Prior’s Turn to Medieval Logic

The peculiar aspect of medieval logic, that the truth-value of propositions changes with time, gradually disappeared as Europe exited the Renaissance. In modern logic, it was assumed by W.V.O. Quine that one cannot appreciate modern symbolic logic if one does not take it to be tenseless. A.N. Prior’s invention of tense-logic challenged Quine’s view and can be seen as a turn to medieval logic. However, Prior’s discussion of the philosophical problems related to quantified tense-logic led him to reject essential aspects of medieval logic. This invites an evaluation of Prior’s formalisation of tense-logic as, in part, an argument in favour of the medieval view of propositions. This article argues that Prior’s turn to medieval logic is hampered by his unwillingness to accept essential medieval assumptions regarding facts about objects that do not exist. Furthermore, it is argued that presentists should learn an important lesson from Prior’s struggle with accepting the implications of quantified tense-logic and reject theories that purport to be presentism as unorthodox if they also affirm Quine’s view on ontic commitment. In the widest sense: philosophers who, like Prior, turn to the medieval view of propositions must accept a worldview with facts about individuals that, in principle, do not supervene (present tense) on being, for they do not yet exist.

Pewne zastosowania wybranych rozszerzeń logiki tensalnej w niektórych naukach przyrodniczych

In the article an issue of applicability of tense logic in natural sciences is addressed. I argue that if one reaches the limits of applications of tense logic, then, in some cases, it is possible to apply some extensions of tense logic. Among examples of such systems is the metric tense logic which enables one to express how many units of time have passed since the occurrence of an event, or how many units of time will pass until the event will take place. Another example is the logic with operators Since and Until, which allows to express time dependences of occurring one event upon the occurrence of an another event.

Memory in Terms of Logic and Semiotics

The phenomenon of memory is considered as a component implicitly present in the process of information communication. A short typology of memory kinds that form a referential field around so-called semantic memory is given. Through the approaches of Yu. Lotman and R. Jacobson, the classical notion of time is considered through the relationship "Past-Present-Future", which is closely related to the problems of memory. The focus is on how could the memory be considered within logic and by means of logic? As one of the ways of solving the point, to apply the tools of tense logic to the problem through the analysis of the works of Anatoly Ishmuratov (1946–2017), a prominent Ukrainian logician, is proposed. The classifications of the tenses by O. Jespersen, H. Reichenbach, W. Bull are considered. The subjective and objective axes of orientation, which form the basis of calendars, charts and scales, as fragments of time, are analyzed. According to Ishmuratov, these instruments – schemes, diagrams, etc. can be considered languages. The possibility of language objectification of meaning determines the relationship of logical inference, and thus the structuring of semantic areas, which are memories, by means the language of logic and in accordance with its structures. Through the study of logical and cognitive conditions of action, A. Ishmuratov continued to develop ideas of tense logic and their application to explain the psychological perception of objective time. He construed a scheme of semantic connections of memory as a mental act that reproduces the life path of the individual; he distinguished between memories and "pseudo-memories", which together influence the reassessment of past events, shape the individual`s experience and his ability to construe alternatives to the future and reasoning about it. A special place in A. Ishmuratov's research is occupied by his explication of temporal three-valued logic and application of temporal modalities to the analysis of so-called transient states. Further study of such approaches could help to make sense of rational explication of memory, testimonies, reminiscences of past events and give interesting results.

Display to Labeled Proofs and Back Again for Tense Logics

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics.

On the Decidability of Intuitionistic Tense Logic without Disjunction

Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.

Arthur Prior A ‘Young Progressive’ Letters to Ursula Bethell and to Hugh Teague 1936-1941.

Arthur Prior is scarcely a household name in New Zealand, but in some respects his story repeats a narrative we like to think of as quintessentially Kiwi—that of the small town boy who ‘makes it’ on the world stage. Born and raised in the rural township of Masterton in 1914, Prior became a leading philosopher of the 20th century, feted for his invention of tense logic (or temporal logic as it is now called), invited by no less a figure than Gilbert Ryle to deliver the prestigious John Locke lectures in Oxford in 1956, offered a Chair in Philosophy at Manchester in 1958, then a Fellowship at Balliol College, Oxford, in 1966. Tragically, he died at the relatively young age of 54, but he remains one of the central figures in the development of logic in the 20th century.