The Introduction outlines, in a concise way, the history of the Lvov-Warsaw School – a most unique Polish school of worldwide renown, which pioneered trends combining philosophy, logic, mathematics and language. The author accepts that the beginnings of the School fall on the year 1895, when its founder Kazimierz Twardowski, a disciple of Franz Brentano, came to Lvov on his mission to organize a scientific circle. Soon, among the characteristic features of the School was its serious approach towards philosophical studies (...) and teaching of philosophy, dealing with philosophy and propagation of it as an intellectual and moral mission, passion for clarity and precision, as well as exchange of thoughts, and cooperation with representatives of other disciplines.The genesis is followed by a chronological presentation of the development of the School in the successive years. The author mentions all the key representatives of the School (among others, Ajdukiewicz, Lesniewski, Łukasiewicz,Tarski), accompanying the names with short descriptions of their achievements. The development of the School after Poland’s regaining independence in 1918 meant part of the members moving from Lvov to Warsaw, thus providing the other segment to the name – Warsaw School of Logic. The author dwells longer on the activity of the School during the Interwar period – the time of its greatest prosperity, which ended along with the outbreak of World War 2. Attempts made after the War to recreate the spirit of the School are also outlined and the names of followers are listed accordingly. The presentation ends with some concluding remarks on the contribution of the School to contemporary developments in the fields of philosophy, mathematical logic or computer science in Poland. (shrink)

This paper surveys selected (though arguably representative) versions of metaphysical and epistemological disjunctivism. Although they share a common logical structure, it is hard to find a further common denominator among them. Two main conclusions are: (1) a specific standpoint on the nature of perceptual relation is not such a common denominator, which means that it is very unlikely that all of these views could be refuted with a single objection; (2) contrary to what its name suggests, disjunctivism can be correctly (...) expressed without the employment of disjunction. (shrink)

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. (shrink)

Alfred Tarski frequently declared that his semantic definition of truth was inspired by Aristotle’s views. The present paper discusses this issue in the context of Marian Wesoły’s criticism of the thesis that there is an affinity between Tarski’s views and those of Aristotle. The article concludes with an inquiry into whether Aristotle’s definition of truthfulness can be identified with the correspondence theory of truth.

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 “every sentence is either true or false”. Clearly, some logics are bivalent while others are not. A more general formulation of uses the concept of designated and non-designated logical values and is captured by “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 “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. (shrink)

In this paper I present four interpretations of so-called negative theology and provide a number of attempts to model this theory within a formal system. Unfortunately, all of them fail in some manner. Most of them are simply inconsistent, some contradict the usual religious praxis and discourse, and some do not correspond to the key theses of negative theology. I believe that this paper shows how challenging this theory is from a logical perspective.

Bolzano's theodicy is a very good example of Platonism in the philosophy of religion. Above all, Bolzano believes that there obtains an ideal realm of truths in themselves and mathematical objects, which are independent of God. Therefore, we are allowed to conclude that God is only a contractor; true, more powerful than Plato's demiurge because He created substances and sustains them in existence, but God must follow a project which is independent of Him. Since the world is determined, by the (...) program and God follows the program, then in fact the program is a god, or better, there is no God. Bolzano's project is not related to God's essence, since it is external to God, and is not made by God. Thus, Bolzano's theodicy is also the absolute opposite of the Cartesian theodicy. God in the Cartesian theodicy can change all rules, all scientific laws and, in consequence, He can create any world He wants. Bolzano's God cannot change anything and cannot create a different world than the world determined by the project, a world different than the one He has created. The responsibility of Bolzano's God for the evil in the world is limited by the project of the world. (shrink)

