The bookModeling Reality covers a wide range of fascinating subjects, accessible to anyone who wants to learn about the use of computer modeling to solve a diverse range of problems, but who does not possess a specialized training in mathematics or computer science. The material presented is pitched at the level of high-school graduates, even though it covers some advanced topics (cellular automata, Shannon's measure of information, deterministic chaos, fractals, game theory, neural networks, genetic algorithms, and Turing machines). These advanced (...) topics are explained in terms of well known simple concepts: Cellular automata - Game of Life, Shannon's formula - Game of twenty questions, Game theory - Television quiz, etc. The book is unique in explaining in a straightforward, yet complete, fashion many important ideas, related to various models of reality and their applications. Twenty-five programs, written especially for this book, are provided on an accompanying CD. They greatly enhance its pedagogical value and make learning of even the more complex topics an enjoyable pleasure. (shrink)

There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing, is closely connected to the power-setting formation on the base of some initial truth values. Having a set of generalized truth values, one can introduce fundamental logical notions, more specifically, the ones of logical operations and (...) logical entailment. This can be done in two different ways. According to the first one, advanced by M. Dunn, N. Belnap, Y. Shramko and H. Wansing, one defines on the given set of generalized truth values a specific ordering relation (or even several such relations) called the logical order(s), and then interprets logical connectives as well as the entailment relation(s) via this ordering(s). In particular, the negation connective is determined then by the inversion of the logical order. But there is also another method grounded on the notion of a quasi-field of sets, considered by Białynicki-Birula and Rasiowa. The key point of this approach consists in defining an operation of quasi-complement via the very specific function g and then interpreting entailment just through the relation of set-inclusion between generalized truth values. In this paper, we will give a constructive proof of the claim that, for any finite set V with cardinality greater or equal 2, there exists a representation of a quasi-field of sets isomorphic to de Morgan lattice. In particular, it means that we offer a special procedure, which allows to make our negation de Morgan and our logic relevant. (shrink)

This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

Some people approve of certain general rules of behavior, or some concrete cases. The others disapprove of or are indifferent to them. In this paper I suggest an axiom system which formalizes the use of these utterances. It may be considered as a special (individualistic) approach to deontic logic.

The paper contains an exposition of some non standard approach to gentzenization of modal logics. The first section is devoted to short discussion of desirable properties of Gentzen systems and the short review of various sequential systems for modal logics. Two non standard, cut-free sequent systems are then presented, both based on the idea of using special modal sequents, in addition to usual ones. First of them, GSC I is well suited for nonsymmetric modal logics The second one, GSC II (...) is devised specially for symmetric, i.e. Blogics. GSC I and GSC II are not different formalizations, from the theoretical point of view GSC I may be seen as a simplification of the more general approach present in GSC II. They are considered separately, mainly because Blogics demand different, and more complicated, strategy in completeness proof, whereas non symmetric logics are easily and uniformly characterised by means of Fitting's Consistency Properties. The weakest modal logic captured by this formalization is minimal regular logic C, but many stronger logics are obtainable by addition of suitable structural rules, which conforms to Do en's methodology. Both variants of GSC satisfy also other, besides cut-freedom, desirable properties. (shrink)

It is commonly held that the rise and development of quantum mechanics forces us to reject the idea of objective knowledge and the notion of truth in science. In the article I critically analyse arguments against possibility of objective knowledge in quantum mechanics, which were formulated by philosophizing physicists (Bhor, Heisenberg, Weizsacker). I point out that the term „objectivity” used by those physicists, in ambiguous. They do not distinguish epistemological and ontological notions of „objectivity”, different meanings of the ontic objectivity (...) itself, and they do not separate the objectivity of cognitive acts from the objectivity of cognitive results. (shrink)

Metafizyczny kreacjonizm a paradoksy teizmu ewolucyjnego: przyczynek do dyskusji w ramach współczesnego tomizmu Autor artykułu dowodzi, że metafizyczny kreacjonizm, z którym spotykamy się w filozofii św. Tomasza z Akwinu, w odróżnieniu od kreacjonizmu amerykańskiego oraz teologiczno-‑biblijnego, jest teorią, która wyrasta z czysto filozoficznego wyjaśnianie początków świata i człowieka. Nie jest zatem ideą biblijną przeniesioną na teren filozofii. Podobnie jak teizm metafizyki Arystotelesa, a także teizm metafizyki św. Tomasza z Akwinu nie jest teizmem religijnym, lecz teizmem czysto filozoficznym, gdyż wyrasta z (...) metafizycznego wyjaśniania rzeczywistości. Kreacjonizm metafizyczny jest ostatecznym wyjaśnieniem źródła istnienia bytów, które dane są nam w doświadczeniu, jako niekonieczne w istnieniu i zmienne. Natomiast kreacjonizm amerykański, jest interpretacja biologiczno-kosmologiczną biblijnej prawdy o stworzeniu świata w określonym przedziale czasowym i w punkcie wyjścia odwołuje się do danych Objawienia, które chce naukowo potwierdzić Artykuł został podzielony na dwie części. W części pierwszej zostały przedstawione węzłowe elementy metafizycznej teorii stworzenia ex nihilo i jej rozumienie. W drugiej zaś części artykułu zostały przywołane elementy teizmu ewolucyjnego, które z punktu metafizycznego kreacjonizmu są źródłem różnych paradoksów, a niekiedy i absurdów oraz domagają się ponownego przemyślenia. (shrink)

