Models for normal intuitionistic modal logics

Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given for analogues of the modal systemK based on Heyting's prepositional logic. It is shown that these two relations can combine with each other in various ways. Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both. Embeddings in modal systems with several modal operators, based on classical propositional logic, are also considered. This paper lays the ground for an investigation of intuitionistic analogues of systems stronger thanK. A brief survey is given of the existing literature on intuitionistic modal logic.     

Systems of Quantum Logic

Logical implications are closely related to modal operators. Lattice-valued logic LL and quantum logic QL were formulated in Titani S (1999) Lattice Valued Set Theory. Arch Math Logic 38:395–421, Titani S (2009) A Completeness Theorem of Quantum Set Theory. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of Quantum Logic and Quantum Structures: Quantum Logic. Elsevier Science Ltd., pp. 661–702, by introducing the basic implication → which represents the lattice order. In this paper, we fomulate a predicate orthologic provided with the basic implication, which corresponds to complete ortholattices, and then formulate a quantum logic which is equivalent to QL, by using a modal operator instead of the basic implication.     

Combining linear-time temporal logic with constructiveness and paraconsistency

It is known that linear-time temporal logic (LTL), which is an extension of classical logic, is useful for expressing temporal reasoning as investigated in computer science. In this paper, two constructive and bounded versions of LTL, which are extensions of intuitionistic logic or Nelson's paraconsistent logic, are introduced as Gentzen-type sequent calculi. These logics, $\mathrm{IB}[l]$ and $\mathrm{PB}[l]$, are intended to provide a useful theoretical basis for representing not only temporal (linear-time), but also constructive, and paraconsistent (inconsistency-tolerant) reasoning. The time domain of the proposed logics is bounded by a fixed positive integer. Despite the restriction on the time domain, the logics can derive almost all the typical temporal axioms of LTL. As a merit of bounding time, faithful embeddings into intuitionistic logic and Nelson's paraconsistent logic are shown for $\mathrm{IB}[l]$ and $\mathrm{PB}[l]$, respectively. Completeness (with respect to Kripke semantics), cut–elimination, normalization (with respect to natural deduction), and decidability theorems for the newly defined logics are proved as the main results of this paper. Moreover, we present sound and complete display calculi for $\mathrm{IB}[l]$ and $\mathrm{PB}[l]$.In [P. Maier, Intuitionistic LTL and a new characterization of safety and liveness, in: Proceedings of Computer Science Logic 2004, in: Lecture Notes in Computer Science, vol. 3210, Springer-Verlag, Berlin, 2004, pp. 295–309] it has been emphasized that intuitionistic linear-time logic (ILTL) admits an elegant characterization of safety and liveness properties. The system ILTL, however, has been presented only in an algebraic setting. The present paper is the first semantical and proof-theoretical study of bounded constructive linear-time temporal logics containing either intuitionistic or strong negation.     

Partiality and Its Dual

This paper explores allowing truth value assignments to be undetermined or "partial" (no truth values) and overdetermined or "inconsistent" (both truth values), thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's (first-degree) relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson's "constructible falsity".     

Decidability of Quantified Propositional Intuitionistic Logic and S4 on Trees of Height and Arity ≤ω

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers p, p, where the propositional variables range over upward-closed subsets of the set of worlds in a Kripke structure. If the permitted accessibility relations are arbitrary partial orders, the resulting logic is known to be recursively isomorphic to full second-order logic (Kremer, 1997). It is shown that if the Kripke structures are restricted to trees of at height and width at most , the resulting logics are decidable. This provides a partial answer to a question by Kremer. The result also transfers to modal S4 and some Gödel–Dummett logics with quantifiers over propositions.     

Models for stronger normal intuitionistic modal logics

This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated.This paper presents results of an investigation of intuitionistic modal logic conducted in collaboration with Dr Milan Boi.     

Propositional Epistemic Logics with Quantification Over Agents of Knowledge

The paper presents a family of propositional epistemic logics such that languages of these logics are extended by quantification over modal (epistemic) operators or over agents of knowledge and extended by predicate symbols that take modal (epistemic) operators (or agents) as arguments. Denote this family by \({\mathcal {P}\mathcal {E}\mathcal {L}}_{({ QK})}\). There exist epistemic logics whose languages have the above mentioned properties (see, for example Corsi and Orlandelli in Stud Log 101:1159–1183, 2013; Fitting et al. in Stud Log 69:133–169, 2001; Grove in Artif Intell 74(2):311–350, 1995; Lomuscio and Colombetti in Proceedings of ATAL 1996. Lecture Notes in Computer Science (LNCS), vol 1193, pp 71–85, 1996). But these logics are obtained from first-order modal logics, while a logic of \({\mathcal {P}\mathcal {E}\mathcal {L}}_{({ QK})}\) can be regarded as a propositional multi-modal logic whose language includes quantifiers over modal (epistemic) operators and predicate symbols that take modal (epistemic) operators as arguments. Among the logics of \({\mathcal {P}\mathcal {E}\mathcal {L}}_{({ QK})}\) there are logics with a syntactical distinction between two readings of epistemic sentences: de dicto and de re (between ‘knowing that’ and ‘knowing of’). We show the decidability of logics of \({\mathcal {P}\mathcal {E}\mathcal {L}}_{({ QK})}\) with the help of the loosely guarded fragment (LGF) of first-order logic. Namely, we generalize LGF to a higher-order decidable loosely guarded fragment. The latter fragment allows us to construct various decidable propositional epistemic logics with quantification over modal (epistemic) operators. The family of this logics coincides with \({\mathcal {P}\mathcal {E}\mathcal {L}}_{({ QK})}\). There are decidable propositional logics such that these logics implicitly contain quantification over agents of knowledge, but languages of these logics are usual propositional epistemic languages without quantifiers and predicate symbols (see Grove and Halpern in J Log Comput 3(4):345–378, 1993). Some logics of \({\mathcal {P}\mathcal {E}\mathcal {L}}_{({ QK})}\) can be regarded as counterparts of logics defined in Grove and Halpern (J Log Comput 3(4):345–378, 1993). We prove that the satisfiability problem for these logics of \({\mathcal {P}\mathcal {E}\mathcal {L}}_{({ QK})}\) is Pspace-complete using their counterparts in Grove and Halpern (J Log Comput 3(4):345–378, 1993).     