In this paper, I try to accomplish two goals. The first is to provide a general characterization of a method of proofs called — in mathematics — the diagonal argument. The second is to establish that analogical thinking plays an important role also in mathematical creativity. Namely, mathematical research make use of analogies regarding general strategies of proof. Some of mathematicians, for example George Polya, argued that deductions is impotent without analogy. What I want to show is that there exists (...) a direct line leading from Cantor’s diagonal argument to constructions that underlies of the proofs of several important theorems of the mathematical logic (in particular, Church’s theorem concerning the undecidability of formal arithmetic, Gödel’s theorem concerning the incopleteness of formal arithmetic, Tarski’s theorem concerning truth, and Turing’s theorem concerning the Halting Problem), and that the line could be described as an analogical mapping. In other words, Cantor’s diagonal argument and the proofs of the limitative theorems are structurally the same. Hence they can be represented as instances (or special cases) of the same general scheme. (shrink)

O presente artigo aborda a especificidade do vivido intencional e a sua relação com as sensações não intencionais. Em seguida, examina a relação entre a noese e o noema, além de analisar a estrutura completa do noema. Mostra que o objeto intencional oscila entre o caráter imanente do noema e o que transcende o próprio noema. Ele traz como conclusão, então, que a análise da estrutura completa do noema evidencia uma dupla concepção do objeto intencional na subjetividade transcendental.

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...) dominance principle. (shrink)

In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure cap-semilattice. These constructions are introduced for the first time.

Philosophers of religion of the Cracow Circle (1934-1944) are the principal precursors of what is now called the analytic philosophy of religion. The widespread claim that the analytic philosophy of religion was from the beginning an Anglo-American affair is an ill-informed one. It is demonstrable that the enterprise, although not the label "analytic philosophy of religion," appeared in Poland in the 1930’s. Józef Bochenski’s postwar work is a development of the Cracow Circle’s prewar work in the analytic philosophy of religion, (...) or at least of important elements of that earlier work. Bochenski’s approach in his ’Logic of Religion’ is quite original and might still be profitably studied and discussed by philosophers of religion of the analytic persuasion. (shrink)

Paraconsistent logics may be viewed as one of the last elementsin a series of rapid developments in science in the 19th and early 20th c.,triggered by the appearance of non-Euclidean geometries. The philosophyof conventionalism, which gave a metatheoretical framework to the basicchanges involved, may also help in evaluating the truth import of logic and in determining its relation to ontology.

This paper represents such an amateur approach; hence any comments backed up by professional erudition will be highly appreciated. Let me start from an attempt to sketch a relationship between professionals’ and amateurs’ contributions. The latter may be compared with the letters to the Editor of a journal, written by perceptive readers, while professionals contribute to the very content of the journal in question. Owing to such letters, the Editor and his professional staff can become more aware of the responses (...) of educated public to the journal’s output. (shrink)

The aim of the paper is to analyze the views of Willard van Orman Quine and compare them with the views of Kazimierz Ajdukiewicz, an eminent philosopher from the Lvov-Warsaw School. I will argue that Ajdukiewicz's approach to ontology is deationary and, in that respect, similar to Quine's. In my analysis of these two ontological stances, I would like to refer to Price's deationist interpretation of Quine's views in order to highlight the similarity between Ajdukiewicz's views and Quine's stance on (...) ontology. Additionally, as both Ajdukiewicz and Quine used a method of paraphrase, my paper also discusses similarities and differences in the methods used by these central representatives of two philosophical environments { Polish and Anglosphere. (shrink)

This article will address the views of Kazimierz Ajdukiewicz - the leading representative of the Lvov-Warsaw School. I will present arguments proving that the Polish philosopher could have anticipated contemporary metaontological discussions. -/- In the first part, I will provide a profile of Ajdukiewicz as a representative of the Lvov-Warsaw School. I will outline the assumptions of his metaepistemological projects: radical conventionalism and semantic epistemology. In the second part, I will argue that the former project resulted in views on existence (...) similar to Hilary Putnam’s and Eli Hirsch’s, whereas the outcomes of the other project are views similar to those of Amie Thomasson and her easy ontology project. (shrink)

