Within the current mainstream research in the foundations of physics, much attention has been turned to the program of Axiomatic Reconstruction of Quantum Theory in terms of Information-Theoretic principles (ARQIT). ARQIT aims at finding a few general information-theoretic principles from which, once translated into mathematical terms, one can formally derive the structure of quantum theory. This chapter explores the role of mechanistic explanations and mathematical explanations (in particular, structural explanations) within ARQIT. With such considerations as a point of departure, we (...) investigate how ARQIT contributes to the explanation of quantum phenomena, and the possible prospects for explanations provided by mechanical interpretations of quantum theory. (shrink)

TheGenerales Inquisitiones de Analysi Notionum et Veritatumis Leibniz’s most substantive work in the area of logic. Leibniz’s central aim in this treatise is to develop a symbolic calculus of terms that is capable of underwriting all valid modes of syllogistic and propositional reasoning. The present paper provides a systematic reconstruction of the calculus developed by Leibniz in theGenerales Inquisitiones. We investigate the most significant logical features of this calculus and prove that it is both sound and complete with respect to (...) a simple class of enriched Boolean algebras which we call auto-Boolean algebras. Moreover, we show that Leibniz’s calculus can reproduce all the laws of classical propositional logic, thus allowing Leibniz to achieve his goal of reducing propositional reasoning to algebraic reasoning about terms. (shrink)

New light is shed on Leibniz’s commitment to the metaphysical priority of the intensional interpretation of logic by considering the arithmetical and graphical representations of syllogistic inference that Leibniz studied. Crucial to understanding this connection is the idea that concepts can be intensionally represented in terms of properties of geometric extension, though significantly not the simple geometric property of part-whole inclusion. I go on to provide an explanation for how Leibniz could maintain the metaphysical priority of the intensional interpretation while (...) holding that logically the intensional and the extensional stand in strictly inverse relation to each other. (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics. The authors cover themes such as the knowability paradox, tableaux and sequent calculi, natural deduction, definite descriptions, identity, truth, dialetheism and possible worlds semantics. The developments presented here focus on challenging problems in the specification of fundamental philosophical notions, as well as presenting new techniques and tools, thereby contributing to the development of the (...) field. Each chapter contains a bibliography, to assist the reader in making connections in the specific areas covered. Thus this work provides both a starting point for further investigations into philosophical logic and an update on advances, techniques and applications in a dynamic field. The chapters originate from papers presented during the Trends in Logic XI conference at the Ruhr University Bochum, June 2012. (shrink)

This article deals with an alternative interpretation of syllogistics, different from the classical (extensional) one: an intensional one, in which subject and predicate are not associated with a set of individuals (the extension of the concept) but a set of attributes (the content of the concept). The authors of the paper draw attention to the fact that this approach was first proposed by Leibniz in works on logical calculus, which for a long time remained in the shadow of his other (...) philosophical works. Currently, the intensional approach is gaining more and more popularity due to the development of non-classical logics, and the article will present several existing intensional formal syllogistic semantics. The paper will also consider another historical approach to syllogistics, associated with the name of the Russian logician Nikolai Vasiliev, who is not only one of the founders of non-classical (non-Aristotelian logic) but also of a different intensional interpretation of such logic. The authors, along with the already known formalizations of Vasiliev’s ideas, present two new systems. One of them is a reconstruction of one type of imaginary logic with statements of three qualities: affirmative and two types of negative statements (with absolute and ordinary negation). The second system is the one that is adequate to semantics, in which instead of the four classical ones, only three types of statements are presented (two particular statements are replaced by one - accidental), and their significance is determined through the relation of the classical logical entailment. Both of them are interpreted intensionally. The intensional approach in logic and, in particular, in syllogistics allows us to expand the class of accepted principles (which occurs due to the expansion of the class of correct moods of syllogisms). (shrink)

Through the reconstruction of Leibniz's theory of the degrees of knowledge, this e-book investigates and explores the intrinsic relationship of imagination with space and time. The inquiry into this relationship defines the logic of imagination that characterizes both human and non-human animals, albeit differently, making them two different species of imaginative animals. -/- Lucia Oliveri explains how the emergence of language in human animals goes hand in hand with the emergence of thought and a different form of rationality constituted by (...) logical inferences based on identity and contradiction, principles that are out of reach of the imagination. The e-book concludes that the presence of innate principles in human animals transforms the way in which they sense-perceive the world, thereby constantly increasing the distinction between human and non-human animals. -/- Keywords: human and non-human animals, Leibniz and Locke on ideas, Leibniz on bodies, Leibniz on conceivability, Leibniz on degrees of knowledge, Leibniz on degrees of perception, Leibniz on innate ideas, Leibniz on modality, Leibniz on similarity and congruence, Leibniz on space and time, Leibniz’s philosophy of language, theory of types. (shrink)