Suchergebnisse

Over the past several decades, in the field of temporal logic there have been created a great number of semantical theories that provide different truth conditions for tensed propositions. In this article we deal with five non-bivalent semantical interpretations of the temporal logic systems CL (Cocchiarella Linear) and Kb (Kripke Branching): 1) Ł3 by J. Łukasiewicz; 2) K3 by S. C. Kleene; 3) Ockhamism by A. Prior; 4) supervaluationism by R. Thomason; 5) relativism by J. MacFarlane. The aim of this article is to present a detailed typology of the five semantical theories based on these criteria: a) the ability to deal with the problem of retrospective evaluation of future contingent propositions; b) the ability to deal with the problem of divine omniscience and free will; c) their relation to the law of excluded middle; d) their relation to other formulas that are intuitively acceptable in an intederministic context. It is argued that the only theory that satisfies all four criteria is the relativism of J. MacFarlane; however, it faces some serious challenges when dealing with the problem of retrospective evaluation of future contingent propositions in the theological context.

The aim of the article is to present the results of research conducted as part of the project Polonica Philosophica Orientalia: namely, to give an overview of the most important logical and metaphysical treatises (both manuscripts and printed editions) written in Vilnius between the sixteenth and eighteenth centuries that are currently accessible in some of the Vilnius libraries. Although the research focused primarily on the Vilnius University Library and its resources, some interesting results were also obtained while researching the Wróblewski Library of the Lithuanian Academy of Sciences. Most sources containing information about the state and the nature of metaphysical and logical investigations conducted in Vilnius during the period discussed are the manuscripts of lecture courses delivered for the students of Vilnius University and other schools. The analysis of those manuscripts has revealed a strong and long-lasting influence of scholastic Aristotelianism in both logic and metaphysics. Namely, up to the mid-eighteenth century, the main questions discussed in logic were Aristotelian syllogism, the square of opposition and the medieval topics of semantical antinomies, modalities and supposition theory, while investigations into metaphysical issues were limited to commentaries on Aristotle's theoretical treatises without seriously questioning their main theses. In the second part of the eighteenth century, a moderate shift towards subjectivism and psychologism was observed in both of these disciplines. This was influenced by modern epistemologists (George Berkeley, John Locke and others). Logicians and metaphysicians of Vilnius University developed an interest in the topics of human understanding and cognition. However, this shift did not take a radical form – while the majority of eighteenth-century authors sought a combination of scholastic and modern ideas, a critical and even hostile stance towards modern philosophy and science is still noticeable in many of the analysed sources. An overview of the research supported by statistical data is followed by some preliminary remarks on how and where investigation of this topic might be continued in the future.

[tekstas lietuvių kalba]

[full article, abstract in English; only abstract in Lithuanian]
The paper deals with the problem of the "two Barbaras" in the Aristotelian modal syllogistic. The problem consists in Aristotle's differing views on two at a first sight similar in nature syllogisms of mixed assertoric (X) and necessary (L) premises: Barbara LXL and Barbara XLL. The fact that Aristotle believed the first syllogism to be valid and the second one – not, has been received either 1) negatively, because both Barbaras have been held to be invalid, or 2) negatively, because both Barbaras have been held to be valid, or 3) positively, by giving a reason why the two Barbaras differ. We commit ourselves to the position (3) by proving that modal propositions for Aristotle have their modalities de dicto and that Aristotelian modal operators act according to their own separate rules where only the type of the modality of a major premise is relevant for the modal status of the conclusion.

...

Straipsnio objektas yra teiginių su tuščiais terminais aristoteliškajame loginiame kvadrate analizė. Moderniojoje logikoje vyrauja nuostata, jog teiginiai su tuščiais terminais yra neteisėto egzistavimo importo (undue existential import) priežastis – siekiant jo išvengti, atsisakyta priešingumo, popriešingumo ir pavaldumo ryšių. Teiginių su tuščiais terminais problema straipsnyje pristatoma paradokso pavidalu: 1) teiginiai su terminais, neturinčiais referento, funkcionuoja loginiame kvadrate; 2) dalinis teiginys O su tuščiu terminu negali būti teisingas (dėl egzistavimo importo); 3) dalinis teiginys O su tuščiu terminu yra teisingas (dėl loginio kvadrato ryšių). Aptarus kitus pagrindinius paradokso sprendimo būdus, įrodinėjama, jog tradicinėje Aristotelio logikoje nei bendriesiems, nei daliniams teiginiams nebuvo būdingas egzistavimo importas – taigi, atmetama antroji prielaida. Sprendimas pristatomas kaip modifikuota tradicinės kvadrato interpretacijos versija: sutikdami su pagrindine jos teze, kad Aristotelio logikoje terminai nebuvo "tušti" šiuolaikine prasme ir todėl teiginiams su tokiais terminais galioja tie patys principai kaip ir bet kuriems kitiems, nemanome, jog jungtis "yra" išreiškia bet kokio pobūdžio egzistavimą, ir klausimą apie objektų egzistavimą paliekame už aristoteliškojo loginio kvadrato ribų. Siūlomas paradokso Aristotelio sistemoje sprendimas grindžiamas pastarųjų metų bandymais interpretuoti terminų logiką intensiniu pagrindu.

...

In recent years modal syllogistic provided by 14th century logician John Buridan has attracted increasing attention of historians of medieval logic. The widespread use of quantified modal logic with the apparatus of possible worlds semantics in current analytic philosophy has encouraged the investigation of the relation of Buridan's theory of modality with the modern developments of symbolic modal logic. We focus on the semantics of and the inferential relations among the propositions that underlie Buridan's theory of modal syllogism. First, we review all inferences between propositions of necessity, possibility, contingency, and non-contingency, with or without quod est locution, that are valid in Buridan's semantics, and offer a comprehensive diagrammatic representation that includes them all. We then ask the question if there is a way to model those results in first order modal logic. Three ways of formalizing Buridan's propositions in quantified modal logic are considered. Comparison of inferences between the quantified formulas and Buridan's propositions reveals that, when supplied with a suitable formalization, Buridan's semantics of categorical statements and immediate inferences among them can be fully captured by the quantified modal system T.

Tense logic is a branch of contemporary logic which includes formal devices that allow us to deal with the temporal relations between propositions. The aim of our paper is threefold: 1) to reveal how Aristotelian philosophical ideas about time, truth, possibility and necessity were reinterpreted by the founder of contemporay tense logic Arthur Prior; 2) to discuss what novel solutions to the classical problem of future contingents are available using Priorean invention; 3) to describe how the tools of tense logic have transcended their original theoretical purposes.
Keywords: Tense Logic, Sea-Battle Paradox, Future Contingents, Arthur Prior, Aristotle