I am a theoretical physicist and currently Director of 
January 28, 2005
Science and proof II
In his comment on my earlier posting on "Science and Proof", Kurtiss Hare raises an interesting point about the value of religion and what kind of validity criteria I was referring to, so I thought I would elaborate.
When it comes to the *value* of belief structures to an individual, then there are really no external criteria that can be imposed. For example, for someone who has experienced a personal tragedy, a belief in God and a divine purpose for life may be of far more value than all the science in the world.
The point I was trying to muddle through to about science is that it is not being "proven true" that gives scientific theories their credibility, but the fact that they seem to work well, are reliable, and can be used to make predictions.
The probability argument that Kurtiss raises is interesting but has two directions in which it can be taken. The first (which I think is the one he makes) is that the fact that very few planes crash means that the probability of that particular application of the scientific theories (i.e., arriving safely) is high.
But does that translate into a high probability of the underlying scientific theories being true? No, because if you you want to assign a "truth probability" to a scientific theory then you have to compare (for any given theory) the number of predictions that are confirmed to the total number of predictions that are conceivable. Since for any non-trivial theory the number of possible predictions is infinite, the truth probability for *any* theory (however "good") turns out to be zero!
This seems paradoxical but philosophers of science have not been able to get around it.
Comments
Mano:
I might be missing the point you are trying to make here but I have a problem with the lines I have quoted below.
> No, because if you you want to assign a "truth
> probability" to a scientific theory then you
> have to compare (for any given theory) the
> number of predictions that are confirmed to the > total number of predictions that are
> conceivable. Since for any non-trivial theory
> the number of
> possible predictions is infinite, the truth
> probability for *any* theory (however "good")
> turns out to be zero!
I don't follow your reasoning here. Why would you
want to consider the total number of conceivable predictions? The "space" of all conceivable predictions seems to me be ill-defined and guaranteed to stacks things against even the best of theories. Are you saying that no matter how many accurate predictions have been made by a theory, there is an infinite sea of potential predictions out there that diminish the validity of the theory?
Yes, that is exactly what I mean, although it only diminishes the validity of the theory if you use probability arguments to establish degrees of validity.
For some time, people had been using probabilistic notions somewhat loosely to measure the relative truth value of theories. But Karl Popper argued that the term was being used in an ill-defined way and that it was not possible to construct a probabilistic measure for theories that was not purely ad-hoc or that could not be manipulated or that did not lead to zero probability.
His discrediting of probabilism was a prelude to introducing his own ideas of falsificationism to replace it. Although falsificationism also got shot down later, probabilistic notions never recovered from his assault.
Okay, do you have a quick explanation for why falsification is not the distinction between science and religion?
On a day to day level, it works for me. If someone says there exist leprechauns, but they are invisible, and leave no trace in our world, I know that the statement can not be proven wrong so it is not worth arguing against. But if someone says that species evolve from other species, it is conceivable that it could be proven wrong, so it is worth taking seriously. And if enough people try to disprove it and fail, that is good evidence that it might have explanatory power.
(the mix of philosophy and politics/comtemporary events is a good one, and perhaps blog-unique.)
For a response to Dan's comment, see the new posting Science and proof III
Indeed, I was making the argument that the probability of success for a theory's application is what actually adds value to life. I absolutely cannot justify the validity of a theory as being valuable unto itself, without justifying the validity of religion in all it's purely spiritual applications. (In fact I justify both of these, but that is neither here, nor there.) As far as the calculation of the probability for success of a theory's application is concerned, there are finite and meausurable quantities that give people a great deal of confidence in that particular application. In a sense, it doesn't matter what scientific theories underly an application, except to the degree that a solid understanding of those theories might bring about an even more valuable application.If one argues there is value in the truth or validity of a pure scientific theory, then I would be hard pressed to understand any justification for demoting a religion, philosophy, or belief system below the likes of science. To prove that both are valuable beyond their real-world application, I need only mention that both exist and have competing/evolving followers. It is of little value to believe that David Koresh was the messiah, which is why such a following absolutely cannot compete on the level of Science, Christianity, Secularism, etc...