In this paper we investigate AGM belief contraction operators by using the tools of algebraic logic. We generalize the notion of contraction to arbitrary finitary propositional logics, and we show how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions, as studied (...) in the final part of the paper. (shrink)

The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic \. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic \ is related to the construction of Płonka sums of the matrix models of \. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate (...) them in the Leibniz hierarchy. (shrink)

The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a time-honoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, (...) showing their equivalence with the known semantics by Dunn and Epstein. We also show that DAI is algebraisable and we identify its equivalent quasivariety semantics. This class turns out to be a linguistic and axiomatic expansion of involutive bisemilattices, a subquasivariety of which forms the algebraic counterpart of Paraconsistent Weak Kleene logic. This fact sheds further light on the relationship between containment logics and logics of nonsense. (shrink)

In this paper, first, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic ⊢ with a composition term. Then, we investigate their position into the lattice of co...

This article explores the relation between cinema and philosophy through the lens of interest shown by some filmmakers in the lives and works of philosophers. It begins by delving into contemporary perspectives on the relationship between philosophy and cinema. In order to assess how the constitutive dissimilarity of the two terms and the ways in which they can be brought together are at the origin of speculative short circuits and experiences of wonder, it brings together the works of thinkers – (...) Cavell, Benjamin, and Kracauer; and filmmakers Rossellini, Montaldo, Keaton, and Jarman. Reflecting on the aesthetic and cultural impact of cinema is all the more important given the current omnipresence of images and prosthetic technologies that, with their incessant solicitations, threaten the processes of apprehension, learning, and conveying of knowledge. Thinking and perceiving differently thus becomes an essential function of cinema, one keenly performed in Safaa Fathy’s Derrida’s Elsewhere, analyzed in the last two sections. (shrink)

The paper studies the containment companion of a logic \. This consists of the consequence relation \ which satisfies all the inferences of \, where the variables of the conclusion are contained into those of the set of premises, in case this is not inconsistent. In accordance with the work started in [10], we show that a different generalization of the Płonka sum construction, adapted from algebras to logical matrices, allows to provide a matrix-based semantics for containment logics. In particular, (...) we provide an appropriate completeness theorem for a wide family of containment logics, and we show how to produce a complete Hilbert style axiomatization. (shrink)

Paraconsistent Weak Kleene Logic is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK.

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The (...) level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

A key role in inference is played by randomization, which has been extensively used in clinical trials designs. Randomization is primarily intended to prevent the source of bias in treatment allocation by producing comparable groups. In the frequentist framework of inference, randomization allows also for the use of probability theory to express the likelihood of chance as a source for the difference of end outcome. In the Bayesian framework, its role is more nuanced. The Bayesian analysis of clinical trials can (...) afford a valid rationale for selective controls, pointing out a more limited role for randomization than it is generally accorded. This paper is aimed to offer a view of randomization from the perspective of both frequentist and Bayesian statistics and discussing the role of randomization also in theoretical decision models. (shrink)

Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued logic, (...) unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models. (shrink)

I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...) the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B. We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?". (shrink)

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next twenty (...) or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

Introduction -- The self-interest based contractarian response to the skeptic -- A feminist ethics response to the skeptic -- Deformed desires -- Self-interest versus morality -- The amoralist -- The motive skeptic -- The interdependency thesis.

This collection addresses a post-WWII shift in the hierarchy of scientific explanations, where the highest goal moves from reductionism towards some ...

One of our great behavioral scientists, the bestselling author of Behave, plumbs the depths of the science and philosophy of decision-making to mount a devastating case against free will, an argument with profound consequences Robert Sapolsky's Behave, his now classic account of why humans do good and why they do bad, pointed toward an unsettling conclusion: We may not grasp the precise marriage of nature and nurture that creates the physics and chemistry at the base of human behavior, but that (...) doesn't mean it doesn't exist. Now, in Determined, Sapolsky takes his argument all the way, mounting a brilliant (and in his inimitable way, delightful) full-frontal assault on the pleasant fantasy that there is some separate self telling our biology what to do. Determined offers a marvelous synthesis of what we know about how consciousness works-the tight weave between reason and emotion and between stimulus and response in the moment and over a life. One by one, Sapolsky tackles all the major arguments for free will and takes them out, cutting a path through the thickets of chaos and complexity science and quantum physics, as well as touching ground on some of the wilder shores of philosophy. He shows us that the history of medicine is in no small part the history of learning that fewer and fewer things are somebody's "fault"; for example, for centuries we thought seizures were a sign of demonic possession. Yet, as he acknowledges, it's very hard, and at times impossible, to uncouple from our zeal to judge others and to judge ourselves. Sapolsky applies the new understanding of life beyond free will to some of our most essential questions around punishment, morality, and living well together. By the end, Sapolsky argues that while living our daily lives recognizing that we have no free will is going to be monumentally difficult, doing so is not going to result in anarchy, pointlessness, and existential malaise. Instead, it will make for a much more humane world. (shrink)

This book argues that Plato's Charmides presents a unitary but incomplete argument intended to lead its readers to substantive philosophical insights.

At the beginning of his Metaphysics, Aristotle attributed several strange-sounding theses to Plato. Generations of Plato scholars have assumed that these could not be found in the dialogues. In heated arguments, they have debated the significance of these claims, some arguing that they constituted an 'unwritten teaching' and others maintaining that Aristotle was mistaken in attributing them to Plato. In a prior book-length study on Plato's late ontology, Kenneth M. Sayre demonstrated that, despite differences in terminology, these claims correspond to (...) themes developed by Plato in the Parmenides and the Philebus. In this book, he shows how this correspondence can be extended to key, but previously obscure, passages in the Statesman. He also examines the interpretative consequences for other sections of that dialogue, particularly those concerned with the practice of dialectical inquiry. (shrink)