Wouldn't appeal to some common prolepsis (on the question of gods’ existence) be subject to the ad populum fallacy?
Yes, it would be such a fallacty if Cicero/Cotta's interpretation of what Epicurus is saying were correct, that Epicurus held that he believed in gods "because 50 million Frenchmen say that there are gods."
But that's not the correct interpretation of prolepsis. Cicero should have known (and probably did know) better than that.
If prolepsis is a "canon of truth" (which it is), then prolepsis is no more an opinion than any other perception or sensation is an opinion. We don't test opinions against other opinions - that would be circular reasoning. A test of an opinion cannot itself be an opinion, but must be evidence in the form of an irreducible given against which we compare and then process in our minds to determine what is true and consistent with that given. If so, a prolepsis is best thought of as an irreducible perception, just like a sensation of sight or sound or a feeling of pleasure and pain.
Quote from Lucretius 4:478 (Brown / Dunster)[478] But you will find that knowledge of truth is originally derived from the senses, nor can the senses be contradicted, for whatever is able by the evidence of an opposite truth to convince the senses of falsehood, must be something of greater certainty than they. But what can deserve greater credit than the senses require from us? Will reason, derived from erring sense, claim the privilege to contradict it? Reason – that depends wholly upon the senses, which unless you allow to be true, all reason must be false.
A true opinion corresponds with what we conclude are the facts of reality after repeated observations produce the same results. A single glimpse of light or color by the eyes is not an opinion, a particular sound heard by the ear is not an opinion, and neither is a single "anticipation" an opinion. A true opinion (what we label to be a "fact") is an opinion concluded by the mind after the receipt and processing of streams of evidence. An "opinion" is held to be true if it is consistent with the evidence, and not contradicted by evidence. Therefore individual perceptions, whether received by the senses, or by prolepsis, or by feelings of pleasure and pain are not "opinions" or "facts." True opinions require consistent streams of perception over time, and individual perceptions (even those of prolepsis) can and often are interpreted incorrectly in ways that are not true to what we eventually conclude to be the ultimate facts after we receive additional data.
[34] Opinion they also call supposition, and say that it may be true or false: if it is confirmed or not contradicted, it is true ; if it is not confirmed or is contradicted, it is false. For this reason was introduced the notion of the problem awaiting confirmation: for example, waiting to come near the tower and see how it looks to the near view. The internal sensations they say are two, pleasure and pain, which occur to every living creature, and the one is akin to nature and the other alien: by means of these two choice and avoidance are determined. Of investigations some concern actual things, others mere words. This is a brief summary of the division of their philosophy and their views on the criterion of truth.
The opinion that gods are living beings blessed and imperishable is an "opinion" which is held by Epicurus to be true for reasons that are not stated in full in the letter to Menoeceus. As Joshua is saying, the letter is definitional: Epicurus tells us the true opinions, and that the opinions of many about the gods are false. He also tells us why the opinions of the many are false: the opinions of the many are false because they are logically inconsistent with a being that is truly blessed and imperishable.
But that does not mean that the many did not base their false opinions about the gods on anticipations they received about the gods, it only tells us that the many misinterpreted the anticipations that they received by not processing them correctly. They let their disposition to believe that the gods are like themselves prejudice their opinions, rather than sticking strictly to the first premises that gods are fully blessed and do not suffer from the weakness of needing to reward friends and punish enemies.
What is an anticipation then? I think the best definition as to what Epicurus was saying (which various people here on the forum have stated in the past) is that prolepsis is a form of "pattern recognition." Through prolepsis we perceive relationships between the data (perceptions) that we receive. These patterns can be found in any or all of the perceptions, not only through the perceptions of the five senses and the feelings of pleasure and pain, but also by the perceptions of the mind received through the "images." But perceiving patterns in these perceptions does not in itself give us a correct opinion about what the perceptions are reflecting. We may in fact be perceiving a centaur in the images, but we know that centaurs do not exist in reality.
In the context of gods, a pattern we perceive about one or more gods in dreams, images received by the mind, seeing paintings or statues of gods, hearing mystical music, feelings of holiness or fear of lightning, or perceptions in any other manner do not in themselves constitute true or false opinions. Just as with centaurs, people can receive all sorts of anticipations about the gods, some of which we will conclude to be true and some of which we will conclude to be false. Epicurus gives us the core opinions that we conclude to be true (living beings blessed and imperishable), and says in the letter to make sure that any other opinions you form about the gods are consistent with those basic truths. If any other opinion you consider is inconsistent with total blessedness and imperishability, that opinion is immediately ruled out of court and deemed to be false.
As Joshua indicates, the reasons given by Epicurus for belief that the gods about which we have anticipations are blessed and imperishable are not in the letter, but and the best indication we have of those reasons are as given by Velleius. The foundations seem to include the "supremely potent principle of infinity," wherein we conclude that in an infinite universe, those things which are possible will occur an infinite number of times. Living beings which are happy and continue to live over time are known to use through our experience here on earth, and logical extensions of those things (including Joshua's example of the existence of oceans even if we have only seen small bodies of water in the past) are believable and expectable to be true.
Those things which are not possible (supernatural gods or supernatural anything) will never occur because they are not possible. I do not think the concern that this amounts to an ontological argument is valid because these ontological arguments for the existence of supernatural gods rely on imagination which postulates supernatural things which cannot exist by definition (based on experience). The principal of infinity may be very powerful, but it cannot break the laws of nature, and the supernatural is impossible - full stop.
I think most of us have come to the conclusion that a prolepsis is not an opinion, but that's clearly the first step in this chain of thought which has to be confronted. If you think that a prolepsis is an opinion, and that the opinion in this case is that there are gods, and you should believe in gods because lots of people say that there are gods, then you've reached the conclusion that Epicurus believed in gods because 50 million Frenchmen say that there are gods, and if you believe that then Epicurus was such a fool that nothing else Epicurus held should be believed either, and if you're a fan of Epicurus at all it's because you're a Stoic or Buddhist looking for justification for your devotion to tranquility in the phrase "absence of pain." Obviously in my case I reject that entire line of thought as absurd.
The second key issue is the implication of infinity, which Epicurus clearly tells us to study as a central matter, and Velleius tells us why. Were it not for Cicero preserving this in "On The Nature of the Gods" we'd have almost nothing to go on about why Epicurus stressed that it is important. In the case of infinity, we're facing another set of headwinds similar to the Stoic/Buddhist problem. A certain set of modern scientists allege that the universe is not infinite, and that Epicurus has been refuted on that point. As with the Buddhists and Stoics, Epicurus rejected the logic of that conclusion and considered it to be absurd to argue that the universe has an "end" on the other side of which there is something "outside" of reality.
There are all sorts of ways to respond to those who say the universe is not infinite today, but the one I would point to primarily is that they are misinterpreting the data in a way that they should have rejected out of hand because it never made and can never make any sense. The "universe as a whole" is all that there is, and it can never have a "limit" or an "end" outside of which is "something else" or "nothing." Infinity has always been and always will be the most compelling opinion as to the nature of the universe, regardless of the religions who say that "god" created the universe, or anyone else on any other theory, has to say.