The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics (...) that are sound and complete with respect to varieties of distributive lattices with operators in the above-mentioned classes. (shrink)

We explore the possibilities for elementary embeddings $j : M \to N$, where M and N are models of ZFC with the same ordinals, $M \subseteq N$, and N has access to large pieces of j. We construct commuting systems of such maps between countable transitive models that are isomorphic to various canonical linear and partial orders, including the real line ${\mathbb R}$.

We show that any symmetric, Baire measurable function from the complement of $\ezero$ to a finite set is constant on an $\ezero$-nonsmooth square. A simultaneous generalization of Galvin's theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equivalence relations on $E_0$-nonsmooth sets, this result is proved by relating $\ezero$-nonsmooth sets to embeddings of the complete binary tree into itself and appealing to a version of Hindman's theorem on the complete binary tree. We also establish (...) several canonization theorems which follow from the main result. (shrink)

We present an algebraic approach to canonical embeddings of arbitrary residuated algebras into powerset residuated algebras. We propose some construction of powerset residuated algebras and prove a representation theorem for symmetric residuated algebras.

Ifκis a measurable cardinal, let us say that a measure onκis aκ-complete nonprincipal ultrafilter onκ. IfUis a measure onκ, letjUbe the canonical elementary embedding ofVinto its Ultrapower UltU. Ifxis a set, say thatUmovesxwhenjU≠x; say thatκmovesxwhen some measure onκmovesx. Recall Kunen's lemma : “Every ordinal is moved only by finitely many measurable cardinals.” Kunen's proof and Fleissner's proof are essentially nonconstructive.The following proposition can be proved by using elementary facts about iterated ultrapowers.Proposition.Let ‹Un: n ∈ ω› be a sequence (...) of measures on a strictly increasing sequence ‹κn: n ∈ ω› of measurable cardinals. Let U = ‹ Wα: α < ω2›, where Wωm + n= Um. Then, for each θ inUltU,if E is the support of θ inUltU,then, for all m ∈ ω, Ummoves θ iff E ∩ [ωm, ω)≠ ∅. (shrink)

The analysis of the temporal structure of canonical general relativity and the connected interpretational questions with regard to the role of time within the theory both rest upon the need to respect the fundamentally dual role of the Hamiltonian constraints found within the formalism. Any consistent philosophical approach towards the theory must pay dues to the role of these constraints in both generating dynamics, in the context of phase space, and generating unphysical symmetry transformations, in the context of a (...) hypersurface embedded within a solution. A first denial of time in the terms of a position of reductive temporal relationalism can be shown to be troubled by failure on the first count, and a second denial in the terms of Machian temporal relationalism can be found to be hampered by failure on the second. A third denial of time, consistent with both of the Hamiltonian constraints roles, is constituted by the implementation of a scheme for constructing observables in terms of correlations and leads to a radical Parmenidean timelessness. The motivation for and implications of each of these three denials are investigated. (shrink)

By extending geometrodynamical phase space by embeddings and their conjugate momenta, one can homomorphically map the Lie algebra of space-time diffeomorphisms into the Poisson algebra of dynamical variables on the extended phase space.

This article tackles Giorgio Agamben's critique of Michel Foucault's genealogy of governmentality in two ways: first, by presenting an alternative model of the relations between pastoral and theological economy and, second, by conducting a genealogy of the former as revealed in the state of exception, when canon law is suspended. Following the author's genealogy of oikonomia in the state of exception, he argues that politics and economy are distinct from one another by virtue of the fact that the primary relation (...) of the latter is one of inclusion while that of the former is one of exclusion. Finally, the author traces three of oikonomia's prolific qualities in the operation of governmentality in civil society and of market economy: (i) its inclusiveness; (ii) the constant representation of the irreconcilability of law and authority; and (iii) its operation by accommodating to the ways of the governed. (shrink)

The concept of political obligation has not attracted much attention within Heideggerian scholarship. In this paper, we identify and explicate Heidegger’s conception of political obligation embedded in his pre-Kehre works. It will be argued that Heidegger’s magnum opus Being and Time and his address as Rector of Freiburg contain a latent associative account of political obligation. We argue that the ontological framework disclosed in Being and Time and the more concrete policy prescriptions of the Rectoral Address reveal a communitarian ethos (...) which animates the early Heideggerian canon and grounds his account of political obligation. For Heidegger, Dasein must be connected to a particular community’s ontological heritage in order to delimit its ontical possibilities in concrete situations. It will be argued that this relationship between ontological heritage and ontical possibilities is what defines political obligation for Heidegger. (shrink)

Let \(2 (...) It is shown that \(\mathbf{K_n}\) is not finitely axiomatizable and that it coincides with the class of atomic algebras in the elementary closure of \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{\omega}\) where \(\mathbf{S_c}\) is the operation of forming complete subalgebras. For any class \(\mathbf{L}\) such that \({\sf At}{\sf Nr}_n{\sf CA}_{\omega}\subseteq \mathbf{L}\subseteq {\sf At}\mathbf{K_n}\), it is proved that \({\bf SP}\mathfrak{Cm}\mathbf{L}={\sf RCA}_n\), where \({\sf Cm}\) is the dual operator to \(\sf At\); that of forming complex algebras. It is also shown that any class \(\mathbf{K}\) between \({\sf CRCA}_n\cap \mathbf{S_d}{\sf Nr}_n{\sf CA}_{\omega}\) and \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{n+3}\) is not first order definable, where \(\mathbf{S_d}\) is the operation of forming dense subalgebras, and that for any \(2shrink)

This article considers the various emergence of an explicitly recognized right to life in papal teaching and the canon law of the last century and a quarter. The Church's opposition to abortion is deeply embedded within the tradition and law of the Church. It was, however, only in recent times, since the middle twentieth century, really, that the Church began to speak explicitly of a right to life. This paper explores the consequences for papal thought of this explicit recognition of (...) rights. By speaking of a right to life, the Church has moved beyond the abortion debate to embrace a variety of other concerns. This is not to say that abortion does not remain important. Direct participation in abortion is a crime at canon law that results in automatic excommunication. But the language of rights has allowed the Church to address such matters as the protection of refugees; the moral requirement of adequate health care; the odious use of child-soldiers; and the use of economic embargoes that have the effect of destroying the civilian infrastructure (and public health systems) of entire societies. (shrink)

Every transformation monoid comes equipped with a canonical topology, the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This phenomenon is called automatic homeomorphicity. In this paper we show that whenever the automorphism group of a countable saturated structure has automatic homeomorphicity and a trivial center, then the monoid of elementary self-embeddings has automatic homeomorphicity, too. As a second result we strengthen a result by Lascar by (...) showing that whenever \ is a countable \-categorical G-finite structure whose automorphism group has a trivial center and if \ is any other countable structure, then every isomorphism between the monoids of elementary self-embeddings is a homeomorphism. (shrink)

We generalize the incompleteness proof of the modal predicate logic Q-S4+ p p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed.

