Now, if you've studied philosophy (as I have, from time to time), you'll know who Hume is and what he did9.5. 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:
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 world9.9 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 incorrect. 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!
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.