Wednesday, August 31, 2016

Faith and credence

Alice: I just saw a giraffe in my yard.
Bob: I always trust you about what's in your yard. So I think it's 55% likely there is a giraffe in your yard.
No, Bob doesn't trust Alice. If he trusted her, his credence that she's telling the truth would have been high.

I am not claiming that we always assign high credence in the assertions of someone we trust in a given matter. This dialogue is perfectly sensible.

Alice to Carla: I just saw a giraffe in my yard.
Bob to Dave: I always trust Alice about what's in her yard. I think I might have just overheard her saying that she saw a giraffe in her yard. So now I think it's 25% likely there is a giraffe in her yard.
In the second dialogue, the reason Bob's credence that there is a giraffe in Alice's yard is lowish has little to do with not trusting Alice about these matters. Rather, it is that he doesn't trust his hearing--he's far from sure that he heard her report a giraffe. I assume in the first dialogue, Bob is quite confident that Alice reported a giraffe--if he isn't, there is no problem.

Trust doesn't require high credence in the assertions of the person we trust. But:

  1. If one trusts x with regard to p-type propositions, one assigns high credence to non-exclusive disjunctions like: p is true or x did not assert p.
When I started thinking about this, I also thought it required a high conditional probability P(p | Alice asserted p). But it doesn't require that. Suppose I trust Alice about mathematics and I hear her confidently say something that vaguely sounded like "The derivative of a sine function is a tangent." My unconditional probability that the derivative of a sine function is a tangent is very low (I can just see in my mind that the slope of a sine is bounded and a tangent is unbounded), but even my conditional probability on Alice's asserting it is very low. It's not that I actually don't trust Alice. Rather, it's that if she asserted that the derivative of a sine were a tangent, I would lose my trust in her mathematical knowledge. (It might be a bit more complicated. Trust might be compatible with accepting minor occasional slip-ups. So I might think it's one of those. So maybe even if she said this, I would be trusting her in general--but not in this circumstance.) And it's compatible with trust that there be possible circumstances where one would rationally stop trusting.

Now, here is a question that has had some discussion in the literature: Is it rationally possible to have explicit Christian faith (I am using "explicit" to distinguish from the kind of faith that an "anonymous Christian" might have) and assign only a modest (not at all high) credence to the proposition that God exists? I think that given fairly uncontroversial historical evidence, this can't happen. Here is why:

  1. One has explicit Christian faith only if one trusts Jesus in central parts of his teaching.
  2. The historical evidence clearly shows that Jesus existed and that a central part of his teaching is that God loves us.
Given the uncontroversial historical evidence, a rational person will accept with very high credence that a central part of Jesus's teaching is that God loves us. By (1) and (2), if she has explicit Christian faith, she will also assign a high credence to the disjunction that God loves us or Jesus didn't centrally teach that God loves us. Since the second disjunction is uncontroversially historically false, the credence will transfer to the first disjunct, and she will assign a fairly high credence to the claim that God loves us. But that God loves us obviously entails that God exists. So she will assign a fairly high credence to that, too. And hence her credence won't be modest (i.e., not at all high).

Interestingly, as far as arguments like this go, it might be possible to have faith in God while only assigning a modest credence to the existence of God. Someone who has faith in God will trust God. So she will assign a high credence to disjunctions like: God loves us or God didn't say God loves us. But while it's uncontroversial that Jesus said God loves us, it's controversial that God said God loves us, since it's controversial whether God exists, but the existence of Jesus is an uncontroversial historical matter (I understand that even the Soviet historians eventually stopped saying that there was no Jesus).

1 comment:

Avi said...

You can still have conditional probability by defining "p-type propositions" as to exclude statements that would cause you to lose trust. That is, you trust them with regard to statements you don't already have strong reason to disbelieve.