we know this problematic from the Questions series,
from later dealings with the perceptual judgement and lots of
other occasions. In my opinion Sleutels in taking the best
of both is approaching a Peircean perspective, but falls for
interesting reasons short. I will not dwell on that now.
AB: A relevance of that dispute for peircean philosophy
might be the help by thinking about details.
AB: In the Question series Peirce hit upon the unknowable rock of pure,
atomic individuality in the stimulation of a single nerve cell.
The unknowable that runs in a continuous stream through our
lives, as he called it.
But our knowledge of neurons,
like our knowledge of egos,
is inferential and mediated,
is it not?
AB: Later he reworks this in ideas about the percept and perceptual
judgement. The over all picture is that in an out of our control
process by the stimulation of nerves a percept is generated [all
individual receptor excitations being indexicaly connected with
the object], the perceptual judgement takes a bundle of them as
iconical related with a dynamical object (recognizes it as such
through the abductive reduction of the manifold to unity and
transforming the resulting iconical rhematic percept into
a proposition by recognizing, as it were, the indexical
relation of the constituent qualia with the dynmical object).
Thus a perceptual fact is made. It is tempting to look at the
relation between percept and perceptual fact as the relation
between token and type or replica sinsign and legisign.
This looks a bit too much like
Quine's concoction to mix well
with Peirce's solution.
AB: I hope this will do as a first answer.
I am working on an exposition of this
matter in sign diagrams. Comment is
welcome.
Many thanks for the explanations ...
Discussion Note 14
JA = Jon Awbrey
TG = Tom Gollier
Re: EOI-DIS 12. http://stderr.org/pipermail/inquiry/2004-November/001772.html
As Amended At: http://stderr.org/pipermail/inquiry/2004-November/001773.html
In: EOI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
TG: Ah hah! At last I think I see where our disagreement is arising. But I also think
you're catching some of that schizo-speak that has been going around to call a fact
that's 100% certain a "conclusion". If it's 100% certain, we don't need any argument,
and if it's a conclusion, it's not 100% certain. After all, *modus tollens* is always
just as valid as *modus ponens* in any given argument.
Yes, I was undermind by a colloquial phrasing,
but I mean that it's 100% certain relative to
the certainty of the major and minor surmises.
Incidentally, this does serve to bring up the
analogy between exact and probable deduction.
TG: But I have to admit, even though I knew it wasn't "case, rule,
and fact", I was too lazy to look it up. And besides, the thing
I like about Peirce (along with Dewey) is the view that the result
or conclusion is a fact, just a fact predicted or otherwise not
present at the moment. Anyway, to be clearer about the diagram,
I think it should be more like:
o-----------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `Air Cool ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` A ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` Case` | ecudbA` o Rain ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` `/ `Result` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` C ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `Current Situation` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-----------------------------------------------------------o
Figure 7'. Abducing a Case from a Rule and a Result
TG: I doubt if this makes it anymore agreeable to you, but it's clearer
vis-a-vis the texts in Peirce. And at least this way we don't have
to worry about those mythological facts that are not true or false,
but certain, creeping into the analysis.
The designations Case, Fact, Rule on this stage are more like roles that
statements play than anything essential about the statements themselves,
so I often capitalize them when intended as these peculiar terms of art.
The vertical dimension of the syllogistic diagrams is meant to indicate
the comparative order, if comparable, of concepts or terms in a lattice
or "partially ordered set" (more cutely referred to as a "poset").
Read under these conventions, Figure 7' indicates that
Rain => Air Cool, which is not a hard and fast fact,
in any sense of the word.
Of course, everybody knows that you can only go so far
whith these purely propositional or syllogistic forms,
but one of the reasons that I am pushing the edge of
the envelope as far as I can is to see how Peirce
was forced to develop the logic of relatives
in order to explain how explanation works.
Discussion Note 15
JA = Jon Awbrey
TG = Tom Gollier
Re: EOI-DIS 12. http://stderr.org/pipermail/inquiry/2004-November/001772.html
As Amended At: http://stderr.org/pipermail/inquiry/2004-November/001773.html
In: EOI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
TG: Sorry, I'm reading your messages backwards again.
Maybe that's why they make sense to me? Anyway:
TG: - Cool air is an indication of rain
JA: For this to be a Rule in the deductive sense, you would have to delete
the expletive fudge factor "indication" and state simply that A => B,
in other words, "If the Air is cooler then it's Bound to rain".
