Jan Wolenski

There are many versions of the Liar Paradox. J. Agassi names 13 of them. But the most important one is related to Tarski’s theorem that the truth predicate is non-definable for systems that are sufficient for the formalisation of elementary arithmetic of natural numbers. Let S be such a system. We assume that S is consistent and that the syntax of S has been arithmetized as understood by G¨odel. Let E be any sentence of S. E ∗ is the symbol of the G¨odel number of E. If formula A belongs to the language of system S, then formula E is a constant point for formula A if and only if S ⊢ E → A. It can be proved that every formula A ∈ S has a constant point in S.

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical problems.

This book presents the heritage of the Lvov-Warsaw School from both the historical and the philosophical perspective. The historical view focuses on the beginnings and the dramatic end of the School brought about by the outbreak of World War II. The philosophical view, on the other hand, encompasses a broad spectrum of issues, including logical, epistemological, axiological, and psychological problems, revealing the interdisciplinary nature of studies carried out by Kazimierz Twardowski and his students. With thirteen diverse and original essays this volume is split into three parts: History, Culture and Axiology; Psychology; and Logic and Methodology. Exploring not only the history of philosophy represented by the Lvov-Warsaw school, the book also reflects on the condition of contemporary philosophy from the perspective of concepts developed by its representatives. Furthermore, the studies presented in this book delve into problems of contemporary science and its distinctive interdisciplinary character. This volume is, therefore, not only a collection of analyses of the Lvov-Warsaw School philosophy, but also an investigation into the interdisciplinarity of science and philosophy itself.

The paper discusses some logical problems concerning analogy. The traditional understanding of analogy as _proportion_ (proportion) is inadequate, at least if proportionality is taken in mathematical sense. This situation is clear if we considered various special cases of analogy for instance _analogia legis_ and _analogia juris._ Since analogy assumes a similarity of analogata (items being or investigated) as analogical, a general analysis of analogical relation must begin with the concept of similarity. It can be defined as possessing a common property. This idea is formalized by devices borrowed from logic and set theory.

This paper is inspired by Marcin Tkaczyk’s works and discusses the problem of the necessity of the past (is the past determined?) and its role in the analysis of future contingents. The discussion centers on the statements (accepted by Tkaczyk, but slightly paraphrased)) firstly, that every past state of affairs is determined, and, secondly, that at least some some future states of affairs are contingent. The paper argues that because the first assertion is not justified, the antinomy of future contingents does not arise. The argument uses modal and metalogical devices.

Analytic philosophy is one of the dominant styles of philosophizing. On the other hand, every philosopher, past or contemporary is (or even must be) analytic to some extent because he or she intends to explain or clarify something, offers explicit or provisional definitions, divides things and perform critical or approving comparisons of his/her doctrines with proposals of other thinkers. All these activities require more or less analytical work. Yet, restricting our attention to the past, the degree of the analyticity of particular philosophical theories varies from case to case. Socrates was more analytical than Parmenides, Aristotle more so than Plato, the Stoics more so than the Epicureans, St. Thomas Aquinas more so than St. Augustine, Hume more so than Berkeley, Leibniz more so than Spinoza and Kant more so than Hegel and so on. Clearly, there is no minimal amount of analysis in a particular philosophical enterprise. Consequently, we can start the history of analytic philosophy at any arbitrary historical moment, but it is conventional historical-philosophical wisdom to say that proper analytic philosophy arose at the end of the nineteenth century because some philosophers, let’s call them the founding fathers of the analytic movement, like Gottlob Frege, Bertrand Russell or G. E. Moore, considered analysis to be the only (or to be more temperate, the main) method of doing philosophy. This leads to speaking of analytic philosophy as a part of the scenario of contemporary philosophy and not as something cultivated in earlier epochs.

This paper discusses the concept of nothing (nothingness) from the point of logic and ontology (metaphysics). It is argued that the category of nothing as a denial of being is subjected to various interpretations. In particular, this thesis concerns the concept of negation as used in metaphysics. Since the Leibniz question ‘Why is there something rather than nothing?’ and the principle of sufficient reason is frequently connected with the status of nothing, their analysis is important for the problem in question. Appendix contains a short critical analysis of Heidegger’s famous statement Das Nichts nichtet.

The paper discusses the concept of adequacy central for Pertażycki’s methodology. According to Petrażycki any valuable scientific theory should be adequate, that is, neither limping (to broad with respect its actual scope) nor jumping (too narrow with respect to its actual scope). Consequently, adequacy of a theory is a stronger condition than its truth. Every adequacy theory is true, but not conversely. However, there is problem, because scientific laws are conditionals (implications). This suggests that adequacy is too strong conditions, because the consequence of an implication has a wider scope than its antecedent. Thus, laws should have the form of equivalence. The paper shows how model-theoretic characterization of theories allows to recognize truth and adequacy, consistently with Petrażycki’s claims.

. The classical Liar paradox is as follows We can construct several Liar-like paradoxes, for instance of meaninglesness: An additional principles: A is meaningful  A is meaningful; A is meaningful if and only if A is true or false; is not meaningful; is true  is not meaningful; Assume that is true; hence is not meaningful; but is meaningful as true; Assume that is false; hence is meaningful, but  jest meaningful and true; hence   is meaningful; hence  is not meaningful; hence we return to the former case; Analogical paradoxes can be formulated for rationality, testability, etc. A general lesson: If a principle P establishes meaning of a predicate W referring to properties of sentences such that T-scheme is applicable, we can expect that the predicate in question can generate a Liar-like paradox. However, it does not mean that philosopher must resign from P. Generalizing the truth case P is formulated in ML and apply to items formulated in L. The only moral is that the criteria from L have to be supplemented by something else.

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. 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.

Logical theory codifies rules of correct inferences. On the other hand, logical reasoning is typically considered as one of the most fundamental cognitive activities. Thus, cognitive science is a natural meeting-point for investigations about the place of logic in human cognition. Investigations in this perspective strongly depend on a possible understanding of logic. This paper focuses on logic in the strict sense; that is, the theory of deductive inferences. Two problems are taken into account, namely: do humans apply logical rules in ordinary reasoning?; the genesis of logic. The second issue is analyzed from the naturalistic point of view.

This paper analyses proofs of impossibility of epistemology formulated by Leonard Nelson. He proposed two such demonstrations. The first proof tries to show that no criterion of knowledge is possible. Nelson's second argument considers the sentence B 'A is a piece of knowledge' as being synthetic. On the other hand, Epistemology cannot employ problematic premises. Hence, it consists of analytic sentences. Now, epistemology is impossible because synthetic sentence cannot be derived from purely analytic ones. The analysis conducted in the papers intends to locate Nelson's arguments in contemporary discussions about the status of epistemology. In particular, it is argued that the second proof deserves attention of contemporary epistemologists.

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.