in response to Benjamin Udell's message On Fri, 17 Feb 2006 22:31:19 +0100
Ben,
thanks for your response. You write:
I read about his Three Worlds picture in an earlier book of his, one
which I understood only middlingly well. I once read a whole book
explaining Goedel's incompleteness proof, but I just don't feel
sure-footed on the subject, so I won't be the one to convince Penrose of
anything if that's what it takes!. Penrose's Three Worlds strike me as
possibly Peircean in ancestry, but it's not clear to me how best to
align it with Peircean conceptions. Its structure, a cycle though the
Worlds that gives you A, B, C, A, B, C... etc., doesn't seem a typically
Peircean kind of determinational structure.
Well, if it gives you A, B, C, A, B, C... etc., then it equally
gives you B, C, A, B, C, A... etc. and C, A, B, C, A, B... etc..
And somehow these three sequences are the same sequence. Well, it's
a very far cry ideed, but thinking along these lines you'll have in germ
part of the keynote of the proofstructure of Robert Burch's "Peircean
Reduction Thesis". Hope this is cautiously enough expressed;-)
I disagree with both Penrose and Peirce on "Three Worlds", but I think
Peirce's view is better thought out. Tegmark's four "Levels," though
more physics-oriented, and philosophically less explicit (unless I'm
discerning too much into it), make more sense to me, which is not to say
that I think that Tegmark's Multiverse theory or his views of what
comprises math are true.
Never heard about Tegmark, but such ideas seem to me to be quite common.
Reminds me of Gotthard Guenther's "Pluriversum" and his "non-aristotelean
logic". Royce is similar too. Decidedly Hegelian all that.
Well, peirce-l isn't really a "project."
Sure. It'not a project. It's a community. That's more isn't it?
Ben, you write:
I don't take a view on whether asymmetry or symmetry is more basic. If I
see an equivalence in place A, and a strict implication in place B, and
a strict reverse implication in place C, then I try to figure out a
place D & figure out what take the form of the mutual non-implication
there. I like to trace out, extend, & complete patterns, usually by
finding a pair of mutually independent yet logically "twinned" bivaluate
parameters.
and
You're the first person since I joined peirce-l who has suggested that I
might be on the right track with structures even though they're
noticeablyfourfold rather than Peirceanly threefold. If you hadn't
really noticedtheir fourfoldness, you may wish now to reconsider!
For me this sounds very much like you are replacing Peirce's categorial
structure with a boolean lattice: two "poles" "intertwined" and in between
two other "poles". So you make this Peircean structure "stronger". Very
remarkable what Joe Ransdell recently replied to you saying: "Is a
fourthness
required for the analysis of number? As I recall it the Peano Postulates
make
do with 0 through 3."
Yes, Hegelian philosophy is in a certain sense just a philosophical/logical
interpretation of number theory.
I do not say that there is anything "wrong" with your approach. It's very
strong
indeed. Only maybe some time you'll have to choose whether you prefer
incompleteness
or undecidability;-)
I would say that we have to go into the direction of "weakness", however
tempting and
even fruitfull in certain aspects the other direction may be.
Thirdness is just the personified violation of the "law of excluded
middle".
With fourfoldness as a stronger system you exactly close the door to this.
But Peirce doesn't simply introduce an additional "truth value". He does
something
exceedingly subtle, so that in a sense the "tertium non datur" isn't even
really violated. His tertium is "form" and not "truth value".
[Thomas] I guess we should discuss this "how it pulls double-direction
"trick" off" further. No mercy!-) This is very important and something
that seems to me to have been neglected as yet!
I've wondered about it. I've been toying with the idea of intelligence
as a kind of localized or individualized sink for a while now, involving
both the "running uphill" and "running downhill" of the system, somehow.
Toying is about all that I can do with it. I don't know whether it's
original. I mean, obviously things like "the soul is memory" have been
said since as long as anybody can remember. Yet to try to take that
retention idea seriously in terms of entropy, order, etc., that's
something such that I wonder whether anybody has done it. (Less work for
me down the road.) A sink of what, exactly?--a sink of something
sufficiently general in conception to relate it to biological, material,
& dynamic systems. And again, obviously it's been taken seriously in
some sense, because of computers retaining memory (and, among other
things, overheating). But I don't know what the "big picture" is between
(a) memory, attachment, skill, adherence, and (b) things like entropy,
order, energy, and thermodynamics.
[Thomas] You write: "anyway it is a RECOGNITION which we are"
This "RECOGNITION effect, this is tremendously important. You've got
it! That's it! We'll get that! We'll get that damned thing out. Be sure.
I'm glad that you think that it's important, and I'd be interested to
know why you think so. I know more or less why I think so. In using it
in a series that begins with "object, sign, interpretant," what I'm
doing is saying that semiosis is tetradic, not triadic. You may not
want to go along with this!
Well, what I meant was that in abductive inference you have this
recognition
effect in the sense that a discovery often seems like recalling what one
already knew all along and did all along without being able to express
it (clearly). It is "as if" it was the insight that you *now* have guided
you
all along. Now, then you must have had certain perceptions, but it
evidently
can't have been the object that you now perceive as a new insight.
"But how can it be that a conclusion should necessarily follow from a
premiss
which does not assert the existence of that whose existence is affirmed by
it,
the conclusion itself? The reply must be that the new individual spoken of
is
an ens rationis; that is, its being consists in some other fact." (CP
4.464)
Yes, upon further investigation you would find some other fact. But
doesn't that
nevertheless mean that you must have a direct perception of forms, "laws"
without
perceiving them as "facts", in the sense that we perceive melody and not
just only
tones etc.? How could we make a guess, if we didn't go beyond mere "facts"?
I am in a terrible hurry and I can only hastily write down some things.
Hope this does not come out as sheer nonsense.
Recently I made the surprising (for me) discovery that the cut in EG is an
asymmetric tesselation of the plane. Well, the cut represents a transitive
relation, of course.
A certain Mr. Charles Peirce writes: "What is the peculiarity of the
relation
of wholly enclosing [...] we anser, "It is a dyadic relative, r, such that
to say
that any place, X, wholly encloses a place, Y, is equivalent to saying
that X
is at once r of Y and is r of everything that is r'd by Y.""
And that means that r is exactly a transitive relation.
The word "tessellate" is derived from the Ionic version of the Greek word
"tesseres",
which in English means "four". The first tilings were made from square
tiles.
Thomas;-)
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