TG: allows our hero to deduce rain may very well be in the offing.
JA: But the deductive inference is apodictic, bound, certain,
demonstrative, exact, and does not allow of the modality
that you admit as "may very well be" in your conclusion.
TG: What a narrow, formalistic view of deduction. But yet our pace quickens, no?
Well actually not mine in these situations, because I also believe in the old
gambling maxim that scared money never wins, so if I quicken my pace, I'm going
to get rained on for sure. But they sure seem like deductions -- applications
of a case to a rule so as to produce a predicted fact/result -- to me.
I see this another way. Logic is the "theory of inquiry" (TOI). Catchy title, no?
And deduction is the straight and narrow arrow (=>=> = =>). It would be myopic of
me if I identified deduction with the whole of inquiry, the whole of reasoning,
but I do not, there is the whole world of abductive and inductive reasoning,
at the very least, else wise. Abductive and inductive inference play and
work by their own rules, which joy and job is ours to articulate as best
we can.
And so it goes ...
Discussion Note 16
AB = Auke van Breemen
JA = Jon Awbrey
KM = Kirsti Maattanen
Re: EOI-DIS 13. http://stderr.org/pipermail/inquiry/2004-November/001784.html
In: EOI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
I took a Master's in Psych in 1989, for which I read
a lot of behaviorist, clinical, cognitive, neuropsych,
quantitative/stats, and systems/cybernetic literature.
Aside from teaching math, my grad asst jobs were mostly
as a comp/data/stat asst in biosci/med school settings,
so I kept up with the literature enough to have a feel
for the datasets that I had to work with in those areas.
I put Peirce and Freud in comparison as keen observers of
persistent psychological phenomena, with the speculative
power to anticipate explanatory mechanisms of a complexity
that many of our more reductionist thinkers hardly match
to the present day. It may be that Ockham's razor will
always shave as close to the spinal cord as possible,
but there are treasures yet to be explored in both
of these prescient but not pre-scientific lights.
KM: Just some comments on your latest discussion on "neural epistemic":
KM: I was left wondering on the interest on what Peirce,
as well as Freud in his 'Project', wrote on neurons
and the brain. Surely that has only historical
relevance, serving mainly critical purposes.
(There is a wealth of empirical findings
nowadays, although I don't find the
approaches in main-stream brain
research reconcilable with
a Peircean approach).
KM: I personally do not find what Peirce -- very tentatively -- wrote on
neurons etc something to rely on, nor do I think Peirce meant it to
be taken. Still, I do not recognize the overall picture you, Auke,
gave in the following -- if I understood correctly -- as Peirce's
view. Do you really mean that this is what Peirce had in mind?
(I have underlined the sentences I find most problematic)
AB: In the Question series Peirce hit upon the unknowable
rock of pure, atomic individuality in the stimulation
of a single nerve cell. [...]
JA: But our knowledge of neurons,
like our knowledge of egos,
is inferential and mediated,
is it not?
AB: Later he reworks this in ideas about the percept
and perceptual judgement. The over all picture
is that in an out of our control process by the
stimulation of nerves a percept is generated
[all individual receptor excitations being
indexicaly connected with the object], the
perceptual judgement takes a bundle of them
as iconical related with a dynamical object
(recognizes it as such through the abductive
reduction of the manifold to unity and
transforming the resulting iconical
rhematic percept into a proposition
by recognizing, as it were, the
indexical relation of the
constituent qualia with
the dynmical object).
Thus a perceptual
fact is made.
KM: I haven't been following the discussions in the list
for quite some time, and catching up with the huge
amount of mails has been somewhat overwhelming.
So, my apologies in probable failings to take
into account earlier relevant messages.
Discussion Note 17
JA = Jon Awbrey
KM = Kirsti Maattanen
Re: EOI-DIS 16. http://stderr.org/pipermail/inquiry/2004-November/001841.html
In: EOI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
KM: Thanks, Jon, for providing a context for bringing up Freud's Project.
KM: In the main I can agree with the following:
JA: I put Peirce and Freud in comparison as keen observers of
persistent psychological phenomena, with the speculative
power to anticipate explanatory mechanisms of a complexity
that many of our more reductionist thinkers hardly match
to the present day.
KM: But why do you say "our MORE reductionist thinkers"?
Do you consider Peirce a reductionist?
Freud certainly was, but not Peirce.
Freud in 1895 was still reductionist, of the old Helmholtz school,
but already beginning his transition to another order of thinking.
