The same difficulty exists in math that exists in theology. When debate centers on "logic" any logic applied is only true within the given data sets used to prove said logic. However, when variables of infinity, of infinite negatives, of infinite paradox(es) are introduced into the logic sequences and data sets, they break down in incompleteness and non provability.
Logical arguments are only true when they are based on limited and defined data sets, only provable by the limits or imposed choices of input of the sets themselves. Logic can only assert itself as far as the data used to derive it is capable of encompassing, which, in both math and theology technically disappear when engaging the larger (infinite) reality(s).
Which is why logic is somewhat irrelevant when employed in theology. It is always a "limited" engagement.