The analytic movement advertised its 'linguistic turn' as a radical break from the two-thousand-year-old substance tradition. But this is an illusion. On the fundamental level of ontology, there is enough reformulation and presupposition of traditional 'no entity without identity' themes to analogize Frege, Russell, Wittgenstein, and Quine to Aristotle as paradigmatic of modified realism. Thus the pace of ontology is glacial. Frege and Russell, not Wittgenstein and Quine, emerge as the true analytic progenitors of 'no entity without identity,' offering between (...) them at least twenty-nine private language arguments and sixty-four 'no entity without identity' theories. (shrink)

Prominent thinkers such as Kripke and Rescher hold that Russell has no modal logic, even that Russell was indisposed toward modal logic. In Part I, I show that Russell had a modal logic which he repeatedly described and that Russell repeatedly endorsed Leibniz's multiplicity of possible worlds. In Part II, I describe Russell's theory as having three ontological levels. In Part III, I describe six Parmenidean theories of being Russell held, including: literal in 1903; universal in 1912; timeless in 1914; (...) transcendental in 1918–1948. The transcendental theory underlies the primary level of Russell's modal logic. In Part IV, I examine Rescher's view that Russell and modal logic did not mix. (shrink)

I SHOW THAT THE COSMOLOGICAL ARGUMENT OF AQUINAS FOR THE EXISTENCE OF GOD COMMITS A RATHER TRIVIAL LINGUISTIC FALLACY, BY SHOWING THAT (1) SOME OF ZENO'S PARADOXES COMMIT A TRIVIAL LINGUISTIC FALLACY, AND THAT (2) THE COSMOLOGICAL ARGUMENT IS SUFFICIENTLY SIMILAR TO THESE PARADOXES THAT IT COMMITS THE SAME FALLACY. COPLESTON'S VIEW THAT "MENTION OF THE MATHEMATICAL INFINITE SERIES IS IRRELEVANT" TO "ANY" OF AQUINAS'S ARGUMENTS FOR GOD'S EXISTENCE IS THUS SHOWN FALSE.

What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...) Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains. (shrink)

Do any significant philosophical differences between Quine and Carnap follow from Quine’s rejection of Carnap’s analytic-synthetic distinction? Not if they both understand empirical evidence in merely observational terms. But it follows from Quine’s rejection of the distinction that empirical evidence has degrees of holophrastic depth penetrating even into logic and ontology. Thus his reasons to prefer realism to idealism are holophrastically empirical. I discuss Quine’s holist sectarian realism on private languages, externalism versus internalism, unobserved objects, unobservable abstract entities, bivalence, ecumenicism (...) versus sectarianism, and on gradualism itself. (shrink)

This paper continues Michael Dummett's and my discussion of Frege in The Philosophy of Michael Dummett [2007]. Most of it is about Dummett’s change in view on Frege’s senses and objects. The issues include: the cognitive order versus the ontological order for the forward road; the nature and identity of senses and the different senses of "intension;" the nature of saturation; whether special quantifiers are now needed for senses; and Frege’s earlier and later permutation arguments. I discuss the implications of (...) the forward road for intuitionism as well. (shrink)

Shaughan La Vine, Understanding the Infinite.Cambridge, Massachussets :Harvard University Press, 1994, ix + 372 pp.£31.95/$47.95 B.Russell, Foundations of logic 1903‐05, The Collected Papers of Bertrand Russell, Volume 4, Edited by Urquhart, A.with the assistance of Lewis, A.C.London and New York:Routledge, 1994, Hi+ 743 pp.£100 Ray Monk and Anthony Palmer, Bertrand Russell and the Origins of Analytical Philosophy.Introduction by Ray Monk and Anthony Palmer.Bristol, U.K.:Thoemmes Press, 1996. xvi + 383 pp.£48.00/$78.00 ; £16.95/$29.95 T.J.Holopainen, Dialectic & Theology in the Eleventh Century.Leiden:E.J.Brill, 1996. (...) vii+171pp.$78. (shrink)

E. Husserl, Logik und allgemeine Wissenschaftstheorie. Vorlesungen 1917/18, mit ergänzenden Texten aus der ersten Fassung 1910/11. Introduction by U. Panzer. Dordrecht:Kluwer, 1996. lxii + 554 pp. £130. ISBN0 792 33731 X D. Jacquette, Meinongian logic. The semantics of existence and nonexistence. Berlin and New York:Walter de Gruyter, 1996. xiii + 297 pp. DM 198. ISBN 3 11 014865 X M. Beaney, The Frege Reader. Blackwell Publishers, 1997. xv + 409 pp. £14.99/$21.95. ISBN 0 631 194 452 Elliott Mendelson, Introduction to (...) formal logic, fourth edition. London:Chapman & Hall, 1997. x + 440 pp. £45.00. ISBN 1 412 808307 Samuel Guttenplan, The languages of logic. An introduction to formal logic, second edition. Oxford:Blackwell, 1997. x + 429 pp. No price stated. ISBN 1 55786 988 X A.C. Grayling, An introduction to philosophical logic, third edition. Oxford:Blackwell, 1997. vii + 343 pp. £15.99/$27.99. ISBN 0 631 19982 9 Lewis Carroll, Das Spiel der Logik. Edited with an afterword by P. Good. Translated by M.Zöllner. Cologne:Propen Verlag/Frommann-Holzboog, 1997. 120pp. 32 DM. ISBN 3 7728 1998 2. (shrink)

This paper continues my discussion with Michael Dummett on Frege’s senses, published in The Philosophy of Michael Dummett and further developed in Diametros. In his reply to my original paper, Dummett came to agree with me that senses are neither objects nor functions, since they have a categorially different kind of linguistico-metaphysical function to perform. He then asks how we might quantify over senses, if they are neither objects nor functions. He discusses two main options, and finds one unviable and (...) the other “very un-Fregean.” I then offer a Fregean or neo-Fregean option in my rejoinder. And I still hold that this way out will do the job, or is at least plausible enough that the burden of persuasion is on those who disagree. But I hope to show in this paper that on a more complete examination of Frege, there are at least twenty Fregean or neo-Fregean ways out, with the one I proposed being option. (shrink)

Ray Monk and Anthony Palmer (eds.), Bertrand Russell and the Origins of Analytical Philosophy. Introduction by Ray Monk and Anthony Palmer. Bristol, U.K.:Thoemmes Press, 1996. xvi + 383 pp. £48.00/$78.00 (cloth); £16.95/$29.95 (paper).

First published in 1999, this volume re-examines Bertrand Russell's views on modal logic and logical relevance, arguing that Russell does in fact accommodate modality and modal logic. The author, Jan Dejnozka, draws together Russell's comments and perspectives from throughout his canon in order to demonstrate a coherent view on logical modality and logical relevance. To achieve this, Dejnozka explores questions including whether Russell has a possible worlds logic, Rescher's case against Russell, Russell's three levels of modality and the motives and (...) origins of Russell's theory of modality. (shrink)

The analytic movement advertised its 'linguistic turn' as a radical break from the two-thousand-year-old substance tradition. But this is an illusion. On the fundamental level of ontology, there is enough reformulation and presupposition of traditional 'no entity without identity' themes to analogize Frege, Russell, Wittgenstein, and Quine to Aristotle as paradigmatic of modified realism. Thus the pace of ontology is glacial. Frege and Russell, not Wittgenstein and Quine, emerge as the true analytic progenitors of 'no entity without identity,' offering between (...) them at least twenty-nine private language arguments and sixty-four 'no entity without identity' theories. (shrink)