περὶ τῶν ἀμφισβητησίμων ἀγωνιζόμεθα, ‘we discuss matters which admit of dispute.’
πίστεσιν: here a rhetorical technical term, ‘arguments’, ‘proofs’, lit. ‘means of persuasion’. Aristotle (Rhet. 1355^{a} 4 ff.) defines πίστις as a proof which is of a moral rather than a scientific kind, the latter being called ἀπόδειξις.
ῥητορικούς, ‘clever orators.’ For the force of adjectives in -ικός see note on δημοτικός, E. 46.
αὐτοὶ πρὸς αὑτούς, ‘in their own minds.’