FOM: objectivity, postmodernism, multiculturalism, feminist etc.
Charles Silver
csilver at sophia.smith.edu
Sun Jan 11 08:46:22 EST 1998
I am going to sketch a kind of view that could possibly extricate
Hersh from various criticisms of his views that have been expressed in
this list. Before doing this, I want to make it clear that I am not taking
sides. I too have wondered how Hersh can maintain the "objectivity" and
"reproducibility" of mathematical results, given other things he's said. I
tried to get at this concern with my example of two scenarios involving
King Kong, but I now think the example wasn't as apt as I'd thought.
Here goes:
I think Hersh must say something like the following: There is a *causal
relation* between underlying reality and the kinds of consensus formed by
mathematicians,, such that when (and only when) certain things are *true*
of that underlying reality, that consensus obtains. To put it another
way, there is some underlying reality that *causes* mathematical consensus
to obtain. For this view to be made out, the kind of mathematical
consensus must differ in certain important ways from other forms of
consensus, especially those where we know there is no underlying support
provided by reality. For example, take the consensus reached by those
persons who think they've been abducted by extraterrestrials. For this
causal-type view to work, significant differences must be found between
the claims by these "abductees" about the truth of their being probed,
say, and the claims of mathematicians about the truth of 31 being prime,
say.
That is, as far as I can tell, some unique features must be found
about mathematical agreement to distinguish it from other sorts of
agreement (especially the types where we know there's no underpinning from
reality). I have framed this in terms of "causality" because it's all the
rage these days. I think very similar points could be made without using
the notion of a "causal relation," though. One contemporary favorite is
to weaken "causality" and refer to "supervenience." I personally think
"supervenience" is a philosophical perversion and would not like to see it
used here, but I want to acknowledge that "causality" (which I think also
has problems) is dispensable. So, to weaken the above, Hersh could deny
the specific role of "causality" and still be able to stress that there is
some sort of "if and only if" between reality (of some kind) and the
nature of mathematical consensus.
At any rate, my main point is that I think Hersh can glue
"reality" to the special features of mathematical consensus in order to
claim that even though mathematical consensus is what mathematics is
"really" about, there's an underlying reality (of something or other) that
makes this kind of consensus obtain.
I don't know of course whether Hersh wishes to avail himself of
the above type of explanation. Maybe he has something else in mind.
Take these points that Hersh made (which seemed odd to me at
first):
> > 'A world of ideas exists, created by human beings, existing in their
> > shared consciousness. These ideas have objective properties, in the
> > same sense that material objects have objective properties.
After saying this, Hersh asked whether this was enough
objectivity, whereupon Steve Simpson (rightly in my view) said it wasn't.
I think what makes the above seem wrong is that we think the material
world exists independently of us, whereupon the "world of ideas" seems
surely dependent on us. But, I think if we consider our consensus of what
the material world is like to be causally dependent on the way the world
really and truly is, we can say that we've reached a certain kind of
mental consensus about the world because of its causal impact on us.
I'm not saying there aren't problems with making this view work,
and I'm not saying that Hersh holds such a view. I don't know what his
exact position on these matters is (or would be). One thing that bothers
me still, even though Hersh has answered me personally on this question,
is the "really". If we take as a hypothesis something akin to my attempt
to provide a glue between underlying reality and social consensus, then
(acc. to this hypothesis) mathematics wouldn't "really" be mere consensus.
It would be a very particular, special kind of consensus that obtains when
(and only when) reality (of some sort) supports it. The "really" would
consist then in distinguishing unique features of "mathematical
consensus," as opposed to, say "abductee consensus". Then, I think a
"because" would also need to be added. That is, I think one would have to
add that mathematical consensus is what it is "because"...., where the
dots are filled in with some view of the underlying reality of
mathematics. I think this "underlying reality" could be Platonism or it
could even be Feferman's view of metaphorical abstractions in our
imagination, which in turn spring from our everyday experience of concrete
reality.
I have two questions, the first is for Hersh critics: (1) Does the
type of view proposed above extricate Hersh? My second question is to
Hersh: (2) Do you wish to embrace a view related to the one proposed?
(And, could you please be as specific as possible?)
Charlie Silver
Consulting Film Editor for "A Brief History of Time" and "N is a Number"
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