ONT Re: Inquiry Into Inquiry
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
H H Pattee wrote:
>
> Jon,
> Our discussion is diverging into too many issues. I began this discussion because I wanted to know
> how Peirce's methods of inquiry fundamentally differed from the types of inquiry I know in physics.
> Specifically, I asked,first, if Peirce's logic was treated as a formal logic, ...
Peirce defines "logic" as "formal semiotic".
In this he uses his definition of "formal".
¤~~~~~~~~~¤~~~~~~~~~¤~ARCHIVE~¤~~~~~~~~~¤~~~~~~~~~¤
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largely unpublished mathematical work, edited by Carolyn Eisele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 will use single quotes for Peirce's italics.]
¤~~~~~~~~~¤~~~~~~~~~¤~CITATION~¤~~~~~~~~~¤~~~~~~~~~¤
Vetsion 1.
| 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. (CSP, NEM 4, 20-21).
Version 2.
| 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. (CSP, NEM, 54).
¤~~~~~~~~~¤~~~~~~~~~¤~NOITATIC~¤~~~~~~~~~¤~~~~~~~~~¤
http://suo.ieee.org/email/msg00829.html
¤~~~~~~~~~¤~~~~~~~~~¤~EVIHCRA~¤~~~~~~~~~¤~~~~~~~~~¤
> ... and second, if his method of inquiry tries to separate the syntax of logic
> from the semantics (i.e., the interpretations of the logical signs). This seems
> to me to be necessary, but I do not understand Peirce. Maybe he has other ideas.
You asked:
HP: Does Peircean inquiry strictly separate
the logical syntax of signs from
the semantics of observation?
I replied:
JA: I do not know what you mean by "strictly separate" in this context.
I understand the relations among objects, signs, and ideas to make
sense only within the context of one or another 3-adic sign relation.
I've been told that Peirce seldom if ever used the term "semantics" --
no matter, he recognized the denotative or the referential relation
of signs and ideas to actual, imaginary, or intentional objects,
so that is what we may call his sense of "semantics". Are you
asking whether objects and signs, as absolute categories, are
mutually exclusive?
You responded:
HP: Hertz's epistemic condition is also irreducibly triadic with
the same terms (object, image/sign, observer/interpreter), but
he goes on to explain the necessary conditions for a good model,
a homomorphism. When we want to use a formal symbol system to
model a physical system we have to assign observable qualities
to some of the otherwise meaningless symbols and then provide
initial conditions for them by measurement. If you do not make a
strict distinction between the formal rule-system that represent
universal, inexorable laws and the initial conditions which may
be different for every observer, the model no longer makes sense.
To survive, inquiring physicists (bacteria and all living systems)
want to know what they cannot influence and what they can change.
This led to many interesting further discussions, but I am still waiting for you to tell me
what you mean by "strictly separate". Perhaps you think that this phrase is monosemic, but
it is not. I know of very many radically different possible meanings, myself. Chomsky once
described syntax as an "independent component", using these words in the mathematical sense.
Some people read "independent" as "autonomous", which he never said, but now there is this
entire cottage industry obliterature devoted to mining the maps their own mis-readings.
So I have learned that it pays to be careful in these things.
HP: To answer this question you needed to understand what I meant by a "formal system",
but in spite of my identification of formal with standard definitions and my agreeing
with your own suggestions (axiomatic systems, formal logic, formal languages, algorithm,
effective procedure, etc.) you still say you are at a loss to understand. You appear to
evade my questions by saying you can't think that way. I also do not understand why you
are impervious to my repeated denials that I am promoting a philosophical "line" that
you don't like and that I have stated I don't like either. You appear to be looking
for monsters under the bed. So, only for purposes of answering my questions, not
promotion, I will try again to identify what I mean by "formal system."
I know about axiom systems, formal grammars, formal languages, formal logics,
algorithms, effective descriptions, etc. But what I know tells me that your
notion of "just follow the rules" is not well-defined in any empirical or
formal sense, as best as my fuzzy recall can remind me. I pointed to
intuitive examples and theorems of recursion theory that I remember
as once impressing this impression on me. I could be wrong about
the theorems -- I will have to go check my old textbooks -- but
I think that my concrete counter-examples are fairly clear.
HP: But before that, let me say why I am not promoting formal systems
over any other system or aspect of inquiry, and why my meaning of
formal procedure has no relation to the metaphysical view of some
mathematicians often called formalists. I regard formal procedures
as just one of many essential tools or techniques of scientific inquiry,
and as I emphasized in my first comment on this thread, it is almost never
the first tool used in creative inquiry, but rather is useful only after
playing with many vague, ambiguous images that have no formal expression.
Howard, I gather that your working method is quite practical and reasonable,
but the question that you keep asking me strikes me like a line from a movie:
| I am not a racist, just tell me
| if it's true what they say that
| white guys can't jump.
Just because some folks are called "Formalists"
does not mean that they hold the patent on the
definition of "Form". If that was all it took,
all religions would dub themselves "Truism" and
be done with it. You are viewing the scene the
way that the formalists have formerly painted it.
One of the chief difficulties that I have telling
people what Peirce said is getting it through to
them that he did not just check a different foil
on what they cannot seem to help thinking is the
"all-purpose universal multiple choice exam".
HP: There are an unlimited number of possible formal systems.
Actually, they are countable.
HP: The basic elements are a finite, fixed sets of symbols, axioms, and rules
for reading and writing these symbols. The basic restriction is that the
reading and writing of the symbols is determined only by the axioms and rules
and depends on the symbol vehicles alone (this is sometimes called syntax), and
not on any referents or meanings or interpretations (sometimes called semantics).
In other words, whether they have interpretation or not is irrelevant to their
formal manipulation. Formal languages, formal logics, algorithms, and mechanical
procedures are common names for types of formal processes.
HP: I am feel sure you know what I'm talking about.
I am puzzled by why my questions are so difficult
for you to discuss.
The formal arena, to wit, the rational domain, is one thing.
The bearing of the conceivable tests in experience upon it
is a whole nuther question, and right at the moment it is
my impression that you are confounding the two reigns.
I believe in trying to integrate the empirical domain
and the rational realm, but that is not the same as
confounding them.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