AI,ME AND LEWIS (ABELIAN IMPLICATION,MATERIAL EQUIVALENCE AND C I LEWIS 1920)

C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. This accords with the treatment of negation in the Abelian l-group logic A of Meyer and Slaney (Abelian logic. Abstract, Journal of Symbolic Logic 46, 425–426, 1981), which also defines ∼A inferentially with no special conditions on f. The paper then concentrates on the pure implicational part AI of A, the simple logic of Abelian groups. The integers Z were known to be characteristic for AI, with every non-theorem B refutable mod some Zn for finite n. Noted here is that AI is pre-tabular, having the Scroggs property that every proper extension SI of AI, closed under substitution and detachment, has some finite Zn as its characteristic matrix. In particular FL is the extension for which n = 2 (Lewis, The structure of logic and its relation to other systems. The Journal of Philosophy 18, 505–516, 1921; Meyer and Slaney, Abelian logic. Abstract. Journal of Symbolic Logic 46, 425–426, 1981; This is an abstract of the much longer paper finally published in 1989 in G. G. Priest, R. Routley and J. Norman, eds., Paraconsistent logic: essays on the inconsistent, Philosophica Verlag, Munich, pp. 245–288, 1989). Meyer was supported in this work as a Visiting Fellow in the College of Engineering and Computer Science, ANU.     

Kurt Gödel and the Foundations of Mathematics: Horizons of Truth

MEDIEVAL LOGICS

P. 0 . LEWRY (ed.), The rise of British logic. Acts of the sixth European Symposium on mediaeval logic and semantics, Balliol College, Oxford, 19-24 June 1983. Toronto: Pontifical Institute of Mediaeval Studies, 1985. xii+421 pp. $34.50.

L. M. ,DE RIJK, La philosophie au moyen cige. Translated from the Dutch by P.Swiggers, Leiden: E. J. Brill, 1985. xi + 244 pp. 50 Hfl.

RAIMUNDUS LULLUS, Die neue Logik. Logica nova. Textkritisch herausgegeben von Charles Lohr. Übersetzt von Vittorio Hösle und Walburga Büchel. Mit einer Einführung von Vittorio Hosle. (Lateinisch-deutsch.) Hamburg: Felix Meiner Verlag, 1985. xciv + 3 17s. 64DM.

PAULUS VENETUS, Logica parva. Translation of the 1472 edition, with introduction and notes by Alan R. Perreiah. Miinchen and Wein: Philosophia Verlag, 1984. 372 pp. DM 138.

E. J. ASHWORTH, Studies in post-medieval semantics. London: Variorum Reprints, 1985. x + 342 pp. £32.00.

D. GABBAY and F. GUENTHNER (eds.), Handbook of philosophical logic. Volume 2: Extensions of classical logic. Dordrecht, Boston and Lancaster: D. Reidel Publishing Company, 1984. xi + 779 pp. Dfl. 31 5/$12O.OO/£80.25.

THOMAS M. SEEBOHM, Philosophie der Logik. Freiburg: Alber, 1984. 364 pp. DM 74.

WERNER STELZNER, Epistemische Logik. Zur logischen Analyse von Akzeptationsformen.Berlin: Akademie-Verlag, 1984. 206 pp. No price stated.

JAMES BOGEN and JAMES E. MCGUIRE (eds.), How things are: studies in predication and the history and philosophy of science. (Philosophical studies series in philosophy, Volume 29.) Dordrecht: D. Reidel, 1985. 345 pp. US $46.00.

GEORG HENRIK VON WRIGHT, Truth, knowledge, and modality. (Philosophical papers, Volume 3.) Oxford: Basil Blackwell, 1984. ix + 155 pp. 15.00.

JEAN VAN HEIJENOORT, Selected essays. Naples: Bibliopolis, 1985. 166 pp. No price stated.

H. WANG, Beyond analytic philosophy. Doing justice to what we know. Cambridge (Massachusetts) and London: The MIT Press, 1986. xii + 273pp. No price stated.

TEXTBOOKS

R. L.VAUGHT, Set theory: an introduction. Boston, Basel, Stuttgart: Birkhäuser, 1985. x+141 pp. SFr. 76.

W. H. NEWTON-SMITH, Logic: An introductory course. London, Melbourne and Henley: Routledge and Kegan Paul, 1985. x+ 230 pp. £5.95 (paper).

MISCELLANEOUS

PIERRE DUHEM, Medieval cosmology. Edited and translated by Roger Ariew.Chicago and London: University of Chicago Press, 1985. xxxi+ 601 pp. £24.75.

DAVID A. WHITE, Logic and ontology in Heidegger. Columbus: Ohio State University Press, 1985. xiv + 245 pp. $22.50.

J. W. DEGEN, Systeme der kumulativen Logik. Miinchen und Wien: Philosophia Verlag (Reihe Analytica), 1983. 265pp. DM 128.

GABRIELE LOLLI, La ragioni jisiche e la dimonstrazioni matematiche. Bologna: I1 Mulino, 1985. 365 pp. 30,000 lire.     

