SUO: Re: Building Ontologies Through Signs And Inquiries (BOTSAI)
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JM = Jean-Marc Orliaguet
JM: Remember that there are only two kinds of people:
those who put things into various categories and
those who don't.
And I always thought that it was the 'sui generis' versus the 'gui senilis' --
JM: Each new division obtained from a previous division
adds more determination to the conception being analysed.
It is done by selecting at each new generation an essential
aspect pertaining to the conception, in order to list the
three ways in which a genuinely triadic idea can degenerate
(if the conception involves three objects), or the two ways
in which a genuinely dyadic relation can degenerate (if the
conception involves only two objects). Because of this,
once an essential aspect has been selected there is no
way to get back to a less determinate conception (e.g.
from abduction to arguments to symbols to signs to
triadic relations) without making a logical mistake
if one does not redefine all the terms by making
explicit the essential criteria that are driving
the divisions. The major problem in that case
is that Peirce over a timespan of 40 years
used his universal categories to define
and generate most of his conceptions ...
No, he did not.
Universal positive categories are just not generative enough to do that.
JM: The three types of arguments (abduction, deduction, induction) are obtained,
as you write below, by considering the three ways in which the premise of
the argument form a representation of the conclusion. This is an essential
determination in the conception of an argument because just every argument
has a set of premise and a conclusion which are logically related. In L75,
written in 1902, 35 years after "the New List", Peirce links again the three
types of arguments to the three categories (in no special listing order):
JM, citing CSP:
| I shall then come to the important question of the classification of arguments.
| My paper of April 1867 on this subject divides arguments into deductions, inductions,
| abductions (my present name, which will be defended), and mixed arguments. I consider
| this to be the key of logic. In the following month, May 1867, I correctly defined the
| three kinds of simple arguments in terms of the categories.
JM: In my opinion, there is no doubt that abduction is linked to firstness,
deduction to secondness and induction, to thirdness, as long as one considers
the following essential determination: "what is the mode of being of the premise
in relation to the conclusion?"
JM: You may divide arguments again in your own manner and thereby redefine
'abduction' by selecting another essential determination of arguments
to find out that abduction is of a thirdness type, but unfortunely by
seeing what you wrote below you chose exactly the same determination
as Peirce did in 1867.
I have settled on nothing. I am merely trying to trace, as carefully as I can,
the intellectual trajectories of this or that planetary light in the night sky,
or is it a firefly in the wind? I will puzzle it out from further observation.
You used the word "essential" six times in the above remarks.
Can you tell me what you mean by it?
What exactly do these categorical remarks and these essential classifications do for you?
What function do they serve in your thinking? Do they lend a hand to inquiry into things
apart from themselves or do they merely munch on their selves with a self-satisfied grin?
Will they help me chip out a 3-duction e-calculator in aide of even the simplest inquiry?
That is the sort of stuff that I worry about these days.
Jon Awbrey
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> Jean-Marc,
>
> Let me see if I have built up enough of my stock material
> to begin to address one or two or three of your questions,
> say, this one:
>
> JM: Now the fact that one looks upon abduction from a different perspective,
> i.e. considered as the relatively genuine genus (thirdness) of a previous
> division instead of being the most degenerate (firstness), would in principle
> give in the next generation three subclasses of abductions. In that case, since
> there is a perspective from which you see it that way, can you make explicit the
> three distinct ways in which abduction can "mediate" between deduction and induction?
>
> No, not yet.
>
> First of all, let me be honest and say that I do not really understand all this
> classification mania, whether it's pragmatists or ontologists that fall into it.
> I know, you will say that whatever it is, one thing for sure is that Peirce had
> it bad, but even there I do not read him quite the same way. Maybe it's due to
> the historical accident that I happened on his work by chance, without the boon
> of any professorial guidance, and only delved into the logical and mathematical
> source materials, soaking them up solely for the lights that they threw on my
> early questions about the grounds of reasoning. So now whenever I run into
> one of Peirce's more "classical" stretches, it does not seem out of place,
> because I think back to concrete material that it organizes, and I never
> get the impression, as I do with many of our contemporary writers on
> both pragmatism and ontology, that he was doing it for its own sake.
