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RE: Warning: Actual Philosophy, Redifining Knowledge
Let's take a basic example, 2+2=4.
If you memorize the sentence "two plus two equals four" but have no idea what makes it true (despite justifiably believing it via authority), I'd be hesitant to call it knowledge.
To have understanding, you're justification for believing 2+2=4 needs to be the thing that makes it true, i.e. that 2 and 4 are numbers, and that + is a mathematical operator for addition, etc. etc.
But if you just memorize the sentence "two plus two equals four" and you don't understand what it means, then do you really believe it? I agree that this is not knowledge, because belief is missing.
Because 2+2=4 is something that you can realise by reason alone, it is hard to see how you can fail to believe it without understanding it and being justified in the belief.
But isn't it otherwise with empirical knowledge?