In this paper, we will explore two initiatives that focus on the importance of employing logical theories in educating people how to think and reason properly, one in Poland: The Lvov-Warsaw School; the other in North America: The Informal Logic Initiative. These two movements differ in the logical means and skills that they focus on. However, we believe that they share a common purpose: to educate students in logic and reasoning (logical education conceived as a process) so that they may (...) be able to apply their skills to analyze the issues in their society (logical culture as a result of logical education). The aim of the paper is to justify this claim by exploring research objectives and products that are common to both movements. (shrink)

The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a new (...) paradigm is hindered by the Strong Church–Turing Thesis (SCT), the widespread belief that Turing Machines (TMs) capture all computation, so models of computation more expressive than TMs are impossible. In this paper, we show that SCT reinterprets the original Church–Turing Thesis (CTT) in a way that Turing never intended; its commonly assumed equivalence to the original is a myth. We identify and analyze the historical reasons for the widespread belief in SCT. Only by accepting that it is false can we begin to adopt interaction as an alternative paradigm of computation. We present Persistent Turing Machines (PTMs), that extend TMs to capture sequential interaction. PTMs allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of TMs and of the CTT. The paradigm shift to interaction provides an alternative understanding of the nature of computing that better reflects the services provided by today’s computing technology. (shrink)

Recent scholarship indicates that Quine’s “Truth by Convention” does not present the radical critiques of analytic truth found fifteen years later in “Two Dogmas of Empiricism.” This prompts a historical question: what caused Quine’s radicalization? I argue that two crucial components of Quine’s development can be traced to the academic year 1940–1941, when he, Russell, Carnap, Tarski, Hempel, and Goodman were all at Harvard together. First, during those meetings, Quine recognizes that Carnap has abandoned the extensional, syntactic approach to philosophical (...) analysis, an approach espoused in Carnap’s 1934 Logical Syntax of Language, and which Quine endorsed his entire career. Second, Tarski presents Quine with a philosophically well-motivated reason to think that an apparently analytic discipline, arithmetic, could be synthetic; this reflects one of the central assertions found in “Two Dogmas” but not in “Truth by Convention.” I use this account of Quine’s development to resolve a dispute between Creath and Mancosu concerning the timeline for Quine’s evolving critiques of analyticity. (shrink)

W rozważaniach tych podejmuję próby pokazania, że w myśli filozoficznej XVII i XVIII stulecia pojawiły się zarówno takie formy agnostycyzmu, które określały swoją ideową tożsamość poprzez odwoływanie się do wiary religijnej, jak i takie, które określały ją poprzez opozycję do niej. Spotykały się one i niejednokrotnie spotykają do dzisiaj z surową oceną zarówno ze strony niektórych Kościołów, jak i zdeklarowanych ateistów. Warto się nieco uważniej przyjrzeć argumentacji zwolenników tych form agnostycyzmu. Być może pozwoli to uniknąć przynajmniej niektórych nieporozumień związanych z (...) ich stanowiskiem. (shrink)

The current discussion of the intentionality nature has become more sophisticated and complex. In this paper I will delineate a number of approaches to intentionality in contemporary philosophy: 1 mentalistic; 2 semantic / linguistic; 3 pragmatic; 4 somatic; 5 and naturalistic. Although philosophers identify and analyse many concepts of intentionality, from the author point of view, there is only one intentionality: mentalistic intentionality. Furthermore, there are the pre-intentionality in the physical world and the meta-intentionality in the world of culture.