We study concepts of decidability for subsets of Euclidean spaces ℝk within the framework of approximate computability . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff's concept of resolvable sets, and it modifies and generalizes notions of recursivity known from computable analysis, formerly used for open or closed sets only, to more general types of sets. Approximate decidability of sets can equivalently be expressed by computability of the (...) characteristic functions by means of appropriately working oracle Turing machines. The notion fulfills some natural requirements and is hereditary under canonical embeddings of sets into spaces of higher dimensions. However, it is not closed under binary union or intersection of sets. We also show how the framework of resolvability and approximate decidability can be applied to investigate concepts of reducibility for subsets of Euclidean spaces. (shrink)

We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a (...) connection between our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article provides a bridge between Colombeau theory of generalized functions and non-standard analysis. (shrink)

A μ-algebra is a model of a first-order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms where μx.f is axiomatized as the least prefixed point of f, whose axioms are equations or equational implications.Standard μ-algebras are complete meaning that their lattice reduct is a complete lattice. We prove that any nontrivial quasivariety of μ-algebras contains a μ-algebra that has no embedding into a complete μ-algebra.We then focus on modal μ-algebras, i.e. (...) algebraic models of the propositional modal μ-calculus. We prove that free modal μ-algebras satisfy a condition–reminiscent of Whitman’s condition for free lattices–which allows us to prove that modal operators are adjoints on free modal μ-algebras, least prefixed points of Σ1-operations satisfy the constructive relation μx.f=logical and operatorn≥0fn. These properties imply the following statement: the MacNeille–Dedekind completion of a free modal μ-algebra is a complete modal μ-algebra and moreover the canonical embedding preserves all the operations in the class image of the fixed point alternation hierarchy. (shrink)

Let ${\mathbb{B}}$ and ${\mathbb{C}}$ be Boolean algebras and ${e: \mathbb{B}\rightarrow \mathbb{C}}$ an embedding. We examine the hierarchy of ideals on ${\mathbb{C}}$ for which ${ \bar{e}: \mathbb{B}\rightarrow \mathbb{C} / \fancyscript{I}}$ is a regular (i.e. complete) embedding. As an application we deal with the interrelationship between ${\fancyscript{P}(\omega)/{{\rm fin}}}$ in the ground model and in its extension. If M is an extension of V containing a new subset of ω, then in M there is an almost disjoint refinement of the family (...) ([ω]ω) V . Moreover, there is, in M, exactly one ideal ${\fancyscript{I}}$ on ω such that ${(\fancyscript{P}(\omega)/{{\rm fin}})^V}$ is a dense subalgebra of ${(\fancyscript{P}(\omega)/\fancyscript{I})^M}$ if and only if M does not contain an independent (splitting) real. We show that for a generic extension V[G], the canonical embedding $$\fancyscript{P}^V(\omega){/}{\rm fin}\hookrightarrow \fancyscript{P}(\omega){/}(U(Os)(\mathbb{B}))^G$$ is a regular one, where ${U(Os)(\mathbb{B})}$ is the Urysohn closure of the zero-convergence structure on ${\mathbb{B}}$. (shrink)

A variety V of Boolean algebras with operators is singleton-persistent if it contains a complex algebra whenever it contains the subalgebra generated by the singletons. V is atom-canonical if it contains the complex algebra of the atom structure of any of the atomic members of V.This paper explores relationships between these "persistence" properties and questions of whether V is generated by its complex algebras or its atomic members, or is closed under canonical embedding algebras or completions. It (...) also develops a general theory of when operations involving complex algebras lead to the construction of elementary classes of relational structures. (shrink)

We prove, by using the concept of schematic interpretation, that the natural embedding from the category ISL, of intuitionistic sentential pretheories and i-congruence classes of morphisms, to the category CSL, of classical sentential pretheories and c-congruence classes of morphisms, has a left adjoint, which is related to the double negation interpretation of Gödel-Gentzen, and a right adjoint, which is related to the Law of Excluded Middle. Moreover, we prove that from the left to the right adjoint there is a (...) pointwise epimorphic natural transformation and that since the two endofunctors at CSL, obtained by adequately composing the aforementioned functors, are naturally isomorphic to the identity functor for CSL, the string of adjunctions constitutes an adjoint cylinder. On the other hand, we show that the operators of Lindenbaum-Tarski of formation of algebras from pretheories can be extended to equivalences of categories from the category CSL, respectively, ISL, to the category Bool, of Boolean algebras, respectively, Heyt, of Heyting algebras. Finally, we prove that the functor of regularization from Heyt to Bool has, in addition to its well-known right adjoint (that is, the canonical embedding of Bool into Heyt) a left adjoint, that from the left to the right adjoint there is a pointwise epimorphic natural transformation, and, finally, that such a string of adjunctions constitutes an adjoint cylinder. (shrink)

For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical (...) class='Hi'>embedding algebras. Taken together, these properties imply that results about a Sahlqvist variety V van be obtained by reasoning in the elementary class of canonical structures of algebras in V.We give an example of this strategy in the variety of Cylindric Algebras: we show that an important identity calledHenkin's equation is equivalent to a simpler identity that uses only one variable. We give a conceptually simple proof by showing that the first-order correspondents of these two equations are equivalent over the class of cylindric atom structures. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. Motivated by results of Bagaria, Magidor and Väänänen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifically, we aim to characterize notions from the lower end of the large cardinal hierarchy through the principle [math] introduced by Bagaria and Väänänen. Our results isolate a narrow interval in the large cardinal hierarchy that is bounded from below by total indescribability and from above by subtleness, (...) and contains all large cardinals that can be characterized through the validity of the principle [math] for all classes of structures defined by formulas in a fixed level of the Lévy hierarchy. Moreover, it turns out that no property that can be characterized through this principle can provably imply strong inaccessibility. The proofs of these results rely heavily on the notion of shrewd cardinals, introduced by Rathjen in a proof-theoretic context, and embedding characterizations of these cardinals that resembles Magidor’s classical characterization of supercompactness. In addition, we show that several important weak large cardinal properties, like weak inaccessibility, weak Mahloness or weak [math]-indescribability, can be canonically characterized through localized versions of the principle [math]. Finally, the techniques developed in the proofs of these characterizations also allow us to show that Hamkin’s weakly compact embedding property is equivalent to Lévy’s notion of weak [math]-indescribability. (shrink)

In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the (...) class='Hi'>canonical extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in [FIT 92a]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. (shrink)

Every second-countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space can be considered computationally as a subspace of some computable metric space [15]. While Schröder's construction is “pointless”, i. e., only sets of a countable base but no concrete points are known, for a computable metric space a concrete dense set of computable points (...) is needed. But there may be no computable points in X. By converging sequences of basis sets instead of Cauchy sequences of points we construct a metric completion of a space together with a canonical representation equation image, equation image. We show that there is a computable embedding of in with computable inverse. Finally, we construct a notation of a dense set of points in with computable mutual distances and prove that the Cauchy representation of the resulting computable metric space is equivalent to equation image. Therefore, every computably regular space has a computable homeomorphic embedding in a computable metric space, which topologically is its completion. By the way we prove a computable Urysohn lemma. (shrink)

