Now, if you've *studied* philosophy (as I have, from time to time),
you'll know who Hume is and what he did^{9.5}. On the other hand, if
you are a professional philosopher who (like Harlie) relies on having a
few fundamentally unanswerable pseudoquestions around to work on for a
meager living (in which case, my dear fellow snake-oil salesman, you
have my deepest sympathies, based on my own long, pecuniarily
impoverished experience working a crowd) then you'll know what he did
*and* you'll be secretly hoping that nobody else does, especially
your employers.

The rest of you, listen up now. Hmmm, historical context and punch line, or punch line and then historical context. Let's try the latter:

David Hume is the philosopher best known for proving, beyond any
possible doubt, that *Philosophy is Bullshit*.

To be more explicit and precise (although I do love a nice, pithy,
sound-bite) he proved *rationally*,*mathematically* that most of
the questions asked by philosophers from the very beginning simply
couldn't be answered, if by an ``answer'' you meant that you wanted
something that could be proven using the methodologies of logic,
mathematics, and pure reason. If you like, he deduced that our
knowledge of reality is based on two things:

- Our empirical experience of existence, as of
*right now*, the act of*perceiving*itself (in the present tense only). - Axioms, from which we could derive and conclude
*whatever we like*about the reality presumed to underlie our ongoing instantaneous consciousness depending on what axioms we choose^{9.6}.

As we have taken such pains to assert, axioms are *not* self-evident
truths, they are *fundamentally unprovable assumptions*. That is,
personal opinions. That is, hot air, moonshine, speech out of your
nether regions, *bullshit*. We know what *we are experiencing
right now* and every thing else is *inferred*. I have no problem at
all with the inferences - my axioms allow, nay, *require* them.
Hume was less easy - it bothered him to ``know'' so little even as he
(like us all) went about his quotidian existence as if he knew much
more.

Humian philosophers such as Bertrand Russell also worked on the
principle of inference, that is to say, induction. Russel argues in
*Problems of Philosophy* that there is a *probabalistic* element
to the law of induction, that if we recall that certain things have been
always observed in some particular association in the past, that there
is an increased *probability* that they will be observed in the same
association in the future. However, his argument in favor of this
principle is weakened by two critical things.

First is his acknowledgement that the law of induction (in whatever form
one chooses to state it) is in fact an assumption that cannot itself be
proven by reason or human experience. To attempt to prove induction
itself as a basis for reasoning out of what is ``probably true'' on the
basis of induction (``induction seems to work so we can prove that it is
probably true using induction?'') flogs the question to its knees
begging for its very life, and while so *much* of what has been put
forth as ``philosophy'' is nothing more than question begging, Russell
was too honest to be comfortable with it. We will have much to say
about this later, although we will discuss the axiom known as the law of
causality as the basis of our utilization of the law of induction, as
induction *can* be said to follow from causality, but induction
without causality is frankly very worrisome.

Second, and perhaps more serious, is his abuse of a *mathematical*
concept - probability - in a metaphysical argument or statement. At
the very least this is sloppy beyond all reasonable bounds; at worst it
is simply egregiously incorrect and misleading. It is worth taking a
moment to digress on this subject.

Considerable work has been done on the mathematics of probability.
There is trouble *even* in mathematics right from the start. For
one thing, there are two very different definitions of probability that
often lead to the same numerical result but which have very different
axiomatic developments. One is the frequency definition, where the
probability of an event is explicitly defined to be the number of
occurrences of the event divided by the total number of trials in which
the event *could* have occurred, in the limit that the latter goes
to infinity. While this is a perfectly reasonable definition, it leaves
one with a number of serious problems such as the best way to *compute* the probability of nearly anything from a finite number of
trials.

The second is the Bayesian theory of probability, based loosely on Bayes
theorem (and developed in applications to physical science by Jaynes and
by Shannon's Information Theory). The mathematical details of Bayesian
analysis, while interesting, are not important to us here. The idea is
that Bayesian analysis provides an explicit (if controversial, as it
appears to rely on several additional assumptions or axioms in
application) way of ascribing a probability as a *degree of belief*.
It is *only* with these additional assumptions that *either*
interpretation of probability yields a prediction in the form of a
statistical inference.

Neither of these definitions, then, can be made to apply to the concept
of inference itself without more axioms to bolster it, and *with*
those axioms the statements they make about real-world probabilities are
very precise and limited. Just to give you a tiny bit of the flavor of
some of the problems that one can encounter, imagine an urn containing
balls of some unknown color(s)^{9.7}. The urn belongs to a
guy down the street named Polya, if you care; it is ``Polya's
Urn''^{9.8}. You reach your hand
in and draw out four white balls in rapid succession.

What is the probability that the next ball you draw out is white?

This, in a nutshell, is the problem of inference. The problem is that
*there is no completely satisfactory answer that we'd all agree on a
priori* for this problem. There are too many things we don't know. We
don't know how many balls the urn contains (could be as few as four,
right?) We don't know how many *colors* of balls that the urn *might* contain other than white, although I can get around that by
considering them all to be "non-white" if they are classical balls and
not quantum particle balls with peculiar statistics (which, alas, exist
in tremendous profusion in every atom of existence). We don't know how
the urn was prepared - it might have been picked out of a large number
of urns that were filled with white and nonwhite balls according to
uniformly selected random probabilities (this is what makes it *Polya's Urn* in proper fashion and solvable by a pretty application of
Bayesian analysis that is extremely relevant to quantum theory). Or it
could just be a single urn filled by a curmudgeonly individual who
doesn't like non-white balls (he was once beaned with an eight ball
while playing pool) and won't under any circumstances place them in
urns. In the real world^{9.9} I could
even be reaching my hand into the urn to draw another ball and the Sun
could explode, blasting both me and the urn into a plasma before I
actually draw another ball!

