The series offers a publication forum for innovative works on all topics of analytic philosophy. The focus is on the disciplines of theoretical philosophy: metaphysics, ontology, epistemology, philosophy of language, logic. Furthermore, works that additionally include contributions to the history of philosophy are also welcome.

The aim of the book is to show that the Five Ways of Thomas Aquinas, i.e. his five arguments to prove the existence of God, are logically correct arguments by the standards of modern Predicate Logic. In the first chapter this is done by commenting on the two preliminary articles preceeding the Five Ways in which Thomas Aquinas points out that on the one hand the existence of God is not self-evident to us and on the other hand, that, similar (...) as in some scientific explanations, the mere existence of a cause for an effect which is evidently known to us can be proved. In the second chapter every argument is translated into the symbolic form of Predicate Logic and its logical validity is shown. Additionally a detailed and critical discussion of the premises of each argument is given. (shrink)

The aim of the book is to refute the claim that God's omniscience, omnipotence and benevolence on the one hand and the existence of evil on the other are together inconsistent. This is shown first by unmasking many types of such claims as either logical fallacies or as presupposing false assumptions. Secondly the author formulates God's attributes of omniscience, omnipotence and benevolence and the existence of 10 types of evil in an axiomatic system. This contains the theorems about God's knowledge, (...) will, causation and benevolence without leading to any inconsistency. It proves the compatibility between God's attributes of omniscience, omnipotence and benevolence with the fact of existence of evil. The author offers a consistency proof for the whole axiomatic system with the help of a model in which all axioms and theorems are satisfied"-- Back cover. (shrink)

The contributions to this volume are from participants of the international conference "Kreisel's Interests - On the Foundations of Logic and Mathematics", which took place from 13 to 14 2018 at the University of Salzburg in Salzburg, Austria. The contributions have been revised and partially extended. Among the contributors are Akihiro Kanamori, Göran Sundholm, Ulrich Kohlenbach, Charles Parsons, Daniel Isaacson, and Kenneth Derus. The contributions cover the discussions between Kreisel and Wittgenstein on philosophy of mathematics, Kreisel's Dictum, proof theory, the (...) discussions between Kreisel and Gödel on philosophy of mathematics, some bibliographical facts, and a collection of extracts from Kreisel's letters. (shrink)

The volume deals with the history of logic, the question of the nature of logic, the relation of logic and mathematics, modal or alternative logics (many-valued, relevant, paraconsistent logics) and their relations, including translatability, to classical logic in the Fregean and Russellian sense, and, more generally, the aim or aims of philosophy of logic and mathematics. Also explored are several problems concerning the concept of definition, non-designating terms, the interdependence of quantifiers, and the idea of an assertion sign. The contributions (...) concerned with Wittgenstein's investigations into the philosophy of logic and mathematics pursue issues relating to logical necessity, the undeniability of the law of the excluded middle, and the source of self-evidence, often characterized in the literature as the "rule-following considerations". Additionally, they examine Wittgenstein's attitudes towards the very idea of set-theory as a possible foundation for arithmetic. The volume also includes a number of contributions on specific issues concerning Wittgenstein's views on moral and religious judgements. (shrink)

Zawiera materiały konferencji zorganizowanej przez Instituts Görresgesellschaft für interdisziplinäre Forschung (31.8-5.9.1989).

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts , content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but (...) in agreement . We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6). (shrink)

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in (...) agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic versus semantic formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence. (shrink)

There are basic questions concerning truth that have been perennial throughout the history of philosophy from the Ancient Greeks onwards: Is 'true' a ...