The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math.38(1) (1971) 69–83] and denoted H3, is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.I, eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in work (...) of Sauer [Coloring subgraphs of the Rado graph, Combinatorica26(2) (2006) 231–253] and Laflamme–Sauer–Vuksanovic [Canonical partitions of universal structures, Combinatorica26(2) (2006) 183–205], the Ramsey theory of H3 had only progressed to bounds for vertex colorings [P. Komjáth and V. Rödl, Coloring of universal graphs, Graphs Combin.2(1) (1986) 55–60] and edge colorings [N. Sauer, Edge partitions of the countable triangle free homogenous graph, Discrete Math.185(1–3) (1998) 137–181]. This was due to a lack of broadscale techniques. We solve this problem in general: For each finite triangle-free graph G, there is a finite number T(G) such that for any coloring of all copies of G in H3 into finitely many colors, there is a subgraph of H3 which is again universal homogeneous triangle-free in which the coloring takes no more than T(G) colors. This is the first such result for a homogeneous structure omitting copies of some nontrivial finite structure. The proof entails developments of new broadscale techniques, including a flexible method for constructing trees which code H3 and the development of their Ramsey theory. (shrink)

We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.

In this paper I present both a critical appraisal of Humphreys' probabilistic theory of causality and a sketch of an alternative view of the relationship between the notions of probability and of cause. Though I do not doubt that determinism is false, I claim that the examples used to motivate Humphreys' theory typically refer to subjective rather than objective chance. Additionally, I argue on a number of grounds that Humphreys' suggestion that linear regression models be used as a canonical (...) form for the description of causal relations is untenable. I conclude by exploring the variety of ways in which probabilistic elements can be embedded into the structure of causal mechanisms. This investigation suggests both that deterministic mechanisms can produce stochastic behavior and stochastic mechanisms can produce deterministic behavior. Note: Link is to the article in a subscription database available to users affiliated with Butler University. Appropriate login information will be required for access. Users not affiliated with Butler University should contact their local librarian for assistance in locating a copy of this article. (shrink)

The general purposes of this essay are as follows: First, to outline an ecological model of autobiographical remembering by examining the purposes, processes, and products of reconstructing meaningful memories. Second, to argue that autobiographical remembering is embedded in affective, interpersonal, sociocultural, and historical contexts. Improvised selves are created in present contexts to serve psychosocial, cultural, and historical purposes, and third, to demonstrate essential constraints on the construction of coherent personal narratives that give meaning and purpose to our everyday lives. -/- (...) The specific aim of this essay is to illustrate that the subjective experiences of trauma and atrocity often lack the essential narrative elements needed to give coherence to those experiences as well as affectively grounded evaluative information. Evaluations of experiences give meaning to our lives. Evaluative information leads to culturally recognized coherent stories structured by known canonical narrative forms because affect conveys how subjective experiences should be interpreted and understood. On this view, autobiographical memories that are the essence of one's personal history can appear as coherent or incoherent to others to the extent others are familiar with the narrative structure used to reconstruct the past and the coherence inherent in autobiographical memories associated with the temporal and evaluative structure of those recollections. -/- I claim that autobiographical experiences that cannot be reconstructed and shared through spoken or written language, music, movement (e.g., dance), art, literature, or science precipitate feelings of existential stress because articulated deep motivations cannot be related intimately to others. (shrink)

Versions of Laver sequences are known to exist for supercompact and strong cardinals. Assuming very strong axioms of infinity, Laver sequences can be constructed for virtually any globally defined large cardinal not weaker than a strong cardinal; indeed, under strong hypotheses, Laver sequences can be constructed for virtually any regular class of embeddings. We show here that if there is a regular class of embeddings with critical point κ, and there is an inaccessible above κ, then it is consistent for (...) there to be a regular class that admits no Laver sequence. We also show that extendible cardinals are Laver-generating, i.e., that assuming only that κ is extendible, there is an extendible Laver sequence at κ. We use the method of proof to answer a question about Laver-closure of extendible cardinals at inaccessibles. Finally, we consider Laver sequences for super-almost-huge cardinals. Assuming slightly more than super-almost-hugeness, we show that there are super-almost-huge Laver sequences, improving the previously known upper bound for such Laver sequences. We also describe conditions under which the canonical construction of a Laver sequence fails for super-almost-huge cardinals. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Lost Italian Renaissance: Humanists, Historians, and Latin’s LegacyPaul Richard BlumChristopher S. Celenza. The Lost Italian Renaissance: Humanists, Historians, and Latin’s Legacy. Baltimore: The Johns Hopkins University Press, 2004. Pp. xx + 210. Cloth, $45.00This is a programmatic book about why and how philosophy should care about Renaissance texts. Celenza starts with an assessment of the neglect of the wealth of Latin Renaissance [End Page 485] sources by (...) nineteenth-century historiography, followed by portraits of two prototypal twentieth-century historians and their philosophical approach. He proposes a method of study for Renaissance thinkers and exemplifies it with two key figures and with the concept of honor. A survey of the field of study and an appendix concerning Renaissance research in the US conclude the book."The Renaissance" as a field of research between the Middle Ages and what is now cowardly called "Early Modern" became legitimate through the awakening of national consciousness in the nineteenth century. Consequently, the emphasis lay on vernacular language works in Italy and elsewhere. Latin Renaissance literature never was worthy of Grossforschung, i.e., of national projects like the academy enterprises concerning world history or classical studies, even though classical philology originated in the humanists' emulation of the ancients. This however would be absorbed by the nineteenth-century idea of national character (12).Italian Hegelianism of the nineteenth and early-twentieth century included Renaissance philosophy in the evolution of national spirit, and the late Eugenio Garin as its pupil spent his scholarly life portraying with astounding precision and detail Italian Humanism and Renaissance as a dialectic and rational development. Equally diligent was the German born Paul Oskar Kristeller, clinging, however, to a very different understanding of philosophy, which Celenza describes as rationalist in the Kantian and metaphysical in the Platonico-Aristotelian tradition (41). Here the author underestimates the influence of Heidegger on Kristeller: his dissertation was clearly an interpretation of Plotinus in the light of existentialism, which still transpires in his famous Ficino book and many later philosophical statements. The problem with both approaches, that of Garin and that of Kristeller, is that those philosophers who ignore history (deliberately or incidentally) and those who lost an understanding of metaphysics do not know how to read Renaissance thinkers.'Microhistory' is the formula Celenza proposes: Richard Rorty's abolishing the notion of 'representing' reality in favor of evocation and conversation—both for the interpretation of the past and the past itself—and Pierre Bourdieux's notions of 'field' and 'relational thinking' open the possibility of locating past thinkers in their community and, consequently, the meaning of their philosophical endeavor. What Celenza exercised with Garin and Kristeller applies also to Renaissance authors. Under the heading 'Orthodoxy,' Celenza shows that it is unfortunate to censure Lorenzo Valla (+ 1457) or Marsilio Ficino (+ 1499) as being unorthodox or as precursors to the Reformation, because this perspective misses the point of their lives' work—namely, to find out what makes Christian beliefs and their sources Christian. Valla's discoveries in Greek and Latin philology and Ficino's experiments with magic are part of their scrutiny of orthopraxy (my term), the right way of Christian life, and are embedded in their conversations with friend and foe, who in some cases still await discovery. The far-reaching message of these two samples is: reading their work and studying their conversations is the way to study philosophy in the fifteenth century.The same is proven by engaging in social concepts such as 'honor.' Starting with a surprising appreciation of gender studies, Celenza suggests taking a look at intellectual masculinity among courtiers and writers. Then it turns out that Machiavelli bequeathed to modernity—perhaps as a caricature—the structure of struggle for power, ideas, and provision in which humanists were engaged, being the first large generation of intellectuals outside the safe haven of cathedrals and convents."What is really there?" is the concluding question. A new canon, the prelude to early modern sociology of scholarship, and models of—presently highly acclaimed—contextualization of intellectual productivity. Returning to the Latinity of Renaissance sources Celenza shows that even the emergence of vernacular literature, which bewitched nationalist historiography, was by itself a fruit... (shrink)

