We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda \, | \, (...) V_{\lambda } \prec _{{\Sigma }_{n}}V\}$ ; moreover the theory of such models is invariant under ZFC-preserving extensions. They also all have a rich structure satisfying many of the usual combinatorial principles and a definable wellorder of the reals. The inner model constructed using definability in the language augmented by the Härtig quantifier is thus also characterized. (shrink)

A correction is needed to our paper: to the definition contained within the statement of Lemma 1.5 and thus arguments around it in §3.

We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal functions are not computable by any function of the class over which they diagonalise, there is no ?logical incomputability? in their being computed over a wider class. Hence this ?logical incomputability? regrettably cannot be used in his argument that no hypercomputation can compute the Halting problem. This seems to lead (...) him into a further error in his analysis of the supposed conventional status of the infinite time Turing machines of Hamkins and Lewis ([2000]). Theorem 1 refutes this directly. The diagonalisation misunderstanding Infinite computation Conclusion. (shrink)

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.

We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma _{1}$ -definability at uncountable regular cardinals. In particular we give its exact consistency strength first in terms of the second uniform indiscernible for bounded subsets of $\kappa $ : $u_2$, and secondly to give the consistency strength of a property of Lücke’s.TheoremThe following are equiconsistent:There exists $\kappa $ which is stably measurable;for some cardinal $\kappa $, $u_2=\sigma $ ;The $\boldsymbol {\Sigma }_{1}$ -club property holds (...) at a cardinal $\kappa $.Here $\sigma $ is the height of the smallest $M \prec _{\Sigma _{1}} H $ containing $\kappa +1$ and all of $H $. Let $\Phi $ be the assertion: TheoremAssume $\kappa $ is stably measurable. Then $\Phi $.And a form of converse:TheoremSuppose there is no sharp for an inner model with a strong cardinal. Then in the core model K we have: $\mbox {``}\exists \kappa \Phi \mbox {''}$ is -generically absolute ${\,\longleftrightarrow \,}$ There are arbitrarily large stably measurable cardinals.When $u_2 < \sigma $ we give some results on inner model reflection. (shrink)

The use of Extended Logics to replace ordinary second order definability in Kleene’s Ramified Analytical Hierarchy is investigated. This mirrors a similar investigation of Kennedy, Magidor and Väänänen [11] where Gödel’s universe L of constructible sets is subjected to similar variance. Enhancing second order definability allows models to be defined which may or may not coincide with the original Kleene hierarchy in domain. Extending the logic with game quantifiers, and assuming strong axioms of infinity, we obtain minimal correct models of (...) analysis. A wide spectrum of models can be so generated from abstract definability notions: one may take an abstract Spector Class and extract an extended logic for it. The resultant structure is then a minimal model of the given kind of definability. (shrink)

We show that the predicate “x is the power set of y” is ‐definable, if V = L[E] is an extender model constructed from a coherent sequences of extenders, provided that there is no inner model with a Woodin cardinal. Here is a predicate true of just the infinite cardinals. From this we conclude: the validities of second order logic are reducible to, the set of validities of the Härtig quantifier logic. Further we show that if no L[E] model has (...) a cardinal strong up to one of its ℵ‐fixed points, and, the Löwenheim number of this logic, is less than the least weakly inaccessible δ, then (i) is a limit of measurable cardinals of K, and (ii) the Weak Covering Lemma holds at δ. (shrink)

We prove that a form of the $Erd\H{o}s$ property (consistent with $V = L\lbrack H_{\omega_2}\rbrack$ and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle $\psi_{AC}$ holds, and therefore 2ℵ0 = ℵ2. We also prove that $\psi_{AC}$ implies that every function $f: \omega_1 \rightarrow \omega_1$ is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum (...) fails. (shrink)

We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order ) equal to κ++, and use it to prove the following theorem on mutual stationarity at n.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1.TheoremIf every sequence n m. In particular, there is such a model in which for (...) all sufficiently large m<ω, the class of measurables λ with oM≥ωm is, in V, stationary below m+2. (shrink)

We set $\mathscr{D} = \langle\mathscr{D}, \leq_L, \tt\#\rangle$ , where D is the set of degrees of nonconstructibility for countable sets of countable ordinals. We show how to define inductively over this structure the degrees of such sets of ordinals in K, the core model, and the next few core models thereafter, i.e. without reference to mice, premice or measurable cardinals.

