On Epistemology, Belief, and the Methods of Knowledge

all beliefs should be considered justified enough by default to be tentatively held until reasons can be found to reject them....... Beliefs can only be shown false, or not yet shown false; never positively shown true.

Beliefs not yet shown false can still be more or less probable than others, as calculated by methods such as Bayes' theorem.

Synthetic a posteriori knowledge is the intersection of two distinctions that philosophers often make between different kinds of knowledge: the distinction between synthetic and analytic knowledge.

for example, one person in a discourse insists that to be a bachelor only means to live a carefree life of alcohol, sex, and music (ala the Greek god Bacchus from whose name the term is derived), with no implications on marital status, while another person insists that to be a bachelor only means to be a human male of marriageable age who is nevertheless not married, with no implications on lifestyle besides that, then they will find no agreement on whether or not it is analytically, a priori, necessarily true that all bachelors are unmarried

Also, it is unlikely that people knowingly hold false beliefs, which is why a scientific position would be to consider ideas held as true be viewed as tentative hypotheses that have not yet been disproved.

Beliefs about the same phenomenon or fact? Ex: the creatures of the Earth were placed here by God; they were placed here by advanced aliens; they evolved from earlier forms; they spontaneously popped into existence.

Should this be synthetic a priori?

But this involves synthesizing information that was obtained through experierience.

That’s why that passage leads into a discussion of analytic a posteriori knowledge: the meaning of words (analytic) is obtained from experience (a posteriori).