You are the only who is making assumptions without evidence and ignoring what I'm saying- that contrary to what you think you do not in fact know the Earth exists, your memories are reliable etc and therefore that your argument, which assumes such, falls apart.
You also fail to comprehend that probabilities have implicit axioms which must be accepted in order to accept probability. There is induction (e.g.- Sun risen X times already so it will probably rise again tonight), the Memory assumption (if my memories say I have done X then that is evidence in probabilities I have done X), the Reality assumption (seeing something is evidence in probabilities for it's existence) etc. None of these can be demonstrated- they are starting assumptions taken on faith.
In the real world, as I said, it depends on what the person asked for. If I believe they were implicitly asking for a faith-based answer I would give that, if I believe an answer based on pure reason I would say neither.
The truth is that anything an agent believes to be true they have no way of justifying, as any justification ultimately appeals to assumptions that cannot themselves be justified.
You also fail to comprehend that probabilities have implicit axioms which must be accepted in order to accept probability.
I do not thus fail, and am aware of the specific assumptions you have in mind. I just deny that their existence implies what you say it implies.
OK. Let me try to restate your argument in terms I can better understand. Tell me if I'm getting this right.
(1) Let A = any agent and P = any proposition
(2) Define "justified belief" such that A justifiably believes P iff the following conditions hold:
a. P is provable from assumpt
I've raised arguments for philosophical scepticism before, which have mostly been argued against in a Popper-esque manner of arguing that even if we don't know anything with certainty, we can have legitimate knowledge on probabilities.
The problem with this, however, is how you answer a sceptic about the notion of probability having a correlation with reality. Probability depends upon axioms of probability- how are said axioms to be justified? It can't be by definition, or it has no correlation to reality.