a Study in the Temporal Ontology of Tense Logic
Abstract
In his 1957 work, Time and Modality, Arthur Prior reflects on the Barcan Formulas (so called after Ruth Barcan Marcus) "P(Sigmax)A to (Sigmax)PA" and "F( Sigmax)A to ( Sigmax)FA". Take "P" to be read "It was the case that", "F" to be read "It will be the case that", and "(Sigmax)" to be the existential quantifier. The former formula can be read "If it was the case that there existed something such that A is true, then there exists something such that it was the case that A was true". In order for the formula to hold, whenever there was something that existed that made the formula A true, it must be true that there is something currently existing that makes A true. Prior's tense logic was a direct response to this unintuitive result for modal and tense logics: he thought that the Barcan Formulas should not hold. Whether or not one agrees with Prior may depend on what one takes as existing. For example, if one were to hold that past individuals do in fact exist, then the former Barcan Formula would seem unproblematic. Similar things can be said for the latter Barcan Formula. Special relativity is usually taken to suggest that this is the case, namely, all individuals past, present, and future, all exist in the fourdimensional spacetime continuum. Nino Cocchiarella took this view in his 1966 dissertation. In that work Cocchiarella developed a tense reflecting his intuitions. I argue that special relativity does not commit one to such a view of spacetime. Instead, we should take only presently existing individuals as existing. I reconstruct Prior's primary tense logical system from its axiomatically presented modal fragment. I then evaluate this system in light of my view of time. Next, I reconstruct Cocchiarella's tense system in the same terms with which I reconstruct Prior's logic. Then I evaluate that system. I conclude that both systems lead us to radically solipsistic results. In the final chapter I suggest some lines of inquiry in special relativity that may lead to a solution for the problems that Prior's system and Cocchiarella's systems face.
 Publication:

Ph.D. Thesis
 Pub Date:
 1996
 Bibcode:
 1996PhDT........16Z
 Keywords:

 ARTHUR PRIOR;
 BARCAN FORMULA;
 Philosophy; Physics: General