I don't know what it is all about and am by no means confident that I would
be able to figure this out by myself. I'm not starting the discussion from
the position of someone who thinks they already understand it. I don't
know what the proper context for this paper is as regards his other work in
the period of the turn of the century and a few years thereafter. I have a
hunch that it might be occasioned by his review of Royce's The World and the
Individual or some subsequent reflection on that. The date assigned to the
New Elements (1904) seems to be tentative so it could perhaps have been
written several years earlier than that, but 1904 may be correct
nonetheless. But it just doesn't seem to me to have the feel to it that
suggests a thematic affinity with the various attempts to formulate
pragmatism that came to dominate his attention from around 1903 on nor does
it seem to be of a piece with the Syllabus of Logic stuff of 1903 or with
the Classification of the Sciences stuff or with the Normative Science
material or with the Minute Logic, which he abandoned work on after 1902,
when the Carnegie Application fell through around the beginning of 1903.
But it does seem to me to be the sort of stuff he might be likely to be
talking about if he had already done the reviews of Royce's The World and
the Individual (both volumes) and decided subsequently to accommodate
himself to Royce's sensibility as much as possible. I mean, why is he
getting into all of that metaphysical stuff about the entelechy and the
Absolute and doing so in the context of discussion of the basis of formal
logic in the theory of the proposition and the assertion?
I haven't made any attempt to verify that by digging into the
Royce-connected stuff of the early 1900's or thereabouts but am wondering if
anyone else has any opinion on that? It is not my favorite topic, as I am
very uneasy with that sort of metaphysics, but Peirce certainly had good
reason to want to accommodate Royce's interests along that line, given the
latter's position at Harvard and the fact that there was some real affinity
with Royce -- some disagreement, to be sure, but some real affinity
nonetheless. Did you ever get into Royce, Clark? It is the sort of stuff
you are probably at home with, and I am sure there are others as well who
know something about Royce. Kelly Parker does but I don't know if he is
currently on the list, and there was somebody else who mentioned Royce not
too long back as well. (Gary Richmond, maybe?) It's just a guess, and I
have nowhere in particular to go with it myself at this point, but it seems
worth mentioning in an attempt to reduce the bewilderment of it.
Joe Ransdell
I would suggest to take another direction to try answering the question of what the New Elements are about. Not to try searching into the context of his work at this time, which would certainly be useful but for which we will find nothing but indices. It would be more fruitful to examine the text we have at hand, some kind of "endoporeutic" method if I can say so.
The first thing that always appeared strange to me is that Peirce is beginning with a long development about Euclid's exposition. But we know that precisely a great revolution had already taken place in mathematics under the auspice of non euclidian geometries. I think Peirce is here just saving what had made the value of euclidian geometry in his view, the deductive method as well as the associated style of exposition. This style amounts to some general and abstract statements, which are just set down in order to show their necessary consequences. The logical structure of the exposition has not to be made explicit because it is to the reader's activity to realize it for himself. Finally, what Peirce is undertaking here is to deliver elements of his semiotic doctrine in a related form:
"A scholium is a comment upon the logical structure of the doctrine. This preface is a scholium." (EP2, p. 303). In brief I think Peirce is revisiting the basic points of his semiotic doctrine of the time, in order to see what he could further make of it, but without ordering nor explaining it, that is to say without making any kind of argument in the proper sense. Probably, there is one recurring topic among others to which Peirce was giving a special attention, the properties of a final (and future) cause which has actual consequences (in the present). Everyone will recognize here the problem of the truth of the pragmatic maxim. This is to my sense what Gary has noticed just in time in his recent post :
"The essence of the relation [of interpretation of a sign in another sign] is in the conditional futurity; but it is not essential that there should be absolutely no exception." (Peirce, CP 8.225)
In this order of things, the problem of methods is crucial and this same problem makes the distinction between Theory and Practice one of the basic points he is revisiting. Martin has given us a superb comment on this, very much clearer than I could do. So I just reproduce it below for the sake of the discussion:
---------------------------Martin Lefevre quote-----------------------------------------
In "New Elements", Peirce begins by telling us that "Theory" seeks to discover deductivelly all that which applies to a sign (which is what Peirce means by reaching a "direct perception of the entelechy": the perception of truth through necessary reasoning or, to put it differently, the recognition that "a conception can only be admitted into a hypothesis in so far as its possible consequences would be of a perceptual nature" -- Harvard Lecture #6). Semeiotically this implies elucidating an object through (the discovery of) its qualities and proceeding in deductive manner. Knowing that all men are mortal, I discover that Sorcates, in being a man, is mortal. This will be the case for all men to which, therefore, "__is mortal" applies. Symbols require interpretation and arguments indicate their interpretants. But this they can do only if they combine denotation and connotation (indices and icons). Indices are such that they build on an genuine dyadic relation with their object. Whence the importance of perception (which Peirce construed in a broad, logical not psychological, way) which he also saw as relevant in mathematics (the deductive science par excellence). Practice, on the other hand, seeks to discover all that to which a sign can be applied to by considering the predicates that can apply for each instance of it. Practice seeks to generalize the object of a sign. This, says, Peirce is done through exertion rather than perception. As arguments inductions (this is also true for abductions) also require the service of indices, but these are, in a sense, continually discovered with every new experiment (every new induction offering a new index) -- what is sought here is the production (exertion) of entelechy. Now I'm no mathematician (nor logician, for that matter) but it seems to me that these distinctions would've been quite valuable for mathematicians (the intented audience of "New Elements") whom Peirce saw as working with deductions -- as opposed to lab scientists whose discovery of the Truth lies chiefly in exertion (lab work). Moreover, Peirce recognized that mathematical deductions, in requiring indices (and icons), were also "perceptual" in a logical sense; such deductions discovering "not so much how things are, but how they might be supposed to be" in relation to objects that, unlike those of the natural sciences, are "creations of our own minds" (but no less Real for though they are not independent of our collective minds they are still independent from the accidents of what you or I think). One key for this line of argument is found in lecture 6 of the Harvard Lectures when Peirce asserts: "...perception being for the logician simply what experience, that is, the succession of what happens to him, forces him to admit immediately and without any reason."
---------------------------End Quote -------------------------------------------------------
The unique little reservation I could suggest is that the distinction between exertion and perception is not something primarily addressed to a mathematical audience but probably to the semiotic theory itself when it encounters the problem of interpretants qua interpreted signs, that is to say the dynamic interpretant.
Let us see if the examination of the rest of the text will confirm or not this first sight impression.
Bernard
Bernard Morand
Département Informatique
Institut Universitaire de Technologie BP53 14123 Ifs Cedex France
TEL (33) 02 31 52 55 34 FAX (33) 02 31 52 55 22
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http://www.iutc3.unicaen.fr/~moranb/
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