Thursday, September 24, 2009

Verifiability

I am back from the Philosophy of Cosmology conference at Oxford. There are probably going to be several posts inspired in various ways by the conference.

For now, here is a cheap remark but one that I think worth making: while being verified obviously increases the likelihood of a theory (if "verified" means "conclusively verified", then obviously it increases it to close to one), being verifiable does nothing by itself to contribute to the theory's likelihood of being true.

10 comments:

enigMan said...

Well, we must get our theories from somewhere. If a theory was not verifiable, it would raise a big doubt about its connection with reality. A theory that has been plucked from the air is unlikely to be true. Whereas a theory that has been constructed in light of observations is likely to be verifiable. Consequently being verifiable contributes to a theory's likelihood of being true, arguably.

enigMan said...

...incidentally, do you know if antimatter standing waves (like electron shells attracted around atomic nuclei, but gravitationally repelled into low-energy resonance with the entire universe) are a good explanation of dark matter, dark energy and the overall uniformity and large-scale rippling of ordinary matter?

Eric Telfer said...

Typically when we speak of 'being verifiable' we mean in a certain sense. And, of course, x can be verifiable in one sense, though not necessarily verified, while not being verifiable in other senses, under certain conditions and given certain limitations.

Mike Almeida said...

Maybe following up on Enigman, I'm not sure how you'd know that being verifiable does not confer greater likelihood on a theory. Wouldn't you have to know that it is as likely as not that a true theory is verifiable? But that's a pretty substantive claim.

Alexander R Pruss said...

enigMan:

It's very easy to come up with non-verifiable theories that are more likely true than not. Here's such a theory: the number of hairs that Napoleon had on his head when he died was not divisible by three. This non-verifiable theory has probability 2/3.

And it's very easy to come up with dozens of verifiable theories that are epistemically worthless. For instance, here is an explanation proposal for why the sky is blue: Elephants fly up and scatter powdered emeralds.

At least at the conference, I heard nothing about antimatter standing waves. My understanding is that the one really plausible explanation of dark energy is the cosmological constant, and no really good explanation of dark matter is presently available.

Mike:

Well, here is a thought experiment. You come up with a theory to explain some phenomenon. Now, after some work, you figure out that the theory has a lot of empirical consequences. It does not seem to me that finding out that the theory has a lot of empirical consequences does anything to increase the probability that the theory is true.

Mike Almeida said...

It does not seem to me that finding out that the theory has a lot of empirical consequences does anything to increase the probability that the theory is true.

I know it doesn't seem so to you. But the matter is an empirical one, not an apriori one. You simply could not know apriori how many true theories are verifiable. You'd have to have some empirical basis on which to generalize.

enigMan said...

Hi Alex; my ASW speculation is a handy (for me) example of an informal proto-theory. It would need a lot of work to get it to being a formal theory, much of it in the foundations of physics which are currently not suited to it. But from a proto-theory rough and ready consequences follow, which is why one thinks of it in the first place. If one thinks of theories that arise from such proto-theories, such as most of the modern scientific models, then your examples would be excluded. I was thinking implicitly of such a limitation to the theories being considered, that we would be considering the sort of theories that would arise within science.

Heath White said...

I think here is a way to defend Alex's claim (I don't know whether it's a way *he'd* like):

Very plausibly, *being verifiable by the naked eye* does nothing to epistemically improve a theory. Lots of things aren't available to the naked eye. Likewise, *being verifiable by using a microscope* is no big deal either, since microscopes can't tell us lots of things. Un-microscopability certainly is no indicator of falsehood.

We could generalize: for all methods M, "being verifiable by M" is no tremendous epistemic virtue, and no indicator of falsehood.

Now (this is not precisely a quantifier inversion but) invert the quantifiers and claim, "being verifiable by any method M" is no tremendous epistemic virtue either, and no indicator of falsehood. If there is a weak spot in the argument, this step is it; you might think that lots of little virtues add up to one big virtue. But I don't think it works that way.

I've always thought that verifiability or falsifiability had whatever importance it does, not as an indicator of truth or falsity, but as an indicator of the worthwhileness of spending time reflecting on a theory. If you can't know whether it's true or false, why bother? (I realize there are sophisticated answers to that question, but it's a good starting point.)

Alexander R Pruss said...

I like Heath's argument.

Here's a way to think about it. Suppose that you have a theory that predicts that there is a parallel universe, and predicts nothing about this universe. Suppose that years later, (a) somebody shows that if the theory were true, there would be a very subtle distortion of the cosmic microwave background in the parts of our universe closer to the other one, and (b) somebody else shows that this distortion would be observable with equipment that we could develop if we put a ten trillion dollars into it. Now, the theory has become verifiable, but not practically so. I don't see how discoveries (a) and (b) did anything to increase the probability that the theory is true.

And surely the probability of a theory's truth has little to do with the cost of verification.

Here is another example. I form the hypothesis that when Genghis Khan died, he had an even number of hairs on his head. This seems unverifiable. Nonetheless, I assign probability 1/2 to the hypothesis. Years later, it turns out that Genghis really died in a very cold place, and his body, perfectly preserved, has been found. So now my hypothesis becomes verifiable. But surely the probability is still 1/2, until the verification is done, after which it jumps to close to 0 or close to 1.

Something has occurred to me: One might, however, think that verifiability increases the likelihood of a hypothesis by decreasing the likelihood that the hypothesis is nonsense. Thus, the hypothesis that jabberwockies are mimsy is nonsense and non-verifiable.

Here, I would say that a hypothesis is a proposition, and no proposition is nonsense.

Verifiability does, however, ensure that we are dealing with a sentence that expresses a proposition. So if we consider not propositions but apparent sentences stating hypotheses, then maybe verifiability increases the likelihood of the apparent sentence's being expressive of a proposition, and hence being expressive of a proposition that's true. This qualifies my original claim. Modulo knowing that the sentence makes sense, verifiability gains nothing.

Alexander R Pruss said...

Mike:

"You simply could not know apriori how many true theories are verifiable."

Right, and as long as one doesn't know this, finding out that a theory is verifiable should not affect one's credence in that theory.