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 119 Der Verf. bedient sieh in Verfolgung seines Ziels der fibliehen historischen Methode, die er mit Meistersehaft handhabt. Doch ist er keineswegs ein typischer Vertreter des modernen Historismus. Als Philosoph ist er gefesselt von den Problemen, die sich in der dreifachen Thematik seiner Untersuehung verbergen. Er begibt sich in die Gesehichte, aber doch nur, um yon Zeit zu Zeit aus ihr herauszutreten und i)berlegungen nachzugehen, die er (...) selbst, anlfifilieh einer methodologisehen Bemerkung in der Einleitung, als eine "Typologie yon LSsungen" (3) bezeiehnet. Aber das ist ein understatement, keine exakte Besehreibung. Die unbefangene und nfiehterne Kfihnheit dieser seiner trans-historisehen Reflexionen durehweht als ein frischer Luftzug die Welt der Gelehrsamkeit und Vielbelesenheit, die sich in diesen Seiten aufbaut. Freilieh, wo der Verf. selbst steht, gibt er uns nur gelegentlieh zu verstehen, so z.B. wenn er mit Entsehiedenheit die averroistisehe Depotenzierung des Einzelnen gegenfiber der Mensehheir zurfickweist. Aber, wiederum im Zusammenhang mit Averroes, legt er Gedanken zu der berfihmten oder auch berfiehtigten Lebre yon der doppelten Wahrheit vor, die uns in Zweifel darfiber lassen, ob und wie weit sich der Verf. hier verbirgt oder d~couvriert. M. gesellt sich nicht zu denen, die Averroes entlasten woUen, indem sie die fatale Lehre als eine spatere Zutat erkl~ren. Vielmehr mSchte er das Anathema dadurch fortnehmen, daB er die grobe und beleidigende Darstellung der Lehre dutch eine subtile Deutung ersetzt, die sie als konsequent, als vernfinftig und schlie61ich als wahr erscheinen l~Bt (107 ft.). Der Mensch, so argumentiert er, drfickt sich in einer Mehrheit yon "Sprachen" (universes of discourse) aus, die sich nieht ineinander fibersetzen lassen--der Sprache der Kunst, der Dichtung, der Philosophie, der Religion usw. So kann ein und derselbe Menseh ohne Selbstwidersprueh oder Unredliehkeit als Philosoph sagen: die individuelleSeele ist sterblich, als Gl~ubigerhingegen: sie ist unsterblich. Denn sowohl "Seele" wie "Individuum" wie aueh "Unsterblichkeit" meinen etwas anderes je nach dem universe of discourse, dem philosophischen oder religiSsen, in welchem sie gebraueht werden. Freilich, man kann den Versueh maehen, in langagestart in einer der vielen langues zu reden, und die Theologie kann nicht umhin, eben dies zu wagen. Ffir die Theologie aber~ so bekennt der Verf., ist kein Raum in seinem "scheme of things" (109). Das ist ein erschreckendes Wort, und nieht blofi ffir den, der die Theologie erhalten mSchte. Denn es besteht begrfindete Sorge, dab der Ruin der zwisehen den versehiedenen langues zerriebenen Theologie auch die Philosophiepulverisiert. Die verschiedenen"Spraehen" miissen doch wohl in der einen mensehlichen Person sinnvoll zusammengeordnet sein. Welche Wissenschaft aber wenn nicht die Philosophie darf sich diese Zusammenordnung zum Gegenstand ihres Forschens und Sagens machen? Wir schliefien also unseren Bericht fiber ein bedeutendes Buch mit einer Frage, nicht aber der Kritik oder gar des Besser-wissen-wollenswegen, sondern um auszudrficken, dab der Autor uns nicht nur als gelehrter Kenner unterrichtet, sondern als Philosoph zum Denken zwingt. Mi~nchen, Germany HELMUT KUHN Diogenis Laertii Vitae Philosophorum. Recognovit brevique adnotatione critica instruxit H. S. Long. 1 vol. in2. (Oxford: 1964.Pp. xx ~ xiv W 597. $11.20.) Der Hg erinnert uns, dass seit der Cobetsehen (1850), leider apparatlosen, keine kritische Ausgabe des Diogenes im ganzen ersehlenen ist. Immerhin gibt es abet die Ubersetzung yon M. Gigante (DiogeneLaerzio, Vite dei filosofi, Bari 1962), die so annotiert ist, dass sie vielfach anstatt einer Edition gebraucht werden kann. Man bedauert, dass der Hg sie offenbar noch nicht benutzen konnte (sein Buch ist wohl 1964erschienen, doch ist die Vorrede 1961datiert). Der Hg schliesst sich der Meinung an, dass nut 3 der existierenden Diogenes-Hss den Wert unabh~ngiger Zeugen besitzen. Vorsichtiger beurteilt den Sachverhalt z.B.H. Erbse in: Geschichte der Text~berlieferung, I. Band (1961), S. 306f., doch wollen wir die These des Hg akzeptieren. Wie allgemein zugestanden, gehen diese drei auf eine gemeinsame Vorlage zur~iek. Unter diesen Ums~nden ist es die Pflicht des Hg, uns verl~sslich und eindeutig fiber den Text dieser drei (BFP aus dem 12.u. 13.Jh.) zu informieren, eine Entscheidung zu treffen, wo diese 120 HISTORY OF PHILOSOPHY nicht tibereinstimmen, darfiber hinaus Textverderbnisse anzuzeigen und womSglich zu emendieren, entweder dureh eigene Vermutungen (in Buch VI und IX, e. 19% des Ganzen, habe ich nur zwei gefunden, beide einleuehtend... (shrink)