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory that distinguishes between ordinary and abstract objects. This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex (...) terms is simply adjoined to AOT’s specially formulated comprehension principle for relations. This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. Its discovery is the highlight of our joint project and provides strong evidence for a new kind of scientific practice in philosophy, namely, computational metaphysics. Our results were made technically possible by a suitable adaptation of Benzmüller’s metalogical approach to universal reasoning by semantically embedding theories in classical higher-order logic. This approach enables one to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT. Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics. (shrink)

This paper reformulates some of the questions raised by extended mind theorists from an enactive, life/mind continuity perspective. Because of its reliance on concepts such as autopoiesis, the enactive approach has been deemed internalist and thus incompatible with the extended mind hypothesis. This paper answers this criticism by showing (1) that the relation between organism and cogniser is not one of co-extension, (2) that cognition is a relational phenomenon and thereby has no location, and (3) that the individuality of a (...) cogniser is inevitably linked with the question of its autonomy, a question ignored by the extended mind hypothesis but for which the enactive approach proposes a precise, operational, albeit non-functionalist answer. The paper raises a pespective of embedded and intersecting forms of autonomous identity generation, some of which correspond to the canonical cases discussed in the extended mind literature, but on the whole of wider generality. In addressing these issues, this paper proposes unbiased, non-species specific definitions of cognition, agency and mediation, thus filling in gaps in the extended mind debates that have led to paradoxical situations and a problematic over-reliance on intutions about what counts as cognitive. (shrink)

Burke proved that the generalized nonstationary ideal, denoted by NS, is universal in the following sense: every normal ideal, and every tower of normal ideals of inaccessible height, is a canonical Rudin‐Keisler projection of the restriction of NS to some stationary set. We investigate how far Burke's theorem can be pushed, by analyzing the universality properties of NS with respect to the wider class of ‐systems of filters introduced by Audrito and Steila. First we answer a question of Audrito (...) and Steila, by proving that ‐systems of filters do not capture all kinds of set‐generic embeddings. We provide a characterization of supercompactness in terms of short extenders and canonical projections of NS, without any reference to the strength of the extenders; as a corollary, NS can consistently fail to canonically project to arbitrarily strong short extenders. We prove that ω‐cofinal towers of normal ultrafilters, e.g., the kind used to characterize I2 and I3 embeddings, are well‐founded if and only if they are canonical projections of NS. Finally, we provide a characterization of “ is Jónsson” in terms of canonical projections of NS. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Russell's Naturalistic Turn 37 INTRODUCTION L RUSSELL'S NATURALISTIC TURN RUSSELI.?S NATURALISTIC TURN NED S. GARVIN Philosophy I Albion College Albion, MI 49224 I Quine, Ontological Relativity (New York: Columbia U. P., 1969), p. 83. 1 Russell advocated this hypothetical acceptance of science much earlier, e.g., in AMa, pp. 398-9. Here we have many of the hallmarks of naturalized epistemology: (I) fallibilism, (2) the "best theory" account of science, (3) (...) the view that "knowing" is a natural phenomenon not confined to humans, and (4) the embedding of epistemology in behavioural psychology. But in 1940 Russell was a foundationalist (though an increasingly moderate one) who insisted that normative, or as he called it, "critical" epistemology must be distinguished from natural epistemology, and that critical epistemology is philosophically more important: "Within its limitations, theory of knowledge of the above sort is legitimate and In the nrst form of theory of knowledge, we accept the scientific account of the world, not as certainly true, but as the best at present available. The world, as presented by science, contains a phenomenon caIled "knowing", and theory of knowledge, in its first form, has to consider what sort of phenomenon this is. Viewed from the outside, it is, to begin with, a characteristic of living organisms, which is (broadly speaking) increasingly displayed as the organism becomes more complex. (Pp. 12-13)2 Both knowledge and error, at this stage, are observable relations between the behaviour of the organism and the facts of the environment. (P. 14) Quine argued that traditional justification requires non-scientific propositions that are more secure than scientific propositions, and we see there are none: science is providing the best account of the world and our knowledge of it. Though we abandon the attempt to justify science, we still attempt to understand it for nearly the same reasons that always motivated epistemology: "in order to see how evidence relates to theory, and in what ways one's theory of nature transcends any available evidence".I Russell contemplated a naturalistic turn of his own in 1943, shortly after writing An Inquiry into Meaning and Truth and nearly twentyfive years before Quine's landmark address. In the introduction to his Inquiry Russell claims that there are "two different inquiries, both important, and each having a right to the name 'theory of knowledge '" (IM~, p. 12). The first is recognizably natural epistemology: n.s. 11 (summer 1991): 36-S1.SSN 0036-016p ru•••II: the Journal of the Bertrand Russell Archives McMaster University Library Press w. V. Quine's address to the Fourteenth International Congress of Philosophy in 1968, published a year later as "Epistemology Naturalized " in Ontological Relativity and Other Essays, is a landmark of recent epistemology, marking the turn from traditional critical epistemology to a descriptive epistemology firmly embedded within natural science. I n 1943 Bertrand Russell wrote a little-known, three-page document he titled "Project of Future Work". It outlines the descriptive project of examining non-demonstrative inference that eventually becomes the focal point of Human Knowledge: Its Scope and Limits. More remarkably, this document anticipates many salient features of naturalized epistemology, e.g., Russell argues that (I) an answer to scepticism is futile, we cannot justify scientific method; (2) the Humean Predicament arises from a traditional insistence on an unrealistic, demonstrative canon of justification; (3) non-demonstrative, fallible inference is already firmly embedded in scientific practice as a canon of inference, and should augment the demonstrative canon; and (4) the primary epistemic· problem is descriptive: in what circumstances does scientific method allow us to infer the existence of something unobserved from what we observe. These claims, in the wake of An Inquiry into Meaning and Truth, suggest that Russell was on the verge of his own naturalistic turn. I argue that, despite striking anticipations of naturalized epistemology, Russell develops his descriptive project within a more traditional, critical epistemic perspective. 38 NED S. GARVIN important. But there is another kind of theory of knowledge which goes deeper and has, I think, much greater importance" (IMT;., p. 14). Russell observes that behavioural psychologists omit that they are fallible observers, and this fallibility introduces doubt into their results. Further, naive... (shrink)

