Sunday, January 21, 2018

Very High credence is Not belief

Imagine a spherical die with thousands of tiny faces. You can roll the die around in your hand, surveying all the faces and thinking, of each face, how unlikely it is to end up on top when you roll the die, but that it might. For each face, you have a very high credence in the proposition that it will not end up on top, but it seems that you do not believe that it will not end up on top; it seems so because for some such face you are not at all surprised when it does end up on top.

What would be surprising would be guessing which face it was before it ended up on top; and doing so repeatedly would be so surprising it would suggest some sort of trickery (or psychic power) was present. But that is, of course, quite different; and similarly, the fact that it is unsurprising that our beliefs should sometimes turn out to have been false is a different thing entirely.

The thing is, the Lockean assumption that belief is sufficiently high credence is similarly refuted by almost all of our quotidian beliefs. Consider an ordinary view from some window, for example:

The chance of any particular arrangement of cars, leaves et cetera is low, and so your expectation of having that view is low. Conversely, your expectation of not having that view, and your credence that you won't have that view, are high. But it is of course not the case that you tacitly believe that you won't have that view. On the contrary, you know that you will probably have some such unsurprising view.

Now, a high credence for each possible view not being the actual view is quite compatible with a high credence of one of them being it, of course; but not only is that compatibility paradoxical given the Lockean assumption (it is then the Preface paradox), I just do not believe that anyone really did tacitly believe, before they looked, that the particular possible view that would turn out to have been the actual one was not going to be the actual view. They just are not ever surprised by such an ordinary view.

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