It seems to me that we conceive of possible worlds, but do not imagine them. ‘Conceiving’, here, refers to that intensional cognitive act, the object of which is a particular scenario obtaining in a world, described by complete and compossible propositions. The world is complete in that every proposition or its negation describe the world such that no aspect of the world is left undescribed by a proposition. These proposition are compossible in that the conjunction of all of them is able to be real. Whereas ‘imagining’ refers to that intensional cognitive act, the object of which is a particular scenario which isn’t able to be real.
This is why, for example, we can mentally ‘picture’ impossible scenarios like me running faster than the speed of light without assistance.
Now, I take the relevant probability to be a measure of our confidence that certain propositions bare particular truth-values. Because we may be ignorant of certain things, we can be unsure of the truth-values certain propositions may bare.
So, it makes sense to me that we can be unsure of whether we’re ‘conceiving’ or ‘imagining.’ In so far as we are, it makes sense that we’re unsure of whether a proposition is necessarily true or impossible: we’re ‘picturing’ the relevant scenario, but don’t know if it’s obtaining in a possible world or not. All the probability is doing is numerically representing the ignorance we actually have, or variant degrees of confidence perhaps. Without such numerical representation, our confidence would still exemplify in shades.
We do know as a consequence of our assumed, Anselmian God-concept, though, that the proposition at issue must be non-contingent, that it’s definitely either necessary or impossible, and not anywhere between those two extremes. You agree to that much, correct? Once that’s granted, however, we arguably run into trouble upon the slightest attempt to calculate probability-confidence and/or weigh the evidence surrounding even our very determination of just whether we’re engaging in conception or merely imagination.
Since they put it in clearer words, from here I’m simply going to copy and paste a few substantial portions of the following combox discussion, which ensued under that blog post to which I linked before. Peter Lupu of Arizona State criticized:
"*Subjective or Bayesian probability can only say something about the degree of belief regarding the truth of a proposition, given evidence. However, I fail to see how such a notion of probability can apply to the truth, per se, of necessarily true or necessarily false propositions.
Consider a simple example. The proposition ‘P & ~P’ is necessarily false. Does it makes sense to say that the falsity of this proposition has a high probability based upon evidence consisting of a large number of instances of the same form all of which were found to be false?
I don’t think it makes sense to say that.*"
Further along those lines, Bill, the host, added:
“
‘There are evils that are not explainable by free human agency’ is an empirical, contingent proposition. ‘There is no God’ is a necessary proposition if true. What inference principles could license the move from the first to the second?”
. . ."*Suppose God exists. Then he nec. exists. It follows that any evil there is just has to be logically consistent with the existence of God.
Now turn it around the other way. Here is some evil that cannot be laid at the doorstep of a free agent, e.g. Bambi being burned alive in a forest fire. Assume that this is indeed an evil, and assume that God is noncontingent. How can this natural evil provide any evidence for the nonexistence of God? If God exists, then the counterevidence is merely apparent. If God does not exist, then he is impossible. But how can I infer the impossibility of God from a mere contingent fact, namely, that there is natural evil?*"
. . .“
One question is how the Bambi example provides any evidence of GRATUITOUS evil. Let’s agree that the suffering of the fawn is evil (not exactly obvious, but close enough) and let’s agree that the suffering – the felt suffering, not mere behavior – is empirically detectable. It seems to me that the GRATUITOUSNESS of the suffering is not empirically detectable. After all, if God exists then there cannot be any gratuitous evils. What is empirically detectable is the same whether or not the sufering is gratuitous. To say of some suffering that it is gratuitous is equivalent to saying that the universe is godless.”
. . ."*I agree that just one case of gratuitous evil refutes the proposition that God exists. But how do you know that a given case of evil is a case of GRATUITOUS evil? Is gratuitousness an empirically detectable feature?
To avoid begging the question you need an independent way of establishing that your favorite example of evil is gratuitous, a way independent of just assuming that there is no God.
If God exists, then there are no gratuitous evils. Contrapositively, if there are some gratuitous evils, then God does not exist. Now how will you establish that there are some gratuitous evils?
If x is apparently F it doesn’t follow that x is F. So you can’t appeal to the appearance of gratuitousness.*"
Of course, on the other hand, supposing we actually considered all the various implications, it seems that this tactic might very well end up proving
way too much. For both of us. (Thus, perhaps every one of us just possesses an innate knowledge of the answer. Except, to our frustration, it dwells deep in darkness, beyond our current epistemic reach, underneath layer upon subconscious layer of muddled mental infrastructure – a profundity entangled somewhere between our preferences for surprisingly-dense distraction and disturbingly-adaptive self-deception.)