Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work (...) together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation. (shrink)

Leibniz may be considered as the first computer scientist. He made major contributions to engineering and information science. He invented the binary system, fundamental for virtually all modern computer architectures. He built a decimal based machine that executed all four arithmetical operations and outlined a binary computer. The concepts of lingua characteristica (formal language, programming language) and calculus ratiocinator (formal inference engine or computer program) are the base of the modern logic and information science. Leibniz was groping towards hardware and (...) software concepts worked out much later by Charles Babbage and Ada Lovelace. He anticipated the universal Turing machine. (shrink)

The well known Master Argument of ancient Stoic logician Diodorus Cronus is an argument in favour of the philosophical doctrine of fatalism. Perhaps in antiquity this argument was a subject of the most celebrated controversy about temporal truth and modality. This argument is a subject of logical analysis, especially in connection with temporal logic, also today. 1 The most elegant tense-logical formulation of the Master Argument has been given by A. N. Prior. Discreteness and irreflexivity of time are semantical assumptions (...) of Prior’s formulation of the argument. The assumption of discreness is troublesome. 2 The problem of this assumption is a subject of M. J. White’s paper “The Necessity of the Past and ModalTense Logic Incompleteness”. 3. (shrink)

Scientific knowledge is acquired according to some paradigm. Galileo wrote that the “book of nature” was written in mathematical language and could not be understood unless one first understood the language and recognized the characters with which it was written. It is argued that Turing planted the seeds of a new paradigm. According to the Turing Paradigm, the “book of nature” is written in algorithmic language, and science aims to learn how the algorithms change the physical, social, and human universe. (...) Some sources of the Turing Paradigm are pointed out, and a few examples of the application of the Turing Paradigm are discussed. (shrink)

Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for (...) example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications. Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration. (shrink)

We ask which ideas of cognitive science have their roots in traditional logic, grammar and rhetoric.We also emphasize the presence of cognitive science in the pages of Studies in Logic, Grammar and Rhetoric since its very beginning.

In the introduction to the volume on negation, first the source ways of understanding it from antiquity to modern times are presented, as well as the basic points of contention connected with it. Subsequently, the works contained in this volume are briefly presented in the order in which they appeared.

Concepts of infinity have been subjects of dispute since antiquity. The main problems of this paper are: is the mind able to acquire a concept of infinity? and: how are concepts of infinity acquired? The aim of this paper is neither to say what the meanings of the word “infinity” are nor what infinity is and whether it exists. However, those questions will be mentioned, but only in necessary extent.

Artificial Intelligence, both as a hope of making substantial progress, and a fear of the unknown and unimaginable, has its roots in human dreams. These dreams are materialized by means of rational intellectual efforts. We see the beginnings of such a process in Lullus’s fancies. Many scholars and enthusiasts participated in the development of Lullus’s art, ars combinatoria. Amongst them, Athanasius Kircher distinguished himself. Gottfried Leibniz ended the period in which the idea of artificial intelligence was shaped, and started the (...) new period, in which artificial intelligence could be considered part of science, by today’s standards. (shrink)

Leibniz zamierzał stworzyć lingua characteristica universalis – język, w którym dałaby się zapisać wszelka wiedza, oraz calculus ratiocinator – metodę umożliwiającą rachunkowe określenie prawdziwości dowolnego zdania tego języka. Taka idea leży u podstaw współczesnej logiki. Taka idea w odniesieniu do poprawności sprzętu i programów leży u podstaw metod logicznych weryfikacji systemów informatycznych.Dziś widzimy, że dalszy rozwój informatyki zależy istotnie od postępu badań logicznych, a logika – ta starożytna dyscyplina – znalazła nowe bogate pole dociekań, zyskała nowe perspektywy badań. Jej zastosowania (...) mogą mieć tak znaczący wymiar praktyczny, o jakim nie śniło się filozofom. (shrink)

Infinity and negation are in various relations and interdependencies one to another. The analysis of negation and infinity aims to better understanding them. Semantical, syntactical, and pragmatic issues will be considered.

The position of Polish informatics, as well in research as in didactic, has its roots in achievements of Polish mathematicians of Warsaw School and logicians of Lvov-Warsaw School. Jan Lukasiewicz is considered in the world of computer science as the most famous Polish logician. The parenthesis-free notation, invented by him, is known as PN (Polish Notation) and RPN (Reverse Polish Notation). Lukasiewicz created many-valued logic as a separate subject. The idea of multi-valueness is applied to hardware design (many-valued or fuzzy (...) switching, analog computer). Many-valued approach to vague notions and commonsense reasoning is the method of expert systems, databases and knowledge-based systems. Stanis3aw Jaokowski's system of natural deduction is the base of systems of automatic deduction and theorem proving. He created a system of paraconsistent logic. Such logics are used in AI. Kazimierz Ajdukiewicz with his categorial grammar participated in the development of formal grammars, the field significant for programming languages. Andrzej Grzegorczyk had an important contribution to the development of the theory of recursiveness. (shrink)