Future directions in engineering ethics research: microethics, macroethics and the role of professional societies

Three frames of reference for engineering ethics are discussed—individual, professional and social—which can be further broken down into “microethics” concerned with individuals and the internal relations of the engineering profession and “macroethics” referring to the collective social responsibility of the engineering profession and to societal decisions about technology. Few attempts have been made at integrating microethical and macroethical approaches to engineering ethics. The approach suggested here is to focus on the role of professional engineering societies in linking individual and professional ethics and in linking professional and social ethics. A research program is outlined using ethics support as an example of the former, and the issuance of position statements on product liability as an example of the latter. An earlier version of this paper was presented at the International Symposium on Technology and Society 2000 (ISTAS 2000), Rome, Italy, 7 September 2000. Joseph R. Herkert directs a dual-degree program in engineering and humanities/social sciences and is editor of Social, Ethical, and Policy Implications of Engineering (Wiley/IEEE Press).     

Betting on transitivity in probabilistic causal chains

Causal reasoning is crucial to people’s decision making in probabilistic environments. It may rely directly on data about covariation between variables (correspondence) or on inferences based on reasonable constraints if larger causal models are constructed based on local relations (coherence). For causal chains an often assumed constraint is transitivity. For probabilistic causal relations, mismatches between such transitive inferences and direct empirical evidence may lead to distortions of empirical evidence. Previous work has shown that people may use the generative local causal relations A → B and B → C to infer a positive indirect relation between events A and C, despite data showing that these events are actually independent (von Sydow et al. in Proceedings of the thirty-first annual conference of the cognitive science society. Cognitive Science Society, Austin, 2009, Proceedings of the 32nd annual conference of the cognitive science society. Cognitive Science Society, Austin, 2010, Mem Cogn 44(3):469–487, 2016). Here we used a sequential learning scenario to investigate how transitive reasoning in intransitive situations with negatively related distal events may relate to betting behavior. In three experiments participants bet as if they were influenced by a transitivity assumption, even when the data strongly contradicted transitivity.     

Books Received

Unnecessary Evil: History and Moral Progress in the Philosophy of Immanuel Kant, Sharon Ander son-Gold. Albany, New York: State University of New York Press, 2001, xiii +138 pp., $49.50, pb. $17.95.

Knowledge and Reference in Empirical Science, Jody Azzouni. International Library of Philosophy. London/New York: Routledge, 2001, xi + 259 pp., $50.00.

Philosophy of Science: Contemporary Readings, Yuri Balashov and Alex Rosenberg (eds). Routledge Contemporary Readings in Philosophy. London/New York: Routledge, 2002, xiii + 522 pp.

Of Myth, Life, and War in Plato's Republic, Claudia Baracchi. Bloomington, IN: Indiana University Press, 2002, ix + 249 pp., $49.95, pb. $24.95.

Ethics in Context: The Art of Dealing with Serious Questions, Gernot Böhme. Trans. Edmund Jephcott. Cambridge: Polity, 2001, ix + 189 pp., £45.00, pb. £13.99.

The Philosophical Theory of the State and Related Essays, Bernard Bosenquet. Ed. with intro. Gerald F. Gaus and William Sweet Key Texts. Classic Studies in the History of Ideas. South Bend, IN: St Augustine's Press, 2001, xxxvii +388 pp., pb. no price given.

Belief and its Neutralization: Husserl's System of Phenomenology in Ideas I, Marcus Brainard. SUNY Series in Contemporary Continental Philosophy. Albany, NY: State University of New York, 2002, xvii + 331 pp., $86.50, pb. $29.95.

The Nature of Research: Inquiry in Academic Contexts, Angela Brew. London/New York: Routledge, 2001, v + 205 pp., pb. £18.99.

Critical Thinking: A Concise Guide, Tracy Bowell and Gary Kemp. London/New York: Routledge, 2002, x + 275 pp., (pb.) No price given.

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Essay on the Origin of Human Knowledge, Etienne Bonnot de Condillac. Ed. and trans. Hans Aarsleff. Cambridge Texts in the History of Philosophy. Cambridge: Cambridge University Press, 2001, xlv + 225 pp., $59.95, pb. $21.95.

Theories of Democracy: A Critical Introduction, Frank Cunningham. Routledge Contemporary Political Philosophy. London/New York: Routledge, 2002, vi + 248 pp., pb. £13.99.

Self-Identity and Personal Autonomy: An Analytical Anthropology, Stefaan E. Cuypers. Ashgate New Critical Thinking in Philosophy. Aldershot/Burlington USA/Singapore/ Sydney: Ashgate, 2001, ix + 172 pp., £37.50.

Stream of Consciousness: Unity and Continuity in Conscious Experience, Barry Dainton. International Library of Philosophy. London/New York: Routledge, 2000, xvi + 254 pp.

Kierkegaard After MacIntyre: Essays on Freedom, Narrative, and Virtue, John J. Davenport and Anthony Rudd (eds). Replies by Alasdair Maclntyre and Philip L. Quinn. Chicago/La Salle, IL: Open Court, 2001, xxxix + 363 pp., £47.95, pb. £22.50.

What Distinguishes Human Understanding? John Deely. South Bend, IN: St Augustine's Press, 2002, xiv + 178 pp., £17.50.

Acts of Religion, Jacques Derrida. Ed. with intro. by Gil Anidjar. London/New York: Routledge, 2002, vi + 436 pp., pb. £15.99.

Religion and Media, Hent de Vries and Samuel Weber (eds). Cultural Memory in the Present. Stanford, CA: Stanford University Press, 2001, xvii + 649 pp., $69.00, pb. $29.95.