But my point is this: A criterion of scientific thinking is that
our theoretical models be adequate to the phenomenon in question.
Freud's 'Project' contains the seeds of many ideas that we do not
see prevalent in mainstream psychological and psychiatric thought
until after the cognitive revolution on the one hand and the rise
of object relations theories on the other.
KM: The main issue, however, is about the relationship between the
mind and the brain, or psychological phenomena and neural processes.
Freud explicates with admirable clarity his reductionistic aim and
his devotion to the (outdated) ideals of natural science of his time
in the introduction to the Project (see below an excerpt from the link
you provided).
Once again, the feature of principal interest to me is whether the
theoretical models are adequate to the complexity of the phenomena.
It is the form and function of these models that gives them their
explanatory power, and not the labels that we pin to their parts,
whether we call them "physical" or "psychical". The fact is that
Freud was articulating models of a recognizably cybernetic cast,
with neural structures that were complex enough to serve much
in the way that dynamic data structures do in current AI work,
that is, sufficient to the tasks of knowledge representation,
plus a markedly recursive analysis of psycho-social functions.
KM: With the following I cannot agree:
JA: there are treasures yet to be explored in both
of these prescient but not pre-scientific lights.
KM: I can't see any treasures following from Freud's aim
to "represent psychical processes as quantitatively
determined states of material particles" [= neurons].
This is not what is valuable in Freud's work; the
treasures to be cherished are to be found elsewhere.
(Unfortunately it's not uncommon to find the errors
and limitations of eminent and famous scientists
cherished as much or more than the treasures.)
Again, I do not care if a thinker thinks that all the cosmos
is made of water, or fire, or whatever -- it is the form and
the functioning of that substance that makes the explanation
explain phenomena, if it does at all.
I'll pick out some of my more
treasured nuggests tomorrow,
but I have to break for today.
Discussion Note 18
Auke, Kirsti, List, I'm preparing to return to this more systematically, but here is one incidental, rather more interesting point of comparison between Peirce and Freud that I had been studying: Cf: ESD 1. http://stderr.org/pipermail/arisbe/2003-February/001628.html Copied here: =================================================== Expectation, Satisfaction, Disappointment Compare and Contrast: Exhibit 1 | Reasoning and Expectation | | But since you propose to study logic, you have more or less faith | in reasoning, as affording knowledge of the truth. Now reasoning | is a very different thing indeed from the percept, or even from | perceptual facts. For reasoning is essentially a voluntary act, | over which we exercise control. If it were not so, logic would | be of no use at all. For logic is, in the main, criticism of | reasoning as good or bad. Now it is idle so to criticize | an operation which is beyond all control, correction, | or improvement. (CP 2.144). | | You have, therefore, to inquire, first, in what sense you have | any faith in reasoning, seeing that its conclusions cannot in | the least resemble the percepts, upon which alone implicit | reliance is warranted. Conclusions of reasoning can little | resemble even the 'perceptual facts'. For besides being | involuntary, these latter are strictly memories of what | has taken place in the recent past, while all conclusions | of reasoning partake of the general nature of expectations | of the future. What two things can be more disparate than | a memory and an expectation? (CP 2.145). | | The second branch of the question, when you have decided in what | your faith in reasoning consists, will inquire just what it is | that justifies that faith. The stimulation of doubt about things | indubitable or not really doubted is no more wholesome than is | any other humbug; yet the precise specification of the evidence | for an undoubted truth often in logic throws a brilliant light | in one direction or in another, now pointing to a corrected | formulation of the proposition, now to a better comprehension | of its relations to other truths, again to some valuable | distinctions, etc. (CP 2.147). | | As to the former branch of this question, it will be found | upon consideration that it is precisely the analogy of an | inferential conclusion to an expectation which furnishes the | key to the matter. An expectation is a habit of imagining. | A habit is not an affection of consciousness; it is a general | law of action, such that on a certain general kind of occasion | a man will be more or less apt to act in a certain general way. | An imagination is an affection of consciousness which can be | directly compared with a percept in some special feature, and | be pronounced to accord or disaccord with it. Suppose for | example that I slip a cent into a slot, and expect on pulling | a knob to see a little cake of chocolate appear. My expectation | consists in, or at least