How can you raise the probability of the impossible?
How can you lower the probability of the necessary?

Do you understand the analytic/synthetic distinction with regards to what is true in reality vs. what is true by virtue of definitions? You have seemed to struggle mightily with this as you keep trying to come back to this point.

you first need to show that god is necessary. You are assuming that that is the case, and therefore you think that what you are saying is valid and meaningful.

As aaron points out, you are claiming a conclusion from a definition. You are defining god as "necessary, must exist", and using that definition as proof that he exists. Thats not a valid argument.

I’m doing so because my point is about logical necessity and logical impossibility. If something is logically impossible, it’s physically impossible. So there’s no point in looking for empirical evidence for something like a plane figure that is both round and square to raise or lower the probability it exists.

I’m not using the definition of God as a necessary being to prove he exists. I’m using the definition to show that either God’s existence is necessary or God’s existence is impossible.

then you are incorrect. If god is not necessary, he could still exist. Unless, of course, you are defining god as being necessary.

You realize that this is an incomplete schema, right? The set of things that are "not logically necessary" is not equivalent to the set of things that are "logically impossible."

There are plenty of things that not logically necessary that are still logically possible. Your false dichotomy seems to be rendering your point useless.

Okay. So by the contrapositive, if something is physically possible, then it's logically possible. How does any of this tie in with God being logically necessary?

What definition of God are you using? Please be explicit here.

See above. You have erected a false dichotomy.

Your mistake here is that you are conflating an a priori claim with a metaphysically necessary claim. These are conceptually separate ideas - one refers to an epistemic characteristic while the other is a claim about the nature of reality. For instance, an identity claim like:

Mark Twain (if he exists) is Samuel Clemens.

is plausibly a metaphysically necessary claim (true in all possible worlds) since it is an identity statement with two proper names, but this is not an a priori truth of the world, but rather something we discover empirically.

The claim that p is evidence for a necessarily true (if true) claim d should be understood as an epistemic claim, as updating our Bayesian prior of the probability that a necessarily true (if true) claim d is actually true. For instance, if someone announces a new math proof, we often initially do not believe it is true until it has been checked by experts, while still acknowledging that if true it is necessarily true. A second announcement that it is sound after being checked by independent experts would still function as evidence for it being true.

Prior to checking it, what probability would an expert ascribe to a new math proof being true?

That’s the crux of my problem: I don’t understand how or why an expert would say anything other than 0 or 1.

Sure. There are plenty of things that don’t violate LNC so they’re logically possible. But I don’t think “a thing that must exist but doesn’t exist” is one of them. And that’s one of the evidentiary trails we need to follow to establish probability.

That "God is a necessary being" seems to be the most common definition, so that's what I'm running with.

Most experts start with a prior probability based on the reputation and credentials of the person putting forward the proof, the difficulty of the problem, the mode in which it is put forward, etc. Also, I explained exactly how an expert says something other than 0 or 1: they distinguish between metaphysical and epistemic necessity. A claim can be metaphysically necessary while not being epistemically necessary.

This conceptualization of God is merely understood as a characteristic of God, and not the definition. And in particular, one need not accept that this characterization is valid. I can reject the claim/definition that God is a necessary being untrue or invalid.

Then what do you have?

Interestingly, in mathematics we run into situations where we claim a thing must exist and end up with contradictions all the time. In fact, that's one of the most common techniques for proving something doesn't actually exist.

ok, but that doesnt get you anywhere.

I guess a being that’s dependent on something else for its existence.

It saves time. Ultimately God exists or he doesn’t. If he does the reasoning that led one to raise the probability he doesn’t was faulty, and vice versa.

Okay. And... ?

I will also note that the further down this path you go, the closer you get to some generic form of deism. (Which is fine, but I just want to be clear that this is where we're headed.)

My conception of a necessary being is a being whose existence isn’t dependent on anything outside itself. So when you asked if God is not such a being then what do you have?—I’m thinking it would mean a conception of God whose existence is dependent on something outside itself.

Okay. Now tell me why such a thing exists in reality and not just as a conception in your mind.

Or perhaps we have no conception of God. There is no specific reason for me to even grant this idea.

Or if we grant that God (as such) exists, so what? You now have an object whose only property is its own existence. What exactly does this give you? What do you do with this?

You will find that these sorts of strictly formal arguments about God go through rather difficult constructions and tend not to reveal much of anything about anything. It's more an exercise of logic than it is an exercise of learning about the physical universe.

Specifically, you still have not provided a reason that this existence is necessary. You've only posited the rather circular idea that if such a thing must exist then it exists.

I’m not conflating its mode of existence (necessary) with its existence (being). What I’m saying is if a necessary being exists in reality then it exists necessarily (impossible that it couldn’t exist). Conversely, if a necessary being doesn’t exist in reality then its existence is impossible (couldn’t possibly exist).


No. I haven't claimed a necessary being pops into existence out of the laws of thought.

It seems that you are making an assertion about a particular type of probability statement of which statements about God's existence is just one example. For example it seems that you are saying that it makes no sense to say "the probability that the Riemann Conjecture is true is such and such", even though we presently do not know whether it is true.

Am I correct about that? If so I believe that you are not alone in thinking that even among the well educated. But I also believe that almost all the experts disagree with you and them.

I wouldn’t go as far as saying it makes no sense. I just don’t understand how we can apply probability to necessary truths. And I don’t see how the analytic/synthetic distinction or epistemic/metaphysical necessity factors in. I don’t know what to call it, but it looks something like using inductive reasoning to justify a belief in a categorical proposition.

Then what exactly have you accomplished?