[Inquiry] Re: Futures Of Logical Graphs -- Discussion

[Jon Awbrey]

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FOLG.  Discussion Note 13

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JA = Jon Awbrey
JR = Joe Ransdell

Re: FOLG-DIS 6.  http://stderr.org/pipermail/inquiry/2005-October/003140.html
In: FOLG-DIS.    http://stderr.org/pipermail/inquiry/2005-October/thread.html#3135

Joe, Peirce List,

Comments interspersed ...

JR: As regards the following interchange between me and Jon::

JR: Third, you cite as a premiss in your argumentation that "what
    goes for the medium must go for all the signs that it mediates".
    Is that supposed to be a self-evident truth?  I would say that it
    is not at all obvious, and that accepting a dictum like that as
    a premiss is like "buying a pig in a poke", i.e. buying something
    without knowing what in the world you might be buying.  Most unwise.

JA: No doubt there are many ways to misinterpret this humble heuristic, but
    in the setting where it was deployed it merely served to call attention
    to the fact that the initial interpretation, Entitative or Existential,
    of the simplest formal constant, the unmarked space, reflects a bit of
    freedom in the logical interpretation of every other expression that
    is marked therein or thereon.

JR: But what is the evidence to the effect that Peirce put forth
    a logical view which includes the permission to decide between
    the entitative and the existential interpretation?  I recall
    nowhere in which he suggests such a thing.  

There is no requirement that a person say every obvious thing.
Once a formal duality, triality, or higher order symmetry has
been noted, the corresponding interpretive options are simply
properties of the formal system in view.  Peirce explored the
formal symmetries that are present in various formulations of
logic in a painstakingly systematic fashion, following themes
that would have been utterly familiar from basic knowledge of
algebra and geometry.  What the axioms do not determine about
the primitive entities, whether points and lines or operators
of logic, an interpreter has to make an arbitary choice about.

JR: On the contrary, he talks instead as if, having first tried
    the entitative understanding of the formal elements of the
    graphical system, he realized that it should be construed
    as in Existential Graphs, and one major reason for that
    would surely be that he regarded the latter as iconic
    in a way that the entitative graph system is not.

One tends to pick a favorite interpretation, but
this has more to do with habit than anything else.

JR: (And considering two assertions inscribed on the same planar space as
    representating conjoint assertion of the two propositions so inscribed
    surely does seem to be more iconic of an act of conjunctive assertion
    than considering them, so inscribed, as representing the assertion of
    an inclusive alternative:  it would not be difficult to spell out in
    an intuitive way what that similarity is in the case of conjunction,
    whereas I can hardly imagine where to start in trying to point out
    a likeness in the case of assertion of inclusive alternatives.)

It is rather easy to accustom oneself to either convention.
Though I tend the prefer Ex myself, others seem to like En.
Peirce actually considered far more options than this, and
about all we can presently say about the different choices
is that their potential advantages have yet to be explored
sufficiently to this date.

JR: Moreover, besides that, there is the problem of how to understand
    the idea of a universe of discourse when inscription on the sheet
    of assertion is construed as in the the entitative graph version.

I do not see any problem there, unless someone is perhaps confusing the
sheet of assertion, the sign, with the universe of discourse, the object.

JR: Apart from tracing out what the implications of that way of construing
    inscription might turn out to be for the idea of a universe of discourse,
    there is no way of knowing whether the difference between the two ways of
    understanding inscription is indeed such that we have a choice about that,
    given the aims of logic.  In any case, Peirce himself clearly regarded the
    difference between the two systems as important enough to insist upon the
    latter interpretation himself and never, as far as I am aware, suggests that
    one can choose one or the other as one sees fit and still be doing what one
    should be doing in developing a notation for formal logic.  If you know of
    some statement of his to the contrary you should cite it.  On the other hand,
    if you regard him as mistaken in that -- a disagreement which you are certainly
    free to express here -- you should just say so, and of course provide reasons
    in justification of that claim.   Are you going to cite Carnap's "Principle
    of Tolerance", perhaps?  Is that what your invoking of the syntax-semantics
    distinction is all about?

To say that Peirce "insisted" on one interpretation is really too strong.
The fact that he explored these alternatives, and many more, demonstrates
his awareness that many paths were open.  Here I merely exercise the habit
of paying as much attention to what people do as to what they say, and when
there is a contradiction I will take the doing as definitive of their belief.
I will try eventually to take up some sections of the "Simplest Mathematics"
where Peirce exhibits the methods of operator variables and formal symmetries.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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