Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions (...) and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK. (shrink)

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.

In a rather general setting, we prove a number of basic theorems concerning computational complexity of derivability in adaptive logics. For that setting, the so-called standard format of adaptive logics is suitably adopted, and the corresponding completeness results are established in a very uniform way.

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics for independence-friendly first-order logic, but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump (...) semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas. (shrink)

We shall be concerned with the modal logic BK—which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding ‘strong negation’. Though all four values ‘truth’, ‘falsity’, ‘neither’ and ‘both’ are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for ‘neither’ or/and ‘both’ leads to quite unexpected results. To be more (...) precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics. (shrink)

The article is devoted to the analysis of the legal theories of P.I. Novgorodtsev and B.A. Kistyakovsky, based on the moral philosophy of I. Kant in comparison with the psychological theory of law of L.I. Petrazhitsky. The unity of the positions of Novgorodtsev and Kistyakovsky in focusing on the ethical aspects of law, as well as highlighting morality as the highest principle, is revealed. Attention is paid to the disclosure of neo-Kantian motives in the philosophy of law and in the (...) context of the development of the theory of natural law in Russia. The main content of the article is a consistent analysis of Novgorodtsevʼs ideas in their dynamics, compared with the neo-Kantian philosophy of law of Kistyakovsky. It is emphasized that the psychological theory of the source of Petrazhitskyʼs legal relations is in the same intention of thought with the motives of the Russian neo-Kantians, which allows them to be compared in the history of the development of the Russian theory of law. The modern scientific literature is analyzed in order to identify the problem of comparing different approaches in the history of Russian philosophy of law, in which German transcendental philosophy is one of the key foundations. The question of the independence of Russian scientists in the construction of ethical and legal doctrines is actualized, but, at the same time, a single motive is emphasized with the Kantian provision on the need to establish a general civil society on the principles of a developed system of rules and norms. (shrink)

This article examines some of S. Lem’s statements about his philosophical and worldview positions regarding the mysterious nature of language and the linguistic sign, the connection between language, mind and reality. The main goal of the paper is to understand what texts on the philosophy of language the Polish thinker read and what attitude he has formed towards them. Lem is the follower of an analytical intellectual culture that focuses on the naturalistic worldview and the consequences of the “linguistic turn” (...) in Western philosophy. For Lem, language is not only an interesting philosophical object, but also a complex precise instrument of his own creative thinking. In this regard, the philosophy of language for a writer cannot be based only on logical-linguistic atomistic methodology. Lem seeks in his contemporary interdisciplinary methods ways to combine realistic and anti-realist positions. Many concepts, such as “the effect of semantic transparency”, “polymorphic language model”, “variation model” are quite correlated with modern theories of language and require additional philosophical comments. (shrink)

We prove that all algebras P/IR, where the IR-'s are ideals generated by partitions of W into finite and arbitrary large elements, are isomorphic and homogeneous. Moreover, we show that the smallest size of a tower of such partitions with respect to the eventually-refining preordering is equal to the smallest size of a tower on ω.

This paper is a book review of 'A Treatise of Master Hervaeus Natalis († 1323), The Doctor Perspicacissimus, On second Intentions' by John P. Doyle.

In recent years, many philosophers of modern physics came to the conclusion that the problem of how objectivity is constituted (rather than merely given) can no longer be avoided, and therefore that a transcendental approach in the spirit of Kant is now philosophically relevant. The usual excuse for skipping this task is that the historical form given by Kant to transcendental epistemology has been challenged by Relativity and Quantum Physics. However, the true challenge is not to force modern physics into (...) a rigidly construed static version of Kant's philosophy, but to provide Kant's method with flexibility and generality. In this book, the top specialists of the field pin down the methodological core of transcendental epistemology that must be used in order to throw light on the foundations of modern physics. First, the basic tools Kant used for his transcendental reading of Newtonian Mechanics are examined, and then early transcendental approaches of Relativistic and Quantum Physics are revisited. Transcendental procedures are also applied to contemporary physics, and this renewed transcendental interpretation is finally compared with structural realism and constructive empiricism. The book will be of interest to scientists, historians and philosophers who are involved in the foundational problems of modern physics. (shrink)

The place of the emotions among the passions -- The analytic of the emotions I -- The analytic of the emotions II -- The dialectic of the emotions -- Pride, arrogance, and humility -- Shame, embarrassment, and guilt -- Envy -- Jealousy -- Anger -- Love -- Friendship -- Sympathy and empathy.

Frankish's argument for illusionism -- the view that there are no real instances of phenomenal consciousness -- depends on the claim that phenomenal consciousness is an 'anomalous phenomenon', at odds with our scientific picture of the world. I distinguish two senses in which a phenomenon might be 'anomalous': its reality is inconsistent with what science gives us reason to believe, its reality adds to what science gives us reason to believe. I then argue that phenomenal consciousness is not anomalous in (...) the first sense, and the fact that phenomenal consciousness is plausibly anomalous in the second sense is only problematic if it can be shown that our introspectively-based reasons for believing in consciousness are epistemically problematic. I finish by suggesting that Frankish might be motivated to adopt radical naturalism because he takes doing so to be the appropriate response to the incredible success of natural science. I outline a way of thinking about the history of science which undermines this motivation. (shrink)

Gordon Baker and I had been colleagues at St John’s for almost ten years when we resolved, in 1976, to undertake the task of writing a commentary on Wittgenstein’s Philosophical Investigations. We had been talking about Wittgenstein since 1969, and when we cooperated in writing a long critical notice on the Philosophical Grammar in 1975, we found that working together was mutually instructive, intellectually stimulating and great fun. We thought that we still had much to say about Wittgenstein’s philosophy, and (...) it seemed to us that misinterpretations of passages in the Investigations were so extensive that it would be worth trying to write a detailed analytical commentary. It is difficult to recapture the excitement of those early days in being among the first to work on the microfilms and, subsequently, on the photocopies of Wittgenstein’s Nachlass. We spent many hundreds of hours poring over the typescripts and the often only semi-legible manuscripts, fascinated and privileged to be able to try to follow the development of the thoughts of a great philosophical genius. We talked endlessly about what we had found in Wittgenstein’s manuscripts and typescripts, and debated how it should be understood. The first fruit of our labours was Wittgenstein – Understanding and Meaning. Its guiding idea was to draw attention to the manner in which Wittgenstein linked the concepts of meaning, understanding and explanation, and so to bypass the connections between meaning, truth and truth-conditions that so fascinated philosophers of the 1970s, and to abandon the red-herring of assertion-conditions and anti-realism. After a hiatus of four years, during which time we wrote a controversial book entitled Frege – Logical Excavations and a polemical book on contemporary philosophy of language – Language, Sense. (shrink)

We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates. BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ’learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the (...) relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system. (shrink)