The aim of this paper is to show that the operations of forming direct products and submatrices suffice to construct exhaustive semantics for all structural strengthenings of the consequence determined by a given class of logical matrices.

In the paper some consequence operations generated by ukasiewicz's matrices are examined.

This paper, which in its subject matter goes back to works on strongly nite logics , is concerned with the following problems: Let Cn1; Cn2 be two strongly nite logics over the same propositional language. Is the supremum of Cn1 and Cn2 also a strongly nite operation? Is any nite matrix axiomatizable by a nite set of standard rules? The rst question can be found in [9] . The second conjec- ture was formulated by Wolfgang Rautenberg, but investigations into this (...) problem had been carried out earlier in works of many logicians . Moreover, Stephen Bloom [1] posed a conjecture stronger than that: the consequence de- termined by a nite matrix is nitely based, i.e. it is the consequence generated by a nite set of standard rules. This hypothesis was, however, disproved by Andrzej Wronski [10] . In the present paper it is shown that neither nor holds true. The negative answer to can be viewed as a generalization of the result given by Andrzej Wronski [10]. (shrink)

This is an expository paper on the problem of independent axiomatization of any set of sentences. This subject was investigated in 50's and 60's, and was abandoned later on, though not all fundamental questions were settled then. Besides, some papers written at that time are hardly available today and there are mistakes and misunderstandings there. We would like to get back to that unfinished business to clarify the subject matter, correct mistakes and answer questions left open by others. We shall (...) deal with results of many authors. However, they will be exposed in a different manner, with complete proofs and, often, with refinements and supplements. Some questions will be brought up to date and related to other questions in logic. New results and questions will also be added. Stress will be laid on constructive aspects; that is, we will examine the problem of the possibility of independent axiomatization as well as algebraic means by use of which independent sets of axioms can be given. (shrink)

We consider the notion of structural completeness with respect to arbitrary (finitary and/or infinitary) inferential rules. Our main task is to characterize structurally complete intermediate logics. We prove that the structurally complete extension of any pure implicational in termediate logic C can be given as an extension of C with a certain family of schematically denned infinitary rules; the same rules are used for each C. The cardinality of the family is continuum and, in the case of (the pure implicational (...) fragment of) intuitionistic logic, the family cannot be reduced to a countable one. It means that the structurally complete extension of the intuitionistic logic is not countably axiomatizable by schematic rules. (shrink)

An operation on inferential rules, called H-operation, is used to minimize the axiom basis for classical logic.

We characterize all finitary consequence relations over S4.3, both syntactically, by exhibiting so-called passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic L extending S4 has projective unification if and only if L contains S4.3. In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known (...) results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relations over S4.3 is countable and distributive and it forms a Heyting algebra. (shrink)

This paper develops a proof theory for logical forms of proofs in the case of monadic languages. Among the consequences are different kinds of generalization of proofs in various schematic proof systems. The results use suitable relations between logical properties of partial proof data and algebraic properties of corresponding sets of linear diophantine equations.

An operation on inferential rules, called H-operation, is used to minimize the axiom basis for classical logic.

We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.

Topic modeling—a text‐mining technique often used to uncover thematic structures in large collections of texts—has been increasingly frequently used in the context of the analysis of scholarly output. In this study, we construct a corpus of 19,488 texts published since 1971 in seven leading journals in the field of bioethics and philosophy of medicine, and we use a machine learning algorithm to identify almost 100 topics representing distinct themes of interest in the field. On the basis of intertopic correlations, we (...) group the content‐based topics into eight clusters, thus providing a novel, fine‐grained intellectual map of bioethics and philosophy of medicine. Moreover, we conduct a number of diachronic analyses, examining how the “prominence” of different topics has changed across time. In this way, we are able to observe the distinct patterns in which bioethics and philosophy of medicine have evolved and changed their focus over the past half a century. (shrink)

Leading authors in their fields present an interdisciplinary panorama of vital themes of the philosophy of language and track their historical origins. This book gives new life to historical ideas and additional depth to current debates.

Contributed papers presented at seminar held at Warsaw University, Poland, 8-9 September, 2000.

All through the XXth century it has been repeated that "there is an exact correspondence, almost coincidence between Euclid's definition of equal ratios and the modern theory of irrational numbers due to Dedekind". Since the idea was presented as early as in 1908 in Thomas Heath's translation of Euclid's Elements as a comment to Book V, def. 5, we call it in the paper Heath's thesis. Heath's thesis finds different justifications so it is accepted yet in different versions. In the (...) paper its historical and mathematical version is reconstructed. We next reconstruct Eudoxos' theory of proportions in an axiomatic fashion. Finally, we show that Heath's thesis both in the historical and mathematical version is false. To this end a counterexample is given; it is based upon a specific interpretation of the uniform distribution theorem. (shrink)

In its attempt to come to grips with the nature of the human mind idealism employs such terms as "pure self," "transcendental apperception," "pure con sciousness" and so on.

