200 research outputs found
Paraconsistent Logics!
No full textIn this note I respond to Hartley Slater's argument [12] to the effect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency (which rejects the possible truth of any contradictions). Against this position Slater's argument has no bite at all. Secondly, while the argument does show that for dialethic paraconsistency (according to which contradictions can be true), certain other contradictions must be true, I show that this need not deter the dialethic paraconsistentist from their position. Paraconsistent Logics! Greg Restall [email protected] http://arp.anu.edu.au/arp/gar/gar.html Automated Reasoning Project Au..
/ Lukasiewicz, Supervaluations, And The Future
No full textIn this paper I consider an interpretation of future contingents which motivates a unification of a / Lukiasiewicz-style logic, and the more classical, supervaluational semantics. This in turn motivates a new non-classical logic modelling what is "made true by history up until now". I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models. / Lukasiewicz, Supervaluations, and the Future Greg Restall [email protected] http://www.mq.edu.au/~phildept/staff/grestall.html School of History, Philosophy and Politics Macquarie University Sydney 2109, Australia Will there be a sea battle tomorrow? If we wish to take indeterminism seriously, we might agree that there is, as yet, no fact of the matter about a sea battle tomorrow. It is neither the case now that there will be a battle tomorrow, nor the case now that there won't be a battle tomorrow. However, once we agree on that, there are (at least) tw..
The geometry of nondistributive logics
No full textIn this paper we introduce a new natural deduction system for the logic
of lattices, and a number of extensions of lattice logic with different
negation connectives. We provide the class of natural deduction proofs
with both a standard inductive definition and a global graph-theoretical
criterion for correctness, and we show how normalisation in this system
corresponds to cut elimination in the sequent calculus for lattice
logic. This natural deduction system is inspired both by Shoesmith and
Smiley's multiple conclusion systems for classical logic and Girard's
proofnets for linear logic
/ Lukasiewicz, Supervaluations, And The Future
No full textIn this paper I consider an interpretation of future contingents which motivates a unification of a / Lukiasiewicz-style logic, and the more classical, supervaluational semantics. This in turn motivates a new non-classical logic modelling what is "made true by history up until now". I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models. / Lukasiewicz, Supervaluations, and the Future Greg Restall [email protected] http://www.mq.edu.au/~phildept/staff/grestall.html School of History, Philosophy and Politics Macquarie University Sydney 2109, Australia Will there be a sea battle tomorrow? If we wish to take indeterminism seriously, we might agree that there is, as yet, no fact of the matter about a sea battle tomorrow. It is neither the case now that there will be a battle tomorrow, nor the case now that there won't be a battle tomorrow. However, once we agree on that, there are (at least) tw..
Logic:an introduction
No full textGreg Restall's Logic provides concise introductions to propositional and first-order predicate logic while showing how formal logic intersects with substantial philosophical issues such as vagueness, conditionals, relevance, propositional attitudes, and opaque contents. The author also examines the ideas behind modal logic, free logic, and other non-standard logics and discusses the nature of logic itself. The book covers both natural deduction and tree methods for proving validity. Each chapter includes excellent suggestions for further reading and both elementary and more advanced exercises, with solutions provided on a website. It is flexibly designed to be useable for half or full-year courses, for courses focusing exclusively on formal logic, or for a variety of approaches that would integrate topics in philosophical logic.</p
WHAT IS LOGICAL PLURALISM? (J.C. BEALL’S AND GREG RESTALL’S STANDPOINT)
No full textC. Beall and Greg Restall are advocates of a comprehensive pluralist approach to logic, which they call Logical Pluralism (LP). According to LP, there is not one correct logic, but many equally acceptable logical systems. The authors share Tarski’s conviction and follow the mainstream in thinking about logic as the discipline that investigates the notion of logical consequence. LP is the pluralism about logical consequence – a pluralist maintains that there is more than one relation of logical consequence. According to LP, classical, intuitionistic and relevant logics are not rivals, but they all are equally correct, they all count as genuine logics.
The purpose of this paper is to present some remarks concerning J.C. Beall’s and Greg Restall’s exposition of LP. At the beginning, the definition of the relation of logical consequence, which is central to their proposal, is shown. According to Beall and Restall, argument is valid if, and only if, in every case when the premisses are true, then the conclusion is, too. They argue that by considering different types of cases the logical pluralist obtains different logics.
The paper — apart from presenting LP — also gives a critical discussion of this approach. It seems, that the thesis of LP is far from being clear. It is even unclear what exactly LP is and where is stops. It is unclear what “equally good”, “equally correct”, “equally true” mean. It is not clear, how to explain, in scope of logic, that the system of logic, is a model of real logical connections
On permutation in simplified semantics
No full textThis note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J Philos Logic 22(5):481–511, 1993) concerning the modelling conditions for the axioms of assertion A → ((A → B) → B) (there called c6) and permutation (A → (B → C)) → (B → (A → C)) (there called c7). We show that the modelling conditions for assertion and permutation proposed in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent. This problem is not restricted to ‘Simplified Semantics.’ The techniques of that paper are used in Graham Priest’s textbook An Introduction to Non-Classical Logic (Priest, 2001), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose two different corrections.33
Los alcances del pluralismo lógico
No full textAccording to logical pluralism there is not one true logic, there are many. The most well-known pluralism is the view defended by J.C. Beall and Greg Restall. They are pluralists about logical consequence. In this paper, I adhere to the logical pluralism but I hold that the Beall-Restall pluralism has many unsolved problems. I will show that there are important reasons to search for another kind of pluralism.Según el pluralismo lógico no hay una lógica verdadera, sino varias. El pluralismo más conocido es el defendido por J.C. Beall y Greg Restall. Ellos son pluralistas respecto de la noción de consecuencia lógica. En este artículo, me adhiero al pluralismo lógico, pero sostengo que el pluralismo de Beall y Restall tiene problemas sin solución. Mostraré que hay importantes razones para buscar otro tipo de pluralismo
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