Ludwik Borkowski’s vast knowledge of philosophy allowed him to put his logical studies in a philosophical context. As a logician, he continued the tradition of the Lvov-Warsaw school. He dealt with the basic issues of the widely understood logic as well as with those having strong philosophical implications (e.g. non-classical logics, the theory of truth, natural deduction, the theory of consequence). He also worked on the theory of definition and the intuitive interpretation of logical results. For Borkowski, logic was an (...) autonomous science whose function is supposed to be ancillary towards the other sciences. Although he did not write any typical philosophical-logical works, investigating philosophical sources, inspirations and the implications of logical results was something he did throughout the whole period of his creative activity. (shrink)

Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version (...) of the Church–Turing Thesis is unaffected by SAD computation. (shrink)

Both through his own work and that of his students, Franz Clemens Brentano had an often underappreciated influence on the course of 20 th - and 21 st -century philosophy. _The Routledge Handbook of Franz Brentano and the Brentano School_ offers full coverage of Brentano’s philosophy and his influence. It contains 38 brand-new essays from an international team of experts that offer a comprehensive view of Brentano’s central research areas—philosophy of mind, metaphysics, and value theory—as well as of the principal (...) figures shaped by Brentano’s school of thought. A General Introduction serves as an overview of Brentano and the contents of the volume and three separate bibliographies point students and researchers on to further avenues of inquiry. Systematic and detailed, _The Routledge Handbook of Franz Brentano and the Brentano School_ provides readers with a valuable reference to Brentano’s work, and to his lasting importance in the history of philosophy and in contemporary debates. (shrink)

In this paper I briefly discuss principles of “independent ethics” formulated and popularized by the Polish philosopher Tadeusz Kotarbiński. I focus on the notion of “conscience” which seems to play a fundamental role in this moral theory.

In the period after the First World War when the various national-ideological “truths” that led to it were not well resolved which resulted in the Second World War, one of the greatest world crises occurs. In those turbulent times, one philosopher renounces his national identity (changes his religion and name), wanting not to save himself from an evil world that is emerging but to join the creation of a completely new world – the world of modern logic. This man is (...) Alfred Tarski, whom many recognize as “the man who defined truth”, linking him to the formulation of the distinction between object and metalanguage. In the paper, I argue with historians of philosophy who claim that this distinction was first set by the logician and philosopher of the Lvov-Warsaw school Stanislaw Leśniewski (whose Tarski was the only doctoral student) accusing Tarski of violating professional laws without attributing the authorship of this distinction to Leśniewski. I show that this is not true and I cite the places where Tarski clearly emphasizes Leśniewski ‘s contribution. (shrink)

The paper depicts the evolution of the conception of the method of analytical description of Czeżowski, one of the most important figures of the Lvov-Warsaw School of Philosophy. It portrays Czeżowski as an author, whose voice on relation between theory and experience, as well as language and empirical reality, can be still considered important and significant. Generally speaking, Czeżowski distinguishes between two kinds of methods: the inductive ones and the no inductive, i.e. the method of analytic description. The results of (...) the former are the base of every further scientific activity, from the empirical sciences to philosophy. The method serves, first of all, to define abstract concepts and to precise scientific terms, what allow next to set and to express relations between them. Its application is an indispensable and essential part of process of building every abstract scientific theory. Despite some similarities between Czeżowski’s method and other methods of conceptual analysis, the former is not subjected to the paradox of analysis, according to the author of the paper. (shrink)

The article aims to determine whether it is possible to build the reliably practiced classical philosophy, understood as a metaphysical research, directed towards the nature of objective reality. The purpose of this kind of philosophizing is knowledge and truth. Moreover, the practice of such philosophizing and its results should meet some of the characteristics of science. The paper establishes a set of conditions that have been imposed on the science of metaphysics by Kazimierz Twardowski. Among the conditions of such philosophizing (...) are anti-dogmatism, criticism, inter-subjectivity of philosophizing and its results, proper epistemic justification of philosophical beliefs, application of the analysis method, rigorous language and reasoning, the use of experience and scientific knowledge. The paper considers these conditions to be correct in most cases and argues that metaphysics can meet them. The existing cases of analytical metaphysics show that metaphysics is possible as a science. Next, the article argues that the late Twardowski failed to substantiate his claim that metaphysical positions which he classified as a world-view philosophy could not be scientifically justified, which could have been possibly done with differentiating ways of understanding what such a scientific justification should be. The article argues that he did not take into account a reductive conception of the metaphysical philosophy, which even though it allows the plurality of metaphysical explanations and does not force anyone to accept one position as the only possible and correct explanation, would have an objective value, if such metaphysics were elaborated indeed. (shrink)

