## Monday, October 5, 2015

### The Principles of Indifference and Sufficient Reason

The Principle of Indifference says that we should assign equal probabilities to outcomes that are on par. Why? The thing to say is surely: "Well, there is no reason for one outcome to be more likely than another." But the equal probability of outcomes only follows from this remark if the Principle of Sufficient Reason holds so that when there is no reason for something, it doesn't happen. So it seems that the Principle of Indifference presupposes some version of the Principle of Sufficient Reason.

SMatthewStolte said...

The second step of your post (asking “Why?” on the assumption that there must be an answer) requires that there be some reason for PI. So I take it that this argument is not supposed to be an independent support for PSR. Is that right? It only shows that, given PSR, PI presupposes PSR. The point is something to do with the way these principles are ordered to each other?

Heath White said...

SMS,

I take it that the argument is this. The PI argues

There is no reason probabilities should be different.
Therefore, the probabilities are not different.

This form of argument is an instance of the general form

There is no reason that P, therefore not P

or contrapositively,

If P, then there is a reason that P

which is the PSR.

Alex,

The PI has always puzzled me. Surely there are some things we just have no idea the probabilities of, and assigning them equal probabilities is foolish in that context. For example, what is the probability of a manned mission to Mars in the next 100 years? I have no idea. But probably not 50/50.

Alexander R Pruss said...

Heath:

I agree that the PI is problematic. I think it is least implausible in cases of clear symmetry. The Mars mission case doesn't seem quite so symmetric: the two events are not sufficiently alike.

Heath White said...

When cases are symmetric, that seems like a reason probabilities would be the same (or close). Perhaps we should distinguish between

Principle of Indifference: If there is no reason for probabilities to be different, they are (best treated as) the same

versus

Principle of Similarity: If there is a reason for probabilities to be the same, they are (best treated as) the same

PS strikes me as way better than PI. A different way to put it would be to say that, when there is reason to think probabilities are not different, there is (to that extent) no reason to think they are different; but the converse does not hold.

David Gordon said...

"There is no reason that P, therefore not P" is a stronger principle than
"There is no reason that the probabilities are different, therefore the probabilities are not different", though of course the latter proposition follows from the former. The Principle of Indifference does not rule out cases in which an event happens, though there was no more reason for it to happen than some other event, if these two events have an equal probability of occurrence. But this appears inconsistent with
"There is no reason that P, therefore not P"

Alexander R Pruss said...

An explanation of p doesn't require that there be more reason for p than for some other event.

Consider a crooked coin that has probability 0.6 of heads. Then you understand why it landed heads. But its landing tails is no less understandable. And understanding seems to require knowing the explanation.

David Gordon said...

I suspect that I'm venturing into territory you have mapped out long ago, but if a small probability of an event's happening counts as an explanation of the event's happening,doesn't this threaten to render the PSR innocuous?