There are inferences from a sentence or a set of sentences to a question. The relation between the premises and conclusions of such inferences is sometimes called arising.

In this article, the author notes that Thomas Aquinas, in his brief work entitled De Ente et Essentia, proved that at the base of understanding the world, the human being, and God in particular, there is our understanding of being and its essence. When we make a small mistake at the beginning in our understanding of being and its essence, it will turn to be a big one in the end. And what is “at the end” of our knowledge is (...) the discovery of the First and Ultimate Cause of all things, known as: Ipsum Esse, God, the Absolute, The Most Perfect Substance, on whom everything depends, and who depends not on anything else. These present inquiries about the proper understanding of being and its essence are aimed at formulating proof of the necessity of existence of a Being that is the First Cause, and which, existing as Ipsum Esse, is the source and reason of existence of all beings. Without these inquiries, the proof itself would be incomprehensible, and more importantly it would be a purely a priori one. Furthermore, without the existential conception of being, which Thomas first formulated, one could not discover the First Cause which, as Ipsum Esse, is the source of the existence of every being. This issue seems to have escaped the attention of the author of the book Aquinas’s Way to God. The Proof in “De Ente et Essentia.”. (shrink)

In this paper we show that some standard topological constructions may be fruitfully used in the theory of closure spaces (see [5], [4]). These possibilities are exemplified by the classical theorem on the universality of the Alexandroff's cube for T 0-closure spaces. It turns out that the closure space of all filters in the lattice of all subsets forms a generalized Alexandroff's cube that is universal for T 0-closure spaces. By this theorem we obtain the following characterization of the consequence (...) operator of the classical logic: If is a countable set and C: P() P() is a closure operator on X, then C satisfies the compactness theorem iff the closure space ,C is homeomorphically embeddable in the closure space of the consequence operator of the classical logic.We also prove that for every closure space X with a countable base such that the cardinality of X is not greater than 2 there exists a subset X of irrationals and a subset X of the Cantor's set such that X is both a continuous image of X and a continuous image of X. (shrink)

The author reflects on the moral attitudes displayed by Poles fighting in the Warsaw Uprising. He believes that the sacrifice and selflessness with which Varsovians battled for their city had its roots in the general mentality of the Poles, who for generations had been raised in the spirit of “mutual and willing endowment”. He also notes that the noble ideals of the wartime generations have today been largely replaced by mercenary selfishness.

Artykuł stanowi syntetyczna próbę spojrzenia na historyczny rozwój filozofii życia z perspektywy pytań o człowieka. W jej dziejowej ewolucji wyodrębniono trzy okresy z uwzględnieniem specyfiki każdego z nich. Spoiwem wszystkich odmian filozofii życia jest otwarta, dynamistyczna koncepcja człowieka, będąca częścią wizji nieustannie stającego się świata. W takim ujęciu pytanie o człowieka odnosi sie do przesłanek rozumienia: naturalnych korzeni, dziejowej egzystencji czy ładu aksjologicznego.

This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see [6]). We shall prove many properties of -conjunctive closure spaces (X is -conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:1. For every closed and proper subset of an -conjunctive closure space its interior is empty (i.e. it is a boundary (...) set). 2. If X is an -conjunctive closure space which satisfies the -compactness theorem and [X] is a meet-distributive semilattice (see [3]), then the lattice of all closed subsets in X is a Heyting lattice. 3. A closure space is linear iff it is an -conjunctive and topological space. 4. Every continuous function preserves all conjunctions. (shrink)

Political thought of the war and occupation period continued the ideological and program searches started already before 1939. The concept of democracy was mostly associated with the values such as individual freedom, civil rights, safety of citizens, society of the state; cooperation among nations in the fields of politics, economy and protection of peace. The author deals with topics like: democratic international order; democratic political order and economic system. The author concludes the article with a few synthesizing remarks.