While total skepticism is entirely refuted by the necessary nature of logical axioms and the truths that follow from them, some skeptics of the self-refuting variety mistakenly claim that knowledge of every distinct worldview and fact is required to have even foundational knowledge. To deny axioms is to affirm them, but I have addressed this contradiction extensively. There is an alternate way to demonstrate the intrinsic errors of total skepticism (legitimate skepticism acknowledges that anything that cannot be logically proven is ultimately unknown). The very nature of reason allows for knowledge of necessary truths even if one is not familiar with every worldview.
I do not need to know exactly what the sum of 32,541 and 78,905 is to know with absolute certainty that the answer is not five. To refute any contrary claims in full, I only need to show that two plus three (like four plus one or five plus zero) is five; this alone proves that adding larger numbers by necessity results in a greater sum. There is always a way to disprove every incorrect mathematical conclusion about which combinations of numbers equal five without resorting to something so simple. Despite this, it is not as if one has to prove that three plus four--or four plus five, five plus six, and so on--does not equal five in order to know that two plus three infallibly amounts to five.
Mathematical truths form only a subset of logical truths. Logical truths, therefore, are far broader than those merely pertaining to numeric values. Proving any logical fact, like proving a specific truth about addition, automatically refutes all possible alternative claims, even if someone is not aware of just how many alternative ideas there are. No one needs to comprehend how many different forms of theism there are, for example, to know with absolute certainty that there is an uncaused cause [1]. Similarly, no one needs to know how many different epistemological frameworks (rationalism, empiricism, sensory empiricism, etc.) there are to know that reason is true by necessity.
Epistemology is far more complex and simplistic than many people realize all at once. Many articles of knowledge are far more difficult to obtain than the average person would like to pretend; simultaneously, many articles of knowledge are also far easier to obtain than is commonly imagined. There is a vast sea of worldviews, but reason provides epistemological solidity due to the absolute certainty it imparts. Refuting a host of philosophical positions is often as simple as proving a basic logical truth. Cling to reason, and a legion of demonstrable truths will never be distant, even if some truths remain unknown or unknowable.
[1]. https://thechristianrationalist.blogspot.com/2017/04/the-uncaused-cause.html
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