The quantization of gravity represents an important attempt at reconciling the two seemingly incompatible frameworks that lie at the base of modern physics, quantum theory and general relativity. The dissertation begins by looking at the incompatibilities between the two frameworks. The incompatibility with quantum theory, it is argued, is rooted in the profound differences between general relativity and ordinary field theories. The dissertation goes on to look at how, in practice, these incongruities are treated in the canonical quantization program, (...) and argues that their treatment is such that it is unlikely to lead to a satisfactory physical theory. The dissertation concludes by arguing that quantum theory only makes sense when embedded in a classical theory. Thus the reconciliation of quantum theory and general relativity suggests that we look outside the bounds of ordinary quantum theory for the proper theoretical framework. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Cross-Cultural Encounters and ExclusionEun-Jeung Lee (bio)There are only a handful of comprehensive studies about the role that knowledge of non-European civilizations and ideas played in the formation of early modern and Enlightenment European thought. Any in-depth treatment of how European thinkers understood China and India between 1600 and 1744 is therefore a more than welcome addition to existing research in this area. During this period, new information about Chinese (...) Confucian culture reached Europe through reports and writings of Jesuit missionaries. It was also during this time that Chinese and Indian ideas started to be excluded from the category of world philosophy.Early modern European thinkers who came into contact with reports about non-European cultures, such as China and India, embraced, rejected, or criticized the transmitted ideas in relation to their own system of thinking. In that sense, European thinkers were not much different from those East Asian scholars who in the seventeenth century first encountered translated Western books and books on the West written in classical Chinese, for [End Page 215] example the Korean literati of the Chosŏn dynasty. These scholars, in a fashion strikingly similar to how their contemporary European thinkers dealt with Chinese Confucian culture, accepted, rejected, or criticized Western knowledge based on their own canon of thought.1 This process can be said to be a ubiquitous response to such cross-cultural encounters. Today, it is generally accepted that it is through such reactions that we can understand the spiritual and social conditions of a society.2 The way European thinkers discussed Chinese or Indian thought throughout the seventeenth and eighteenth centuries allows important insights into Western thought at the time, but not so much that of China or India.The eventual exclusion of Chinese and Indian thought from "world philosophy" in the eighteenth century, scholars agree, had its roots in the belief of the superiority of European civilization. "Histories of world philosophy" became mainstream in the latter half of the eighteenth century, forming the global standard for a very long time due to the effects of European imperialism and European intellectual hegemony. Current debates on the decolonization of philosophy recognize the importance of how to approach depictions of the history of philosophy from a practical and global perspective.3 A critical and systematic study of the process of exclusion of non-European cultures from histories of philosophy compiled in Europe are therefore crucial to such discussions. Selusi Ambrogio's study forms an important contribution to this area of inquiry.Chinese and Indian Ways of Thinking in Early Modern European Philosophy spans the seventeenth and early eighteenth centuries, when the arrival of information about the history and culture of China in Jesuit treatises and reports came as a great shock to European philosophers. Especially Chinese history and its ancient tradition of written culture, much older than Christian historiography, became the focus of interest in European intellectual circles. It is no coincidence that Descartes, widely considered the founder of modern philosophy, in his Discours de la méthode mentions China as a prime reason for the existence of a new uncertainty in European philosophy.4In his book, Ambrogio systematically shows how the philosophical dispute over the evaluation of Chinese philosophy was embedded within a paradigm shift from the older Philosophia perennis to the newer Philosophia sectaria and eclectica. This shift not only shaped the scientification of the history of philosophy in the eighteenth century, but also redefined European conceptions of time and history. In the debates about the correct paradigm for the history of philosophy, Confucian philosophy, as transmitted by the Jesuits, played a key role due to the long tradition of its canonical texts.Ambrogio summarizes how histories of philosophy written in Europe first included China but subsequently began a process of exclusion of Chinese thought. He does this by placing a special focus on the tension between theology and philosophy before the time of Hegel. In the first chapter, [End Page 216] Ambrogio shows how the Chinese were seen "as contemporaries" but, at the same time, "as ancient barbaric peoples inserted within the biblical history of philosophy" (p. 56). The second chapter deals with discussions that define... (shrink)

RESUMEN Partiendo de la exposición que el propio Giorgio Agamben hace de sus intenciones teóricas y prácticas al inicio de Homo sacer I, así como del método con el que pretende afrontarlas, este ensayo muestra, mediante un análisis pormenorizado de dicho método, algunos de los límites del proyecto. Esta tarea crítica negativa se ve complementada con 1) una defensa de algunos de los gestos teóricos agambeanos frente a una cierta recepción de sus ideas sobre la "nuda vida", y 2) la (...) propuesta metodológica de una "precaución etnográfica" que posibilitase un saneamiento del proyecto y una superación de los límites descubiertos. Tales cuestiones se enmarcarían en una indagación en torno a la interdisciplinariedad y el canon y la esencia de la filosofía crítica. ABSTRACT Starting from the exposition provided by Giorgio Agamben himself of his theoretical and practical intentions at the beginning of Homo sacer I and from the method with which he intends to face them, this essay shows, through a detailed analysis of that method, some of the limits of the project. This negative critical task is complemented by 1) a defense of some of Agamben's theoretical gestures against a certain reception of his ideas about "bare life", and 2) the methodological proposal of an "ethnographic precaution" that would permit to sanitize the project and to overcome the discovered limits. Such questions would be embedded in an inquiry about interdisciplinarity and the canon and essence of critical philosophy. (shrink)

