FOM: Tennant/Hersh exchange

[steel@math.berkeley.edu]

   One reservation about the method of analytical philosophy, as outlined
by Tennant: the appeal of the perverse counterexample is surely limited to
professional philosophers of a certain bent. Mathematicians who have made
a definition or two know that there are often "garbage cases" in which
you just don't care how the concept you are defining behaves. I think the
same should be true of philosophical attempts to elucidate basic concepts.
For example, who cares how the concept of time applies in a universe with
just 5 sounds? ( I'm not sure what is even meant there.)

   This reservation does not apply to the thought experiments Tennant
presented to Hersh, however. There were some far-fetched details to these
scenarios, but they made clear sense, and an account of mathematical truth
ought to be able to deal with them. Anyway one can make the same point
without them. After all, humans have not always existed. If Hersh is
right, then "the number of moons of the Earth is equal to the number of
electrons in the hydrogen atom" actually became true at some point in
history AFTER the Earth-Moon system appeared.( When? Was the existence of
Lucy and her friends good enough? Did the number 1 begin to exist with the
Neanderthals?) 

   Mathematics IS a human institution ( as is Physics, Chemistry, Music,
...), but it is not ABOUT human institutions. Sociology, Politics,
History, etc., are sciences which are ABOUT human institutions, but
mathematics is not of this nature. Martin Gardiner made this point several
times in his exchanges with Hersh, and I believe Tennant has made it too,
but it doesn't seem to register. 

   Mathematics is about sets, numbers, functions,... If there are no real
numbers, for example, then I and many others have been publishing
mountains of lies and getting paid for it. The taxpayers of California
have paid me to tell their kids about the real numbers for 20 years. I
wasn't paid to tell them about my/our imaginings, or teach them how
mathematics fits into human society, I was paid to teach them useful
truths about real numbers. 

John Steel