This article performs a word history on correspondentia, a neo-Latin construction by Thomas Aquinas in Scholastic thought attempting to interpret Aristotle on the perception of truth, and then tracks succeeding circles of the neologism’s utility. The new term “correspondentia” performs a crucial role in shaping correspondence theory in early modern hermetic thought and again in modern neo-Cartesian thought. A thread of shared discourse demonstrates an ­interconnected journey for the neologism from Aquinas through these contiguous ­conversations all the way to Swedenborg’s (...) sophisticated esoteric “science of correspondences.” Typical of figures in Western esoteric and New Religious Movements, Swedenborg makes claims of ahistorical and direct apprehension of theosophical information regarding unseen realms, providing a useful case study for contextual analysis of how cultural transmission and interdiscursivity shape transcendental traditions. Swedenborg claims an ahistorical reception of his “science of correspondences” in his eight-volume masterwork Arcana Coelestia, where he lays out his first and most exhaustively demonstrated declarations of correspondences as the key to sacred scripture and to a vast bank of information on unseen realms. Analysis of primary sources and his environment of thought, however, betrays the Swedish polymath as deeply embedded in kabbalist, hermetic, and neo-Cartesian discourse for his impressive development of correspondence theory. (shrink)

This text analyzes the concept of philosophical superstition according to Joseph Maria Bocheński. It specifies sufficient conditions for beliefs and statements to be a philosophical superstition. Philosophical superstitions consist in specific contradictions in beliefs or statements: (a) Superstitions assume or contain contradictory beliefs or statements or/and (b) they are inconsistent with direct experiences or (c) beliefs of their followers, or/and (d) without sufficient reasons superstitions contradict what has already been sufficiently justified or/and (e) they contradict semantic rules of reference of (...) a language in which they are formulated. (shrink)

Tematyka niniejszego referatu wpisuje się w badania nad jedną z najważniejszych formacji filozoficznych w XX wieku – Szkołą Lwowsko-Warszawską. W pracy dokonano analizy fenomenu Szkoły Twardowskiego z perspektywy dotychczas przez badaczy tego zagadnienia nie branej pod uwagę – a mianowicie uwzględniającej wielokulturowy charakter Lwowa, jako kolebki Szkoły. Uzasadnienie głównej hipotezy komunikatu, polegającej na stwierdzeniu przynależności szeregu czołowych przedstawicieli ukraińskiej myśli filozoficznej w przedwojennej Galicji do tradycji tzw. filozoficznej Szkoły Lwowskiej, wypełnia istotną lukę w badaniach nad Szkołą Lwowsko-Warszawską i rozszerza perspektywę (...) jej pojmowania jako wielokulturowej formacji intelektualnej. (shrink)

Traditional theism (in Christianity, Judaism and Islam) understands God as possessing certain attributes including omnipotence. God is omnipotent in the sense that God possesses unlimited (maximal) power. For some classical philosophers and theologians (PetrusDamiani, René Descartes) God’s omnipotence requires his being able to do absolutely anything, including the logically impossible. But in Thomas Aquinas’ opinion, to do what is logically impossible is not an act of power but is self-contradictory action. For Aquinas, a logically impossible action is not an action. (...) The contemporary British philosopher of religion, Richard Swinburne, considers omnipotence from an analytic perspective and, partially,within Aquinas’ tradition. For Swinburne, omnipotence includes the power to perform only logically possible and consistent tasks. In this paper, I discuss systematically (§§ 3-6) the philosophical and logical problems of omnipotence and the relation between God and logic from the perspective of Jan Łukasiewicz’s logical investigations. Keywords: Omnipotence, God, logic, rationality, Richard Swinburne, Jan Łukasiewicz. (shrink)