Knowledge Of What Follows

One reason why absolute certainty extends far beyond basic logical axioms and the immediate thoughts within one's consciousness is that even concepts that cannot be proven or falsified can still be used to establish knowledge of what follows from those concepts.  Whether the concept is merely scientific or wholly centered on abstract metaphysics, some things would follow from it if it is true, and other conclusions are red herrings to the idea and its ramifications.  Awareness of what these ideas would mean about the nature of reality is not contingent on awareness of whether these ideas are true.

There are, in fact, scores of logical facts simply pertaining to what does or does not follow from an idea that is itself ultimately unverifiable.  Although one cannot know if the premise is true, one can still know that it is true that the premise would necessitate certain facts if it does correspond to reality.  There are thus always some truths about a given concept that can be known--strictly logical truths--regardless of whether the concept is true, demonstrable, or even supportable by mere evidence.  Knowledge of what follows from a true or false idea requires only that one consults reason soundly.

Knowable facts inevitably reduce down to aspects of reality that can be proven by reason, either by self-evidence (in a small number of cases) or sound deduction.  However, even proving what is true if a concept is valid still establishes a logical fact about reality and simultaneously rules out other possibilities.  The nature of knowledge is more nuanced than simply knowing or not knowing if a given idea is true, as there are always some truths that can be reasoned out about things that are otherwise unknowable.

There is no way to prove that one is in a simulation that has misdirected one's visual sensory perceptions, but one can still know that the "brain in a vat scenario" requires the existence of matter, without which a brain and a vat could not exist.  There is no way to prove if the Civil War happened or not, but one can still prove that nothing has historically occurred that has violated the laws of logic, as such a thing is inescapably impossible.  Many other examples could be provided, but no specific examples are even required for someone to realize that knowing what follows from a premise does not hinge on knowing if the premise is true.