Art and Value, George Dickie. Oxford: Blackwell, 2001, vi + 114 pp., £45.00, pb. £11.99.

Modern Philosophy from Descartes to Nietische: An Anthology, Steven M. Emmanuel and Patrick Goold (eds). Blackwell Philosophy Anthologies. Maiden, MA/Oxford: Routledge, 2002, xvii + 525 pp.

The Basic Writings of Bertrand Russell (1903-1959), Robert Enger and Lester Denonn (eds), with new intro. by John Slater. London/New York: Routledge, 1992, reissue: 2001, 736 pp., pb. $26.95.

Democracy, David Estlund (ed.). Blackwell Readings in Philosophy. Maiden, MA/Oxford: Blackwell, 2001, xii + 310 pp., £55.00, pb. £15.99.

Philosophy Goes to the Movies: An Introduction to Philosophy, Christopher Falzon. London/New York: Routledge, 2002, ix + 230 pp., pb. £11.99.

Arresting Language: From Leibniz to Benjamin, Peter Fenves. Meridian: Crossing Aesthetics. Stanford, CA: Stanford University Press, 2001, xiii + 379 pp., $55.00, pb. $24.95.

Richard Rorty: Critical Dialogues, Matthew Festenstein and Simon Thompson (eds). Cambridge: Polity, 2001, ix + 241 pp., £50.00, pb. £14.99.

Berkeley and the Principles of Human Knowledge, Robert J. Fogelin. Routledge Philosophy Guidebooks. London/New York: Routledge, 2001, x + 166 pp., pb. £8.99.

Intellectual Trust in Oneself and Others, Richard Foley. Cambridge Studies in Philosophy. Cambridge: Cambridge University Press, 2001, x + 182 pp., $55.00.

Thomas Kuhn: A Philosophical History for Our Times, Steve Fuller. Chicago/London: University of Chicago Press, 2000, pb. 2001, xvii + 472 pp., pb. $22.50, 314.50.

A Common Humanity: Thinking about Love and Truth and Justice, Raimond Gaita. London/New York: Routledge (1998), 2002, xiii + 293 pp., pb.

Stochastic Causality, Maria Carla Galavotti, Patrick Suppe s and Domenieo Costantini (eds). CSLI Publications. Chicago, IL: University of Chicago Press, xii + 275 pp., $65.00, pb. $25.00; £41.00, pb. £16.00.

Introduction to Logic, Harry J. Gensler. London/New York: Routledge, 2002, ix + 399 pp., pb. £15.99.

Walter Benjamin: Critical Constellations, Graeme Gilloch. Key Contemporary Thinkers. Oxford: Polity, 2002, xi + 304 pp., £50.00, pb. £14.99.

Between Ethics and Aesthetics: Crossing the Boundaries, Dorota Glowacka and Stephen Boos (eds). Albany, NY: State University of New York, 2002, v + 310 pp., $81.50, pb. $27.95.

Practical Rules: When We Need Them and When We Don't, Alan H. Goldman. Cambridge Studies in Philosophy. Cambridge: Cambridge University Press, 2002, xi + 210 pp., $54.95.

Manners and Violence, Ignacio L. Götz. Westport, CN/London: Praeger, 2000, xiii +131 pp., £44.50.

Dummett: Philosophy of Language, Karen Green. Key Contemporary Thinkers. Cambridge: Polity, 2001, xi + 236 pp., £55.00, pb. £14.99.

Wittgenstein: Connections and Controversies, P. M. S. Hacker. Oxford: Clarendon Press,2001. xxiv + 375 pp., £35.00.

India: A Financial Sector for the Twenty-first Century, James A. Hanson and Sanjay Kathuria (eds). Oxford India Paperbacks. Oxford: Oxford University Press, 2002 (first publ. 1999), xv + 446 pp., pb. £13.99.

Socialism, Michael W. Howard (ed.). Key Concepts in Critical Theory. New York: Humanity Books, 2001, 408 pp., pb. $29.00.

Ontology and the Art of Tragedy: An Approach to Aristotle's Poetics, Martha Husain. SUNY Series in Ancient Greek Philosophy. Albany, NY: State University of New York,2002. ix + 152 pp., pb. $16.95.

Why Good is Good: The Sources of Morality, Robert A. Hinde. London/New York: Routledge, 2002, xiv + 241 pp., pb. £15.99.

Logical Investigations, Edmund Husserl. Two vols. trans. J. N. Findlay, revised Dermot Moran with new preface by Dermot Moran and new introduction by Michael Dummett. International Library of Philosophy. London/New York: Routledge, 2001, vol. 1, Ixxxvii + 331 pp., pb. $29.95; vol. 2, xiv + 364 pp., pb. $29.95.

The Shorter Logical Investigations, Edmund Husserl. Abridged ed. and trans. J. N. Findlay, abridged and revised by Dermot Moran with new preface by Dermot Moran and new introduction by Michael Dummett. London/New York: Routledge, 2001, Ixxxv + 422 pp., pb. $27.95.

The Political, David Ingram (ed.). Blackwell Readings in Philosophy. Maiden, MA/ Oxford: Blackwell, 2001, xii + 310 pp., £60.00, pb. £15.99.

Hegel, M. J. In wood. Arguments of the Philosophers. London/New York: Routledge (1983 and 1998), xxxiv + 582 pp., pb.

Reconsidering Michael Polanyi's Philosophy, Stefania Ruzsits Jha. Pittsburgh, PA: University of Pittsburgh Press, 2002, viii + 318 pp., $32.00.

Speaking the Unspeakable: Religion, Misogyny, and the Uncanny Mother in Freud's Cultural Texts, Diane Jone-Pace. Berkeley: University of California Press, 2001, x + 190 pp., $45.00, pb. $17.95, £29.95, pb. £12.95.

