I was listening to science Friday’s discussion with Sam Harris. For those who don’t know, Sam Harris is currently pushing the idea that science can determine ethics. I suspect this is not the case, but more importantly, I found his arguments problematic. I haven’t read his book, so I won’t make a critique of it here.
I did however make a critique on twitter. Interestingly, I got a few comments bringing up the Problem of Induction. The basic idea is this: there is no proof that the future will be like the past. This might seem innocuous until you realize that it includes the view that all science stands on an uncertain foundation.
I confess that, although I’m a strong believer in science, I would normally concede the problem of induction. That is, I’d have to agree that science is based on the assumption that the past will be like the present. Today, I changed my mind a bit on this, and I’ll tell you the line of reasoning.
First, let me define “science.”
My philosophy of science (as a theory) is this: Science is the assumption that facts are knowable by repeated observation (1) and that logic is real (2).
My notion of science the method is this: Using 1 and 2, perform experiments to determine facts.
There’s obviously a bit more to it, but I think everything else can be built on the above. For example, the idea of a scientific “theory” is essentially a logical framework you use to suggest experiments. So, even though I don’t reference it directly, it’s in there.
My basic view as of this morning was that in order to do science, you assume 1 and 2. They *seem* to be true and to produce results, but they can’t be proven. This is probably true, but leaves out an import fact: they also can’t be disproved.
Why? Well, let’s look at 1 and 2.
I’ll start with 2, since it’s the easier one to explain.
If you wanted to disprove the realness of logic, you are obligated by the nature of the task to use logic. That is, in order to “disprove” logic, you must use logic. If you disproved logic, you’d then have disproved the logic you used to disprove logic. So, your conclusion that logic was non-logical would be wrong. You see how you quickly end up going in a loop, somewhat like the “This statement is a lie” paradox. Or, to put it more succinctly, the demand to “prove logic is real,” is tantamount to saying “create a paradox.”
From here, it’s easy to see how 1 also breaks down. In order to make an experiment that falsifies 1, I’d have to make observations. In other words, I’d have to make observations that disprove the idea that making observations is meaningful. Again, you get a paradox.
Lest you think this sort of argument could be made against any assumption, let me provide an illustrative example: Say someone says “the sky is blue.” Well, I can easily make observations that suggest it’s blue and do experiments to prove it. For example, I could say “If the sky is blue, I should be able to detect a lot of blue wavelength light if I point a detector at the sky.”
So, you see there is a qualitative difference between these types of assumptions. I put it to you that there are not simply “assumptions,” but rather there are certain cases of assumptions:
A) Normal assumptions – assumptions that can be proved or disproved. (E.g. the sky is blue, 2+2 = 4)
B) Unprovable assumptions – assumptions that can neither be proved or disproved. (E.g. polygamy is bad, Santa Claus exists, etc.)
C) Weird assumptions – assumptions that cannot strictly speaking be proved from earlier assumptions, but whose disproving implies a contradiction (E.g. Logic is logical, observations can be observed).
The assumptions that underlie daily life are in A. The assumptions that underlie theology and some philosophy are in B. The assumptions of science, I believe, are entirely in C.
Science indeed does rest on assumptions, but they are not assumptions in the typical sense. They’re a bit stronger than that.
Additionally, the problem of induction as stated “we can’t assume the future will be like the past” contains logical problems as well. Let’s parse out what this statement means.
We can safely say the simple case of this is not a problem. Of course we know there will be some differences between past and present. The universe will expand and the stuff in it will move around. Few have seriously argued against this, unless you believe that Zeno’s paradoxes imply that motion is an illusion. Science, of course, can exist despite these changes.
The next case would be the physical laws. But here too, science requires no changes to accommodate a universe in which physical laws change. Consider, for example, a universe in which the “fundamental constant” G changes over time. This would seem weird to us, but could certainly be understood in scientific terms. Hell, we might even be able to quantify its rate of change, leading to a “deeper” constant. If that one cycled as well, we could go yet deeper. Even if this recursion continued infinitely, science could still grasp it. It is, for example, not a problem for science that there are infinite digits of pi.
Or, to get even weirder, we could imagine a situation in which the law itself changes. Gravity obeys the inverse square law. But, what if it turned out distance squared was just a little off. What if it was actually distance^(2 + (2^-googol)). And, what if it changed by 2^-googol every 10 billion years? This would certainly seem strange, but there’s no reason science couldn’t accommodate it. In fact, the change would be quite easy. We would just insert a time factor into the equation. This would cause plenty of mathematical headaches, but would be no means expel gravity from the realm of science.
So, exactly what is meant by “the future will be like the past?” Or, to put it more illustratively, “what sort of past-future difference would invalidate science as we know it.”
I don’t have an answer to that question, but I tried to think of something. The best I could do was to imagine a universe in which logic doesn’t work how we think it does. Like, perhaps 2+2=4 was right yesterday, but will have a slight rounding around tomorrow. But, this doesn’t work because if 2+2=4.0000000000000000000000000000000000000001, it’s simple algebra to prove weird things like “0=1/0.” Of course, we could then say “well, maybe in this universe algebra works differently too.” But, this is essentially arguing something to the effect of “well, what if I use illogic?” As mentioned above, I believe this sort of thinking fails because it is self contradictory. Using an “if-then” statement to prove illogic results in an internal contradiction.
What if we try assailing assumption 1 this way? I believe we encounter the same problem. You might propose a universe in which the more you observe something the less likely it is to be true. But here again we have internal contradiction. If observation of this rule is made, it makes the rule less likely, which makes observation more valid, which makes it less valid.
After thinking about this for a while, it seemed to me that I’m no longer certain the problem of induction is real.
I admit that it is perhaps disconcerting to think that logic isn’t self proving. But, it is comforting to think that (at least) logic cannot self-disprove.
Hope that all makes sense. I’m sure I’ll get plenty of critique (especially from people familiar with Godel and Hofstadter), and I’m looking forward to it!