The author suggests that law is best represented, understood, and taught in the form of open‐ended, defeasible, normative, conditional propositions. The meaning, role, and significance of defeasibility is explained by presenting three ‘canonical forms’ and by distinguishing exceptions and overrides. The role of equity in the law of contract, as understood by the author, is taken as an exemplar of override and parallels are drawn with policy in the English law of tort and with mercy in the criminal law (...) of England and Wales. The third and preferred canonical form is sequenced and internally differentiated and seeks a satisfactory middle way between all‐or‐nothing rules and wild‐card discretion and a reconciliation of the surface demands of legal rules and the deeper values embedded in law. The suggested approach therefore resists closure and seeks a conceptual restructuring of law which opens it up to the influence of notions such as justice and equity and locates them as open‐ended conditions of defeasance inhabiting the express or implied ‘unless…’ clause which is taken to be an element in every fully‐formed statement of law. This approach accommodates law as a locus not only of traditional rule‐based reasoning, but also of open‐ended internal moral reasoning invoking deeper values inherent in law and only imperfectly captured and implemented by formal legal rules. (shrink)

Birth, suffering, disability, disease and death were by medicine's successes placed within a context of seemingly novel challenges that cried out for new responses. Secular bioethics rose in response to the demands of these new biomedical technologies in the context of a culture fragmented in moral pluralism. While secular bioethics promised to unite persons separated by diverse religious and moral assumption, this is a promise that could not be fulfilled. Reason alone cannot provide canonical, content-full moral guidance or justify (...) a moral community capable of binding all persons. Christian bioethics, as part of a way of life embedded in authentic worship, offers content, meaning and understanding where secular bioethics has failed. For Christians, resolution of bioethical controversies will not be found through appeals to foundational rational arguments or isolated scriptural quotations, but only in a Christian community united in authentic faith. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Style: A Queer Cosmology by S. Taylor BlackJoe Edward HatfieldStyle: A Queer Cosmology. By Taylor Black. New York: New York University Press, 2023. 304 pp. Hardcover $99.00, paper $35.00. ISBN- 10: 147982500X.Style is a perennial concern within rhetorical studies. As one of Aristotle's five canons, style has inspired a great deal of rhetorical theory over the past two millennia and counting. Hence, it would be reasonable to presume (...) that there is not much, if anything, else original to contribute to the well-trodden domain of the stylistic. However, Taylor Black's Style: A Queer Cosmology challenges this assumption by offering a fresh take on its titular concept. The book's grounding in the interdisciplinary field of American Studies allows its author to speak to multiple audiences at once, including those invested in queer theory, race and ethnicity, popular culture, new materialism, and literary criticism. To this inventory, I would add anyone interested in the art of rhetoric, particularly those committed to incorporating new, diverse perspectives into the field's existing analytical tool chest. Tonally whimsical but nonetheless boldly argued, Style dramatically reframes a timeworn concept in the rhetorical lexicon that many of us have likely—and mistakenly—come to take for granted.Readers of this journal will be immediately seduced by Black's provocative rethinking of style as elemental. Here, the term "elemental" directs attention toward style as "the rudimentary source of difference that distinguishes one thing from another, something perhaps, more closely aligned with myth than fact: an immaterial force or energy, perhaps supernatural in essence, that imbues everything under the sun" (5). As Black infers throughout the book's introduction, style is the expression of difference available to all human and nonhuman beings. More than aesthetic ornamentation, or the mere ability to make oneself appear outwardly beautiful, style is a mysterious yet universal condition of possibility underlying the cultivation [End Page 226] of a personality. Style names the intertwined processes of self-fashioning and self-discovery that produce individuation as its outcome. And though everyone "has" a style, Black asserts, "not everyone is a stylist" (15). Black posits the figure of the stylist to denote a minoritarian subject who transmutes the experience of oppression into a purposeful performance of self. Upon realizing their exclusion from a majoritarian social order organized by deeply embedded attachments to a hierarchy of difference that discriminates on bases of race, gender, sexuality, class, and other intersecting codes of identification, stylists turn their failure to conform into an opportunity for opening possibilities for alternative futures.In other words, from the limitations that accompany experiences of structural oppression, style authorizes potential. Referencing Zora Neale Hurston's 1928 essay "How It Feels to Be Colored Me," Black suggests stylists tend to dwell in cosmology, a form of storytelling or narrative fabulation about the universe's origins and one's place in its ongoing unfolding. "Stylists," Black poetically avers, are "naturally drawn to understanding the universe better by virtue of developing a more and more acute consciousness of who and what they are and how they came to be" (20). Black highlights style's fundamental elementality as emerging from cosmic renderings of marginalized experience and the pursuit of a future otherwise. To further illustrate this elemental notion of the stylistic, Black assembles an eclectic corpus of texts by those he calls "subterranean American stylists" (5), namely Quentin Crisp, Bob Dylan, Toni Morrison, Flannery O'Connor, and Edgar Allan Poe, among others, whose lives and work he examines over seven chapters divided into three main parts. Each chapter supplies unique insights on the elementals of style, as well as its subject matter, thus allowing Black to support the thesis constructed in the introduction without ever seeming overly redundant.The first part of Style, "The Mystery of Personality: Queerness as Style," consists of a preface and two chapters oriented around the specific ways stylizations of queer selfhood may function as a survival strategy and, relatedly, a means for exploring elemental mysteries of personality and being. In the initial chapter, Black analyzes texts authored by openly gay memoirist and cultural commentor Quentin Crisp, who became famous for his humorous and often brash... (shrink)

Edward W. Said’s Orientalism has attained canonical status as the key study of the cultural politics of western representation of the East, specifically the imaginative geographies underwriting constructions such as the Middle East and the Islamic world. The Ottoman Empire overlapped both European and exteriorized Oriental space during much of the period that Said dealt with, yet while the existence of the empire is referred to in Said’s study, the theoretical implications of that presence for his critique of Orientalist (...) discourse are not. The material presence of the Ottoman state, in the Arabic-speaking lands, but also crucially, and for a longer period, much of south-east Europe and Anatolia, highlights long-standing Oriental geopolitical and cultural agency in the face of unidirectional narratives of western encroachment. Attention to the specific discursive manoeuvres undertaken by the West to handle that disruptive, intrinsic Ottoman presence in Europe itself may add traction to the notion that the Orient was imagined as a radically exterior point of comparison. It is argued that the history of western representation of the Ottoman Empire constitutes a pre-Orientalist discourse, whose dual, perennial purpose is to make pragmatic accommodation for an Ottoman Oriental material presence in Europe yet never to fully acknowledge its discursive presence as being of Europe. I argue that by supplementing Said’s critique with a full consideration of the Ottoman legacy, a reformulation is possible that integrates the Islamic Orient as an intrinsic component of historically informed notions of European space, while dissolving notions of the absolute distinction of that latter construct from the wider milieus in which it is embedded. (shrink)

