Depends on how you define agnosticism. To use a popular example, I am not agnostic about you having an invisible fire-breathing dragon in your garage despite not being able to put a flat 0% probability on it.
Bayesianism redefines the concept of knowledge, which under Bayesianism is represented as a probability. I have very strong knowledge that there is no god. If given sufficiently strong proof against that, I will update my beliefs about the issue -- but this does not mean the same as being unsure about it now.
You shouldn't have any "knowledge" that there is no god.
The issue isn't that there is a small probability of god existing, but rather there is a vanishingly small probability of your particular brand of god being true versus all the other particular brands of god or gods being true.
The pudding in a Bayesian discussing is as so often in the normalizing factor...
No. I have done quite a lot of observations on the world. Each and every one of those observations has produced a result congruent with a world in which no gods exist, and so has very slightly nudged my P(god) towards zero. Under a Bayesian philosophy, this probability is called knowledge.
Then you have to assume that god fudges with the physics so you can catch him at it. Which means that all faiths on the world must assume a god would interfere in a situation that you utterly and completely observed and understood. Because otherwise there might be a true god from some religion who just doesn't care about you.
> The problem with syllogisms is that they're always valid. [...]
> The Bayesian definition of evidence favoring a hypothesis is evidence which we are more likely to see if the hypothesis is true than if it is false. Observing that a syllogism is logically valid can never be evidence favoring any empirical proposition, because the syllogism will be logically valid whether that proposition is true or false.
> Syllogisms are valid in all possible worlds, and therefore, observing their validity never tells us anything about which possible world we actually live in.
If a proposition is logically possible, there's a non-zero probability it's actually true. E.g. it's possible that God does not exist. It's also possible that God does exist and put dinosaur fossils in the ground to troll us. I say this without sarcasm.
Pure Logic(TM) isn't always pragmatic enough to suit our needs because it restricts its inputs and outputs to 100% certainties. In the real world, nothing is ever 100% certain. Maybe we have a lot of life experiences with gravity. Maybe we predict with seven 9's that objects will continue to fall down like they always have. But can we ever be truly-entirely-perfectly certain that tomorrow, gravity won't be around because God forgot to pay the utility bill? No, actually, we can't. We're just really confident because we've experienced evidence of gravity for our entire lives.
Likewise, you can never be truly certain that the diodes in your computer won't spontaneously reverse current. But we can still rely on diodes to work properly because we predict that such an event is super-ultra-extremely unlikely (has low probability) given the voltages humanity's electrical engineers decided to ram through our circuits.
Bayesianism redefines the concept of knowledge, which under Bayesianism is represented as a probability. I have very strong knowledge that there is no god. If given sufficiently strong proof against that, I will update my beliefs about the issue -- but this does not mean the same as being unsure about it now.