involves, such a habit that when I think | of pulling the knob, I imagine I see a chocolate coming into view. | When the perceptual chocolate comes into view, my imagination of it | is a feeling of such a nature that the percept can be compared with | it as to size, shape, the nature of the wrapper, the color, taste, | flavor, hardness and grain of what is within. Of course, every | expectation is a matter of inference. What an inference is we | shall soon see more exactly than we need just now to consider. | For our present purpose it is sufficient to say that the | inferential process involves the formation of a habit. | For it produces a belief, or opinion; and a genuine | belief, or opinion, is something on which a man is | prepared to act, and is therefore, in a general sense, | a habit. A belief need not be conscious. (CP 2.148). | | Charles Sanders Peirce, 'Collected Papers', CP 2.144-148. Exhibit 2 | The Experience of Satisfaction | | The filling of the nuclear neurones in Psi has as its | consequence an effort to discharge, an impetus which is | released along motor pathways. Experience shows that the | first path to be followed is that leading to 'internal change' | (e.g., emotional expression, screaming, or vascular innervation). | But, as we showed at the beginning of the discussion, no discharge | of this kind can bring about any relief of tension, because endogenous | stimuli continue to be received in spite of it and the Psi-tension is | re-established. Here a removal of the stimulus can only be effected | by an intervention which will temporarily stop the release of quantity | (Q-eta) in the interior of the body, and an intervention of this kind | requires an alteration in the external world (e.g., the supply of | nourishment or the proximity of the sexual object), and this, as | a "specific action", can only be brought about in particular ways. | At early stages the human organism is incapable of achieving this | specific action. It is brought about by extraneous help, when the | attention of an experienced person has been drawn to the child's | condition by a discharge taking place along the path of internal | change [e.g., by the child's screaming]. This path of discharge | thus acquires an extremely important secondary function -- viz., | of bringing about an understanding with other people; and the | original helplessness of human beings is thus the primal source | of all moral motives. | | When the extraneous helper has carried out the specific action in | the external world on behalf of the helpless subject, the latter | is in a position, by means of reflex contrivances, immediately | to perform what is necessary in the interior of his body in | order to remove the endogenous stimulus. This total event | then constitutes an "experience of satisfaction", which | has the most momentous consequences in the functional | development of the individual. ... | | Thus the experience of satisfaction leads to a facilitation between | the two memory-images [of the object wished-for and of the reflex | movement] and the nuclear neurones which had been cathected during | the state of urgency. (No doubt, during [the actual course of] | the discharge brought about by the satisfaction, the quantity | (Q-eta) flows out of the memory-images as well.) Now, when | the state of urgency or wishing re-appears, the cathexis | will pass also to the two memories and will activate | 'them'. And in all probability the memory-image of | the object will be the first to experience this | wishful activation. | | I have no doubt that the wishful activation will in the first | instance produce something similar to a perception -- namely, | a hallucination. And if this leads to the performance of the | reflex action, disappointment will inevitably follow. | | Sigmund Freud, "Project", pages 379-381. | | Sigmund Freud, |"Project for a Scientific Psychology" (1895), | pages 347-445 in 'The Origins of Psycho-Analysis: | Letters to Wilhelm Fliess, Drafts and Notes: 1887-1902', | ed. by Marie Bonaparte, Anna Freud, Ernst Kris, | trans. by Eric Mosbacher and James Strachey, | intro. by Ernst Kris, Basic Books, New York, NY, 1954.
Discussion Note 19
JA = Jon Awbrey
KM = Kirsti Maattanen
Re: EOI-DIS 16. http://stderr.org/pipermail/inquiry/2004-November/001841.html
In: EOI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1707
Continuing from where I left off ...
KM: As I see it, what Freud in his early work (The Project)
wrote extensively, as well as what little Peirce did say
on the relation between psychological phenomena and neural
processes, need to be critically examined and, if they seem
to serve some reasonable purpose, updated and reformulated.
(The extremely rare occasions I have made a note "outdated"
or something like that in the margins of CP have been with
paragraphs dealing with the nervous system. Once or twice,
if I remember correctly.) Updating, however, I do not see
anything like an easy task, main-stream neuroscience having
not much to offer, especially in terms of a Peircean frame.
KM: You mentioned behaviorism when describing your studies in psychology.
I'll take it as an example: Behaviorism is based on the work of I.P. Pavlov.
