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I'm not a Latin reader, so I don't know anything about "mox"; a few dictionaries I've consulted give the primary meaning as being soon in the respect of being next in time or position (which makes perfect sense, given the dogma-- it's distinguishable from the "soon" that you say to a five year old who asks if you're there yet). But shouldn't the dogma speak for itself, rather than having us have to rely on dictionaries to understand it? Dictionaries aren't infallible. If the Church teaches primarily-- or only-- through solemn definitions, then it follows that she, being capable and divinely equipped to execute her mission, speaks clearly in solemn definitions. Right? If you're finding an ambiguity of language, that's your problem.
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So, we're back to a problem of methodology. Now, for those of us whose methodology allows and encourages us to learn from the Church's ordinary teaching, we find out that the usual translation is immediately simply because the doctrine is that the particular judgment occurs immediately after death, with the sending to Heaven/Purgatory or Hell immediately or instantaneously to the judgment (Parente, 1953). We might, in a manner of speaking, say that such souls do not ascend or descend immediately, but only because they must be judged "first." Not because they can be preserved in a stasis or slumber pending judgment and punishment or reward.
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Interestingly enough, GJC's contention (which you are repeating here) of some stasis or slumber is positively condemned; it's not just a matter of being very difficult to reconcile with Benedictus Deus or any of the other creeds that reinforce the immediacy of Heaven or Hell after death, but "the soul's slumber" is an idea that was tossed around and already condemned (McHugh, 1910).
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So, you see? I am "learning from man." :D
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I agree that you don't need these pious stories as proof of your conclusion. So stop defending them.