SUO: Re: Semiotics Formalization
Adam Pease wrote:
>
> Jon,
>
> You bring up some interesting issues. Someone who is more familiar than
> I with Shannon's information theory may be able to help. However, I think
> we can address the issues of Information and Signs without delving into how
> to represent uncertainty in information and signs. If you agree, maybe you
> could come up with an English definition for Sign to augment the few terms
> I proposed earlier?
>
> Adam
>
<...>
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Adam,
Perhaps we can "address the issues of Information and Signs without
delving into how to represent uncertainty in information and signs" --
the question is whether the things addressed will answer to our call,
since it is by virtue of their power to reduce uncertainty that signs
come to have their remarkably sooth-ing characteristics, in other words,
their function in resolving the "irritation of doubt" that gives rise to
the struggle of inquiry in the first place.
Still, I will give it a try, not in my own words but in those
of C.S. Peirce.
In this connection, I personally prefer the definitions that appear
in 'The New Elements of Mathematics', a set of volumes of Peirce's
largely unpublished mathematical work, edited by Carolyn Eisele
(who passed away at the age of 98 just last January).
Here Peirce defines "logic" as "formal semiotic" and gives
one of his clearest definitions of the concept of a "sign".
The way I read it, this definition places the being of
a sign within a relational context, as a pragmatic role,
not as an essential attribute of the thing that takes up
that role. I will quote two versions of the definition
from NEM 4, pp. 20-21 and 54, nearly the same in both
locations but with a few interesting variations.
[Here, I wiil use single quotes for Peirce's italics.]
#Begin Quotation====#====#====#====#==NEM 4, 20-21#
| No. 12. 'On the Definition of Logic'.
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time. Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'. It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized.
#Begin Quotation====#====#====#====#====#NEM 4, 54#
| No. 12. 'On the Definition of Logic'.
|
| Logic is 'formal semiotic'. 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'. This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident. The word "formal" in
| the definition is also defined.
#End Quotation=#====#====#====#====#====#====#====#
I have placed these 'texts for defining signs' back
into their original 'contexts for defining logic' --
from which many commentators prefer to extract them --
because I think that it remains important to remember
the importance that Peirce attached, not only to these
subjects, but to their relationship, and this is hardly
to mention the fact -- and many there are who hardly do! --
that it is "mathematical reasoning", of all things, that
he says that he uses to "deduce" from this "definition"
of signs the "principles of logic" -- so easy to miss,
to ignore, or to forget that he did not say the reverse!
So much for authority, if not authenticity, but how can
we inquire if these theories make sense if we don't even
track which direction they are pointing!?
There are one or two features that I think we ought to notice
in our reading of these definitions. Some of these features
are borne out on the surface of the text -- others are less
obvious and require some digging into other texts that employ
the same sorts of words (or lower implied sorts).
1. There is the fact that Peirce calls them "definitions".
I used to think that this was a totally trivial observation,
but I have since noticed that people who do not imagine that
there can be a definition usually find it convenient just to
ignore this whole aspect of the issue altogteher, as if there
was never anybody who said there might just happen to be one --
if not this particular one then one that is worth looking for!
But it's become naive -- if not impolite! -- even to bring up
the possibility, and people who would never let you get away
with writing a thirteen line sonnet continue to pretend that
they simply have no use for something so pedantic as a simple
definition. We just generate the world in a narrative way,
and so long as everybody keeps their stories straight, nobody
will ever know the difference -- that's called "solidarity"!
2. Please remember this! A sign is still a sign,
no matter how it goes, interpretant or otherwise,
as time goes by! It seems pretty clear to me that
an 'interpretant' sign is just another sign. Indeed,
the word is only defined here as an adjective and not
as a substantive term, which renders it sort of futile
to go looking for its "essence", much less the specific
difference that would make it what it is. An interpretant
sign is "interpretant" not by dint of any absolute essence
that might be sought in it, but by virtue of its role in a
sign relation, and if it appears to have a "triadic quality"
about it, it is only because this sign relation is triadic.
The following remarks are more impressionistic, as they derive from:
(a) Things that I'm pretty sure I've read in Peirce somewhere
but can't -- don't even want to try -- to locate right now.
(b) Associated experiences using Peirce's ideas in the attempt
to write a few simple "learning" or "reasoning" programs.
It's my impression that what Peirce is referring to by means of phrases
like "in the same way" or "the same sort of correspondence", especially
as hedged by the qualification to "a lower implied sort", is nothing
short of the whole triadic sign relation itself, not limited to any
dyadic aspect of it, much less constrained by the species of sign
that may be but transiently involved in any particular transit
or interval of semiosis.
I mean, think about it. If all your thought takes place in signs, then
there is some big sign relation that covers all that you think throughout
your whole life, part of some even bigger sign relation that covers all of
those triple moments in the history of the universe where something means
something to somebody, but this has just got to be a very heterogeneous mix,
with any agent or community of interpretation passing from moment to moment
through many splintered species of classifriable transitions, all the while
that the overall sign relation is being more or less preserved.
Back to the question of the worth of a definition. Having used these
sorts of definitions to design one or two programs, I am quite aware
of the places where they fall short of being completely satisfactory
as effective specifications -- which is why I sometimes refer to them
as "near-definitions", or as "definitions modulo some other concepts
that themselves cry out for definitions". The places where these
holes seem to be are at the points where Peirce invokes the notions
of "determination", "creation", and "correspondence" -- but he does
define these concepts in other places, or at least the first and the
last, and creation is just a special case of the way that he defines
determination, as "making something other than it would otherwise be" --
so the definition can be completed, but to do it you have to use his
definitions, not just anybody's. In particular, Peirce's concept of
correspondence, as evidenced by locutions like "triple influence" and
(I think even) "triple correspondence", is quite a bit richer in its
structure than that half-baked sort of dyadic mirrorty imaging that
people commonly associate with the "correspondence theory of truth",
and that some people have even written whole books to lambaste, all
without realizing that they were only ridiculing their own weak
notions of an adequate and suitable form of correspondence.
To sum up, one of the most important features of this definition
is the way that signs are bound to a relational context, whether
it is a triadic sign relation formulated as a three-column table,
or an "information channel", that is, a probability distribution
over a formal language or a collection of signs. In accord with
this "contextuality", signs only make sense in some such setting.
From this point of view, I am looking at "sign relations" as a particular
class of mathematical objects, much like graphs or groups, and it makes more
sense to consider sign relations whole and to classify these entire relations
than it does to become too intent on the isolated components of the individual
triples, like the components o, s, i of the triple <o, s, i>, even the latter
of which is just one element of a typical sign relation R.
I don't know if this helps, but it sure seems like enough for now.
Jon
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