SummaryAfter giving examples for different relations of analogy among different objects the gist of analogy relations are interpreted as homomorphism and isomorphism . The main purpose of the paper is to give a number of precise definitions for different kinds of analogy . In chapter 7 definitions are proposed for analogy relations between theories and common features of the relations T1 is anologous to T2 and T1 is interpretable in T2 are discussed. Chapter 8 compares analogy and transformation and chapter (...) 9 proves some theorems on analogy. (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)

With his theory of descriptions Russell wanted to solve two problems concerning denotation and reference, which are formulated here as Problem I and Problem II. After presenting each problem, we describe the main points of Russell’s solution. We deal with Russell’s concepts of existence and then elaborate his presuppositions concerning the relation of denoting and referring. Next we discuss the presuppositions or principles which underlie Russell’s understanding of the _objects_ of reference. These principles are such that if the objects of (...) reference are material objects, they are objects of classical mechanics, or very close to such an interpretation. Finally we show how these principles have to be relaxed if the objects of reference are objects of quantum mechanics or special or general relativity. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

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)

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)

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 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)

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)

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)