[FOM] Permanent Value?
robblin at thetip.org
Thu May 13 03:15:59 EDT 2004
It has been brought to my attention that Mr. Friedman was "calling me
out" (in an email I also missed) and so this humble reply months later,
I haven't been keeping up.
The ongoing debate between formalisms, intuitionisms and platonisms of
various kinds on this list and in recent publications (at least in the
last five years in both philosophy and mathematics) has been
instructive since the time of the original posting. This is because
inasmuch as mathematics is interesting qua enduring value - it is
interesting for philosophical (or practical) reasons - e.g. because it
unearths "the truth" about which we have been instructed not to speak
in this forum.
Mr. Friedman asked genuinely, I think, whether or not Philosophers have
made contributions to "enduring knowledge" in the sense of things known
in the last five years comparable to the kinds of knowledge that
mathematicians (and we'll assume he meant "pure mathematicians" for the
moment) make regularly.
I think the question here is telling for two reasons which I'll make
1) The underlying pragmatism that motivates Mr. Friedman's question is
instructive simply because it betrays the notion of "enduring
knowledge" that he's pushing as a standard of value. If what is
valuable about knowledge is that it endures, then surely philosophers
have made the greatest contributions to knowledge in every era. In our
modern era, in particular, we've seen the fall of this pragmatism of
his to each of foundationalism, coherentism, anti-foundationalism and
out-and-out relativism in the theory of knowledge. Thankfully, the
theory of knowledge has not found its way into a calculus book so few
people are claiming that it really is a form of mathematics. Its
fruitfulness is to be measured not by how many theorems it proves, but
rather by how many theorems may be seen as proved now that were seen as
simply wanting of an adequate theory of knowledge, for instance. As it
stands, mathematics has no adequate theory of knowledge. Recognition
of this fact might lead to more interesting work on both sides (and
In any case, Mr. Friedman's meta-mathematical musings - his
"permanent-value-as-knowledge" and the distinction between leading-to
and being such I find much more interesting. For instance, why should
permanence have anything to do with knowledge and why either of them
should be necessarily be valuable - would be strictly, I think, a
philosophical question. More interesting philosophically would be
looking at why specific kinds of knowledge are deemed valuable (e.g.
physics and computer science) and not, say, grammatology or
communication theory? Could deconstruction be mathematized the same
way that information has been? This is again, no doubt, due to this
notion of endurance as value - the establishment of something that
lasts. But since in Mr. Friedman's terminology "Truth is up for grabs"
the best thing we can hope for is endurance. Who cares about truth?
2) Measuring philosophy's advance in grains of 5-years is unfair.
People don't make important decisions that fast - societies and
cultures more slowly. Philosophy slowest of all. Thankfully, in the
last five years there have been some nice pieces of work released which
may not have created "permanent-value-as-knowledge" but certainly made
an impact about what the options were - and that too is a kind of
enduring knowledge. To stick close to the subject matter, I've
especially enjoyed the work of Claire Ortiz Hill and Guillermo Haddock
on two possible varieties of platonistic interpretation of
number-theory and their, albeit tenuous, insertion of Husserl into the
questions. Have they proved the same number of theorems as a
comparable gaggle of mathematicians? No, but will their work or the
work of, say, J.R. Lucas or Bas Van Frassen last out the century?
Sure. Is that long enough? Who gets to decide? It's certainly not a
mathematical question. And since the issues they're attempting to
address have a preemptive relationship with the work of mathematicians
- if there are no topological spaces, for instance, then we can't call
what topologists do "of lasting value" in any more than the sense that
the story of Santa Claus is of lasting value. Surely - we'll be happy
to allow the matter to gestate a little longer. For instance, we might
find it more interesting to have psychologists, sociologists and
economists examine mathematicians to see what makes them say things
like "a circle is provably topologically equivalent to ..."
The desire to treat of foundations without addressing the philosophical
importance and relations of mathematical issues to other sciences and
arts is itself a philosophical program that falls under a political
program. This program is fascinating in that it is an attempt to
control or undermine (we're not able to tell which) the very inference
schemas which we're allowed to call rational - that is it is an attempt
to define rationality - and this program is thoroughly philosophical.
It is also attempting to do it "outside the ring" that is outside of
what is called philosophy - explicitly rejecting that name. That it
may also be a pragmatic attempt - to define rationality for a reason -
is somewhat chilling. Philosophy's name is tainted everywhere - "there
is nothing so ridiculous that some philosopher has not claimed to have
proved it". But to see only this is to miss the point - philosophers
learn their freedom by being free in their philosophy, mistakes of this
kind ARE knowledge.
