Absoluteness of Truth and the Lvov–Warsaw School (Twardowski, Kotarbiński, Leśniewski, Łukasiewicz, Tarski, Kokoszyńska)

According to Twardowski, truth is if it is independent of temporal coordinates. This understanding was one of the main arguments against truth-relativism. Kotarbiński rejected this view as far the issue concerns sentences about the future, but he did not elaborated this idea from a logical point of view. Leśniewski offered an argument that truth is eternal if and only if it is sempiternal; Twardowski shared this opinion. Łukasiewicz rejected sempiternality but retained eternality. His main novelty consisted in applying three-valued logic to explain how it is possible that truth is not sempiternal. Łukasiewicz also pointed out that bivalence together with the principle of causality implies radical determinism. Kotarbiński accepted Leśniewski’s criticism and he defended Twardowski’s view in Elementy. Tarski did not explicitly addressed to the problem of absoluteness or temporality of truth. On the other hand, Kokoszyńska proposed an interpretation of the semantic theory of truth as absolute. It is possible to justify absoluteness of truth in semantics cum the principle of bivalence and show that bivalence does not imply determinism

Was Gaunilo Right in his Criticism of Anselm? A Contemporary Perspective

Gaunilo argued that Anselm could prove the existence of many perfect objects, for example, the happiest island, that is, happier than any other island. More formally, Gaunilo’s arguments were intended to show that the sentence “God exists‘ does not follow from premises accepted by Anselm. Contemporary versions of the ontological proof use the maximalization procedure in order to demonstrate that God exists as the most perfect being. This paper argues that this method, which is based on maximalization, is not sufficient to prove God’s existence. Thus, a “contemporary Gaunilo‘ can repeat objections raised by his ancestor

Foundations of Mathematics and Mathematical Practice. The Case of Polish Mathematical School

The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed. A natural problem arose, namely of how much the foundations of mathematics influence the real practice of mathematicians. Although mathematics was and still is declared to be independent of philosophy, various foundational controversies concerned some mathematical axioms, e.g. the axiom of choice, or methods of proof (particularly, non-constructive ones) and sometimes qualified them as admissible (or not) in mathematical practice, relatively to their philosophical (and foundational) content. Polish Mathematical School was established in the years 1915–1920. Its research program was outlined by Zygmunt Janiszewski (the Janiszewski program) and suggested that Polish mathematicians should concentrate on special branches of studies, including set theory, topology and mathematical logic. In this way, the foundations of mathematics became a legitimate part of mathematics. In particular, the foundational investigations should be conducted independently of philosophical assumptions and apply all mathematically accepted methods, finitary or not, and the same concerns other branches of mathematics. This scientific ideology contributed essentially to the remarkable development of logic, set theory and topology in Poland

Metalogical properties, being logical and being formal

The predicate ‘being logical’ has at least four applications. We can apply it to concepts, propositions, sets of propositions (systems, theories) and methods. The concepts of quantifier or disjunction are logical but those of horse or water are not. Some propositions, for instance, the principle of excluded middle, are logical, others, for instance the law of gravity, are not. Propositional calculus is a logical theory (belongs to logic), but the theory of evolution is not. In a sense, the problem of logical propositions reduces itself to the question of logical systems, because we can say that A is logical if and only if it belongs to a logical systems (however, see below). Finally, deduction is a logical method of justification, but observation is not

Theory or philosophy of law?

The article discusses the theory of law in terms of the extent to which it is part of jurisprudence, on the one hand, and a philosophical pursuit, on the other. The question is explored considering the historical development of the legal sciences and the situation of Polish theory of law in the latter half of the twentieth century. Also, the author relies on the analysis of selected theoreticallegal concepts, notably the so-called multiplane theory of law and the views thought of Zygmunt Ziembiński. The conclusions suggest that philosophy is inevitable in jurisprudence.The article discusses the theory of law in terms of the extent to which it is part of jurisprudence, on the one hand, and a philosophical pursuit, on the other. The question is explored considering the historical development of the legal sciences and the situation of Polish theory of law in the latter half of the twentieth century. Also, the author relies on the analysis of selected theoreticallegal concepts, notably the so-called multiplane theory of law and the views thought of Zygmunt Ziembiński. The conclusions suggest that philosophy is inevitable in jurisprudence

Truth as Modality

Truth as Modalit

Metalogical properties, being logical and being formal

The predicate 'being logical' has at least four applications. We can apply it to concepts, propositions, sets of propositions (systems, theories) and methods. The concepts of quantifier or disjunction are logical but those of horse or water are not. Some propositions, for instance, the principle of excluded middle, are logical, others, for instance the law of gravity, are not. Propositional calculus is a logical theory (belongs to logic), but the theory of evolution is not. In a sense, the problem of logical propositions reduces itself to the question of logical systems, because we can say that A is logical if and only if it belongs to a logical systems (however, see below). Finally, deduction is a logical method of justification, but observation is not

Universality of Logic

This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, topical neutrality and validity (truth in all models). All theses senses can be proved to be justified. The fourth understanding, namely the amount of expressive power, is connected with the criticism of the first-order thesis: first-order logic is the logic. The categorical approach to logic is presented as associated with the last understanding of universality. The author concludes that two senses of universality should be sharply discriminated and defends the first-order thesis.Zadanie „ Wdrożenie platformy Open Journal System dla czasopisma „ Bulletin of the Section of Logic” finansowane w ramach umowy 948/P-DUN/2016 ze środków Ministra Nauki i Szkolnictwa Wyższego przeznaczonych na działalność upowszechniającą naukę

Truth-makers and Convention T

This papers discuss the place, if any, of Convention T (the condition of material adequacy of the proper definition of truth formulated by Tarski) in the truth-makers account offered by Kevin Mulligan, Peter Simons and Barry Smith. It is argued that although Tarski’s requirement seems entirely acceptable in the frameworks of truth-makers theories for the first-sight, several doubts arise under a closer inspection. In particular, T-biconditionals have no clear meaning as sentences about truth-makers. Thus, truth-makers theory cannot be considered as the semantic theory of truth enriched by metaphysical (ontological) data. The problem of truth-makers for sentences about future events is discussed at the end of the paper

An abstract approach to bivalence

This paper outlines an approach to the principle of bivalence based on very general, but still elementary, semantic considerations. The principle of bivalence states that (a) "every sentence is either true or false". Clearly, some logics are bivalent while others are not. A more general formulation of (a) uses the concept of designated and non-designated logical values and is captured by (b) "every sentence is either designated or non-designated". Yet this formulation seems trivial, because the concept of non-designated value is negative. In order to refine the analysis, the class of anti-designated values has been distinguished. The non-trivial version of the principle of bivalence is expressed by (c) "every sentence is either designated or anti-designated". The last part of the paper mentions some extralogical reasons for considering the principle of bivalence with truth being a designated value as intimately connected to human thinking and behavior