The founding fathers of behaviorism, however, took the notion of conditional
reflex, isolated it from its context, the general theoretical framework of
I.P. Pavlov. They ignored the concept of dynamical stereotypes, which for
Pavlov was the neural correlate (this may not be an adequate term to use
here) of a habit. On this basis the behaviorists then developed their
notion of habit, which became both predominant and popular, to the
degree of being ingrained in ordinary every-day western ways of
thinking. Compared to the notion of habit in Pavlov's works,
the behaviorist variant is one-sided, skewed and simplistic.
KM: Here I want to add: Why I want to bring all this up in the list is not
so just to give a response to Jon, but because -- to my mind -- the ways
Peirce's conception of habit has been understood and interpreted seems to
be continuously muddled with the behaviorist heritage. -- This, of course,
applies to what I'm familiar with. (Recommendations for further reading
are welcome).
Yes, James and Dewey had their infatuations with the young behaviorism,
and the fact is that focusing on behavior is healthy and interesting,
but again the criterion is anti-procrustean: Do we fit our models
to the actual phenomena of action, behavior, conduct -- or do we
lop off nature's givens to to fit the models we can handle?
KM: Then, back to behaviorism and Pavlov:
KM: What behaviorism left out as well from I.P.Pavlov's theory was
the basic approach of viewing the nervous system as a whole.
Exemplified in Pavlov's principle: Any pattern of activation
induces a correlated pattern of inhibition in the system (as
a whole). One of the consequences -- if this is accepted as
a starting point -- for philosophical considerations on the
mind-body problem (or its now popular reductionist variant:
mind-brain problem) is that any attempt based on activation
of single neurons or bundles of neurons and linking them
with -say- a mental image are futile.
I think we are mainly on the same plane here.
KM: We all know that the activity of the nervous system is electro-magnetic
activity. (c.f. Pavlov's principle above). Approaches based on the idea
of single neurons (then to be added up to bundles) take into consideration
electrical impulse passing (or rather hopping) through the neuron and its
synaptical transmission to other neurons. -- What is left out of consideration,
then, is the magnetic "side" of electro-magnetic phenomena. Quite unlegitimate
use of Ockham's razor, I'd say, no matter how common.
KM: I'm not sure I understood the following:
JA: It may be that Ockham's razor will always
shave as close to the spinal cord as possible.
KM: but if I did, I do hope it does not hold.
(Pardon me for saying, but did you notice
that your metaphor limps -- "shaving" sounds
an inadequate here, isn't it a euphemism?)
It connotes the microtome, and anatomical "preparations".
KM: Anyway, it seems to me that the most common and long-standing misuse
of Ockham's razor is that instead of carefully and meticulously shaving
the beard criss-crossing all over the essential features, it is used in
a much simpler and quicker way: to cut the throat. Not taking notice
that if you cut the throat, you cut out life. By this I mean ways of
philosophizing as if the head with the brain inside were all that is
essential in human beings, for epistemological purposes, for instance.
E.g. all epistemologies based on vision, that is: almost all through
the modern era. It does not take very much caricaturing to say that
all that quite often seems to be taken as essential in human body
is one eye (more specifically the dominant eye) and the brain.
Or, in modern neuroscience it is not uncommon to meet with
explicit considerations of how "the brain interacts with
the world". Which is simply nonsense and in dire need
of philosophical criticism.
KM: Well, well, well. It has been quite a while since I read
Pavlov's 'Selected Works' (in German translation). I was
an undergraduate student then, planning my master's thesis.
By then I had read my share of behaviorism, as part of the
psychology curriculum, and I.P. Pavlov was familiar from
those sources. I still vividly remember my astonishment
when I started to read his own writings, none of which
was included in the curriculum. -- And now that I came
to think about it, I don't remember having ever actually
met anyone else who had read Pavlov's own writings, not
even amongs the neuropsychologists I've discussed with
over the years.
KM: Now that I have dwelled this much on Pavlov's work,
my anticipation is that some listers draw the hasty
conclusion that I am an adherent to his theory. That
is not the case. I appreciate and even admire him as
a devoted and original researcher and theorist in his
field, still unequalled in many respects. I took him
up here as an example of a theorist in neuroscience,
whose treasures have been left behind, and a caricature
passed on to future generations.
So you understand how that happens.
KM: To restate my main point here: There is no way out in philosophy
of the trouble of taking into account in general outlines all that
is essential in life. Peirce was exceptional in his capability to
do this, as well as minute work in logic, formal and informal.
KM: To end with a more casual key, I want to tell an story from the writings
of Pavlov. He came to the conclusion that the period of optimal activity
in the brain occurs for some 20-30 minutes after waking up in the morning.