The new concept of lambda calculi with monotone inductive types is introduced byhelp of motivations drawn from Tarski's fixed-point theorem (in preorder theory) andinitial algebras and initial recursive algebras from category theory. They are intendedto serve as formalisms for studying iteration and primitive recursion ongeneral inductively given structures. Special accent is put on the behaviour ofthe rewrite rules motivated by the categorical approach, most notably on thequestion of strong normalization (i.e., the impossibility of an infinitesequence of successive rewrite steps). It (...) is shown that this key propertyhinges on the concrete formulation. The canonical system of monotone inductivetypes, where monotonicity is expressed by a monotonicity witness beinga term expressing monotonicity through its type, enjoys strong normalizationshown by an embedding into the traditional system of non-interleavingpositive inductive types which, however, has to be enriched by the parametricpolymorphism of system F. Restrictions to iteration on monotone inductive typesalready embed into system F alone, hence clearly displaying the differencebetween iteration and primitive recursion with respect to algorithms despitethe fact that, classically, recursion is only a concept derived from iteration. (shrink)

Mill's famous proportionality statement of the Greatest Happiness Principle (GHP) is commonly taken to specify his own moral theory. And the discussion in which GHP is embedded -- Chapter 2 of Utilitarianism -- predominates the interpretation of Mill's normative philosophy. Largely because of these suppositions, Mill is traditionally read as a particular kind of utilitarian: a maximizing act-consequentialist. This paper argues that the canonical status accorded to Utilitarianism is belied by the text itself, as well as by its historical (...) context, and that this point largely undermines the orthodox interpretation of Mill. In fact, GHP was intended as the statement of a common creed, acceptable to the diverse class of philosophers Mill counted as utilitarian. Moreover, the discussion of substantive moral theory in Utilitarianism in several respects does not reflect his own view, and the work itself is much less important than it is almost universally taken to be -- though not, it turns out, by Mill himself. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 121-122 [Access article in PDF] Harold Tarrant. Plato's First Interpreters. Ithaca, NY: Cornell University Press, 2000. Pp. viii + 263. Cloth, $55.00. This is Tarrant's third book on the ancient Platonist tradition, following his Scepticism or Platonism? (1985) and Thrasyllan Platonism (1993). In those earlier volumes his focus was on the first centuries bc and ad. Here his scope is much (...) wider. Stating that "Platonic interpretation is today at a crossroads," he has written a book that explores "ancient attempts to wrestle with this corpus," with the ultimate objective "to encourage a fresh, almost primitive reading of Plato himself" (vii).He begins engagingly by confronting the ancients with questions any modern reader of Plato must ask: What kind of text is this? Are there doctrines here? Where do I look for Plato's doctrines? The second part of his book is a historical survey, taking us from Plato, the early Academy and Aristotle, through the Hellenistic and early Roman Imperial period, and concluding with the principal Neoplatonist interpreters. In the third and longest part, he focuses on the interpretation of specific dialogues, giving most space to the Gorgias and Theaetetus, but also dealing in particular detail with the Meno, Parmenides, and Philebus. Something is said about every dialogue, but Tarrant writes only briefly about such major works as the Republic and Timaeus. He explains his selectivity (not very convincingly) as due to his wish to "discuss issues of meta-interpretation, with emphasis on the period before Plotinus" (198).Taking his book as a whole, one realizes that few strands of modern interpretation were not prefigured to quite a large extent in antiquity. The two most obvious exceptions are the chronological and developmental approach (Early, Middle, and Late), at present under strong attack from some quarters, and the theological, numerological, and allegorical readings practiced by Neoplatonists. Plato's ancient interpreters were doctrinal unitarians, but they implicitly anticipated our tendency to distinguish "Socratic dialogues," which some of them called "gymnastic" and "inquisitive," from such "canonical" works as the Phaedo,Republic, Symposium, and Timaeus, to which they applied the labels "dogmatic" and "expository." And they recognized that both types of characteristics could be found in the same dialogue, as in the Meno and Theaetetus. Plato himself, they proposed, spoke primarily through the voices of Socrates, Timaeus, and the Eleatic and Athenian strangers; but other characters, such as Pausanias in the Symposium, or Protagoras in the dialogue of that name, utter thoughts with some philosophical value. In explaining difficult passages of one dialogue, they would typically refer to passages from other parts of the corpus. An especially intriguing instance is the strategy of the Anonymous Commentator on the Theaetetus, who reads the Meno into the dialogue on which he is officially commenting.Ancient scholars, just like ourselves, asked questions about the unifying themes of complex dialogues. Hence the sub-titles given to certain works: "On the soul" for the Phaedo, and "On justice" for the Republic, etc. For Olympiodorus (whose commentary on the Gorgias Tarrant has recently co-edited [Leiden, 1998]), earlier interpreters have seriously erred by giving too limited an account of that dialogue's scope. It is not, he says, simply about rhetoric, nor about justice and injustice; nor is its theme the divine demiurge (as some Neoplatonists had strangely proposed, on the basis of the concluding myth). Rather, the subject of the Gorgias is "the ethical principles that lead to constitutional well-being" (125). [End Page 121] However, Olympiodorus's eminently "sensible" reading (as Tarrant calls it) is deeply embedded in the Neoplatonic contrast between the "purificatory virtues" of the Phaedo and the "constitutional virtues" of Republic4.Strong or weak scepticism, esotericism, unwritten doctrines, spurious versus genuine, a canon of central dialogues, dramatic considerations, and the philosophical importance or non-importance of the dialogues' prologues—all of these are interpretive approaches that Tarrant surveys in this immensely learned book, and all of them continue to resonate for us. Modern scholars, who emphasize the literary and philosophical unity of each dialogue, are walking... (shrink)

A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on (...) HA op fp can be derived from that of Sh(P 0 ,J 0 ) via the embedding Φ. We also show that the equivalence relations in HA op fp are not effective in general. On the way to these results we establish a new kind of duality between HA op fp and a category of sheaves equipped with certain structure defined in terms of Ehrenfeucht games. Our methods are model-theoretic and combinatorial as opposed to proof-theoretic as in [Pi]. (shrink)

In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. Attention to the gauge generator G of Rosenfeld, Anderson, Bergmann, Castellani et al., a specially _tuned sum_ of first-class constraints, facilitates seeing that a solitary first-class constraint in fact generates not a gauge transformation, but a bad physical change in electromagnetism or (...) General Relativity. The change spoils the Lagrangian constraints, Gauss's law or the Gauss-Codazzi relations describing embedding of space into space-time, in terms of the physically relevant velocities rather than auxiliary canonical momenta. But the resemblance between the gauge generator G and the Hamiltonian H leaves still unclear where objective change is in GR. Insistence on Hamiltonian-Lagrangian equivalence, a theme emphasized by Castellani, Sugano, Pons, Salisbury, Shepley and Sundermeyer among others, holds the key. Taking objective change to be ineliminable time dependence, one recalls that there is change in vacuum GR just in case there is no time-like vector field xi^a satisfying Killing's equation L_xi g_mn=0, because then there exists no coordinate system such that everything is independent of time. Throwing away the spatial dependence of GR for convenience, one finds explicitly that the time evolution from Hamilton's equations is real change just when there is no time-like Killing vector. The inclusion of a massive scalar field is simple. No obstruction is expected in including spatial dependence and coupling more general matter fields. Hence change is real and local even in the Hamiltonian formalism. The considerations here resolve the Earman-Maudlin standoff over change in Hamiltonian General Relativity: the Hamiltonian formalism is helpful, and, suitably reformed, it does not have absurd consequences for change and observables. Hence the classical problem of time is resolved. The Lagrangian-equivalent Hamiltonian analysis of change in General Relativity is compared to Belot and Earman's treatment. The more serious quantum problem of time, however, is not automatically resolved due to issues of quantum constraint imposition. (shrink)