In fact, I have no idea how to compute a probability that the next ball
will be white (or that I'll live to draw another ball) without making a
*bunch* of assumptions - that the urn has more balls and that the
sun won't explode before I draw the next one being just two of the more
colorful (sorry) ones. Somebody else that made different assumptions
might well get a different, and equally justifiable, answer. By the
time we've *specified* enough *unprovable prior conditions* to
get a unique and mathematically defensible answer to this *trivial*
problem in induction, we've basically created a whole Universe of
axioms.

*All human knowledge borne from experience* (or rather our apparent
personal and tribal/cultural memory of experience) is relatable to this
simple example. It doesn't matter if we've drawn out ten *million*
white balls in a row - the next ball we draw could be black (and the
hundred million balls following that). Or the sun could explode,
destroying the urn and all undrawn balls, making the color of the next
ball drawn .

Now, much as we all like to argue about whose axioms, whose prior
assumptions, are ``right'' or ``good'' or ``bad'', the sad truth is that
*reason* cannot provide us with any answer to these *pseudoquestions* for even this simple problem.

We conclude that even if one considers purely abstract mathematical
examples where one can *rigorously justify* the use of the term
``probably'' we have to *specify the underlying assumptions on which
a particular computation of probability is based* and those assumptions
themselves are *not statements that can be asserted to be
``probably'' true*. Sadly, we must conclude that saying that a rational
system is probably correct is as much Bullshit as is saying that it is
inevitably correct or provably *in*correct. Now it isn't clear (to
me, given my laziness and unwillingness to look up any evidence one way
or the other) if Russell was familiar with the actual mathematics of
probability - Bayes' theorem, Shannon's theorem and all the rest - but
it seems unlikely given his casual use of the term ``probably'' in the
context of a discussion of the basis of knowledge of all things (and
elsewhere in those writings I *have* read).

Given that not even *statistical* statements of truth or falsehood
- which are much weaker than the law of exclusion where something is
true or false but never ``probably true'' or ``probably false'' - can
be made without an even *larger* (and more controversial) set of
axioms than those of simple deductive logic, perhaps we should spend a
bit of time examining some of the most prevalent of the *fundamental* axiom sets upon which our understanding of things *is*
based. We'll get on that in a moment. First, though, I want to address
an important issue.

Out there I can almost hear the cleverest readers starting to snicker
inside. If I conclude that Philosophy is Bullshit, and this is a work
on philosophy, isn't this *entire book* just *bullshit*? Of
course it is. My wife would have told you that before you bought it, if
you'd only thought to ask her. Sorry though, can't get your money back.
Philosophers have to eat too, and if nothing else you can view the book
as the capering of a jester for your personal amusement if not
edification.

More seriously, I'm asserting that Hume's proposition is *true*,
that it is *correct*, even though the *proposition itself*
states that Philosophical Propositions (including this one) Cannot Be
Proven Correct (without the use of unprovable assumptions). Is this not
a problem?

Amazingly (and this may be my single original contribution to Western
Thought in this entire document) the answer is *no!* Hume's
assertion is *nothing more than a example of Gödel's
self-referential logic!*. In fact, it asserts that the fundamental
basis of any philosophical system is:

The fundamental basis of any philosophical system cannot be proven.

Whoa, you say. That looks suspiciously like something I read a chapter
or so ago. We can *analyze* this statement quite simply. If it is
false, then any philosophical system *can* be proven using pure
logic. Things that can be proven are true. If this assertion is true,
then it *cannot*, in fact, be proven which is a contradiction so
that this philosophical system cannot be false.

However, the usual logical flip-flop *terminates* at this point.
There is *nothing wrong with it being true*. We just cannot *prove* that it is true. We know that it is not false. We cannot *prove* that it is true, but it certainly *can* be true and in fact
it seems manifestly obvious that it *is* true - we can ``know'' it
to be true without being able to prove it, since if it is true it is
*consistent* but if we were able to prove that it is true then it
would be false which *also* seems like it would make it true. We
are forced to conclude that the fundamental basis of any philosophical
system of pure reason is inevitably *self-referential* and must be
*true but unprovable*.

Fortunately, mathematics has given us a term that beautifully describes things that are true but cannot be proven!

Axioms^{9.10}!

This is the ultimate ontological argument. I have shown that all
philosophical systems are based on something that must be unprovably
true as a truth itself, without proving it (as it cannot be proven).
However, any attempt to *doubt that it is correct* (as our good
friend Descartes would have us do) is foredoomed to failure and that way
madness lies. It is a madness that has consumed thousands of years of
the effort of thousands of philosophers, all generating their own
peculiar brand of Bullshit as they search for a Philosopher's Stone to
turn the dross uncertainty of an axiomatically reasoned world (with its
presumed true but *unprovable* axioms) into the fool's gold of
rational inevitability.

Ain't happenin', my fellow humans. We are doomed to live within our
senses, nothing more, and to *know* nothing beyond what we are *experiencing* save by inference and deduction and reasoning based on
unprovable *assumptions* that might be correct, might be incorrect,
but can never be proven.

It is worth spending a *bit* of time now on one of the most
important and pervasive classes of manifestly self-referential axiom
sets, one that attempts to resolve the problem posed above by adding
*one more axiom*. I speak of the Axioms of Religion. Which
religion? Any religion. The axioms of organized religion share *memes* in order to survive as *social superorganisms*. They bear
some close examination.