Once we've appealed to an authority we can go back and ask "is this person/source really authoritative?"
No. I am not sure why you ask me this question. It´s not what I said or implied. Is it your position?
But my question here is: is an appeal to authority a proper justification for knowledge?
And my answer is no (given that this is all there is for a justification).
If I read the information on Wolfram Alpha, can it be said that I "know"?
You mean "
because I read....?"? Then the answer is no.
Anyway, philosophically speaking the concept of knowledge (and particularly the defining question what is required for to constitute a conviction "knowledge") is very diverse. It starts from "strictly speaking, we can´t know anything" (which I think renders the term "knowledge" useless and makes any further considerations obsolete) and has very different versions of what is a justification for considering something known (or for acting
as though it were known). The best we can strive for is a consistent use of the term (and there could be several different consistent ways of using this term).
However, unless we are determined to think and deal in absolutes (which I think ultimately will kick us in the butt), we will need to take into account the context, the subject, the situation, the purpose etc.
So e.g. when I get a letter from the Ministery for Traffic which tells me I have been speeding on...at...in and I get a fine of... there are (under strict application of the term "knowledge") huge problems to even justify that I "know" this letter is genuine, that comes from where it claims it comes, etc. Furthermore (even if I could verify this - and this would come with the acceptance of further sources, that I can´t know to be reliable), I still wouldn´t "know" whether the measuring method was reliable, whether the apparatus was working properly etc etc. So I could spend years upon years trying to 100% verify the whole thing, and I would still not be there.
Instead I could, for practical purposes, rely on information, sources, institutions, processes etc. that have proven highly reliable, and consider this sufficient justification to say "I know...". In most every instance humans use the word "(justification of) knowledge" (and I think the only exception is abstract epistemology, which does not necessarily help us with anything) as a substitute for "justification
to act as though we know.". Simply because that´s the only workable method, in practice.
Now, asking a concrete, practical question, and then applying abstract (possibly absolutist) epistemological criteria in a very strict way means doing two different things as though they were the same.
Thus, if a certain source has proven reliable time and again (and we know that the precautions against itself relying on misinformation, etc etc. are granting a certain reliability), in our use of language we are justified
to act as though we "know" and to
say we "know".
Simply because the only viable alternative approach would be radical epistemological nihilims (i.e. a definition of "knowledge" that renders knowledge impossible and hence renders the word "knowledge" useless).
Of course, all this has very little to do with the "appeal to authority" fallacy, and I think you know this.