What is hope? A feeling? Something you do? A belief or a cluster of beliefs? A way of perceiving the world? Is hope the same as wishful thinking? Hope is complicated. Nevertheless, hope can make our lives better. In Understanding Hope, Philip Smith combines theology, psychology, philosophy, and his own experience of personal loss to help readers understand and practice hope. Understanding Hope is short, but it requires hard thinking. It's worth the effort.

In Why Faith is a Virtue, Philip D. Smith builds on the work of Alasdair MacIntyre and Robert Adams to argue that faith contributes to human excellence. To make the argument, Smith sorts through conflicting possible "faiths" and shows how some of them are not virtues at all. Nevertheless, he argues that faith, properly understood, contributes to crucial human practices: scientific research, social reform, and parenting.

We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization (...) of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever. With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by ’t Hooft in which a connection between conformal gravity and Einstein gravity has been found. (shrink)

This book addresses a substantive normative issue of contemporary political theory, the issue of political legitimacy, critiquing the mainstream approach of justificatory liberalism and offering an alternative reconstructed from neo-Calvinist social thought, a rich source of insights that might be applied to other issues within political theory.

This book addresses a substantive normative issue of contemporary political theory, the issue of political legitimacy, critiquing the mainstream approach of justificatory liberalism and offering an alternative reconstructed from neo-Calvinist social thought, a rich source of insights that might be applied to other issues within political theory.

According to justificatory liberalism legal coercion is legitimate only when exercised for reasons that all reasonable persons can accept. That is, laws are legitimate only if they satisfy JL’s unanimity condition. This principle entails that if no law meets the unanimity condition, then no law is legitimate. However, given the diversity of persons who meet JL’s own twofold criteria of ‘reasonable’ – commitment to fair cooperation and recognition of reasonable pluralism – no law would be supported by all reasonable persons (...) in JL’s thought experiment, let alone in the real world. I illustrate this diversity of qualified views with an objector inspired by Michael Bakunin, whose revolutionary anarchist views take the state to threaten more than protect equality and pluralism. Therefore, JL would prohibit any use of legal coercion. Nothing would be justified by JL. This result clearly conflicts with commonsense, which recognizes many instances of legal coercion as legitimate even amidst disagreement, and calls into question JL’s plausibility. (shrink)

