Pedro,
I am still having problems with your mailer rejecting my mail as spam. I
went to the page listed below, but it is in Spanish, so I couldn't read
it easily.
John
Date: Mon, 20 Feb 2006 19:05:52 +0200
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The original message was received at Mon, 20 Feb 2006 13:00:37 +0200
from gwpop.ukzn.ac.za [146.230.128.75]
>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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Received on Tue Feb 21 13:07:54 2006