Free Will, Robert Kane (ed.). Blackwell Readings in Philosophy. Maiden, MA/Oxford: Blackwell, 2001, xii + 310 pp., £55.00, pb. £15.99.

Wittgenstein: Biography and Philosophy, James C. Klagge (ed.). Cambridge: Cambridge University Press, 2001, xv + 272 pp., $54.95, pb. $19.95.

Frege and the Logic of Sense and Reference, Kevin C. Klement. Studies in Philosophy: Outstanding Dissertations. New York/London: Routledge, 2002, xiii + 260 pp., $70.00.

The Presence of Myth, Leszek Kolakowski. Chicago, IL/London: University of Chicago Press (1989), pb. ed. 2001, xii + 138 pp., $13.00, £8.50.

Justifying Emotions: Pride and Jealousy, Kristján Kristjansson. Routledge Studies in Ethics and Moral Theory. London/New York: Routledge, 2001, xii + 257 pp., £50.00.

Understanding Philosophy of Science, James Ladyman. London/New York: Routledge, 2002, xiii + 290 pp., pb. £12.99.

Infinite Minds: A Philosophical Cosmology, John Leslie. Oxford: Clarendon Press, 2001, xi + 234 pp., £25.00.

Appositions of Jacques Derrida and Emmanuel Levinas, John Llewelyn. Bloomington, IN: Indiana University Press, 2002, xx + 255 pp., $49.95, pb. $24.95.

Logic, Form, and Grammar. Peter Long. International Library of Philosophy. London/New York: Routledge, 2000, x + 109 pp.

Metaphysics: A Contemporary Introduction, Michael J. Loux. Routledge Contemporary Introductions to Philosophy. London/New York: Routledge, 2002, xiii + 303 pp., pb. £13.99.

Metaphysics: Contemporary Readings, Michael J. Loux (ed.). Routledge Contemporary Readings in Philosophy. London/New York: Routledge, 2002, xii + 555 pp., pb. £16.99.

The Metaphysicians of Meaning: Russell and Frege on Sense and Denotation, Gideon Makin. International Library of Philosophy. London/New York: Routledge, 2000, ix + 229 pp.

Towards a Critical Theory of Society, Herbert Marcuse. Collected Papers of Herbert Marcuse 2. London/New York: Routledge, 2001, xiii + 242 pp., £19.99.

Kierkegaard in the Present Age, Gordon Marino. Pref. by Philip Rieff. Marquette Studies in Philosophy 27. Milwaukee, WI: Marquette University Press, 2001, 124 pp.

An Introduction to the Philosophy of Mind, K. T. Maslin. Cambridge: Polity, 2001, xviii + 332 pp., no price given.

The Philosophy of Merleau-Ponty, Eric Matthews. Continental European Philosophy. Chesham, UK: Acumen, 2002, vi + 186 pp., £40.00, pb. £14.95.

Mind and Mechanism, Drew McDermott. Bradford Books. Cambridge, MA/London: MIT Press, 2001, xv + 262 pp., $32.95.

Approaches to Wittgenstein: Collected Papers, Brian McGuinness. London/New York: Routledge, 2002, xv + 299 pp., £50.00.

Collective Rationality and Collective Reasoning, Christopher McMahon. Cambridge: Cambridge University Press, 2001, ix + 251 pp., $54.95, pb. $19.95.

Authority and Estrangement: An Essay on Self-Knowledge, Richard Moran. Princeton, NJ: Princeton University Press, 2001, xxxv + 202 pp., £35.00, pb. £11.95.

The Sublime in Kant and Beckett Aesthetic Judgement, Ethics and Literature, Bjørn K. Myskja. Kantstudien 140. Berlin/New York: Walter de Gruyter, 2002, xii + 313 pp., no price given.

Spinoza's Heresy: Immortality and the Jewish Mind, Steven Nadler. Oxford: Clarendon Press, 2001, xvi + 225 pp., £22.50.

Arguing About Art: Contemporary Philosophical Debates, Alex Neill and Aaron Ridley (eds). 2nd ed. London/New York: Routledge, 2002 (McGraw-Hill, 1995), xiii + 479 pp.

Building on Frege: New Essays on Sense, Content, and Concept, Albert Newen, Ulrich Nortmann and Rainer Stuhlmann-Laeisz (eds). CSLI Publications. Chicago, IL: University of Chicago Press, xxiv + 351 pp., $65.00, pb. $23.00, £41.00, pb. £14.50.

Naturalism and Religion, Kai Nielsen. Amherst, NY: Prometheus Books, 2001, 506 pp., $40.00.

Beyond Good and Evil: Prelude to a Philosophy of the Future, Friedrich Nietzsche. Ed. Rolf-Peter Horstmann and Judith Norman; trans. Judith Norman. Cambridge Texts in the History of Philosophy. Cambridge: Cambridge University Press, 2001, xxxiv + 193 pp., $38.00, pb. $14.00.

Truth Matters: Realism, Anti-Realism and Response-Dependence, Christopher Norris. Edinburgh: Edinburgh University Press, 2002, viii + 228 pp., £40.00.

Naturalism and the Human Condition: Against Scientism, Frederick A. Olafson. London/ New York: Routledge, 2001, xi + 115 pp., pb. £13.99.

Wittgenstein's Tractatus: A Dialectical Interpretation. Matthew B. Ostrow. Cambridge: Cambridge University Press, 2002, x + 175 pp., $55.00, pb. $20.00.

Land, Value, Community: Callicott and Environmental Philosophy, Wayne Ouderkirk and Jim Hill (eds). Albany, NY: State University of New York, 2002, ix + 358 pp., $73.50, pb. $24.95.

