модальности (10)

[hgr]

почему модальная логика Прайора имеет так мало отношения к логике нашего мышления времени.

расскажу тут и историю. один очень крупный наш логик из старшего поколения, который сам является вехой в развитии модальных логик, недавно писал одну книгу (еще не издана), где о модальной логике времени говорится, примерно, по Прайору. я его спрашиваю: какая же это логика *времени*, если там про алетическую модальность, пусть даже и во времени? -- на это он мне ответил, что он вообще не понимает, как это может быть "просто" логика времени.
но такие логики усиленно разрабатываются с 1980-х годов. computer science простимулировала, хотя в логический мэйнстрим они едва приходят сейчас, уже после 2005 года где-то... (о них -- в след. серии).1 Why Prior is not about time

The logic of time, among other modal logics, ploughed a lonely furrow during the 20^th century. This has drastically affected its development as a logical discipline as well as its applications in other cognitive sciences, including narratology and linguistics.

The first impulse was given by John Ellis McTaggart (1908) who argued that the time in the sense of a series “past—present—future” is non-existent outside our mind, being a derivation of the time in the sense of series “earlier—later.” Arthur Prior in the 1950s answered this philosophical challenge with a theory of time based on then recently published von Wright’s (1951) book on the modal logic (Prior 1969). Prior’s approach consisted in study of “changing truths” rather than the time as such. In his own words, “[c]ertainly there are unchanging truths, but there are changing truths also, and it is a pity if logic ignores these…” (Prior 1996, 46).

Prior’s logic of time, or “Tense Logic,” is a generalization of the alethic modal logic to the changes in time. It is evident from the very beginning, that is, from the nature of Prior’s operators:

P “It has at some time been the case that…”

F “It will at some time be the case that …”

H “It has always been the case that …”

G “It will always be the case that …”

Prior’s logic was, first of all, about causality: necessity and possibility in the past and in the future, a combination of the alethic modal logic with an otherwise unnoticed logic of time. However, until the early 1990s, Prior’s approach (mixing of time modality with alethic modality) remained the predominant style of the logic researches of time (Øhrstrøm, Hastle 1995).

Prior’s logic as such turned out to be inapplicable to reasoning about time in both narratology and linguistics, even though Prior himself was inspired by the facts related to the natural language. When Alice ter Meulen (1995) proposed a model of time representation in natural language, she preferred to leave aside its logical interpretation. She has been told, however, by Johan van Benthem and Jerry Seligman that a modal logic equivalent to her model should have four-place operators (ter Meulen 1995, 129, n. 1).
Indeed, Prior is more about what we are thinking in time than how we are thinking time. But the structures of language and narrative are about how and not about what. Thus, Prior’s enormous influence after his death (1969) until the early 1990s was rather inhibiting the logical analysis of temporal thinking. However, in about 1990, it was catalyzed by the computer science.