(T1) Every expression token (of the sort that is a candidate to have an extension) is associated with a primary intension, a secondary intension, and a two-dimensional intension. A primary intension is a function from scenarios to extensions. A secondary intension is a function from possible worlds to extensions. A two-dimensional intension is a function from ordered pairs of scenarios and worlds to extensions.
(T2) When the extension of a complex expression token depends compositionally on the extensions of its part, the value of each of its intensions at an index (world, scenario, or ordered pair) depends in the same way on the values of the corresponding intensions of its parts at that index.
(T3) The extension of an expression token coincides with the value of its primary intension at the scenario of utterance and with the value of the secondary intension at the world of utterance.
(T4) A sentence token S is metaphysically necessary iff the secondary intension of S is true at all worlds.
(T5) A sentence token S is a priori (epistemically necessary) iff the primary intension of S is true at all scenarios.
(T6) A sentence token S is necessary a posteriori iff the secondary intension of S is true at all worlds but the primary intension of S is false at some scenario.
(T7) A sentence token S is contingent a priori iff the primary intension of S is true at all scenarios but the secondary intension of S is false at some world.
(T8) ‘A≡B’ is metaphysically necessary iff A and B have the same secondary intension.
(T9) ‘A≡B’ is a priori (epistemically necessary) iff A and B have the same primary intension.