The paper offers a matrix-based logic (relevant matrix quantum physics) for propositions which seems suitable as an underlying logic for empirical sciences and especially for quantum physics. This logic is motivated by two criteria which serve to clean derivations of classical logic from superfluous redundancies and uninformative complexities. It distinguishes those valid derivations (inferences) of classical logic which contain superfluous redundancies and complexities and are in this sense from those which are or in the sense of allowing only the most (...) informative consequences in the derivations. The latter derivations are strictly valid in RMQ, whereas the former are only materially valid. RMQ is a decidable matrix calculus which possesses a semantics and has the finite model property. It is shown in the paper how RMQ by its strictly valid derivations can avoid the difficulties with commensurability, distributivity, and Bell's inequalities when it is applied to quantum physics. (shrink)

Der Atheismus erlebte in den letzten Jahren eine Renaissance. Durch verschiedene Publikationen wurde der Atheismus in der Offentlichkeit und in den Wissenschaften wieder zum Thema. Religioser Glaube sei mit einem wissenschaftlichen Weltbild nicht vereinbar, so viele Atheisten. Diese Bewegung fasst man unter dem Namen Neuer Atheismus zusammen. Aber ist tatsachlich etwas neu am neuen Atheismus? Gibt es in den modernen Naturwissenschaften noch einen Platz fur Gott? Konnen Argumente der neuen Atheisten uberzeugend zeigen, dass es unvernunftig und unwissenschaftlich ist, an die (...) Existenz eines Gottes zu glauben? Dies sind nur einige Beispielfragen, die die Autoren dieses Bandes versuchen werden zu beantworten. Die Autoren kommen aus unterschiedlichsten Disziplinen: Aus der Physik, der Biologie, der Mathematik, der Philosophie und der Theologie.". (shrink)

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In part II (...) the authors offer several logics that deviate in different ways from classical logics. The twelve papers in part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Académie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences. (shrink)

The paper discusses problems which arise in attempts to axiomatize parts of religion or religious belief systems. Besides those problems already investigated by Bochenski, like that of the propositional content or the meaning of religious discourse there are several further ones. This paper deals with the question whether full Classical Logic is suitable, whether one universe of discourse is sufficient, how to use definitions and analogous concepts and whether justifications satisfy credibility criteria.

This volume comprises a selection of papers that were contributed to the 7th International Congress of Logic, Methodology and Philosophy of Science, which was held in Salzburg from the 11th - 16th July, 1983. There were 14 sections in this congress: 1. proof theory and foundations of mathematics 2. model theory and its applica ti on 3. recursion theory and theory of computation 4. axiomatic set theory 5. philosophical logic 6. general methodology of science 7. foundations of probability and induction (...) 8. foundations and philosophy of the physical sciences 9. foundati ons and phi 1 osophy of biology 10. foundations and philosophy of psychology foundations and philosophy 11. of the social sciences 12. foundati ons and philosophy of linguistics 13. history of logic, methodology and philosophy of science 14. fundamental principles of the ethics of science In each section, three or four invited addresses were given, which will be published in the Congress Proceedings (Ruth Barcan Marcus, Georg J. W. Dorn and Paul Weingartner, eds. : Logic, Metho dology and Philosophy of Science VII. Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of v PREFACE Science, Salzburg, 1983. - Amsterdam, New York, Oxford: North-Holland Publishing 'Company, 1985. ) Every section with the exception of section 14 also contained contributed papers. (shrink)

This article proposes a basic logic for application in physics dispensing with the Principle of Excluded Middle. It is based on the article “Matrix Based Logics for Application in Physics (RMQ) which appeared 2009. In his article with Stachow on the Principle of Excluded Middle in Quantum Logic (QL), Peter Mittelstaedt showed that for some suitable QLs, including their own, the Principle of Excluded Middle can be added without any harm for QL; where ‘without any harm for QL’ means that (...) the basic desiderata and the basic results (theorems) of those QLs remain satised in the sense that they avoid the well known difficulties with commensurability and distributivity.In the following article I want to show that the basic desiderata and results (theorems) of RMQ (of avoiding the well-known difficulties with commensurability, distributivity, fusion and Bell’s inequalities) remain satised if by introducing a strong negation (or strong negation and disjunction) the resulting weak intuitionist system RMQI dispenses with the Principle of Excluded Middle; it becomes either invalid or not strictly valid. (shrink)

