[FOM] Permanent Value?

[Robbie Lindauer]

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 
plain:

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 
certainly has).

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 
google.

Here are some replies to some specific complaints:

Friedman:

 >1'. Philosophers do not normally engage in the quest for
"permanent-value-as-knowledge", hoping, at most, that it will lead to 
such
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

permanent-value-as-knowledge"?

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 
a lifetime.

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 
member of
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 
you think
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 
thinking in,
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?

Best Wishes,

Robbie Lindauer