I am dissatisfied with the standard two-valued propositional nature of logic.
I keep running into situations wherein someone makes a claim, and the claim either has an unknowable truth value or is incoherent.
As far as I can tell, binary truth values break down for cases where there is (or can be) NO evidence supporting or denying a position.
In this situation, the rational Bayesian gets kinda stuck.
Proposed solution: Add truth values:
True, False, Unknowable, Incoherent
I will use an example here. Atheism is the argument I know the best, and I land firmly in that camp. However, there's all sorts of pitfalls along the way to a coherent/consistent Bayesian Atheism.
So for instance, Tyler Cowen, a relatively well known Athiest, has claimed ~10% likelihood for the existence of (something like) God. It is assumed that he similarly includes ~90% likelihood for God does not exist.
However, (and somewhat unsurprisingly) the doctrinaire atheist position is not there.
First, the doctrinaire atheist has a bunch of logical traps to dodge.
First standard atheist position: A-theism means Without Theism meaning does not believe in a God. This is distinct from the proposition that they believe God does not exist. Burden of proof is elsewhere.
Kinda. I mean, sure, in an argument with other people, you say I don't see it, they say it exists, their burden of proof. But whatever...your job as a functioning rational creature is to make your best assessment of the situation, and as Eliezer Yudkowsky has pointed out more than once, that assessment involves presenting the best argument you can for the opposing position, not just accepting their lame arguments. So...burden of proof is an irrelevant topic in the search for truth, even though it's relevant to debates.
So...given that we have a proposition about "god", and we are responsible for finding the truth value of the proposition, what do we do?
Second standard Atheist position: standard "God" is either inconsistent or incoherent.
Inconsistency is where life gets interesting. A good Bayesian can eliminate some inconsistent "God"s from the possibility set ... while maintaining a healthy 1-3% skepticism that suggests that the individual's inconsistency checker is on the fritz. Hell, I can't expect take a 100 question standardized test on topics I know cold without missing on the order of 1-3 from my errors. And God is a harder topic than all the standardized tests.
Incoherent is where I run into difficulties:
What the do you do with an "incoherent/unknowable" position here?
True, false? No. You label it inapplicable to true/false. But you're still in a place where you may be wrong in your judgement, and that's where the fun comes in.
Roughly the strongest incoherentist position would be:
96% incoherent, 2% true, 2% false.
But then you go back to the Yudkowskian practice of intellectual generosity: If the smartest person you know said "God exists", what would they have meant? In that case...it gets more interesting. I'm going out on a limb here, and suggesting that the essence of the theist position is that there is a sentient creator of the seen universe...think perhaps a jupiter brain playing "Life".
What kind of probability numbers can one place on that? Robin Hanson and others likes to write on the topic. However, I'm going to suggest here that you'd need some evidence one way or another in order to make a decision. And furthermore, I've got a strong inclination to believe that it is impossible to be shown evidence that distinguishes between smart aliens and super-intelligent creators.
Which gives me a 90% epistemically unknowable, 10% unknown?
Oh shucks...I just realized that I should also be putting error bars around my probability estimates. :P
But it's worse than that...suppose you have reason to believe, as per Robin Hanson above, or the standard Unitarian Universalist, that your actions may impact something or not, based on the truthiness of the epistemically unknowable results? That's a hard question.
Anyhow...enough thinking on epaper.