On Fri, 10 Feb 2006 14:32:22 +0100, Joseph Ransdell <[EMAIL PROTECTED]>
wrote:
What I am especially concerned with at present is the distinction he is
often more or less consciously working with between expressedthought and
thought which occurs "silently". In general, he is as muchconcerned to
establish something about unexpressed thought as he is aboutexpressed
thought, though we usually content ourselves with regarding
him as being concerned only with the latter. The philosophical movehe
is making is not merely to establish that expressed thought --taking the
form of word-signs -- has all of the features which arerequired for the
purposes of logic, so that logic can proceed on thebasis of verbal
expressions of thought -- things that appear on blackboards
or pieces of paper -- without being defeated by the inability to access
invisible -- or, more generally, imperceptible -- thought, but also to
establish that unexpressed thought, though often non-linguistic because
it makes do with a person's personal and unshared symbolically
functioningnotation, is nevertheless capable of being regarded AS being
symbolicjust as a word is. In other words, he seems to regard the
introductionof the conception of the symbol as a way of getting past the
limitationsimplicit both in the word "thought" but also implicit in the
word "word". On can thus talk indifferently of words OR thoughts.
The so-called "linguistic turn" is the turn to expressed thought -- the
internal dialogue is just the externally observable dialogue imagined to
be what also transpires imperceptibly because it really makes no
difference
what occurred imperceptibly, anyway -- but Peirce didn't merely make the
linguistic turn but also re-turned to the unexpressed to reclaim it, as
it were, on the basis of its presumed equivalence to what he has
established
about linguistically expressed thought. The linguistic turn replaces
"thought" by "word"; the semiotic turn and return replaces both "word"
and "thought" by "symbol" (though also of course by "icon" and "index" as
appropriate, too). Maybe that is not an important further step but only
a gratuitous addition that really has no logical significance, but I
think
Peirce did regard it as a significant move.
Dear Joe,
I am delighted that you have written the above and I appreciate very much
that
you put Jerry Dozoretz' paper on "The Internally Real, The Fictitious, And
The
Indubitable" on the Arisbe website. Jerry Dozoretz' paper is most
admirable in
its insightfulness and clearness. Now we are really beginning to "bring
things
down to earth". We have here a new aspect of Peirce's work, though it is
certainly not another aspect in the sense of being remote from the main
body or
in any way detached. It, on the contrary, touches the very heart, the
kernel of
it all.
Let me please start with the distinction between a mere fiction and a
mathematical hypothesis, which latter is partly fictious too. Structurally
this
is exactly the difference between the relatives "-- is lover whatever is
loved
by --" and "-- is both lover of and lover of everything loved by --" as
Peirce
compares them in L 224 which I cited in my recent paper that I sent you off
list. The first one amounts to simple transitivity, the second one
embodies what
I sometimes call "super-transitivity" or "general transitivity" (when I
speak
to myself).
There is a most beautiful example for the very keen sense mathematicians
have
for this distinction. Richard Dedekind's epochal work on "Was sind und was
sollen die Zahlen?", where he derives the structure of the natural and real
numbers, though admired for the construction of the real numbers by the
"Dedekindscher Schnitt" (Dedekind Cut), has always been regarded by
mathematicians as dubious concerning his founding of the natural numbers:
The
central element in Dedekind's derivation is "Dies ist ein Gedanke meiner
Gedankenwelt" which exactly amounts to the first relative above, i.e.
simple
transitivity.
So far some very "real world" historical background.
Joe, you write: "What I am especially concerned with at present is the
distinction he is often more or less consciously working with between
expressed
thought and thought which occurs "silently"" and later "...Peirce didn't
merely
make the linguistic turn but also re-turned to the unexpressed to reclaim
it...".
It is at this point perhaps best, if I refer to Jerry Dozoretz' paper in
order
to answer to you as directly as possible, since we have both read the
paper.
I would like to make three points:
The first is, that Jerry Dozoretz' "ground" is the very same "ground"
Peirce
refers to in the New List of 1867. Jerry Dozoretz writes: "there is for
Peirce
a kind of middle ground, as it were, which is neither fictional and thereby
unreal nor yet real in the aforementioned sense. In what follows I shall
endeavor to show that in order to isolate and describe the "middle ground"
mentioned we shall have to make use of Peirce's "internal"/"external"
reality
distinction, and that the distinction between positive truth and
mathematical
truth may be best understood in this context."
Secondly I can show, that the use Peirce makes of the operation of
"precision"
in ยง7 of the New List saying "Reference to a ground cannot be prescinded
from
being, but being can be prescinded from it." is, mathematically
considered, a
"proof of consistency". This can be shown very strictly, but here a mere
illustration should be sufficient for the moment:
In the context of the New List it amounts, by the way of simplifying
circumlocution, to this: you have inserted a new object into the "space",
the
background, under consideration. In order to "experimentally" test whether
this
object has a "stability of its own", you switch the background on and off
(precision) and observe whether the new object remains "referentially
stable".
It might very well be the case that, as happens e.g. in certain kinds of
optical
illusions, that if you "hide from view" certain elements of the picture,
the
rest will "fall apart" or appear to you as something quite different from
what
you originally thought it to be (or even "melt to the background noise").
The third point that I would like to direct your attention to, is
something that
has seemingly not yet been remarked in the literature on Peirce (as far as
I
know). It must be considered in connection with what I have just written
above
about "precision".
The derivation of the categories certainly seems to be a highly abstract
theory
and quite intangible at first. Nevertheless Peirce has tested it
experimentally
in the laboratory. This I do not mean as a figure of speech. He did it very
directly, almost literally so. The experiment he did together with Joseph
Jastrow, and the results of which he then published as "On small
differences of
sensation" (W5, pp.122; 1884), is very cleverly designed. It involves
second
intentions.
I think Peirce knew very well that his Categories would collapse and the
whole
architecture erected on them would immediately fall to the ground, if the
Fechner-Weber Law were strictly true. The necessary condition for the
validity
of the derivation of the categories is that there should be a possibility
for
perception that is at the same time more indirect ("second intentional
guessing") and more immediate then what Fechner and Weber aimed at. It is
of
course a necessary but not a sufficient condition what Peirce here tests.
I take
it to be consensus by now, that it would be ridiculous to assume that logic
should, would or could be based on psychology.
On the contrary: one of the consequences should be, that psychology can
almost
exclusively be based on observation of external behaviour without having
to resort
to some more or less artificially constructed "theory of inner reality" a
la Freud
etc. Since the question of what is "inner" and what is "outer" is a
question of a
"more or less", a matter of degree, a so developed scientific psychology
would
nevertheless be very different from Behaviorism a la B.F. Skinner etc..
A "man" and a "word" have very much in common indeed. But this is only a
remark
aside and beyond what I want to show here.
I could say much more, but I leave it at this here. I hope I have presented
things coherent enough to be understandable. I hope this sheds some more
light
on the problems you address. If you would challenge me, I certainly could
"elaborate" things in far greater detail. It's partly already in what I
recently
sent to you under the heading "How to grow an onion and catch a fly". I
have been
away over the weekend to Berlin (this town always inspires me) to distract
myself a bit in order to get new ideas and as it so happens I have made
another
substantial step ahead in my understanding of the structure of the New
List. I
now have found the "missing link" between the New List and Existential
Graphs
(as soon as one considers the structure of the New List as consisting in
"three Thirds"). But that's another story.
Thomas Riese.
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