Imagination has recently attracted considerable attention from epistemologists and is recognized as a source of belief and even knowledge. One remarkable feature of imagination is that it is often and typically agentive: agents decide to imagine. In cases in which imagination results in a belief, the agentiveness of imagination may be taken to give rise to indirect doxastic control and epistemic responsibility. This observation calls for a proper understanding of agentive imagination. In particular, it calls for the development of a (...) semantics of imagination ascriptions. In the present paper an earlier suggestion by Ilkka Niiniluoto for a logic of imagination is considered. This proposal does not capture the agentive nature of imagination, and an alternative semantics is suggested. The new semantics combines the modal logic of agency with the neighbourhood semantics from alethic modal logic. (shrink)

book I. The nature of the state.-- book II. The social foundations of the state.-- book III. The constitution of the state.-- book IV. The administration of the state.-- book V. The state in international intercourse.

This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N– and N. Doen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to (...) be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. (shrink)

Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In this paper we show that (...) this is not the case. We consider two ways of formalising the notion of external validity, and show that in both of these the paradox is not forthcoming without the appropriate forms of contraction. (shrink)

Reprint. Originally published: T'ubingen: C.F. Osiander, 1822.

"Die Grundlage... ist... ein Programm, welches ich im vorigen Jahre unter dem Titel: "Historische und philosophische Beitr'age zur Erl'auterung des Spinozismus' ausgegeben habe. Aber... hier... sehr erweitert.".

On cover: Zusammenhang des Spinozismus mit der Cartesianischen Philosophie.

Although it is not younger than other areas of non-classical logic, paraconsistent logic has received full recognition only in recent years, largely due to the work of, among others, Newton da Costa, Graham Priest, Diderik Batens, and Jerzy Perzanowski. A logical system Λ is paraconsistent if there is a set of Λ-formulas Δ ∪ {A} such that in Λ one may derive from Δ both A and its negation, and the deductive closure of Δ with respect to Λ is different (...) from the set of all formulas. If from Δ one may derive a formula and its negation, Δ is said to be syntactically inconsistent. But is every syntactically inconsistent set of formulas contradictory? In classical logic and many non-classical logics, every syntactically inconsistent set is unsatisfiable, that is, semantically inconsistent. If contradictoriness means semantical inconsistency, there is, up to logical equivalence, only one contradiction. In paraconsistent logics, there are usually many non-equivalent formulas representing the semantically unique contradiction in a non-paraconsistent logic. So when is a formula the contradiction of another formula, and, moreover, how does the notion of contradiction relate to the notions of contrariety and negation? (shrink)

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...) introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence. (shrink)

Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.

It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.