  Philo and Diodorus each considered the four modalities possibility, impossibility, necessity and non-necessity. These were conceived of as modal properties or modal values of propositions, not as modal operators. Philo defined them as follows: ‘Possible is that which is capable of being true by the proposition’s own nature … necessary is that which is true, and which, as far as it is in itself, is not capable of being false. Non-necessary is that which as far as it is in itself, is capable of being false, and impossible is that which by its own nature is not capable of being true.’ Diodorus’ definitions were these: ‘Possible is that which either is or will be [true]; impossible that which is false and will not be true; necessary that which is true and will not be false; non-necessary that which either is false already or will be false.’ Both sets of definitions satisfy the following standard requirements of modal logic: (i) necessity entails truth and truth entails possibility; (ii) possibility and impossibility are contradictories, and so are necessity and non-necessity; (iii) necessity and possibility are interdefinable; (iv) every proposition is either necessary or impossible or both possible and non-necessary. Philo’s definitions appear to introduce mere conceptual modalities, whereas with Diodorus’ definitions, some propositions may change their modal value (Boeth. In Arist. De Int., sec. ed., 234–235 Meiser).