Re: Proposal for a Mini Slow Read -- Kaina Stoich eia❢

Kristi & All,

I am short on time and concentration and about to get shorter, so all
I can do right now is set the stage for a possible future discussion.
The props on that stage -- more like jigsaw puzzle pieces, actually --
are as follows, just pulled at random from my very fallible memory:

1.  Why did Peirce assign the title "Kaina Stoicheia" to this piece?
     What object did he have in mind for the piece by naming it that?

2.  What's all that fuss about the terms of art from the axiomatic method --
     (1) definitions (2) postulates (3) axioms (4) corollaries (5) diagrams
     (6) letters (7) theorems (8) scholiums?  What purpose did Peirce have
     in mind by introducing that whole panoply of nomenclature at the start?

3.  Why bring signs into the discussion at all, especially if Kaina Stoicheia
     was intended as a preface to a book on the foundations of mathematics, as
     the editors of EP suggest?  I know from my own experience that math folk
     tend to dismiss matters of "mere notation" as being "not of the essence"
     to their subject.  As we know, Peirce had another take on that question,
     but why, exactly?

All I have time for now ...

Jon

KM = Kirsti Määttänen

KM: Well, it may be I attach a different meaning to "formal axiomatic theory".
     To my mind, to express the matter as simply as I can, it deals with logic
     dealing with formulas.  That is, expressing it's ideas in way of formula
     and developing new ones from them in an axiomatic way. -- Any objections
     or corrections are welcomed!

KM: You offered two quotes from Peirce.  One was from one version of
     the Application.  The other from some other writing of Peirce.
     (My internet connection, the one nowadays available, is very
     unreliable. I do get mails, but links quite often fail.
     Quite frustrating.  A got a glimpse, but cannot check
     now.)

KM: I was talking of Kaina Stoichea and that only. -- I can't see any formulas there.
     Except the idea of rhema and rhemata.  Which I take, in relation to formal axiomatic
     logic (as I view it) take to be rather a clue towards, than an expression of formal
     axiomatic logic. -- But just as well a clue away from it.  Which is the direction
     I have taken to my interest to follow.

KM: I've hade my share of formal logic as well as of mathematics in my studies
     at Helsinki University. -- I turned away, in the conviction that there is
     nothing for me in those directions.  -- All this was before I started
     with Peirce. Later, both convictions proved wrong, but only partlally so.

KM: I'ts been decades since I read Euclid's elements, and probably only partially.
     (Available links for the full text heartily welcomed.)

KM: To my mind, Euclid presents an axiomatic system, but not a formal one. --
     He presents his statements in sentences. -- Am I wrong -- or not?

KM: You say that you are following that school of thought that
     stretches its rope from Euclid through Peirce to the present.

KM: Kaina Stoicheia is definitely about Euclid.  But Peirce and the present presents,
     at least to me, a problem.  To me, it is obvious that Peirce is -- still -- about
     the future.  With the present, there are problems.  The rope from Euclid to Peirce
     and thence to the future are still in the process of being weaved.

KM: There are problems with 'the present', taking that in a broad sense to mean 'new age*,
     the modern age etc. Problems, which I view as a heavy burden, in striving to understand
     BOTH Peirce AND Euclid, as threads in the same rope.

KM: In the time of Euclid, there was not, nor could have been,
     an idea of the equation.  The formula: a = a, was unthinkable. --
     Grattan-Guinness is one of the very few historians of mathematics
     who takes this up.  Reading Grattan-Guinness was a great revelation
     to me.  It, for instance, opened up to me some of Peirce's definitions
     of identity in a wholly new way.

KM: You may well be weaving a rope from Euclid to Peirce, no doubt about that.
     And that's something I for my part am deeply interested in. -- But there's
     a lot, a lot to be done to reach the present understanding, even amongst
     Peirce scholars.  And to reach the common sense within the present academe,
     and  those close to it.

KM: I've been reading Goethe's diaries from his journey to Italy.  He mentions
     en passant a book, of which he says: "You do not learn anything from it,
     but you become ... Well, I read a translation to Finnish, and the last word
     used just does not translate itself in my mind into an English one, without
     distorting the idea.  "Someone" is an option, but being well versed with Goethe,
     not one I would choose.

KM: With Peirce, not only your ideas, thoughts and knowledge (information) chance.
     In an ideal case, your way of thinking changes.

KM: Peirce defines logic in many ways, in various times and in different writing.
     In the most general view, he makes a difference between logic in the broad sense,
     and logic in a restricted sense, in a narrow sense.

KM: Formal logic, to my mind, is to Peirce logic in a narrow sense. --
     You, with your skills, can easily find quotes on logic in the
     broad sense.

KM: In formal logic, as well as in mathematics -- in modern ages
     taken in a broad sense meaning times after the enlightenment --
     one of Peirce's definitions of the sign take the fore.  Which
     is the 'standing for'-relation.

KM: A sign is then taken as -- primarily -- standing for something else. --
     Well, there is nothing "primary" with this.  This kind of the various
     triads present a sing presented from the perspective of Secondness. --
     Nothing primary with that.

KM: But, in mathematics (and formal logic) "standing for" relation truly
     comes to the fore as the primary. Along with equations and algebra.

KM: The formula: a = a, as well as: a = xb are both about "standing for"
     relation.

KM: Classical mechanics may have lost it's stand as the ideal of science
     and scientific methods. -- But equations and algebra still go strong.

KM: What is lost is continuity, for one thing. -- (Well, actually never
     reached, in the first place) -- Time-series analysis, as a method,
     e.g., only catches points, not continuity.  As Peirce has proven.

KM: Sorry for taking up so many topics! -- In my mind they are so intertwined.

KM: Anyway, all objections are welcome.

-- 

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