Definitions:
Faith: The absence of doubts and questions, or the condition in which doubts and questions are not allowed.
Skepticism: The condition in which doubts and questions and critical thinking are allowed, or the process by which a position is subjected to questions or doubts, but this is also the name of the belief that knowledge is impossible, as such.
Knowledge: a position or belief which is held with the belief that it cannot be wrong or that its truth is the one and only possibility.
Faith-based knowledge: knowledge that is held without doubt, without question, without testing, without evidence.
Rational knowledge: knowledge that is held, and which is asserted or claimed to be known, but which is, or can be, doubted, questioned, tested, while still maintaining its status as knowledge, or knowledge which exists in a condition where doubts and questions and critical thinking are allowed.
The tradition position holds that you must choose between faith-based knowledge or rational skepticism, but you cannot have rational knowledge. Now the question is: Is rational knowledge possible? If so, how, and under what conditions?
Consider this: Claim, or assert, that you know that X is true. Logic, or science, or math, or history, or whatever, shows that, if X is true, then experience Y will be observed. You can test or question or doubt X by looking for Y in your observations or experience.
Now, you test for Y or not Y, and run an experiment to see if Y is true, or you question or doubt Y and Y withstands the critical scrutiny and proves true, once, and you see that Y is true. Does that mean that you rationally know X?
Consider this: You test X and/or Y an infinite number of times, and X and/or Y is proven true, against doubt and question and test and experiment and experience, an infinite number of times.
Would this, then, be rational knowledge? You know that X is true because X and/or Y withstood doubt and question and critical inquiry and critical thinking, but, for N number of times which X and/or Y did so, X and/or Y might fail a test at the N+1 experiment or test or doubt or question. So you can never rationally know philosophical truth.
Yes. But the problem is: how can you possibly test X and/or Y an infinite number of times?
Consider this: If X is such that if X is true then Y will be observed, and if X is a metaphysical or philosophical principle that is universal and infinite in scope, then (and here is the important part): if X is true, then Y will prove true an infinite number of times, if doubted and questioned an infinite number of times. Y will prove true an infinite number of times, because X is true.
And, if X is true, then the application of logic and reason to thinking about X, will produce knowledge of X.
So it isn't that you rationally know X because X was proven true by an infinite number of doubts and questions being withstood with X's truth intact. Instead, you rationally know X because X is true, and X would prove true in an infinite number of questions and doubts, if such were to exist, because X is true.
But how does one gain rational knowledge that X is true, other than by the satisfaction of an infinite series of doubts of X and/or Y? By means of logic.
What matters for rational knowledge is not whether you know it, what matters is whether or not it is really true. If it is true, then you will come to know it, provided that you use reason and logic.
Contrast this position with the faith-skepticism dichotomy: the claim that knowledge must be based on faith, because reason always allows doubts, and knowledge is that which is known to always be true, so rational knowledge could only come by means of a process of an infinite series of doubts being satisfied, because, if you assert or claim that your knowledge is rational, either you or someone else is always, at any or every point in the future, entitled to question or doubt or test that position which you claim to know, and no position can satisfy every doubt and every question because there could be an infinite series of such leading into the future, so only faith, as the absence of all doubts and questions, or as a condition where you are not allowed to doubt or to question, could make knowledge possible, so you must choose either faith and knowledge, or reason and skepticism, but you can't choose reason and knowledge, you are not allowed to choose to believe that rational knowledge is possible in a practical way in reality for humans.
Objectivism rejects the faith-skepticism dichotomy. The belief that rational knowledge is possible is a core element of the philosophy of Objectivism.
The truth has nothing to fear from skepticism. Indeed, rationality is skeptical knowledge, in a sense. If someone suppresses or avoids being questioned, and seeks to censor doubts, that is the surest sign that they are hiding something, that they fear rational inquiry or critical thinking, that they want you to believe their assertions when what they say is false, and they know it is false, or they themselves don’t know but they fear it is false, in their hearts, so they attack the skeptic who questions and doubts to insulate their own doubts from irritating their guilty conscience, because your doubts become a symbol of their own doubts in their subconscious minds, and they hide from themselves. As Ayn Rand said, “to name the unnamed,” to openly state the doubt or the question or the need for a test, to openly ask why and to call the belief into question, is the surest antidote to this type of fear. When someone has no answers, they seek to avoid the questions, but if they have answers, then they do not fear, or need not fear, skepticism.