[FOM] Infinity and the "Noble Lie"
Timothy Y. Chow
tchow at alum.mit.edu
Sat Dec 10 13:00:15 EST 2005
Joe Shipman wrote:
> My concern is with those who insist that key statements about infinite
> sets are "meaningless" or "fictitious" and refuse to grant axioms like
> the Axiom of Infinity the status of "True", while continuing to conduct
> or refer to ordinary mathematical research which depends in an
> essential way on such an axiom.
Most respondents seem to have slid into familiar grooves of argumentation
and have missed the point of Joe Shipman's question, which is about
ethics, not about mathematical truth.
To clarify the question further, perhaps it will help to push the
religious analogy. Suppose I am the pastor of a church, and suppose I
started down this professional path with naive enthusiasm, but in the
course of studying higher criticism of the Bible, skeptics' writings,
comparative religion, etc., have come to believe that the basic statements
of faith of my church are false when taken at face value (which is how 90%
of my congratation takes them). On the other hand, I haven't totally lost
my faith, and I am comfortable with the religious language of my church,
*provided* that that language is "suitably reinterpreted." If I use
conventional religious language in the pulpit, and operate among my
congregation in a conventional manner, without ever divulging my secret
reinterpretations, am I a hypocrite?
Whether you answer yes or no to this question, you probably *do* perceive
that there *is* an ethical question here. I certainly do. So if the
analogy holds, then my answer to Joe Shipman's original question as stated
("Does anyone perceive an ethical issue here?") is yes.
The analogy might not be quite convincing, so maybe not everyone will
answer yes, but I expect most people will be willing to grant a "yes"
answer, if only for the sake of argument. The more interesting question
then becomes, given that there *exists* an ethical issue, what is the
ethically correct path?
At this point let me drop the religious analogy and speak just to the
mathematical case. I think the answer depends on just how radical your
disagreement with the "establishment view" is. If you believe that their
activity is pernicious, then certainly you should have the courage not to
aid and abet it. But if you believe that their activity is, on the whole,
good and valuable, and the only problem is that they have a somewhat
misguided philosophical view of their own activity, then I see nothing
wrong with participating in and promoting that activity. Even adopting
their misguided language so as to keep things running smoothly without
getting bogged down in interminable and unresolvable philosophical debates
seems acceptable to me up to a point, provided you don't mislead people as
to your true beliefs and provided you don't, for the sake of being a
likable guy, cross the line into activity that your philosophy deems bad.
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