At 01:42 PM 2006/02/20, you wrote:
Dear John:
Thanks a lot for the references. I'll begin by reading your draft.
(Unfortunately, I cannot cc this to the list because of the moderator's
limitations to two contributions each week.)
Obviously, I should not have used the word "mathematical"; perhaps,
"non-linear dynamics" would have done the job? May I take the opportunity to
include below a draft of my abstract for the World Congress of Sociology in
your city (Durban)? I have to remain below 200 words, but I wonder whether
it is understandable:
Yes, it was the 'mathematical' that misled me. I would agree with pretty
much all of what you say below. I think that it is on the right track. [...]
What you say below is untouched by my remarks (it's hardly reductionist!).
Pity you couldn't have replied on the list. I could have approved, and we
could have advanced another step (hopefully) in the collective history of
fis.
Cheers,
John
Modeling Anticipation, Codification, and Husserl�s Horizon of Meanings
Loet Leydesdorff
Social order cannot be expected to exist as a stable phenomenon, but it can
be considered as an order of expectations which are reproduced. Thus, a
non-linear dynamics of meaning is generated: specific meaning can be
stabilized, for example, in social institutions, but all meaning refers to a
global horizon of possible meanings. Using Luhmann�s social systems theory
and Rosen�s (biological) theory of anticipatory systems, I submit algorithms
for modeling the exchange of meaning in social systems and the non-linear
dynamics of expectations. First, a system which contains a model of itself
can use this model for the anticipation. Under the condition of functional
differentiation, the social system can be expected to entertain a multitude
of models; each model contains also a model of all other models. Two
anticipatory mechanisms are then possible: one transversal between the
models, and a longitudinal one providing the system with this variety of
meanings. A system containing two anticipatory mechanisms can become
hyper-incursive. Without taking decisions the uncertainty in a
hyper-incursive system would explode. Under this pressure, informed
decisions tend to replace �natural preferences� of agents. In a
knowledge-based order, action and organization are transformed into
decision-making structures because of uncertainty in the reproduction of
expectations among differently codified meanings.
Is this understandable? See you in Durban, but undoubtedly before that on
the list.
With best wishes,
Loet
________________________________
Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR),
Kloveniersburgwal 48, 1012 CX Amsterdam.
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681;
[email protected]
; http://www.leydesdorff.net/
_____
From: John Collier [ <mailto:collierj@ukzn.ac.za>
mailto:collierj@ukzn.ac.za]
Sent: Monday, February 20, 2006 12:00 PM
To: Loet Leydesdorff; "'Søren Brier'"; 'Stanley N. Salthe';
fis@listas.unizar.es
Subject: RE: Fw: [Fis] art and meaning
At 03:16 PM 2006/02/19, Loet Leydesdorff wrote:
Dear Soeren:
Before we might be able to measure meaning, we would first need to have a
mathematical theory of meaning in order to specify the expectation.
I am pretty sure that a mathematical theory of meaning is not a possibility,
for much the same reason as a purely mathematical theory of induction is not
possible. There are mathematical constraints on a satisfactory theory of
meaning (it must fit model theory, for example, and not contradict the
lambda calculus), and the formal aspects must be able to be embodied in a
suitable metaphysics, but as soon as you get to this point you have left
mathematics. Barwise and Perry's situational semantics offers and embodiable
mathematics, but violates a context free version model theory.
Talmont-Kaminski and myself suggest a modification of the Barwise-Perry
approach inspired by Peirce that allows a Montague style semantics and
pragmatics to be recovered, but that is only after we determine meaning by
non formal techniques. The problems and the solution are outlined in our
"Pragmatist Pragmatics" due out later this year in Philosophica. There is a
draft version at
http://www.ukzn.ac.za/undphil/collier/papers/pragmatist%20pragmatics.pdf
Incidentally, since it is arguable that there is no mathematical theory that
captures exactly the concept of number, the above should not be surprising.
Barwise was motivated by this problem, but we feel he and Perry thew more
out than they needed to. My supervisor, Bill Demopoulos, wrote a paper, The
Philosophical Basis of Our Knowledge of Number, Noûs > Vol. 32, No.
4 (Dec., 1998), pp. 481-503, in which he argues that formal methods can
give us a set of entities suitable for number theory (part of pure
mathematics) but cannot give us a set of entities corresponding to our
everyday use of number. The main problem to overcome has been long known as
the Julius Caesar problem, since Fregean formalism, as Frege knew, cannot
rule out Julius Caesar being a number. Demopoulos'solution is the same one I
would advocate. In any case, since a purely mathematical theory of number is
impossible, it follows directly that a purely mathematical theory of meaning
is impossible. I noted this in my PhD thesis (which, not surprisingly,
Demopoulos supervised), and used the result to argue that Kuhnian
incommensurability cannot be resolved by purely formal approaches (it is not
a purely formal problem). Incommensurability, in fact, is a direct result of
making two assumptions 1) that any difference in meaning must make a
difference to possible experience (Peirce's Pragmatic Maxim) and 2) the
weakest verificationism. The latter, verificationism, is a direct
consequence of thinking that a mathematical theory of meaning can exhaust
meaning. If one holds both 1 and 2, then incommensurability is inevitable,
and there will be an appearance that truth is constructed. However, I would
say that that appearance is an illusion of accepting 2. It is quite easy to
assume 2 without knowing it, but the typical strategy that presupposes some
version of 2 is to identify truth and/or meaning with something else that is
not truth and/or meaning, but something more tractable.
Loet may not have meant that a mathematical theory of meaning would tell us
what meaning is, since he may think that it has other aspects as well that
are not mathematical (as I would say mathematical physics does). If so, I
submit that all the mathematics we need for a theory of meaning are already
available to us. But the hard work is only begun.
Cheers,
John
Professor John Collier
collierj@ukzn.ac.za
Philosophy and Ethics, University of KwaZulu-Natal, Durban 4041 South Africa
T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031
http://www.nu.ac.za/undphil/collier/index.html
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Professor John Collier
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T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031
http://www.nu.ac.za/undphil/collier/index.html
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Received on Thu Feb 23 08:09:54 2006