Like relativity and quantum theory chaos research is another prominent concept of 20th century physics that has triggered deep and far-reaching discussions in the philosophy of science. In this volume outstanding scientists discuss the fundamental problems of the concepts of law and of prediction. They present their views in their contributions to this volume, but they also are exposed to criticism in transcriptions of recordings made during discussions and in comments on their views also published in this book. Although all (...) authors assume familiarity with some background in physics they also address the philosophers of science and even a general audience interested in modern science's contribution to a deeper understanding of reality. (shrink)

It will be shown in this article that a pluralism of causality is needed. Not only, as might be expected, for such different domains as natural sciences and humanities, but even within the domain of physics different causal relations are necessary. This will be illustrated with examples from Classical Mechanics and Special Relativity, Thermodynamics and Quantum Mechanics. In these domains causal relations differ in their properties. A model for five types of causal relations is provided that is based on a (...) decidable 6-valued logic. (shrink)

SummaryIn the first part of the paper necessary conditions for the rationality of the notions of belief, knowledge, and assumption are given: Among the different conditions it is stressed that one needs two different concepts of belief, one such that if someone knows something he also believes it, the other exclusive such that if someone knows something he need not to believe it and if he believes it he does not yet know it. Another important point is that deductive infallibility (...) has to be rejected as not being a property of human rationality. Similarly it is not a property of human rationality to know all logical true statements.The second chapter offers a deductive system which meets these and additional conditions of human rationality. The third chapter contains the semantics of the deductive system.RésuméDans le premier chapitre ľauteur énumére des conditions nécessaires à la rationalité des concepts croire, savoir et admettre. Entre autres, il relève qu'il faut distinguer au moins deux concepts croire, qui satisfont ľun àľénoncé: quand quelqu'un sait quelque chose, il la croit aussi, ľautre plus exclusif à: quand quelqu'un sait quelque chose, il n'a pas besoin de la croire et quand quelqu'un la croit , il ne la sait pas . Un autre point très important est que ľinfaillibilité déductive doit être rejetée comme n'appartenant pas à la rationalité humaine. Idem pour la connaissance de tous les énoncés logiquement vrais.Le deuxième chapitre décrit un système déductif qui remplit ces conditions de rationalité . Le troisième, la sémantique de ce système.ZusammenfassungIm ersten Kapitel werden notwendige Bedingungen für die Rationalität der Begriffe Glauben, Wissen und Annehmen gegeben: Unter anderem wird hervorgehoben, dass minde‐stens zwei verschiedene Begriffe von Glauben nötig sind; einmal so, dass gilt: wenn einer etwas weiss, dann glaubt er es auch, und dann auch im exklusiven Sinn: wenn einer etwas weiss, dann braucht er es nicht zu glauben und wenn einer etwas glaubt, dann weiss er es nicht. Ein anderer sehr wichtiger Punkt ist, dass deduktive Infallibilität (d.h. dass man von dem. (shrink)

The purpose of the paper is to show that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. This kind of cleaning of CL has been done successfully by distinguishing two types of theorems of CL by two criteria. One criterion (RC) forbids such theorems in which parts of the (...) consequent (conclusion) can be replaced by arbitrary parts salva validitate of the theorem. The other (RD) reduces the consequences to simplest conjunctive consequence elements. Since the application of RC and RD to CL leads to a logic without the usual closure conditions, an approximation to RC and RD has been constructed by a basic logic with the help of finite (6-valued) matrices. This basic logic called RMQ (relevance, matrix, Quantum Physics) is consistent and decidable. It distinguishes two types of validity (strict validity) and classical or material validity. All theorems of CL (here: classical propositional calculus CPC) are classically or materially valid in RMQ. But those theorems of CPC which obey RC and RD and avoid the difficulties in the application to empirical sciences and to Quantum Physics are separated as strictly valid in RMQ. In the application to empirical sciences in general the proposed logic avoids the well known paradoxes in the area of explanation, confirmation, versimilitude and Deontic Logic. Concerning the application to physics it avoids also the difficulties with distributivity, commensurability and with Bell's inequalities. (shrink)

INITIAL PROBABILITIES: A PREREQUISITE FOR ANY VALID INDUCTION* * I. INDUCTIVE REASONING AND ITS UNDERLYING ASSUMPTIONS Experience does not tell us anything ...