Abstract:This article correlates the physical composition of the built environment with social interactions and human relationships. The resulting framework draws on an embodied cognitive position through interdisciplinary knowledge with priority given to architectural theory and cognitive linguistics. This approach does not address idiosyncratic, phenomenological descriptions of experiences of place but the potential relationship of human bodies through situated semantics suggested by spatial composition. In this article we ask how the physical arrangement of a space can provide information for analyzing the (...) probable social relations such as positions of hierarchy, power, and authority. We identify two theoretical models, namely latent embodied cognitive operations and space as a situated concept, which can be used to correlate physical arrangements with social meaning. (shrink)

We discuss the circumstances under which gravity might be repulsive rather than attractive. In particular we show why our standard solar system distance scale gravitational intuition need not be a reliable guide to the behavior of gravitational phenomena on altogether larger distance scales such as cosmological, and argue that in fact gravity actually gets to act repulsively on such distance scales. With such repulsion a variety of current cosmological problems (the flatness, horizon, dark matter, universe age, cosmic acceleration and cosmological (...) constant problems) are then all naturally resolved. (shrink)

Our long experience with Newtonian potentials has inured us to the view that gravity only produces local effects. In this paper we challenge this quite deeply ingrained notion and explicitly identify some intrinsically global gravitational effects. In particular we show that the global cosmological Hubble flow can actually modify the motions of stars and gas within individual galaxies, and even do so in a way which can apparently eliminate the need for galactic dark matter. Also we show that a classical (...) light wave acquires an observable, global, pathdependent phase in traversing a gravitational field. Both of these effects serve to underscore the intrinsic difference between nonrelativistic and relativistic gravity. (shrink)

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second-order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's law of gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted (but actually still open to question) assumptions which go into the formulation of (...) the standard second-order Einstein theory in the first place. In particular, we show that while the familiar second-order Poisson gravitational equation (and accordingly its second-order covariant Einstein generalization) may be sufficient to yield Newton's law of gravity they are not in fact necessary. The standard theory thus still awaits the identification of some principle which would then make it necessary too. We show that current observational information does not exclusively mandate the standard theory, and that the conformal invariant fourth-order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the constraints of data, and in fact to do so without the need for any so far unobserved nonluminous or dark matter. (shrink)

Virtue of Civility in the Practice of Politics is a book at the intersection of ethical theory, political philosophy and Christian belief. The book argues that there is a true political virtue: civility. Civility is a virtue that is directed toward the political opponent. MacIntyre's schema for understanding a virtue is used to show how civility contributes to better human living in a variety of contexts: business, family life, church life, and public affairs.

The Factualistic, Positivistic Basis . . . this life of suffering, of doubt, which makes you deeply love naked, living reality. Zola "Gustave Doret,"Mex ...

We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being \ rather than \ itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is (...) obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided. (shrink)

We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais–Uhlenbeck fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais–Uhlenbeck model does indeed contain the negative norm energy eigenstates (...) which are characteristic of higher derivative theories, in the limit in which we switch off the second order action, such ghost states are found to move off shell, with the spectrum of asymptotic in and out S-matrix states of the pure fourth order theory which results being found to be completely devoid of states with either negative energy or negative norm. We confirm these results by quantizing the Pais–Uhlenbeck theory via path integration and by constructing the associated first-quantized wave mechanics, and show that the disappearance of the would-be ghosts from the energy eigenspectrum in the pure fourth order limit is required by a hidden symmetry that the pure fourth order theory is unexpectedly found to possess. The occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure fourth order theories per se, but rather to be one which only arises when fourth and second order theories are coupled to each other. (shrink)

