alethic modalities historically, the four central ways or modes in which a given proposition might be true or false: necessity, contingency, possibility, and impossibility. (The term ‘alethic’ derives from Greek aletheia, ‘truth’.) These modalities, and their logical interconnectedness, can be characterized as follows. A proposition that is true but possibly false is contingently true (e.g., that Aristotle taught Alexander); one that is true and not-possibly (i.e., ‘impossibly’) false is necessarily true (e.g., that red things are colored). Likewise, a proposition that is false but possibly true is contingently false (e.g., that there are no tigers); and one that is false and not-possibly true is necessarily false (e.g., that seven and five are fourteen).
Though any one of the four modalities can be defined in terms of any other, necessity and possibility are generally taken to be the more fundamental notions, and most systems of alethic modal logic take one or the other as basic. Distinct modal systems differ chiefly in regard to their treatment of iterated modalities, as in the proposition It is necessarily true that it is possibly true that it is possibly true that there are no tigers. In the weakest of the most common systems, usually called T, every iterated modality is distinct from every other. In the stronger system S4, iterations of any given modality are redundant. So, e.g., the above proposition is equivalent to It is necessarily true that it is possibly true that there are no tigers. In the strongest and most widely accepted system S5, all iteration is redundant. Thus, the two propositions above are both equivalent simply to It is possibly true that there are no tigers.
See also CONTINGENT , MODAL LOGIC. C.M. Alexander, Samuel (1859–1938), Australianborn British philosopher. Born in Sydney, he was educated at Balliol College, Oxford, and taught for most of his career at the University of Manchester. His aim, which he most fully realized in Space, Time, and Deity (1920), was to provide a realistic account of the place of mind in nature. He described nature as a series of levels of existence where irreducible higher-level qualities emerge inexplicably when lower levels become sufficiently complex. At its lowest level reality consists of space-time, a process wherein points of space are redistributed at instants of time and which might also be called pure motion. From complexities in space-time matter arises, followed by secondary qualities, life, and mind. Alexander thought that the still-higher quality of deity, which characterizes the whole universe while satisfying religious sentiments, is now in the process of emerging from mind. See also PHILOSOPHY OF MIN. J.W.A.