He then bemoans how people usually waste this precious time by getting
dressed and brushing their teeth, whereas he always stays in bed
contemplating the most difficult and pressing scientific problems.
Freud, "Project for a Scientific Psychology" --
I am re-locating and extending these excepts here:
PSY. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1869
Discussion Note 20
KM = Kirsti Määttänen
I am pre-occupied at the moment with other issues,
but I want to flag the following paragraph for
possible future discussion:
KM: The inertia in change is not so much because "the findings are not yet conclusive",
which is usually offered as the reason why. The real issue is about habit change,
both personal and institutional. For a shift to be paradigmatic, it necessarily
involves changes in habits of thinking and acting. This is especially where I
feel that Peircean philosophy of science may have enormous human significance.
But, in order for that to happen, there should be real interdisciplinary
dialogue. Is there, really?
Discussion Note 21
JA = Jon Awbrey
TG = Tom Gollier
Re: EOI 14. http://stderr.org/pipermail/inquiry/2004-November/001908.html
In: EOI. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1704
TG: I think you've caught the nub of our prior disagreements when you write:
JA: We need a word to cover all three uses of the later type of figure --
abductive, deductive, inductive -- since "syllogism" refers to the
deductive use alone, and so I will experiment with using the word
"syzygy" to cover all three ways of reading the same configuration.
TG: For, to my way of thinking it is precisely the syllogistic or deductive
element that puts the teeth, such as they have any, in all the means of
inference. Thus, what makes abduction valid to the extent it is is the
fact it provides an explanation. What makes induction valid to the
extent it is is not analogy (or an inane repetition of white swans)
but the fact the middle term or mediating concept can function
deductively and successfully with all sorts of consequents and
applied in all sorts of situations. Thus, to come up with a
word [that] eliminates deduction, or to restrict deductions
to formal systems only marginally related to the actual
experience, effectively pulls Peirce's teeth.
No, I think that you sum up the situation quite well, and I concur with
the way that you derive the approximate validity of Ab- and In- duction
from the exact validity of the corresponding Deduction. More important,
I think that Peirce, and so far as I remember, Aristotle, would roughly
agree with your derivation. So no root canals are in the offing so far.
I simply found that I had a recurring need for a word that referred to
a particular set of premisses, while being equipotential or neutral in
regard to its reading as an Ab-, or a De-, or an In- ductive inference.
Once again you have caught me just before it's time to go to dinner ---
But I promise to come back re-victualized for your questings ...
Discussion Note 22
JA = Jon Awbrey
TG = Tom Gollier
Re: EOI 14. http://stderr.org/pipermail/inquiry/2004-November/001908.html
In: EOI. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1704
I continue from where I left off ...
TG: Unfortunately, I think making rain the object
in the one diagram and switching the the case
and result/fact in the other has precisely
the same effect.
I'm not sure I understand what you mean here.
TG: The elements and inferences are being illustrated by a the [?] diagram
that resembles faces in the clouds. The mediating aspect of any sign
is lost with rain on the one side as object and rain (as thought) on
the other side as interpretant; while reversing the case and result
renders the deductive inference (from antecedent to consequent) into
an invalid one from consequent to antecedent.
TG: Meanwhile, you seem to insist that "deduction" be sacredly
apodictic, and I guess, not applicable at all until we have
retired to the diagram itself, divorced from any kind of
experiential relevance.
TG: But, all this also explains why I've never been too good at
the scholarly pursuit of philosophy. If you disagree with
the basic presuppositions, how can you keep on trying to
follow all the reasoning that can continues to be piled
on top of them. Philosophers should stick to short,
article- or even email-length, writings.
I guess I don't understand what you want here.
The phenomena of rain and walking and surprise
and thinking and choosing a course of action are
the primary appearances of reality, and it's up to
us to describe them how we may, in ways that explain
what we think needs explaining. All these theories of
weather or signs or inquiry and all these terms of art
are only meant for that. Peirce's mansion has rooms
for all the things that we seem to want, only there
are plaques on the doors, not on our teeth, that
have funny names peculiar to his line of thought
and the tradition of thinking that he carries
not caries forward.
The name "deduction" is pinned on an ideal limiting form
of exact explicative inference that would be what it is
under any name. There are even forms of approximate,
modal, and probable explicative inference where
you can have less than 100% certainty weighing
on the various premisses. If you seek forms
of reasoning to account for the sorts of
approximate amplicative suggestions
that we use everyday, then you
find them described under the
headings of "abductive" and
"inductive" reasoning.
