A logic-based approach to problems in pragmatics

After an exposé of the programme involved, it is shown that the Gricean maxims fail to do their job in so far as they are meant to account for the well-known problem of natural intuitions of logical entailment that deviate from standard modern logic. It is argued that there is no reason why natural logical and ontological intuitions should conform to standard logic, because standard logic is based on mathematics while natural logical and ontological intuitions derive from a cognitive system in people's minds (supported by their brain structures). A proposal is then put forward to try a totally different strategy, via (a) a grammatical reduction of surface sentences to their logico-semantic form and (b) via logic itself, in particular the notion of natural logic, based on a natural ontology and a natural set theory. Since any logical system is fully defined by (a) its ontology and its overarching notions and axioms regarding truth, (b) the meanings of its operators, and (c) the ranges of its variables, logical systems can be devised that deviate from modern logic in any or all of the above respects, as long as they remain consistent. This allows one, as an empirical enterprise, to devise a natural logic, which is as sound as standard logic but corresponds better with natural intuitions. It is hypothesised that at least two varieties of natural logic must be assumed in order to account for natural logical and ontological intuitions, since culture and scholastic education have elevated modern societies to a higher level of functionality and refinement. These two systems correspond, with corrections and additions, to Hamilton's 19th-century logic and to the classic Square of Opposition, respectively. Finally, an evaluation is presented, comparing the empirical success rates of the systems envisaged

Formalization, Mechanization and Automation of G\"odel's Proof of God's Existence

G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction proof. A formalization of the axioms, definitions and theorems in the TPTP THF syntax. Automatic verification of the consistency of the axioms and definitions with Nitpick. Automatic demonstration of the theorems with the provers LEO-II and Satallax. A step-by-step formalization using the Coq proof assistant. A formalization using the Isabelle proof assistant, where the theorems (and some additional lemmata) have been automated with Sledgehammer and Metis.Comment: 2 page

Modality, Potentiality and Contradiction in Quantum Mechanics

In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that, taking into account the square of opposition, quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [17] we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.Comment: Published in: New Directions in Paraconsistent Logic, J-Y B\'eziau M. Chakraborty & S. Dutta (Eds.), Springer, in press. arXiv admin note: text overlap with arXiv:1404.518

Barry Smith an sich

Festschrift in Honor of Barry Smith on the occasion of his 65th Birthday. Published as issue 4:4 of the journal Cosmos + Taxis: Studies in Emergent Order and Organization. Includes contributions by Wolfgang Grassl, Nicola Guarino, John T. Kearns, Rudolf Lüthe, Luc Schneider, Peter Simons, Wojciech Żełaniec, and Jan Woleński

Indispensability Without Platonism

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage

Quine, Ontology, and Physicalism

Quine's views on ontology and naturalism are well-known but rarely considered in tandem. According to my interpretation the connection between them is vital. I read Quine as a global epistemic structuralist. Quine thought we only ever know objects qua solutions to puzzles about significant intersections in observations. Objects are always accessed descriptively, via their roles in our best theory. Quine's Kant lectures contain an early version of epistemic structuralism with uncharacteristic remarks about the mental. Here Quine embraces mitigated anomalous monism, allowing introspection and the availability in principle of full physical descriptions of the perceptual states which get science off the ground. Later versions abandon these ideas. My epistemic-structural interpretation explains why. I argue first-personal introspective access to mental states is incompatible with global epistemic structuralism

Computer Science and Metaphysics: A Cross-Fertilization

Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational philosophy with a focus on metaphysics. In this paper, we (a) develop results in modal metaphysics whose discovery was computer assisted, and (b) conclude that these results work not only to the obvious benefit of philosophy but also, less obviously, to the benefit of computer science, since the new computational techniques that led to these results may be more broadly applicable within computer science. The paper includes a description of our background methodology and how it evolved, and a discussion of our new results.Comment: 39 pages, 3 figure

Logics and Their Galaxies

This article introduces some concepts that help exploring the ontological import of universal logic. It studies the notions of an antilogic and counterlogic associated to each logic and shows some of their properties. It presents the notion of galaxy, as the class of possible worlds compatible with a given logic.We explore some consequences of these developments

The Paraconsistent Approach to Quantum Superpositions Reloaded: Formalizing Contradictory Powers in the Potential Realm

In [7] the authors of this paper argued in favor of the possibility to consider a Paraconsistent Approach to Quantum Superpositions (PAQS). We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints -coming from present technical and experimental developments in QM- that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause have raised several arguments against the PAQS [1, 2, 3]. In [11, 12] it was argued that their reasoning presupposes a metaphysical stance according to which the physical representation of reality must be exclusively considered in terms of the equation: Actuality = Reality. However, from a different metaphysical standpoint their problems disappear. It was also argued that, if we accept the idea that quantum superpositions exist in a (contradictory) potential realm, it makes perfect sense to develop QM in terms of a paraconsistent approach and claim that quantum superpositions are contradictory, contextual existents. Following these ideas, and taking as a standpoint an interpretation in terms of the physical notions of power and potentia put forward in [10, 12, 15], we present a paraconsistent formalization of quantum superpositions that attempts to capture the main features of QM.Comment: 26 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1502.05081, arXiv:1404.5186, arXiv:1506.0737