Philosophy and the Adventure of the Virtual: Bergson and the Time of Life, Keith Ansell Pearson. London/New York: Routledge, 2002, ix + 246 pp., $80.00, pb. $38.95.

Environmental Culture: The Ecological Crisis of Reason, VaI Plum wood. Environmental Philosophies. London/New York: Routledge, 2002, vii + 291 pp., pb. £13.99.

Ethical Life: The Past and Present of Ethical Cultures, Harry Redner. Lanham/Boulder/ New York/Oxford: Rowman and Littlefield, 2001, ix + 348 pp., $80.00, pb. $32.95.

Paradoxes: Their Roots, Range, and Resolution, Nicholas Rescher. Chicago/La Salle, IL: Open Court, 2001, xxiii + 293 pp., £44.50, pb. £20.95.

Medicine, Magic and Religion, W. H. R. Rivers. The Fitzpatrick Lectures (first publ. 1924). Routledge Classics. Preface by G. Elliot Smith. London/New York: Routledge, 2001, viii + 136 pp. (pb.). No price given.

Is it Righteous to Be? Interviews with Emannuel Levinas, Jill Robbins (ed.). Meridian: Crossing Aesthetics. Stanford, CA: Stanford University Press, 2001, ix + 305 pp., $55.00, pb. $24.95.

Philosophy of Science: A Contemporary Introduction, Alex Rosenberg. Routledge Contemporary Introductions to Philosophy. London/New York: Routledge, 2000, x + 191 pp.

ABC of Relativity, Bertrand Russell. 6th ed. with intro. by Peter Clark. London/NY: Routledge, 1992, reissue: 2001, xvi + 155 pp., pb. $15.95.

What is Truth? Richard Schantz (ed.). Current Issues in Theoretical Philosophy 1. Berlin/ New York: Walter de Gruyter, 2002, vi + 338 pp., no price given.

The BlackweU Guide to Social and Political Philosophy, Robert L. Simon (ed.). Blackwell Philosophy Guides. Maiden, MA/Oxford: Blackwell, 2002, xi + 329 pp., £60.00, pb. £16.99.

The Unfinished Project: Toward a Postmetaphysical Humanism, Lorenzo C. Simpson. London/NY: Routledge, 2001, xi +180 pp., $85.00, pb. $22.95.

Hegel and the Phenomenology of Spirit, Robert Stern. Routledge Guidebooks. London / New York: 2001, xviii + 234 pp., pb. £8.99.

Wittgenstein, Avrum Stroll. Oxford: Oneworld Publications, 2002, ix + 162 pp., pb. $14.95.

Matters of Mind: Consciousness, Reason and Nature, Scott Sturgeon. International Library of Philosophy. London/New York: Routledge, 2000, x + 166 pp.

Marx for a Post-Communist Era, Stefan Sullivan. London/New York: Routledge, 2002, x + 191 pp., pb. £14.99.

Critical Reasoning: A Practical Introduction, Arme Thompson. 2nd ed. London/New York: Routledge, 2002, ix + 209 pp., pb. £12.99.

Hyperreality: Paradigm for the Third Millennium, John Tiffin and Nobuyoshi Terashima (eds). London/New York: Routledge, 2001, vvii +165 pp., (pb.) price not given.

Foucault and Latin America: Appropriations and Deployments of Discoursive Analysis, Benigno Trigo (ed.). New York/London: Routledge, 2002, xxi + 305 pp., pb. £16.99.

Knowledge, Michael Welbourne. Central Problems of Philosophy. Chesham, UK: Acumen, 2001, xiii + 143 pp., £35.00, pb. £12.95.

Philosophy, Literature and the Human Good, Michael Weston. London/New York: Routledge, 2001, xix + 198 pp., pb. £14.99.

A Clearing in the Forest: Law, Life, and Mind, Steven L. Winter. Chicago/London: University of Chicago Press, 2001, xvii + 440 pp., $38.00/£24.00.

Kant, Herder, and the Birth of Anthropology, John H. Zammito. Chicago/London: University of Chicago Press, 2002, xii + 576 pp., pb. $29.00, £18.50.     

Dynamic algebras: Examples,constructions, applications

Dynamic algebras combine the classes of Boolean (B 0) and regular (R ; *) algebras into a single finitely axiomatized variety (B R ) resembling an R-module with scalar multiplication . The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result is that free dynamic algebras are residually finite (i.e. factor as a subdirect product of finite dynamic algebras), important because finite separable dynamic algebras are isomorphic to Kripke structures. Applications include a new completeness proof for the Segerberg axiomatization of prepositional dynamic logic, and yet another notion of regular algebra.Dept. of Computer Science, Stanford, CA 94305 This research was supported by the National Science Foundation under NSF grant no. MCS78-04338. Preparation of the present version was supported by the National Science Foundation under NSF grant number CCR-8814921.This paper originally appeared as Technical Memo #138, Laboratory for Computer Science, MIT, July 1979, and was subsequently revised, shortened, retitled, and published as [Pra80b]. After more than a decade of armtwisting I. Németi and H. Andréka finally persuaded the author to publish TM#138 itself on the ground that it contained a substantial body of interesting material that for the sake of brevity had been deleted from the STOC-80 version. The principal changes here to TM#138 are the addition of footnotes and the sections at the end on retrospective citations and reflections.     

