Friday, January 09, 2009

There is No Probability

If we can't get demonstrative truth, then it would seem that the next best we can do is to get probable truth. This seems to me to be the way most of us want to work, and it seems to be the ground for many arguments for one given religious tradition over another ("the historical claims for Christianity may not be certain, but they at least provide good evidence for the faith"). But this probability is a chimera.

Things are probable within a given context; given that miracles can happen, for example, Christ's resurrection becomes decidedly more probable then if one assumes that they don't (and the probability rises as one assumes that more miracles take place). Given certain understandings of the world, living our lives in a properly ordered fashion with analytically deduced relationships and a full political program in place is either the key to virtue and happiness (Confucianism) or their antithesis (Daoism).

Now, if x has a certain probability within a certain context, then x's absolute probability will depend on the probability of the context as a whole. But the context cannot give it's own probability; it may contain the seeds of its own incoherence, but it cannot even prove that it is consistent, let alone likely. So, without an outside assessment of the context's own probability, we have absolutely no idea at all what the probability of x is.

What is left for us to do? We can look between contexts, and judge them by each other's standards. What does the Hindu context, for example, say about the Christian one (and why; of course they disagree, but why precisely must they do so)? In order to truly do this, one must be able to set aside one's own non-truth-conducive biases as much as possible, and judge the new system as sympathetically as if it were her own, and her own system as critically as if it were that of someone else. Only after doing this with several systems would someone start to have any idea about what the probability of x could even be.

Of course, this still does not solve the problem. It could be that every traditional system thinks that a set of principles are probable, but that a new, unforeseen system would not. At this point, all we can do is work the best we can with our relative probabilities (hopefully with better understanding), and keep on searching for the truth as we can.

What are the impacts of this? Not much for practical life; we are always acting within a context to get something done, and this doesn't require anything like an absolute assessment of probability. But any system which purports to give us our values, our aims and meanings, can neither rest stably on such common-sense notions or on evidentalialist arguments which neglect to run the evidence through several different worldviews. Hence, all understanding must remain dialectical, and therefore provisional.

Perhaps all I'm really arguing for, then, is Lessing's ditch: there is an unbridgeable gap between necessary truths (or absolute probabilities) and historical claims (or the things we really want to assign probabilities to).

3 comments:

Beloved said...

The probability of miracles is not abstract and unsupported empirically. The numerous, diverse, broadly dispersed, claims of otherwise reasonable persons to miraculous phenomena frame a plausibility structure for the reality of miracles. For the person who has experienced something materially unexplainable, probability verges on certainty. For the rest of us, there is an obvious element of trust required. Granted trust is grounded to a large degree in correspondence with our own experience, but it is simply irrational to conclude that only those things verifiable by ourselves are true. The trust we have built of another based upon correspondence should hold some sway over non-corresponding claims.

M. Anderson said...

Matt - maybe I'm mistaking your argument for something else; let me know whether I'm understanding it properly.

My argument is not that we need to empirically verify everything ourselves; it is that "probability" is either a mathematical or a practical term. If practical, it tells us nothing about what really happened; it just gives us a clue as to how to live our empirical lives (without telling us anything about what to value, whether there is a God, etc.; just that if we live as if there were a God, we'll feel better, or something like that). So, you may practically believe in the miracle, as something that helps you in life or because you have to do the best you can on limited information, but this does not give you legitimate knowledge of ultimate reality (if nothing else, other people in other religions experience similar things).

Besides, I doubt that there are too many people who qualify as deducing that something is materially unexplainable. A long-established physicist who sees the rules of physics being broken might qualify, but even then I'm doubtful. All that the average person (even someone well-educated) can say is that something has happened which is outside of their own normal experience, which is not enough to establish a miracle. Subjective feelings of certainty may have nothing to do with objective certainty.

We listen to people through testimony because we have no better options. But this may very well be the tragedy of human existence, that we can never have anything even close to certainty about things which matter to us. Just because we want/need certainty or probability, does not mean that it is available.

If mathematical probability is involved, you have to have a set of all possible circumstances and to show how many of those circumstances you are interested in. But, since we are already situated in a context, we never have access to the set of all possible circumstances; we've already thrown some out by fiat. So, we need to have either complete certainty, or else we would have absolutely no idea whether what we are looking it is probable or not (again, subjectively felt certainty is no indication of objective certainty).

It may well be that there is nothing which qualifies for "complete certainty," except for things like math and the logical principle of non-contradiction. But again, just because this is inconvenient for us, doesn't mean that it isn't true.

Beloved said...

"But this may very well be the tragedy of human existence, that we can never have anything even close to certainty about things which matter to us."

Indeed. Why do they matter to us? Rather, when did they start mattering? Was there a "first cause" to begin with?

I don't have the time or the brains to debate these... just offering them for consideration. If you're content believing that human existence is ultimately (in the fullest sense of the word) tragic, then so be it. Your opinion will never change given the criteria you insist upon for knowledge. Maybe Paul was on to something when he said that God and truth are not found by way of human ingenuity. I know, I know, the revelation God has given us seems insufficient. I wrestle with that myself, through much anguish. But I keep coming back to faith... probably out of practical necessity.

Lord, have mercy, right?