"There is always an atheism to be extracted from a religion," Deleuze and Guattari write in their final collaboration, What Is Philosophy? Their claim that Christianity "secretes" atheism "more than any other religion," however, reflects the limits of their archive. Theological projects seeking to engage Deleuze remain embedded within Christian theologies and intellectual histories; whether they embrace, resist, or negotiate with Deleuze's atheism, the atheism in question remains one extracted from Christian theology, a Christian atheism. In Sufi Deleuze, Michael Muhammad (...) Knight offers an intervention, engaging Deleuzian questions and themes from within Islamic tradition. Even if Deleuze did not think of himself as a theologian, Knight argues, to place Deleuze in conversation with Islam is a project of comparative theology and faces the challenge of any comparative theology: It seemingly demands that complex, internally diverse traditions can speak as coherent, monolithic wholes. To start from such a place would not only defy Islam's historical multiplicity but also betray Deleuze's model of the assemblage, which requires attention to not only the organizing and stabilizing tendencies within a structure but also the points at which a structure resists organization, its internal heterogeneity, and unpredictable "lines of flight." A Deleuzian approach to Islamic theology would first have to affirm that there is no such thing as a universal "Islamic theology" that can speak for all Muslims in all historical settings, but rather a multiplicity of power struggles between major and minor forces that contest each other over authenticity, authority, and the making of "orthodoxy." The discussions in Sufi Deleuze thus highlight Islam's extraordinary range of possibilities, not only making use of canonically privileged materials such as the Qur'an and major hadith collections, but also exploring a variety of marginalized resources found throughout Islam that challenge the notion of a singular "mainstream" interpretive tradition. To say it in Deleuze's vocabulary, Islam is a rhizome. (shrink)

Using a densely constructed ethnographic subject, Josephine, the “ugly duckling,” I use Foucault’s complex notion of an Apparatus to examine how Josephine’s decision to have weight-loss surgery is understandable even though it permanently destroys her normally functioning digestive system. I try to illuminate how the decision is deeply embedded in extraordinarily complex neoliberal biopolitical structures and dynamics of fat hatred camouflaged by liberatory discourses that promise “empowerment,” becoming “normal,” and discovery of her “real self.” I argue that in contemporary America, (...) Fat Hatred must be understood as a powerful systemic structure of racialized gendered oppression, that one tactic to normalize weight-loss surgery involves assimilating it to “normal” cosmetic surgery, and that Josephine must be seen, simultaneously, as legitimizing dominant obesity discourses and practices, enacting genuinely liberating personal choices, demonstrating her status as a “good American bio-citizen,” and contributing to the collective physical health and mental health of the nation since “obesity” is soon to be included in the fifth edition of the canonical Diagnostic and Statistical Manual of Mental Disorders as a mental disorder. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:What Has Chalcedon to Do with Lhasa? John Keenan’s and Lai Pai-chiu’s Reflections on Classical Christology and the Possible Shape of a Tibetan Theology of IncarnationThomas CattoiThe starting point of this paper is a critique of John Keenan’s so-called “Mahāyāna Christology” in The Meaning of Christ, in light of Lai Pai-chiu’s “Chinese” response to Keenan’s position. My argument is that Lai correctly construes the Chalcedonian definition as a critique (...) of Hellenist ontology, but fails to critique Keenan’s crucial contention that this same definition ratifies the subjugation of lived spiritual experience to abstract philosophical speculation. I also claim that Lai does not engage Keenan’s flawed use, in his constructive Christology, of the teaching of the Buddha-bodies, which in my opinion could provide an apposite template for the development of a Tibetan contextual Christology. My paper has a twofold purpose: on one hand, I sketch the contours of a possible Tibetan theology of incarnation; on the other hand, I offer a few methodological reflections on the role of classical doctrinal definitions in the development of new contextual theologies.The burden of this paper is to offer a few suggestions toward the formulation of a culturally contextual theology of incarnation, which uses the resources of Mahāyāna speculation on the embodiment of the Buddha. My starting point is Lai’s critique of Keenan’s well-known 1989 volume The Meaning of Christ, in which Keenan sets out to critique traditional Hellenist Chalcedonian Christology and argues for an alternative articulation of the hypostatic union based on the Mahāyāna teaching of the Buddha-bodies.1 Lai’s article revisits Keenan’s critique and argues that the Chalcedonian definition, far from canonizing the uncritical appropriation of a school of thought, evidences the profound limitations of philosophical discourse. Keenan’s underlying contention that traditional Christology subjects the Christian message to the strictures of alien categories is thus deconstructed, although Lai goes on to offer yet one more Christological synthesis based on the Chinese understanding of Buddha nature. In my paper I concur with Lai’s reading of Chalcedonian categories, which I regard [End Page 13] as more accurate and fruitful than Keenan’s, but I also argue that Lai fails to engage the totality of Keenan’s argument and therefore does not appreciate the deeper flaws in Keenan’s appropriation of the Buddhakāya teaching. My constructive suggestion toward the end of this paper is that such teaching could actually provide a most useful template for the development of a “Tibetan” theology of incarnation, which would remain in continuity with the Chalcedonian tradition, and yet resort to the linguistic and philosophical categories of the local culture.Theologians wishing to develop contextual articulations of Christian doctrine often meet considerable resistance, since their emphasis on the culturally contingent nature of traditional formulas is seen as a challenge to their continuing normative character. As early as 1969, Joseph Ratzinger’s Introduction to Christianity expressed serious reservations about the growing tendency to “de-Hellenize” Christian theology and strongly reasserted the enduring “providential” character of traditional Trinitarian and Christological formulas.2 At the same time, the development of a postcolonial Christianity in many Asian and African countries could not but call for inculturated expressions of the Christian faith that embedded the Christian message in the categories of the local culture. Theologian Stephen B. Bevans begins his work Models of Contextual Theology claiming that in the contemporary world, “the contextualization of [Christian] theology [...] is really a theological imperative.” 3 The understanding of theology as an objective and unchanging science of faith is thus superseded by a new approach that gives pride of place to the religious experience of the individual and the community where he or she lives, operates, and worships.4 Bevans’s call for a contextual theology views the “experience of the present” as the ultimately normative benchmark against which the “experience of the past” is assessed, in the search for a new synthesis rooted in a particular cultural and social location.5The development of new Christological formulas that use the resources of Asian Buddhist culture is thus possible only after the... (shrink)