[FOM] The Lucas-Penrose Thesis

[Timothy Y. Chow]

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