Time, Existence, and Identity
Per Hasle, Peter ØHRSTRøM, Torben Braüner, Jack Copeland · 2003
Abstract For some years now a number of us have been working on what is called ‘tense logic’, in which an attempt is made to give something of the rigour of modem logical systems to a language whose sentences resemble those of natural languages in being, in some cases at least, true at one time and false at another. In such a language it is possible to have rudimentary tense-inflections, notably Fp for ‘It will be the case that p\ which is, of course, true whenever p itself is going to be true at some future time, and Pp for ‘It has been the case that p\ which is true whenever p has been true at some past time. The extensions of propositional calculus which we obtain by adding such modifiers to the usual ∼p (‘It is not (now) the case that /?’), p D q (‘If p then q9), p v q (‘Either p or q9), p a q (‘Both p and q9), etc., are now fairly well understood, but we encounter serious problems when we attempt to introduce the same inflections into predicate logic, with quantification over individual variables.