Some results on the Kripke sheaf semantics for super-intuitionistic predicate logics

Some properties of Kripke-sheaf semantics for super-intuitionistic predicate logics are shown. The concept ofp-morphisms between Kripke sheaves is introduced. It is shown that if there exists ap-morphism from a Kripke sheaf ₁ into ₂ then the logic characterized by ₁ is contained in the logic characterized by ₂. Examples of Kripke-sheaf complete and finitely axiomatizable super-intuitionistic (and intermediate) predicate logics each of which is Kripke-frame incomplete are given. A correction to the author's previous paper Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics (Studia Logica, 49(1990), pp. 289–306 ) is stated.Dedicated to Professor Takeshi Kotake on his 60th birthdayThis research was partially supported by Grant-in-Aid for Encouragement of Young Scientists No. 03740107, Ministry of Educatin, Science and Culture, Japan.     

BOOK REVIEWS

Books Reviewed in this Article: Beyond Ideology: Religion and the Future of Western Civilization. By Ninian Smart. Pp.350, London, Collins, 1981, £9.95. Neophtonism and Indian Thought. Edited by R. Baine Harris. Pp.xiii, 353, Albany (New York), State University of New York Press, 1982, $39.00 (hardback), $12.95 (paperback). Monotheism: A Philosophic Inquiry into the Foundations of Theology and Ethics. By Lenn Evan Goodman. Pp.122, Totowa (New Jersey), Allenheld, Osmun, 1981, $13.50. Neoplatonism and Christian Thought. Edited by Dominic J. O'Meara. Pp. xviii, 297, Albany, State University of New York Press, 1981, $39.00 (hardback), $12.95 (paperback). The Path to Transcendence: From Philosophy to Mysticism in Saint Augustine. By Paul Henry, introduction and translation by Francis F. Burch. pp.xxix, 120 (Pittsburgh Theological Monograph Series 37), Pittsburgh, The Pickwick Press, 1981, $10.95. The Adequacy of Christian Ethics. By Brian Hebblethwaite. Pp. 144 (Contemporary Christian Studies), London, Marshall, Morgan & Scott, 1981, £5.95. Ethics. By Wolfhart Pannenberg. Pp. 220, Philadelphia, The Westminster Press, 1981, $10.95. Human Nature, Election, and History. By Wolfhart Pannenberg. Pp. 116, Philadelphia, The Westminster Press, 1982, £2.95. Ethics, Religion and Politics. By G.E.M. Anscombe. Pp.ix, 161, Oxford, Basil Blackwell, 1981, £12.00. Moral Thinking: its Levels, Method and Point. By R.M. Hare. Pp.viii, 242, Oxford University Press, 1982, £11.00 (hardback), £3.95 (paperback). Utilitarianism and Beyond. Edited by Amartya Sen and Bernard Williams. Pp.vii, 290. £7.50 (paperback). Cambridge University Press, 1982, £20.00 (hardback). Language and Political Understanding. By Michael J. Shapiro. Pp.253, New Haven, Yale University Press, 1981, £18.20. Marx's Politics. By Allan Gilbert. Pp.xv, 326, Oxford, Martin Robertson, 1981, £16.50. Feuerbach. By Marx W. Wartofsky. Pp.xx, 460, Cambridge University Press, 1977, £30.00 (hardback), £9.95 (paperback). Nietzsche, Vol. 1: The Will to Power as Art. By Martin Heidegger, translated with notes and an analysis by D.F. Krell. Pp.xvi, 263, London, Routledge and Kegan Paul, 1981, £11.50. Freedom and Karl Jaspers's Philosophy. By Elizabeth Young-Bruehl. Pp.xiv, 233, New Haven & London, Yale University Press, 1981, £14.00. ‘Being and Meaning’: Paul Tillich's Theory of Meaning, Truth and Logic. By I.E. Thompson. Pp.x, 244, Edinburgh University Press, 1981, £15.00. The Rationality of Science. By W.H. Newton-Smith. Pp.xii, 294, London, Routledge and Kegan Paul, 1981, £9.95 (hardback), £5.95 (paperback). Realism and the Progress of Science. By Peter Smith. Pp.viii, 135, Cambridge University Press, 1981, £12.50. Angels and principalities. By Wesley Carr. Pp.xii, 242 (Society for New Testament Studies. Monograph Series 42), Cambridge University Press, 1981, £13.50. Rconciliation: A Study of Paul's Theology. By Ralph P. Martin. Pp.233, London, Marshall, Morgan and Scott, 1981, £8.95. Suffering and Martyrdom in the New Testament. Edited by William Horbury and Brian McNeil. Pp.xxi, 217, Cambridge University Press, 1981, £17.50. Constantine and Eusebius. By Timothy D. Barnes. Pp.viii, 458, Cambridge (Mass.), Harvard University Press, 1981, £24.50. Songs of Glory: the Romanesque Façades of Aquitaine. By Linda Seidel. Pp.x, 220, figs.63, Chicago and London, University of Chicago Press. 1981, £17.50. Marsilio Ficino and the Phaedran Charioteer. Translated and edited by Michael J.B. Allen. Pp.x, 274, Berkeley-Los Angeles, University of California Press, 1981, £18.50. The Letters of Marsilio Ficino, Volume 3. Pp.xiv, 162, London, Shepheard-Walwyn, 1981, £8.00. The World of the Renaissance Jew: The Life and Thought of Abraham ben Mordecai Farissol. By David B. Ruderman. Pp.xvii, 265, Cincinatti, Hebrew Union College Press, 1981, $20.00. A Dialogue Concerning Heresies. Edited by T.M.C. Lawier, G. Marc'hadour and R.C. Marius. Pp.xiv, 888 (The Yale Edition of The Complete Works of St Thomas More, Vol.VI), New Haven, Yale University Press, 1981, £56.00. Canterbury and Rome, Sister Churches: A Roman Catholic Monk reflects upon Reunion in Diversity. By Robert Hale. Pp.xi, 188, London, Darton, Longman and Todd, 1982, £5.95. Rome and Canterbury through Four Centuries: A Study of the Relations between the Church of Rome and the Anglican Churches 1530–1981. By Bernard and Margaret Pawley. Pp.xi, 387, London and Oxford, Mowbray, 1981, £4.95. American Indians and Christian Missions. By H.W. Bowden. Pp.xix, 255, Chicago, University of Chicago Press, 1981, £10.50. Catholics in Western Democracies: A Study in Political Behaviour. By John H. Whyte. Pp.193, Dublin, Gill and Macmillan. 1981, £13.00. Päpstliche Unfehlbarkeit bei Newman und Döllinger: Ein historisch-systema-tischer Vergleich. By Wolfgang Klausnitzer. Pp.280 (Innsbruck theologische Studien 6), Innsbruck, Tyrolia Verlag, 1980, 54 DM. The Letters of Baron Friedrich von Hügel and Professor Norman Kemp Smith. Edited by Lawrence F. Barmann. Pp.353, New York, Fordham University Press, 1981, no price given. Merton: A Biography. By Monica Furlong. Pp.xx, 342, London, Collins, 1980, £6.95. The Autonomy of Religious Belief: A Critical Inquiry. Edited by Frederick J. Crosson. Pp.vii, 162, Notre Dame, University of Notre Dame Press, 1981, £8.95. The Theological Imagination: Constructing the Concept of God. By Gordon D. Kaufman. Pp.309. Philadelphia, The Westminster Press, 1981, $13.95. Spirits of Power: An Analysis of Shona Cosmology. By Hubert Bucher. Pp.231, Capetown, Oxford University Press, 1980, £8.75. Judaism: The Evidence of the Mishnah. By Jacob Neusner. Pp.xix, 419, Chicago, University of Chicago Press, 1981, £17.50.     