The aim of the book is to show that the ’five ways’ of Thomas Aquinas, i.e., his five arguments to prove the existence of God, are logically correct arguments by the standards of modern predicate logic. In the first chapter this is done by commenting on the two preliminary articles preceding the five ways in which Thomas Aquinas points out that on the one hand the existence of God is not self-evident to us and on the other hand, that, similar (...) as in some scientific explanations, the mere existence of a cause for an effect which is evidently known to us can be proved. In the second chapter every argument is translated into the symbolic form of predicate logic and its logical validity is shown. Additionally a detailed and critical discussion of the premises of each argument is given. (publisher). (shrink)

Jaakko Hintikka's concept of belief (aBp) as presented in his Knowledge and Belief is such that in his epistemic logic aKp —> aBp is a thesis. This concept (B-belief) is one important kind of belief and can be contrasted with a different concept of belief (G-belief, denoted by 'aOp') not discussed in Hintikka's book. It is to some extent opposite to the one above in the sense that it is knowledge-exclusive, whereas Hintikka's is knowledge-inclusive. This is shown by the thesis (...) aKp —> —laGp or aGp —> —laKp. My thesis is that this kind of belief is used as the belief in scientific hypothesis and as religious belief. Both G-belief and B-belief are applied to examples from physics and religion and consistency criteria are discussed for either concept. (shrink)

Jaakko Hintikka's concept of belief (aBp) as presented in his Knowledge and Belief is such that in his epistemic logic aKp —> aBp is a thesis. This concept (B-belief) is one important kind of belief and can be contrasted with a different concept of belief (G-belief, denoted by 'aOp') not discussed in Hintikka's book. It is to some extent opposite to the one above in the sense that it is knowledge-exclusive, whereas Hintikka's is knowledge-inclusive. This is shown by the thesis (...) aKp —> —laGp or aGp —> —laKp. My thesis is that this kind of belief is used as the belief in scientific hypothesis and as religious belief. Both G-belief and B-belief are applied to examples from physics and religion and consistency criteria are discussed for either concept. (shrink)

The first part of the papaer contains desiderata for a realistic epistemic system as opposed to idealistic ones. One of the main characteristics of idealistic epistemic systems is their deductive infallibility or deductive omniscience. The system presented avoids deductive infallibility though having a strong concept of knowledge. The second part contains the theorems of the system. The system is detailed in so far as it distinguishes between two concepts of belief and one of assumption and interrelates them to the concept (...) of knowledge. Though all concepts satisfy certain consistency criteria the strongest ones hold for the concept of knowledge; whereas a belief in or a assumption (assertion) of a proposition which has inconsistent consequences (not known or believed or assumed by the believer or assumer) does not entail the commitment of believing in (or assuming of) an explicit contradiction. Moreover the system contains a lot of distinctions and details concerning propositions with a second person involved like "a knows that b knows whether p is the case" etc. The third part of the paper contains the semantics of the system which consists of many-valued truth-tables. Since the matrices are finite the system is consistent and decidable. (shrink)

The first part of the papaer contains desiderata for a realistic epistemic system as opposed to idealistic ones. One of the main characteristics of idealistic epistemic systems is their deductive infallibility or deductive omniscience. The system presented avoids deductive infallibility though having a strong concept of knowledge. The second part contains the theorems of the system. The system is detailed in so far as it distinguishes between two concepts of belief and one of assumption and interrelates them to the concept (...) of knowledge. Though all concepts satisfy certain consistency criteria the strongest ones hold for the concept of knowledge; whereas a belief in or a assumption (assertion) of a proposition which has inconsistent consequences (not known or believed or assumed by the believer or assumer) does not entail the commitment of believing in (or assuming of) an explicit contradiction. Moreover the system contains a lot of distinctions and details concerning propositions with a second person involved like "a knows that b knows whether p is the case" etc. The third part of the paper contains the semantics of the system which consists of many-valued truth-tables. Since the matrices are finite the system is consistent and decidable. (shrink)