What aspects of the problem of induction are simplified if you employ the B-theory of time?

Question

What aspects of the problem of induction are simplified if you consider the problem using the B-theory of time?

A rough idea why this might be relevant:

First consider an urn with a finite number of balls in it. As I successively draw white balls from the urn, it is rational it increase my belief in the proposition "all of the balls in the urn are white". I do not think that this is controversial.

If you "sit out side of space and time" the set of swans in the universe is just a finite assortment like the balls in the urn. Thus, as you go through and sample them, finding each one white, you should increase your belief in the proposition "all swans are white" (up to the point where you find a black one).

There could be nits to pick with respect to the sampling methodology, i.e. we observe subsequent swans later in time, so if their color-state depends on the time we have a correlated sample; even so, our necessarily non-ideal sample still allow us to increase our belief in the global statement when you consider the process using the B-theory of time.

Answer 1

I'm not sure how a B-theory would help. Inductive reasoning can only be based on the information I possess. Whether I regard future events and observations as non-existent until they happen, or existing in reality on a par with the past and present doesn't affect the fact that some information is known to me and some not. The problem of induction is am I justified in projecting generalisations about what I know across to cases that I haven't observed?

To take the example of the swans, on a B-theory we might say that my life is a squiggly timeline in a block universe and there are a bunch of timelines for all the swans that exist. At various points these lines intersect and I make an observation about a swan. But I can't move myself outside the universe and see all the swans. I can only make inductive inferences about the swans I have intersected with and then make projections about other swans that I haven't.

As to whether this projection is justified, the law of large numbers helps here. Suppose we have an urn with 3 million marbles in it, 1 million each of red, green and blue. Now suppose I draw a random sample of 1000 marbles from it. A large majority of such possible samples will be approximately one third red, one third green and one third blue. So from any given sample, it is reasonable to suppose that the distribution of the population of the urn is similar to my sample. Another way to express this is that I am not assuming that my sample is representative, I am only assuming it is random, and the law of large numbers is carrying me from random to (probably) representative. Of course my sample might fail to be random. For a long time Europeans thought all swans were white and then they visited Australia and found black ones - in other words they discovered that their previous samples were geographically biased.

In practice things are never simple. We need to worry about how big our samples are and how to avoid bias, and how our projections fit in with other things we know: in other words all the things that statisticians worry about all the time. But the inductive skeptic is engaging in an absurdity if he claims that observed samples provide no reliable information at all about unobserved ones.

Answer 2

From an externalist theory of time, why would anyone ever have to actually sample? Why not just use the fact that all samples are already presented, but vary across time, to avoid the notion of induction altogether and just use the distribution as a real and independent object?

This is the framing of classical statistics. Classical mathematics just treats time as a dimension, not as a real limiting principle of order, except when it wants an ordering. So classical statistics just idealizes a sample and proceeds. This just gives you the same leverage on induction that you get from the theories of random error and large numbers -- which is pretty good, but nothing new.

So this insight has actually been thoroughly mined, and provides no help that you don't already get from the standard framing of mathematics. It lets you look at theorizing as a process of pattern recognition, rather than a succession of guesses, and it provides a ready set of potential pattern recognition algorithms. (Regression and correlation, cluster analysis, etc.)

But it does not solve the problem of knowing what patterns and what variables to look for in each circumstance or deciding what patterns are illusory and what patterns are present. Whether you think of it as pattern extraction or induction, it still has no good logical basis, and can always mislead you.

Answer 3

You might be interested in The Raven Paradox

• All ravens are black.
• Everything that is not black is not a raven.

First consider an urn with a finite number of balls in it. As I successively draw white balls from the urn, it is rational it increase my belief in the proposition "all of the balls in the urn are white". I do not think that this is controversial.

The Raven Paradox will take this further I will attempt to equate the two change the urn to Earth, and the white balls to swans.

• all swans white.
• everything that is not white is not a swan.
• Time is tenseless (B-Theory)

Now the Raven paradox will ask questions like :

"Does this pair of black sneakers in my closet increase the evidence that all swans are white?"

Note that we changed the urn to the world, this is like if we pulled a pair of all black sneakers out of the urn.

But of course we must ask, what do the sneakers and the white balls have in common? How can we correlate them? Other than there being one more item counted in the world that is not a non-white ball, there is nothing to presuppose what the next item removed from the urn will be, perhaps a black ball? (I know you said not to nit pick this point but....)

That aside... if we pull 7 nonwhite items that are not balls do we increase the belief by a factor of 7 to the original factor of increase?

I think I need to ask you a question of how you are referring to events and such in B-Theory to tie it into this answer.