This thesis looks at explanation in the natural sciences, the social sciences, and in religious reflection. Although these fields differ radically in the objects studied and the methods employed, they do evidence certain formal commonalities when one inquires into the nature of the explanatory endeavor as it is manifested in each. By exploring the links between explanations and the various contexts or disciplines in which they occur, I attempt to provide a general framework for speaking of rational explanations in these (...) diverse areas. ;In an opening chapter I consider several alternatives regarding the epistemic status of religious explanations, focusing finally on the model of "intersubjective explanation." Contemporary defenses of intersubjective religious explanation are placed within the context of the broader faith/reason debate, and a quick survey is made of recent advocates of this position. I then turn to the methodology dispute in the philosophy of the natural sciences . My aim is to mediate between purely formal analyses of explanatory structure and the more recent emphasis on contextual and pragmatic factors. ;In the social sciences, many have argued, explanation is subordinate to intuitive understanding. After tracing the explanation versus understanding debate from Dilthey to the present, I present the recent work of Jurgen Habermas as a case study in the problems of social scientific rationality. Explanations in the social sciences are rational reconstructions of human meaning contexts, and "Verstehen" is required as a precondition for material adequacy. Such explanations are linked to the individual or communal effort to "make sense" of, or bring coherence into, subjective and intersubjective "worlds." ;After an excursus on philosophical explanations and the problem of philosophical rationality, I attempt a brief phenomenology of religious beliefs as explanations. As in the social sphere, religious explanations represent the believer's attempt to "make sense" of her experience in light of a given religious tradition. Although the comprehensive nature of religious explanations makes comparisons difficult--in the limit case they verge on ineffability--the concepts of meaning and coherence allow us to speak of the rationality of religious belief without total equivocation. ;The final chapter turns to the study and evaluation of religious explanations as they occur in the discipline of theology. Under the rubric "theology as a science," I defend theology's dual status as an academic discipline and as believing reflection in the service of the religious community. Through vitally concerned with the truth of its assertions, theology also shares the goals of coherence and intersubjective criticizability with its scientific counterparts. (shrink)

The increasing awareness of the incommensurability between voters’ attitudes about voting and the reality of voting are contributing to the much written-about voter malaise which plagues U.S. elections. Voters who assume their role is to determine the ideal, right, or best candidate confront an election system in our current communication environment that attempts to market candidates to match voters’ ideals, while also providing a surfeit of information that both contradicts the ideal depictions while also making transparent the process by which (...) candidates are packaged. This essay identifies four communication phenomena that contribute to this malaise: campaign transparency; bifurcation of issue and candidate; the abstracted nature of news content; and the glut of information that characterizes our present communication environment. (shrink)

Routledge is proud to reissue these nine pivotal titles from the acclaimed series Studies in Ethics and the Philosophy of Religion. Including key works by Ahern, Beardsmore, Pike, and others, these books are essential for all serious collections. Available as single volumes or as a nine-volume set, the titles in this collection were originally published between 1950-1960 by Routledge and Kegan Paul: Volume 1: The Problem of Evil M.B. Ahern Hb: 0-415-31841-6 Volume 2: Moral Reasoning R.W. Beardsmore Hb:0-415-31842-4 Volume 3: (...) Theology and Intelligibility Michael Durrant Hb: 0-415-31843-2 Volume 4: Humanism and Ideology James R. Flynn Hb: 0-415-31844-0 Volume 5: The Five Ways: St.Thomas Aquinas' Proofs of God's Existence Anthony Kenny Hb: 0-415-31845-9 Volume 6: Moral Practices D.Z. Phillips Hb: 0-415-31846-7 Volume 7: God and Timelessness Nelson Pike Hb: 0-415-31847-5 Volume 8: Without Answers Rush Rhees Hb: 0-415-31848-3 Volume 9: Morality and Purpose J.L. Stocks Hb: 0-415-31849-1. (shrink)

This book is neither a biography nor an in-depth interpretation of Berkeley's philosophical system. There are numerous details about Berkeley's life, social relationships, and intellectual contributions, but Berman neither explores these matters in comprehensive depth nor claims to do so. What, then, does he do? Berman's answer is: "Advancing chronologically, I have focussed on Berkeley as homo religiosus". He uses biographical details to portray Berkeley as a Christian thinker who acted on his commitment both in and out of his study. (...) Berman also locates Berkeley's writings in their specific intellectual and social contexts while tracing a career that spanned over forty years and encompassed a wide range of interests and disciplines, from theology to economics. Attention is paid, for example, to Berkeley's Guardian essays and to Siris, which is characterized as his most popular book during his lifetime. Philosophers now concentrate almost exclusively on the Principles of Human Knowledge and Three Dialogues between Hylas and Philonous, regarding their author only as a technical thinker offering immaterialism as a solution to free-standing philosophical problems. It is therefore salutary to be informed about the wide range of Berkeley's writings and regard them as diverse expressions of Christian idealism, a religiously inspired outlook about God, nature, and humanity which issued in, but transcends, immaterialism, the technical philosophical position. (shrink)