[Inquiry] Re: Logic Of The Sciences -- Discussion

[Jon Awbrey]

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LOTS.  Discussion Note 6

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BM = Bernard Morand
JA = Jon Awbrey

Re: LOTS-DIS 4.  http://stderr.org/pipermail/inquiry/2005-March/002426.html
In: LOTS-DIS.    http://stderr.org/pipermail/inquiry/2005-March/thread.html#2416

JA: It seems that a personal projection will be irresistable in this reconstruction --
    I cannot help thinking of the time that I passed from being a "pure" or perhaps
    "puritanical" mathematician to being more compelled/fascinated by applications,
    and thus being drawn/forced to deal with the brute "impurities" of real data
    and empirical fact.  It was not an easy adjustment, as I recall, even from
    a hazy remoteness.  But one of the things that was key to making the link
    between mathematical forms and empirical material was the association of
    empirical extensions with theoretical intensions, and this meant being
    able to contemplate fairly arbitrary sets of data, not just the kinds
    that were received initially as a-priori familiar natural kinds.

JA: The declared subject of the Harvard & Lowell lectures was the "Logic of Science",
    and this requires a better appreciation of messy experience, where the kinds are
    not so kind as we would like, that is, where the kinds that will seem natural to
    us down the road, if we do indeed adapt, are not the same natural kinds to which
    we have become accustomed through the long acquaintance of evolution and history.

BM: I think that I can see and understand what you are refering to in your
    own understanding of your personal scientific development (in fact mine
    goes roughly the other way).  But I wonder whether it doesn't remain a
    mistake.  You write: "The key to making the link ... was the association
    of empirical extensions with theoretical intensions".  This is carrying
    on some kind of "objectal" vision of the matter, "objectal" as opposed
    to methodological.

Bernard,

I am reminiscing about one of the last big turns in what was always a cyclic,
hopefully helical process, but I wish that some of my old advisors could read
your attributing to me this focus on what they called "substantive" as opposed
to "methodological" matters.  I must be achieving a balanced view at long last.

BM: The problem is not taking into account some new properties of the
    object of scientific interest such as being empirical or extensive
    but it seems more to me a problem of dealing otherwise with the same
    objects (1).  Dealing otherwise with the same objects is, I think, the
    difference between maths and logics.  In its pure abstraction maths will
    deal with axioms relative to imaginary objects (artifacts), will study what
    can be done safely out of them in order to build a system.  For the logician,
    the method begins with an hypothesis about the system itself, independently
    of its naturalness.  In order to control the hypothesis he will construct
    an experiment (so the artifact intervenes here, as the experiment).

I was not contrasting logic and mathematics here, but "pure" and "applied" versions
of both.  It is in the applications that one is forced to consider "real data sets",
and real data sets have a tendency to surprise us, even on those occasions when we
gather them with a narrowly focused hypothesis in mind.  At any rate, the way you
describe a logician as pretending hypotheses and conducting experiments does not
sound like the logician operating qua logician, who pursues a normative, not a
descriptive science.

BM: The difference relies I think, not in the objects but in the method of
    study.  Unfortunately the leading experimental science, namely physics,
    made for more than a century all what it could to mask the distinction.
    In the same vein, I wonder if the "set" concept as it is now understood
    doesn't fulfill just the epistemological role of common place between
    mathematicians and experimental scientists:  each community has his own
    specific conception of it but everybody agrees to meet under its auspices.
    Are you trying otherwise when you equate the sign relation with a set of
    triples?

I'm afraid I could not follow the argument here.

BM: (1) Rereading my message, I see that taking into account new properties
    is also a bad thing for mathematics themselves.  How many times have I
    heard at the end of some theoretical talk in mathematics, the listing
    of the so-called "possible applications" which had nothing to do with
    the subject?  As if an abstract science had to present her own excuses
    for being so.

I think that these are cliches which hide the complexity of the real situation.

JA: To my way of seeing it, the New List is the culmination of a particular direction
    of work -- even though it makes places for approximate reasoning and experimental
    obduracy, it sums up those facets of our perverse reality that can be made pretty
    and almost deceptively a-priori, and is therefore susceptible to misunderstanding
    by those unacquainted with the underlying realities.

JA: In this light, it is not really until the 1870 "Logic of Relatives"
    that Peirce begins to solve, in an instrumentally effective way,
    the problems that he set himself in trying to articulate the
    Logic of Science.

BM: Yes, I agree.  But his logic was kept busy
    with the hypothesis set down in the New List,
    the three categories.

You have hit the nail on the head here.
If people treated the categories as
hypotheses, that would be a start.

Jon Awbrey

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