>
> I am more incited by how inquiry works,
> and how we can learn to work it better,
> than I am by the mere nomination of it.
>
> So let me regress, in the service of the inquiry,
> to a more primitive station in inquiry's journey
> of self-discovery, say here:
>
> | I shall now show how the three conceptions of reference to a ground,
> | reference to an object, and reference to an interpretant are the
> | fundamental ones of at least one universal science, that of logic.
> |
> | CSP, OANLOC, CP 1.559
> |
> | Charles Sanders Peirce, "On a New List of Categories" (1867),
> | Cf. 'Collected Papers', CP 1.545-567.
> | Cf. 'Chronological Edition', CE 2, pages 49-59.
> | http://members.door.net/arisbe/menu/library/bycsp/newlist/nl-frame.htm
>
> I will return to this extremely important paragraph anon,
> but for the moment let us hurry on down to the end of it:
>
> | 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. In deductive argument, the conclusion is
> | represented by the premisses as by a general sign under which it is contained.
> | In hypotheses, something 'like' the conclusion is proved, that is, the premisses
> | form a likeness of the conclusion. Take, for example, the following argument:
> |
> | [Abduction to a Case]
> |
> | 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. That it is different with induction another example
> | will show:
> |
> | [Induction to a Rule]
> |
> | 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's analysis of the patterns of abductive argument
> can be understood according to the following paraphrase:
>
> Fact: S => P^1, S => P^2, S => P^3, S => P^4
> Rule: M => P^1, M => P^2, M => P^3, M => P^4
> ---------------------------------------------------.
> Case: S => M
>
> If X => each of A, B, C, D, ..., then we have the following equivalents:
> 1. X => the greatest lower bound (glb) of A, B, C, D, ...
> 2. X => the logical conjunction A & B & C & D & ...
> 3. X => Q = A & B & C & D & ...
>
> More succinctly, letting Q = P^1 & P^2 & P^3 & P^4,
> the argument is summarized by the following scheme:
>
> | Case Abduction
> |
> | Fact: S => Q
> | Rule: M => Q
> | ---------------.
> | Case: S => M
>
> In this piece of Abduction, it is the glb or the conjunction
> of the ostensible predicates that is the operative predicate
> of the argument, to wit, the predicate that is common
> to both the Fact and the Rule of the inference.
>
> Finally, the reason why one can say that Q is an iconic sign
> of the object M is that Q can be taken to denote M by virtue
> of the qualities that they share, namely, P^1, P^2, P^3, P^4.
>
> Notice that the iconic denotation is symmetric, at least in principle,
> that is, icons are icons of each other as objects, at least potentially,
> whether or not a particular interpretive agent is making use of their
> full iconicity during a particular phase of semeiosis.
>
> The situation is diagrammed in Figure 1.
>
> | P^1 P^2 P^3 P^4
> | o o o o
> | \* \ / */|
> | \ * \ / * / |
> | \ * \ / * / |
> | \ * \ / * / |
> | \ *\ /* / |
> | o Q o |
> | | | * | |
> | | | * | |
> | | | | |
> | | | | * |
> | | | | * |
> | o | o M
> | \ | / *
> | \ | / *
> | \ | / * Case
> | \ | / * S=>M
> | \|/*
> | o
> | S
> |
> | Figure 1. Abduction to the Case S => M
>
> In a diagram like this, even if one does not bother to
> show all of the implicational or the subject-predicate
> relationships by means of explicit lines, then one may
> still assume the "transitive closure" of the relations
> that are actually shown, along with any that are noted
> in the text that accompanies it.
