What this means is that philosophy ultimately becomes an extended argument over which propositions to take as axiomatic. One commonly-used technique in this is the thought experiment, and some well-known, much-debated examples, such as Frank Jackson's "Mary's Room", are not even anecdotal evidence.
While, I suppose, analytical philosophy could always be presented in the form an analysis of what follows from a given set of axioms, what almost invariably happens in practice is that individual philosophers act as advocates for the particular axioms that they believe actually hold.
There also seems to be a pervasive shared assumption in current analytical philosophy that analysis of the use of language can be the ultimate arbiter on questions of how the world actually is - a questionable belief that is not questioned as much as it should be, or so it seems from my very limited perspective.