It's all there.
Document history
Inquiry List (Nov 2004), “Examples of Inquiry”
- http://stderr.org/pipermail/inquiry/2004-November/001704.html
- http://stderr.org/pipermail/inquiry/2004-November/001705.html
- http://stderr.org/pipermail/inquiry/2004-November/001706.html
- http://stderr.org/pipermail/inquiry/2004-November/001709.html
- http://stderr.org/pipermail/inquiry/2004-November/001714.html
- http://stderr.org/pipermail/inquiry/2004-November/001715.html
- http://stderr.org/pipermail/inquiry/2004-November/001732.html
- http://stderr.org/pipermail/inquiry/2004-November/001749.html
- http://stderr.org/pipermail/inquiry/2004-November/001762.html
- http://stderr.org/pipermail/inquiry/2004-November/001808.html
- http://stderr.org/pipermail/inquiry/2004-November/001809.html
- http://stderr.org/pipermail/inquiry/2004-November/001810.html
- http://stderr.org/pipermail/inquiry/2004-November/001811.html
- http://stderr.org/pipermail/inquiry/2004-November/001908.html
- http://stderr.org/pipermail/inquiry/2004-November/001912.html
NKS Forum (Nov 2004), “Examples of Inquiry”
- http://forum.wolframscience.com/archive/topic/595.html
- http://forum.wolframscience.com/printthread.php?threadid=595
- http://forum.wolframscience.com/showthread.php?threadid=595
- http://forum.wolframscience.com/showthread.php?postid=1896#post1896
- http://forum.wolframscience.com/showthread.php?postid=1897#post1897
- http://forum.wolframscience.com/showthread.php?postid=1898#post1898
- http://forum.wolframscience.com/showthread.php?postid=1899#post1899
- http://forum.wolframscience.com/showthread.php?postid=1900#post1900
- http://forum.wolframscience.com/showthread.php?postid=1909#post1909
- http://forum.wolframscience.com/showthread.php?postid=1923#post1923
- http://forum.wolframscience.com/showthread.php?postid=1948#post1948
- http://forum.wolframscience.com/showthread.php?postid=1952#post1952
- http://forum.wolframscience.com/showthread.php?postid=1969#post1969
- http://forum.wolframscience.com/showthread.php?postid=1970#post1970
- http://forum.wolframscience.com/showthread.php?postid=1971#post1971
- http://forum.wolframscience.com/showthread.php?postid=1973#post1973
- http://forum.wolframscience.com/showthread.php?postid=1991#post1991
- http://forum.wolframscience.com/showthread.php?postid=1993#post1993
Inquiry List (Nov 2004), “Examples of Inquiry : Discussion”
- http://stderr.org/pipermail/inquiry/2004-November/001707.html
- http://stderr.org/pipermail/inquiry/2004-November/001708.html
- http://stderr.org/pipermail/inquiry/2004-November/001710.html
- http://stderr.org/pipermail/inquiry/2004-November/001711.html
- http://stderr.org/pipermail/inquiry/2004-November/001712.html
- http://stderr.org/pipermail/inquiry/2004-November/001713.html
- http://stderr.org/pipermail/inquiry/2004-November/001717.html
- http://stderr.org/pipermail/inquiry/2004-November/001718.html
- http://stderr.org/pipermail/inquiry/2004-November/001719.html
- http://stderr.org/pipermail/inquiry/2004-November/001737.html
- http://stderr.org/pipermail/inquiry/2004-November/001767.html
- http://stderr.org/pipermail/inquiry/2004-November/001772.html
- http://stderr.org/pipermail/inquiry/2004-November/001784.html
- http://stderr.org/pipermail/inquiry/2004-November/001806.html
- http://stderr.org/pipermail/inquiry/2004-November/001807.html
- http://stderr.org/pipermail/inquiry/2004-November/001841.html
- http://stderr.org/pipermail/inquiry/2004-November/001865.html
- http://stderr.org/pipermail/inquiry/2004-November/001866.html
- http://stderr.org/pipermail/inquiry/2004-November/001903.html
- http://stderr.org/pipermail/inquiry/2004-November/001909.html
- http://stderr.org/pipermail/inquiry/2004-November/001916.html
- http://stderr.org/pipermail/inquiry/2004-November/001923.html
