A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises (...) designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics. (shrink)
Notices Amer. Math. Sac. 51, 2004). Logically, such a "Grothendieck topos" is something like a universe of continuously variable sets. Before long, however, F.W. Lawvere and M. Tierney provided an elementary axiomatization..
Finitary sketches, i.e., sketches with finite-limit and finite-colimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finite-limit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary first-order logic: they are axiomatizable by σ-coherent theories, i.e., basic theories using finite conjunctions, countable disjunctions, and finite quantifications. The latter result is absolute; the equivalence of geometric and finitary sketches requires (in fact, is equivalent to) the non-existence of measurable cardinals.
This article is a sequel to ‘The Liar Syndrome’. It answers in detail the various criticisms of the latter expressed by Roy T. Cook in his article, ‘Curing the Liar Syndrome’, appearing in SATS/Nordic Journal of Philosophy, 3 (2): 126-141 (2002).
Machine generated contents note: -- Preface -- Acknowledgements -- Notes on Contributors -- Introduction; Z.Radman -- The Mystery of the Background qua Background; H.L.Dreyfus -- PART I: ECHOING SEARLE'S AND DREYFUS' VIEWS ON THE BACKGROUND -- Ground-Level Intelligence:Action-Oriented Representation and the Dynamics of the Background; M.Cappuccio& M.Wheeler -- Exposing the Background: Deep and Local; D.D.Hutto -- The Background as Intentional, Conscious, and Nonconceptual; M.Schmitz -- Social Cognition, the Chinese Room, and the Robot Replies; S.Gallagher -- Contesting John's Searle' Social Ontology: (...) Institutions and Background; J.Margolis -- Music and the Background; D.Schmicking -- PART II: EXTENDED VIEWS ON THE BACKGROUND -- Implicit Precision; E.T.Gendlin -- Enkinaesthesia: The Essential Sensuous Background for Co-Agency; S.A.J.Stuart -- Steps Entailed in Foregrounding the Background: Taking the Challenge of Languaging Experience Seriously; M.Sheets-Johnstone -- The Body as Background: Pragmatism and Somasthetics; R.Shusterman -- The Background: A Tool of Potentiality; Z.Radman -- Embodied Technology as Implicit Knowledge of Modern Civilization; K.Mainzer -- Index. (shrink)
"An American psychologist, Daniel N. Robinson, traces the development of the insanity plea...[He offers] an assured historical survey." Roy Porter, The Times [UK] "Wild Beasts and Idle Humours is truly unique. It synthesizes material that I do not believe has ever been considered in this context, and links up the historical past with contemporaneous values and politics. Robinson effortlessly weaves religious history, literary history, medical history, and political history, and demonstrates how the insanity defense cannot be fully understood without consideration (...) of all these sources." Michael L. Perlin, New York Law School "Daniel N. Robinson has written a graceful history of insanity and the law stretching from Homer to Hinckley. He attempts no final theory as to how the law should cope with the insane; he seeks, rather, to use the shifting notions of when madness exculpates criminal activity to illuminate the core self-perceptions of the cultures developing ever-evolving resolutions of the problem...[T]he grandeur of the theme...commands attention and respect." --Neal Johnston, The Nation . (shrink)
Immanuel Kant is one of Alain Badiou’s principle philosophical enemies. Kant’s critical philosophy is anathema to Badiou not only because of the latter’s openly aired hatred of the motif of finitude so omnipresent in post-Kantian European intellectual traditions—Badiou blames Kant for inventing this motif—but also because of its idealism. For Badiou-the-materialist, as for any serious philosophical materialist writing in Kant’s wake, transcendental idealism must be dismantled and overcome. In his most recent works (especially 2006’s Logiques des mondes), Badiou attempts to (...) invent a non-Kantian notion of the transcendental, a notion compatible with the basic tenets of materialism. However, from 1988’s Being and Event up through the present, Badiou’s oeuvre contains indications that he hasn’t managed fully to purge the traces of Kantian transcendental idealism that arguably continue to haunt his system—with these traces clustering around a concept Badiou christens “counting-for-one” (compter-pour-un). The result is that, in the end, Kant’s shadow still falls over Badiouian philosophy—this is despite Badiou’s admirable, sophisticated, and instructive attempts to step out from under it—thus calling into question this philosophy’s self-proclaimed status as materialist through and through. (shrink)
Is your God really God? -- Believing in God -- On the "names" of God -- The meaning of "God" and the common conception of God -- What is salvation? -- Salvation versus spiritual materialism -- The idolatrous religions -- The ban on idolatry -- Idolatry as perverse worship -- Graven images and the highest one -- Idolatry as servility -- The rhetoric of idolatrousness -- The same God -- The Pharisees' problem with Jesus -- Could we be idolaters? -- (...) Supernaturalism and scientism -- Scientism and superstition -- Supernaturalism -- Legitimate naturalism -- Scientism versus science -- The argument for naturalism from true religion -- The phenomenological approach -- The method and the question -- Yahweh's use of the method -- A criterion or an enclosed circle -- Yahweh's criterion applied to himself -- Forgiving the God -- A reply to yahweh's answer to job -- Is there an internal criterion of religious falsehood? -- The pope's criterion of religious falsehood -- A consequence of the pope's criterion -- Religious and scientific fallibilism -- Why God? -- Doesn't substantive reasonableness suffice? -- The fall -- Homo incurvatus in se -- The redeemer? -- After monotheism -- The highest one -- The tetragrammaton -- The paradox of the highest one -- Speaking of the highest one -- Existents as dependent aspects of existence itself -- An alternative to the thomistic interpretation of the highest one -- Process panentheism -- The goodness of the highest one -- The analogy of logos -- Process panentheism -- The self-disclosure of existence itself -- The problem is with the pantheon -- Panentheism not pantheism -- Distinguishing panentheism and pantheism -- Presence -- Presence as disclosure -- Is being almost entirely wasted? -- Ubiquitous presence -- Against natural representation -- Representation and "carrying information" -- Can causation account for aboutness? -- What could replace the representationalist tradition? -- A diagnosis of the representationalist's mistake -- A transformed picture of "consciousness" and reality -- Confirming the surprising hypothesis -- The mind of God -- The objectivity of the realm of sense -- How the structure of presence might impose evolutionary constraints -- Objective mind and the mind of the highest one -- The doubly donatory character of reality -- Does God exist? -- The highest one -- Christianity without spiritual materialism -- Religion and violence -- The Gospel according to Girard -- Where is original sinfulness? -- Original sinfulness as self-will and false righteousness -- Christ destroys the kingdom of self-will and false righteousness -- The afterlife as an idolatrous conceit -- Against "man's quest for meaning" -- The afterlife as resistance to Christ -- Naturalism's gift : resurrection without the afterlife. (shrink)
The theoretical value of talking to the media isn’t hard to appreciate. Who doesn’t want to shape the public conversation, whether to make it more nuanced and reasoned or to bring injustice and wrongdoing to light? Issues you’ve studied are in the news and you get to be the expert, pointing out what’s wrong, or right, or offering another way of thinking about a difficult question. If you’re lucky, you get your name in print—and in a publication your friends and (...) family actually read. But it can also be intimidating. I used to feel like the hapless witness about to be cross-examined by the wily attorney. I’d heard about the twenty-four-hour news cycle and the push to appeal to the lowest common denominator. .. (shrink)