SUO: Re: What the hell was CSP talking about?
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Pat Hayes wrote:
>
> | A sign is something,'A',
> | which brings something, 'B',
> | its 'interpretant' sign,
> | determined or created by it,
> | into the same sort of correspondence
> | (or a lower implied sort) with something, 'C',
> | its 'object', as that in which itself stands to 'C'.
Pat,
There are a number of things that I usually say on introducing
this definition to any new audience: I would advise them that
it is best to treat this as a definition of a certain type of
3-adic relation, and not a definition of the absolute or the
essential being of any of the things that happen to fill its
roles, whether the sign, the interpretant of a sign, or the
object of a sign, if each should be considered in isolation.
There are many axiomsets and definitions like this in maths,
and I have been contemplating the possibility for a while now
that it might be a good idea, and on several independent grounds,
to begin a comparative and structural exploration of some well-chosen
examples of systems like these. Now you know that I can be just as pithy
as the next person, if I put my mind to it, but I get tired of saying the
same old things over and over, and I cannot imagine that saying it all
one more time is really going to have any novel effects, so at least
this strategy will introduce new material, that may have its own
uses in the long run. Not that I would want to be guilty of
changing the subject, but it will take a while to justify
the comparisons that I am making here, in order to show,
at least, that if Peirce's definition is bizarre, it is
no more outrageous than many other, well-received ideas
in mathematics, which is where I will place this subject.
Compare & Contrast:
| Definition. A nonempty set of elements G is said to form a 'group'
| if in G there is defined a binary operation, called the product and
| denoted by '.', such that:
|
| 0. x, y in G implies that x.y in G, (G closed under '.').
|
| 1. x, y, z in G implies that x.(y.z) = (x.y).z, (associative law).
|
| 2. There exists an element e in G such that
| x.e = e.x = x for all x in G, (identity element).
|
| 3. For every x in G there exists an element
| x^-1 in G such that x.(x^-1) = (x^-1).x = e, (inverse elements).
|
| I.N. Herstein, 'Topics in Algebra', 2nd edition,
| Xerox College Publishing, Lexington, MA, 1975,
| page 28. (a few changes for this plain text).
The first thing to notice about this textbook text is the number of
things that are going on all at once just to define a single notion,
that of a mathematical "group". Strange to say, the practitioners
of this art will commonly refer to the items of this definition
as "axioms", usually taking the 0^th for granted as going with
some more inclusive territory, and speaking of the "3 axioms"
for a group. I will not remark any further on their customs --
it is enough to say that this is the way they actually speak.
The relevance of this example -- I suspect that you are wondering
about that -- is that a binary operation is a 3-adic relation, so
a group G picks out a subset of GxGxG = G^3. Further, the array
and breadth of different systems that can be groups is so diverse
that I would guess that any reasonable person might well be shocked
on first impression to think that any sane folks would lump them all
together in the same boat. These, of course, are properties that we
may find quite comparable to those being attributed to sign relations.
Okay, I have a dental appointment tomorrow, so it may be a time
before I can return to this rather more enjoyable form of drill.
Jon Awbrey
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> This, apparently, is the *definition* of 'sign', that utterly
> central notion of CSP's thought, as provided by CSP himself
> and repeated on several occassions. Evidently he must have
> thought that it meant something, but I am utterly unable to
> make coherent sense of it or to think of a plausible example
> which it could possibly fit.
>
> Here are some of the problems I face.
>
> 1. It seems to be circular, since it defines 'sign' in terms of 'sign';
> the thing B is also a sign. Thus, in particular, this definition
> would be satisfied if there were no signs in the world at all.
> How do signs ever get started, as it were?
>
> 2. Leaving 1. aside for now, it has a second circularity,
> in that the 'correspondence' that A brings about between
> B and C is the same as that which holds between A and C.
> However since we are told nothing about the relationship
> between either B and C or between A and C, there seems
> to be no place to start in trying to apply this, er,
> definition. It doesnt constrain the meaning of the
> terms it uses in any way.
>
> 3. The definition refers to A bringing about something.
> The only way I can make sense of this would seem to
> involve A being an agent of some kind, or at least
> something that can cause a process or event.
> To "bring about" anything at all, something would seem
> to need to *happen*; some change must be taking place;
> something becoming true that was formerly false. And
> indeed, the definition seems to go on in this vein:
> the change is the creation or establishment of a
> relationship, a "correspondence", between B and C;
> the same sort of correspondence that A has to C.
> So this seems to be saying that a change happens
> in which some kind of relationship -- let me call
> it R -- that initially holds between A and C is made
> to also hold between B and C. Moreover, this change
> is brought about *by* A itself, and moreover, it is
> done by A "creating" or "determining" B. Putting all
> this together, it suggests the following kind of example.
> A potter sitting at a wheel creates a pot. The potter (A)
> stands in a certain relationship to something -- say, is
> above (R) the floor(C) -- and by virtue of his creating
> the new thing (B), it is brought into the same relation
> to C that A has to C; the pot, like the potter, is above
> the floor.
>
> OK, so far, so good. We seem to have an example that might,
> at a stretch, be called the creation of a sign: the potter's
> creation could, I guess, be said to indicate the floor in the
> same sense that the potter does. But that is not what the
> definition tells us. The sign is not B, the thing created,
> but the creator, A. In this example, the *potter* is a sign.
> And at this point, I have some sympathy with the crusty
> Harvard professors who refused to let this man give
> a lecture on their campus.
>
> But let me be patient, since so many people seem to think that
> CSP was such a genius. No doubt I have got the wrong end of this
> particular stick, and my example is fundamentally wrong-headed.
> Still, with the best will in the world: the definition does say
> that a sign (A) is something that *does* something: it 'brings'
> something else into a 'correspondence'. And for the life of me,
> I cannot see how anything that could reasonably be called a "sign"
> could actually DO anything TO anything else.
>
> I would welcome any enlightenment on where I might be going wrong.
> Please keep your answers pithy, however, if you possibly can.
>
> Pat Hayes
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