The concern for ethics, ontology and epistemology is important - more
important than choosing between ZF and NF or giving a proof-procedure
for a specific kind of mathematical problem (even though that last
might be very useful for someone some day). Philosophers shouldn't
want to prove things from axioms, but rather find or deconstruct ways
of living that are good - that is to make rational decisions about our
actual lives based on that bogey, again, the truth. The connection
between mathematics and ethics and epistemology is less obvious than in
ontology where several attempts have been made to reconcile the two
already - but they are just as interesting.
Mr. Friedman himself has thought it important to address
epistemological issues in this forum - his certainty machines, aliens
and crystal balls. The arguments there follow the method and tone of
philosophy - if that was mathematics then "anything goes". Whether
email is of enduring value will no doubt depend on the longevity of
Here are some replies to some specific complaints:
>1'. Philosophers do not normally engage in the quest for
"permanent-value-as-knowledge", hoping, at most, that it will lead to
at some future date.
Do you suggest that we pick up the last 5 issues of the Journal of
Philosophy and evaluate the articles strictly in terms of
What conclusions would you draw?
This is not true, philosophers do engage in the quest for "permanent
value as knowledge" that is - knowing particular things. Both in
attempting to provide proofs and in attempting to clarify and extend
our options. BOTH are contributions to our permanent knowledge. As a
result of Peter Klein's essay "Human Knowledge and the Infinite Regress
of Reasons", we can consistently, for instance, claim that for every
claimed piece of knowledge there is a sufficient piece of evidence AND
that no piece of evidence need be self-evident. It is a consistent
position to claim that there is an infinite regress of knowledge-pieces
each of which is a reason for the others and none of which is in its
own antecedent reason-chain. His responses to John Post's criticisms
of the position are cogent and valuable. BUT I don't think that
philosophy can really be evaluated effectively for periods of much
greater than five years - mature philosophical systems are the work of
So the conclusion I draw - to answer you question directly - is that
the issues that philosophers attempt to grapple with are more difficult
than those that mathematicians do and so take much longer to evaluate.
HF - So Shannon was using the philosophy methodology, and was a normal
the philosophy community?
No, Shannon was not a philosopher in the sense that he was
investigating epistemology or ontology or logic for their own sake. On
the other hand, had the foundational work in philosophy and logic not
been accomplished by Boole, Leibniz, Hilbert, Turing, etc.(
"Mathematical Logic and the Origin of Modern Computers" M. Davis) he'd
have been in a complete vacuum AND probably wouldn't have seen the
importance of the work. He was also not a pure mathematician, but an
engineer for the sake of the discussion at hand. This is not a pissing
contest between philosophy and mathematics. Occasionally mathematics,
physics and psychology rise to the level of philosophy (maybe better
"occasionally sink to the level of philosophy"). Occasionally
philosophers are mathematicians and vice versa - like you. But in
particular, when you attempt to answer ontological problems about "Are
any things of the kind being studied by this group of people and are
their methods of justification adequate?", you tend to be doing
philosophy. And when the attempts to decide that external question
becomes important to the science itself (say in the debate between
intuitionism and platonism and logicism or something) it may have some
of the interesting side-effects that you've been hoping for by studing
Foundations in your sense.
The "enduring value" of computers and efficient communication, though,
is hard to evaluate at this point. While you may receive every bit I
send, it's doubtful that we'll communicate.
Also, the notion that there is a "philosophy methodology" or "normal
member of the philosophy community" is absurd. What makes something
philosophy is the essentialness of what is claimed. Shannon did manage
to claim the essential fact that the entropy of a communication channel
is related to the amount of information that can be passed along it.
HF: I am sure that the FOM list would appreciate an accounting of what
are the highlights in philosophy from the last 5 years as far as
Doubtful, but I've really enjoyed "Truth and the Absence of Fact" by
Field and "Mindware" by Andy Clark.
HF: Give us some examples of clear and/or effective philosophical
at least, the writings of contemporary figures in mathematics.
I was thinking most specifically of you and your various "certainty
mechanisms" - the crystal ball, the martians, the hyper-computer.
What I claimed was that your statement that "mathematicians don't
normally engage in philosophical thinking" is not true - here you are
doing it. The boundary between philosophy of mathematics and
mathematics was burst a hundred years ago and the idea that some
particular piece of mathematics definitely isn't ontologically or
epistemologically or even politically charged is outrageous. The
choice of language is politically charged - only a mathematician who
never managed to think about anything else would be "pure" in this
sense. I doubt the existence of this kind of "pure mathematician". If
someone were to spend their whole life working out the consequences of
ZFC without speculating about its ultimate value, that would be a sad
life. If mathematics doesn't take on some kind of philosophical
significance, then why bother?
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