I explained my context was the refutation of philosophical scepticism in general- what I was after should have been clear.
1- You assume that the criterion of self-evidence should be based on being universally convincing. Why should this necessarily be so? Self-evidence comes when the contrary proposition simply doesn't make sense, as it were (simplistic example: free will). The question is how to deal with that with regards to demonstrating the validity of probability/induction. 2- Because the fundamental starting assumption is unjustified, we are no more justified in believing we know the truth than the people who believe in God on faith.
Self-evidence comes when the contrary proposition simply doesn't make sense, as it were (simplistic example: free will).
"Free will" is a concept, not a proposition. What is the proposition about free will that you are claiming to be self-evident, and its opposite "not making sense"?
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.