Of course, the notion that you should choose this standard rather than any other is itself faith-based. I value objectivity, but at the root of Rand's belief system was a stunning failure of consistency.
Reason, based on sensory observation, is man's only means of knowledge -- the knowledge on which his life depends.
This faith-based claim assumes that revelation does not exist, begging the question. (And as a practical matter we all rely very heavily on authority, trusting what others have told us. Otherwise I would have no basis for saying I think I know what the tallest mountain in the world is, or the melting point of lead, or anything else I haven't personally experimented on using tools I built and calibrated myself.)
“Authority” and “Faith” are two different things. One can can double-check authority but one cannot double-check faith.
In other words, anyone can (if they had to) measure a mountain or the boiling point of lead, and prove to themselves the facts of reality, regardless of what authority says.
You cannot do the same for faith — the definition of “faith” is to believe without evidence, or even, despite the evidence. Water into wine? No independent evidence I know of supports that. And everything else I know about the world does not support it, either.
People believe Jesus changed water into wine based on faith — they believe it in spite of the evidence...that’s why they call it a miracle.
Faith cannot be argued against because it is argue-proof — no amount of evidence can be used against it. People believe something no matter what the evidence shows. That’s the heart of what faith means.
Authority on the subject of mountain height and boiling points can always be challenged.
I would question how you would evaluate the validity of "logic" through your 5 senses. And without logic and the law of non-contradiction, you'd have no basis of knowledge.
It's always interesting to watch the naturalists commit the very error they ascribe to others and then work very hard to deny that they did so.