>
> Peirce's analysis of the patterns of inductive argument
> can be understood according to the following paraphrase:
>
> Case: S^1 => M, S^2 => M, S^3 => M, S^4 => M
> Fact: S^1 => P, S^2 => P, S^3 => P, S^4 => P
> ---------------------------------------------------.
> Rule: M => P
>
> If X <= each of A, B, C, D, ..., then we have the following equivalents:
> 1. X <= least upper bound (lub) of A, B, C, D, ...
> 2. X <= the logical disjunction A v B v C v D v ...
> 3. X <= L = A v B v C v D v ...
>
> More succinctly, letting L = P^1 v P^2 v P^3 v P^4,
> the argument is summarized by the following scheme:
>
> | Rule Induction
> |
> | Case: L => M
> | Fact: L => P
> | ---------------.
> | Rule: M => P
>
> In this bit of Induction, it is the lub or the disjunction
> of the ostensible subjects that is the operative subject
> of the argument, to wit, the subject that is common
> to both the Case and the Fact of the inference.
>
> Finally, the reason why one can say that L is an indexical sign
> of the object M is that L can be taken to denote M by virtue of
> the instances that they share, namely, S^1, S^2, S^3, S^4.
>
> Notice that the indexical denotation is symmetric, at least in principle,
> that is, indices are indices of each other as objects, at least potentially,
> whether or not a particular interpretive agent is making use of their full
> indiciality during a particular phase of semeiosis.
>
> The situation is diagrammed in Figure 2.
>
> | P
> | o
> | /|\* Rule
> | / | \ * M=>P
> | / | \ *
> | / | \ *
> | / | \ *
> | o | o M
> | | | | * |
> | | | | * |
> | | | | |
> | | | * | |
> | | | * | |
> | o L o |
> | / */ \* \ |
> | / * / \ * \ |
> | / * / \ * \ |
> | / * / \ * \ |
> | /* / \ *\|
> | o o o o
> | S^1 S^2 S^3 S^4
> |
> | Figure 2. Induction to the Rule M => P
>
> As it happens, I think that I can explain what I once called a "peculiarity"
> of Peirce's language here, simply by referring to our ordinary informal usage,
> and this will save me the trouble of looking through his early writings, where
> I recall seeing this usage before. Remember, our common logical, mathematical,
> and set-theoretic language of "unions" and "intersections" was not fully worked
> out at this time (1860's), at least, not in all the glories or mirages, depending
> on your point of view, of its current axiomatic treatment. Of course, these old
> folks had the concepts, more or less, but if I remember correctly from my first
> encounter with Peirce's work -- and my memory is always a doubtful proposition
> when I'm talking about three days, much less thirty years -- Peirce was still
> at this time, or soon to be, writing about "aggregations" and "compositions",
> and these of two kinds, "absolute" and "relative", but the intuitive meanings
> that were attached to the "absolute" or the "non-relative" variety of terms,
> and bounded by their corresponding concepts and their rudimentary definitions,
> were analogous to but not exactly identical to our modern notions of "unions"
> and "intersections", that is, the set-theoretic operations that are associated
> with the logical usage of "OR" and "AND", respectively.
>
> So what you have to understand -- what all this preambling is leading up to --
> is the following multiplicity of meaning in Peirce's usage at this point,
> namely, that the "AND" in his account of Abduction and the "AND" in his
> account of Induction are two different words, or tokens of the same
> polymorphous sign, if you will, but with a diversity of meanings,
> the first corresponding to conjunction and intersection, and the
> second corresponding to disjunction and union. And this is just
> done in accord with a perfectly natural natural language idiom.
>
> Now, if you will just try to remember the way that we often speak
> in informal circumstances and in ordinary language -- I know, it
> gets harder to remember all the time -- but it is true that we
> often use the word "AND", especially when referring to samples
> of "dry goods", like handfuls of beans and bags of wool, to
> speak of their more aggregarious union, and not so much,
> since it barely makes sense in this setting, of their
> contentious intersection.
>
> Jon Awbrey
>
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