What Can We Know?

At the age of 16,
I realized there's no need to assume God’s existence. Everything
could be explained without a god; in fact, things seemed to me to
make more sense without one. Certainly, a great deal of what was claimed
about the Man made no sense. I became an agnostic.

Nonetheless I felt in terrific need of insight, guidance, and solace,
and began reading philosophy, which I continued to study through college.
I studied most of the big names from the history of Western philosophy,
plus a few others. I became very interested in epistemology--how do
we know anything? how do we know that we know anything?--but also
studied the philosophy of religion, ethics, and other branches.

We know that systems of mathematics can be based upon different sets
of axiomatic principles. For example, Euclidean geometry is based
in part on the axiom or postulate that through any point outside a
straight line, one and only one parallel straight line can be drawn.
In Euclidean geometry, therefore, parallel lines never meet.

As I
understand, a geometry invented by Bernhard Riemann has the same fundamental
axioms or postulates as Euclidean geometry *except *the one just described;
that is, in Riemannian geometry, parallel lines *do *meet. And it is this
Riemannian geometry that Einstein used in his general theory of relativity,
pursuant to which space itself is curved. (See article by J.J. O'Connor and
E.F. Robertson at http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html ; see also http://www.upscale.utoronto.ca/GeneralInterest/Harrison/GenRel/Geometry.html and http://www.cs.ucdavis.edu/~vemuri/EngPopsci/Universe.htm .)

(If, as discussed
in the essay on this site, *Cells
and Systems*, the distinctions we use to define discrete objects
are largely artificial, functions of what we find useful for the purposes
at hand; if everything is really part of one, continuous system; what
does it mean that mathematics seems to work? I.e., math seems to absolutely
depend on the assumption that it is possible to define discrete items,
so as to be able to count them. Could there be a math that omits this
assumption? Could such a math, e.g., better reconcile the Heisenberg
Uncertainty Principle with other physics theories? [See the *Cells
and Systems* essay for a brief description of the Uncertainty
Principle.])

As I proceeded in my studies, it became clear that the only thing
philosophy had arguably proved was that we can’t prove much
of anything. All philosophies or other attempts to understand our
world can be seen to derive from one or more assumptions. Indeed,
our efforts through the ages had brought us to something like Gödel’s
Theorem, which states, roughly speaking, that for any given system,
there will always exist certain propositions that cannot be decided
within that system. The system is never really complete in itself;
in order to prove or derive certain axioms, resort must always be
had to something outside the system. (See http://godel.4mg.com ;
http://www.sciam.com/askexpert_question.cfm?articleID=0002F4F1-B4F3-1C71-9EB7809EC588F2D7 ; http://www.cs.auckland.ac.nz/CDMTCS/chaitin/georgia.html ).

If Gödel's Theorem is generally true, as it seems to me to be,
then we can grasp no absolute truth or knowledge about life so long
as we’re in it, for even our best understandings ultimately
involve irreducible assumptions. Moreover, if any of our assumptions
are like Euclid's axiom regarding parallel lines, it's quite possible
that certain kinds of understanding can be attained only to the extent
we're prepared to reject them.

So yes, I'm
a relativist.

I nonetheless believe, however, that we can reach at least tentative
agreements regarding what we consider to be “true” or
“false” (or as I used to call them, "temporary conclusions"),
at least on a relative, provisional basis. Most of us can probably
agree that the proposition that breathing is required for human life
seems more or less true, while the suggestion that chocolate is required
is more or less false, though we may wish it weren’t.

Indeed, I
believe it is one of our prime responsibilities in life to try to
create articulations of "truth," to understand the context
as best we can, and given that context, to seek to distinguish among
such articulations as to which are in some useful sense which are
more and which are less true.

I think we can even reach tentative agreement on what might be some
principled *bases* for discriminating between relatively “true”
or “false” statements. I believe some useful factors in
making such discriminations might be:

1.**Simplicity**,
i.e., given more than one possible explanation, a simpler one is usually
preferable over a more elaborate one.

2.**Consistency**
with other available data.

3.**Corroboration**
from others--the more heads, and more diverse perceivers and interpreters,
the better; check out *Macbeth* on this point. [There was a
short article in *The New Yorker* within the last few years
that I haven’t had a chance to locate, which as I recall described
research showing that groups of rats in a maze somehow managed to
perform better than single rats, even when none had ever been in the
maze before. I believe it may have been written by James Surowiecki,
who, as of June, 2004 when I add this note, has recently published
a book entitled, *The Wisdom of Crowds: Why the Many are Smarter
than the Few, and How Collective Wisdom Shapes Business, Economies,
Societies and Nations*.]

4.**Elegance**.
May just be shorthand for the first three factors above?

5.**Predictive
power**, i.e., what seems to work; what statements, if assumed
true, give you the power to act in ways that later turn out to have
been appropriate or helpful. Efforts based on relatively untrue statements
usually fail sooner rather than later, while efforts based on relatively
true statements more often succeed.

I can't prove these criteria are the only or best ones any more than
I can prove any purported "truth"; I can only say they do
the best of any I've found so far in satisfying themselves as criteria
. . . though that be unsatisfyingly tautological.

As discussed in the essay on this site entitled, *The
Arts and Literature*, I believe that the arts are expressions of
research and information. In that regard, I’d like to note that
I also believe that works of art and literature, like other expressions
claiming “truth,” can be judged partly by how well they
“work”; i.e., whether or not their effects on us are such
as to help us in one or more ways to cope better with ourselves and
our world.

Also consistently with that essay, I'd like to suggest here that truth
as well as beauty are available to us only to the extent that they
are conscientiously and continually *sought*. A "keeper"
of the truth can only be one who devoutly doubts the possibility of
capturing it but who nonetheless perseveres in its pursuit.

Indeed, I
believe that in some sense, we gain knowledge only through love or
something like it. It is love that shows us how to attend to any person
or thing, at least for a moment, as if that entity were the only one
in the world.

(Proceed to the next Essay, *What Do We Mean by "Meaning"?*, or . . .