Let us, before dissecting Pope's claims, reassure ourselves that Pope is seriously proposing an argument. Wrapped up in flowery language and pretty rhyme as it is, the stanza almost expects to be taken without criticism; but nonetheless, Pope writes imperatively, “Know then thyself, presume not God to scan; the proper study of mankind is Man” (1). While the order feels natural to those who have been raised in Christianity, it bears second examination, even if one is Christian, and feels the order is true. Pope, after stating his thesis, begins to expound on the human situation with a series of claims: man possesses too much knowledge to be skeptical, and too little perserverence to be stoic; he knows not enough to decide whether he is supernatural or natural, whether to rely on reason or passion; man is born only to die, and reasons only to err – and this is the passage upon which we will focus a little later – and is ignorant, with logic such that, however he thinks, everything is chaotic and confused; man is subject to abuse or disabuse, when the two words are taken as antonyms, by himself; was created with apparently contrary impulses; is the only entity which can judge between truth and falsehood, and is always wrong in his descriptions of the world.
Regardless of the accuracy of the more vague descriptions, Pope's central assertion is at least clear: reason is futile; man ought not reflect on the attributes of a deity, but rather must needs examine the state of mankind instead. Since he wishes to comment on the human condition in his work, the conclusion Pope intends his claims to possess substance is not unreasonable; let us, therefore, examine this central proposition.
Ironically, given his outright rejection of logic, since man is a being “reasoning but to err” (10), Pope is internally consistent in a perverse sort of way: he provides no reasons for any reader to believe his bald assertions; without employing logic, he is logically consistent in its denial. He does, however, face, and must somehow deal with, as all apologists must, the notion that an assertion without supporting evidence – and, indeed, without any way to demonstrate its truth – has no reason for an impartial observer to consider it true. Consider, on a visceral level: when any particular person is unsure of the truth of a particular proposition, one searches for conditions sufficient for that proposition: say, e.g., one is unsure of the truth of the claim, “that vending machine exists”; one evaluates the evidence provided by the eyes; if it is insufficient, one may physically examine the object of the claim; if that evidence is still insufficient, one asks one's companion. The entire process is one of finding sufficient conditions to establish the truth of the claim “that vending machine exists”. Similarly, to conclude God is beyond human reason and human reason is fundamentally flawed requires sufficient conditions which are true. Pope presents none.
Moreover, Pope's denial of logic itself lends no credibility to his claims: rather than simply averring his statements are true, as most apologists do, Pope makes the much stronger claim that it is utterly impossible to demonstrate his statements to be true. While not explicit, the statement is necessary for his assertion logic is inherently flawed: should logic be incorrect and flawed, as “reasoning but to err” implies, any sufficient condition for a proposition will not necessarily lead to that proposition. Pope thus destroys his own credibility: in addition to not supplying reasons to believe he is correct, he declares no such reasons exist.
To any rational person, such a position is, by definition, utterly absurd; yet Pope indulges in this sort of repugnant illogical behavior almost without hesitation. Perhaps, given his refusal to apply logic to the situation, he doesn't realize how laughable his assertions are. In any case, presuming for discussion the existence of a deity, let us examine Pope's idea that humans may not apply logic to God.
The claim “humans may not apply logic to God” has a ring of authority to it; perhaps it sounds a little more preposterous when rephrased as “God is absurd”. This is not an exaggeration; the name of a proof which shows a proposition to be self-contradictory, and therefore illogical, is reductio ad absurdum: literally, reduction to absurdity. More to the point, if logic may not be applied to God, God is inherently self-contradictory, for propositions regarding God are not restricted by the laws of logic and therefore a propositional function which is always false -- e.g., “p(X) and ~p(X)”, for any proposition function p(X), to borrow a trivial example -- may be true when X is God.
To wit, consider the paradox of omnipotence: is God capable of creating a rock which he cannot lift? Evasive resolutions aside, some form of this paradox has plagued those who claim God to be omnipotent. Yet, Pope's unestablishable claims would lead to the conclusion not that this paradox is resolvable, but that this is not a paradox!
In the end, it is difficult to communicate how deeply ridiculous the notion that God is beyond logic is: it literally does not make sense. If God is beyond logic, then it is absolutely impossible to determine the truth of any proposition about God; dialogue devolves into a shouting match, with volume determining the winner.