Predictive processing (PP) has been repeatedly presented as a unificatory account of perception, action, and cognition. In this paper, we argue that this is premature: As a unifying theory, PP fails to deliver general, simple, homogeneous, and systematic explanations. By examining its current trajectory of development, we conclude that PP remains only loosely connected both to its computational framework and to its hypothetical biological underpinnings, which makes its fundamentals unclear. Instead of offering explanations that refer to the same set of (...) principles, we observe systematic equivocations in PP‐based models, or outright contradictions with its avowed principles. To make matters worse, PP‐based models are seldom empirically validated, and they are frequently offered as mere just‐so stories. The large number of PP‐based models is thus not evidence of theoretical progress in unifying perception, action, and cognition. On the contrary, we maintain that the gap between theory and its biological and computational bases contributes to the arrested development of PP as a unificatory theory. Thus, we urge the defenders of PP to focus on its critical problems instead of offering mere re‐descriptions of known phenomena, and to validate their models against possible alternative explanations that stem from different theoretical assumptions. Otherwise, PP will ultimately fail as a unified theory of cognition. (shrink)

Public opinion has it that ethics should be concerned with studying and providing precise and reliable rules of conduct. This view is based in a long philosophical tradition which begins with the Stoics and continues at least to Kant; it is, however, a false view. There are good reasons to turn our attention to these aspects of moral thinking which refer to and emphasize the element of risk and uncertainty. In the article I briefly discuss two of such reasons: the (...) problem of moral luck and the problem of action based on ignorance. Consideration of these two problems leads to the conclusion that the most tricky element in moral thinking is the firm belief of the subject in the truth of the premises on which they base their actions and in the irrelevance of external factors to the assessment of their deeds. In this light I argue that the basic requirement for a moral justification of a particular action is not its conformity to a certain set of rules but the subject’s critical reflection on their course of action. Indeed, what turns an attitude into a moral attitude is an amoral, epistemological factor: criticism and openness to uncertainty. (shrink)

Samuel J. Wheeler defends Wittgenstein's criticism of Cantor's set theory against the objections raised by Hilary Putnam. Putnam claims that Wittgenstein's dismissal of the basic tenets of this set theory concerning the noncountability of the set of real numbers was unfounded and ill‐conceived. In Wheeler's view, Putnam's charges result from his failure to grasp Wittgenstein's intention and, in particular, to consider the difference between empirical and logical impossibility. In my paper, I argue that Wheeler's defence is unsuccessful and, at the (...) same time, that Putnam's objections go too far. (shrink)

The article focuses on the anti-naturalism of Menger and Mises. It presents a methodological approach formulated by both scholars as stemming from epistemological anti-naturalism and demonstrating similarities to social phenomenology. The article also discusses the development of the anti-naturalistic perspective on the basis of Hayek’s conception of sensory order. The latter allowed addressing the problem of validity of methodological dualism and established a sound foundation for the methodological approach of the Austrian School of Economics.

Citizen identification systems (known also as ‘ID card systems’, or ‘national identity management systems’, even though those definitions are not identical) are receiving a mixed acceptance, with their privacy, security and usability being criticised, specifically in the UK. This paper investigates whether it is possible to improve social acceptance of such systems in cases where they are incompatible with the perceived value of privacy, but without significantly changing their original architecture. The paper analyses requirements using four different scenarios that address (...) long-term privacy issues. Relatively small alterations to such systems are suggested that may significantly improve their adoption. (shrink)

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...) with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)

The article presents a thought experiment aimed at indicating a possibility for thinking education beyond the logic of progress. In its first part, the argument reconstructs the entanglement of the modern idea of progress (as found in Francis Bacon and Comenius) and education, while tracking down the specific coupling of obedience and conquest at work. Through such an analysis a link between the ideas of progress and of emancipation is determined, which leads to the acknowledgement of the difficulty of the (...) task of imagining education outside of the logic of progress. In the second part an attempt is made to match this task by suggesting that when studying with a teacher, the logic of progress is deactivated. A phenomenological analysis of the practices involved in studying with a teacher points to a specific way of living together that such a collective study involves. This way of living together is formed by continual exercises in the humble equality realized through shared attention to something worthy of study: this stems from attentiveness to what exists, and it develops an attitude of care and respect for being as such. (shrink)

This paper discusses differences between two major schools in philosophy of criminal law, retributivism and consequentialism, with regard to the risk of punishing the innocent. As it is argued, the main point of departure between these two camps in this respect lies in their attitude towards the high evidentiary threshold in a criminal trial: while retributivism seems to strongly support setting this standard high, consequentialists may find it desirable to relax it in some cases. This discussion is set in the (...) context of proxy criminalization, i.e. a situation, in which some suspicious behaviour is criminalized. Since proxy criminalization may be understood as an effective lowering of the evidentiary threshold, its employment is justifiable from the consequentialist perspective, while being highly problematic for the retributivists. (shrink)