[FOM] The Lucas-Penrose Thesis
Timothy Y. Chow
tchow at alum.mit.edu
Mon Oct 2 08:50:07 EDT 2006
Others have provided detailed technical comments about the specifics of
the Lucas-Penrose arguments [note plural], but I want to address a more
generic point that was brought up in F. A. Muller's original message.
F. A. Muller wrote:
> 2. Can someone recommend a paper where it
> is established convincingly, once and
> for all that the argument for the
> Lucas-Penrose Thesis is no good,
Possibly the above sentence is just a locution for "Please recommend a
good paper that argues against the Lucas-Penrose Thesis," but in case it
is intended more literally than that, I suggest that it is almost always
futile to look for a paper---on *any* topic that is even remotely
philosophical---that "establishes convincingly, once and for all" the
correctness of its conclusions. On rare occasions, you may find a paper
that convinces *you* once and for all of the correctness of its
conclusions, and as far as *you* are concerned, that may be a good enough
approximation to a paper that establishes its conclusions once and for all
in the abstract (whatever that means), so it may be worth keeping an eye
out for such a thing. But in general, I find that the attitude underlying
the phrase "established convincingly once and for all" is a highly
unproductive one.
The best illustration for my point here (that I know of) is the surprise
examination or unexpected hanging paradox. I know of no other paradox
that boasts such a phenomenal number of papers that begin with something
to the effect of, "Despite the large literature on the topic, the
definitive solution appears here for the first time." What's happening,
of course, is that there is some intrinsic vagueness about what the
paradoxical argument is, and what constitutes a "resolution" of it,
leading everyone and his dog to a different viewpoint, which he
unhesitatingly assumes is *the* correct viewpoint. You might think that a
few years of studying philosophy seriously would cure people of this naive
tendency, but alas no.
All this applies to the Lucas-Penrose Thesis. As with any philosophical
topic, there is some vagueness, and there are variations on the basic
idea, and there are different counterarguments depending on which version
is being considered. You should not expect to find a single definitive
paper on the topic; that kind of crystalline clarity is to be found only
in strictly technical papers in mathematics and logic. At the same time,
just because a point of view is espoused firmly by a tireless, eloquent,
and clever debater, doesn't mean that it isn't fundamentally flawed for a
rather simple reason.
Tim
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