Book reviews

Religion in Prison: ‘Equal Rites’ in a Multi‐Faith Society James A. Beckford & Sophie Gilliat, 1998 Cambridge: Cambridge University Press xiv + 232 pp., £35.00, US$54.95 ISBN 0–521–62246–8

The Dynamics of Emerging Ethnicities: Immigrant and Indigenous Ethnogenesis in Confrontation Johan Leman, ed., 1998 Frankfurt a. M: Peter Lang 179 pp., DM 32.50 (pb) ISBN 3–631–33107‐X, US ISBN 0–8204–3572–4

Testing the Global Ethic: Voices from Religious Traditions on Moral Values? Peggy Morgan & Marcus Braybrooke, eds., 1998 Oxford: The World Congress of Faiths/Ada, MI: CoNexus Press 172 pp., £11.99, US$19.95 UK ISBN 0–95–24140–1–5, US ISBN 0–9637897–6–7

Embodying Charisma: Modernity, Locality and the Performance of Emotion in Sufi Cults Pnina Werbner & Helene Basu, eds., 1998 London: Routledge 243 pp., £18.99 ISBN 0–415–15100–7

Appropriating Gender: Women's Activism and Politicized Religion in South Asia Patricia Jeffery & Amrita Basu, eds., 1998 New York, London: Routledge 276 + xi pp., £42.50 (hb), £12.99 (pb) ISBN 0–415–91865–0 (hb), ISBN 0–415–91866–9 (pb)

Buddhism and Ecology: The Interconnection of Dharma and Deeds Mary Evelyn Tucker & Duncan Ryuken Williams, eds., 1997 Cambridge, Massachusetts: Harvard University Center for the Study of World Religions xlii + 467 pp., £19.95 (hb), £13.50 (pb) ISBN 0–945454–13–9 (hb), 0–945454–14–7 (pb)

The Book of Enlightened Masters: Western Teachers in Eastern Traditions Andrew Rawlinson, 1997 Chicago & La Salle, Illinois: Open Court Publishing xix + 650 pp, £23.95 (pb) ISBN 0–8126–9310–8

American Buddhism: Methods and Findings of Recent Scholarship Duncan Ryuken Williams & Christopher S. Queen, eds., 1999 Richmond, Surrey: Curzon Press 329 pp., £40.00 ISBN 0–7007–1081–7

China's Catholics: Tragedy and Hope in an Emerging Civil Society Richard Madsen, 1998 Berkeley, Los Angeles, London: University of California Press 183 pp., £19.95 ISBN 0–520–21326–2

Anti‐Catholicism in Ireland, 1600–1998: The Mote and the Beam John D. Brewer with Gareth I. Higgins, 1998 London: Macmillan 248 pp., £47.50 (hb), £16.99 (pb) ISBN 0–333–74634–1 (hb), ISBN 0–333–74635‐X (pb)

Mary and Human Liberation: The Story and the Text Fr. Tissa Balasuriya, 1997 London: Mowbray 262 pp., £14.99 ISBN 0–264–67459–6

Beyond the Darkness: A Biography of Bede Griffiths Shirley Du Boulay, 1998 London: Rider 308 pp., £20.00 ISBN 0–7126–7429–2

Honest to Goddess: Russia, Sophia and the Celtic Soul Geraint Ap Iorwerth, 1998 Foreword by Caitlin Matthews Southampton: Crescent Books 136 pp., £12.99 ISBN 1–844086–001–4

Freud and Jung on Religion Michael Palmer, 1997 London: Routledge 238 pp., £45.00 (hb), £13.99 (pb) ISBN 0–415–14746–8 (hb), ISBN 0–415–14747–6 (pb)

Science Meets Faith: Theology and Science in Conversation Fraser Watts, ed., 1998 London: SPCK 166 pp., £12.99 ISBN 0–281–05112–1