We study the coherence, that is the equality of canonical natural transformations in non-free symmetric monoidal closed categories . To this aim, we use proof theory for intuitionistic multiplicative linear logic with unit. The study of coherence in non-free smccs is reduced to the study of equivalences on terms in the free category, which include the equivalences induced by the smcc structure. The free category is reformulated as the sequent calculus for imll with unit so that only equivalences on derivations (...) in this system are to be considered. We establish that any equivalence induced by the equality of canonical natural transformations over a model can be axiomatized by some set of “critical” pairs of derivations. From this, we derive certain sufficient conditions for full coherence, and establish that the system of identities defining smccs is not Post-complete: extending this system with an identity that does not hold in the free smcc does not in general cause the free smcc to collapse into a preorder. In order to give a larger context to these results, we study the equality of canonical morphisms in non-free symmetric monoidal categories, and establish that w.r.t. a broad subclass of smccs, the equivalences induced by the equality of canonical natural transformations over a model coincide with the equivalences induced by the equality of canonical morphisms for all interpretations in that model. (shrink)

It is known that the Restricted Predicate Calculus can be embedded in an elementary theory, the signature of which consists of exactly two equivalences. Some special models for the mentioned theory were constructed to prove this fact. Besides formal adequacy of these models, a question may be posed concerning their conceptual simplicity, "transparency" of interpretations they assigned to the two stated equivalences. In works known to us these interpretations are rather complex, and can be called "technical", serving only the purpose (...) of embedding. We propose a conversion method, which transforms an arbitrary model of RPC into some model of the elementary theory TR, which includes three equivalences. RPC is embeddable in TR, and it appears possible to assign some "natural" interpretations to three equivalences using the "Track of Relation " concept. (shrink)

We review the equivalence of the two-flavor Skyrme-Witten model and the two-flavor large-N c quark model. The claimed equivalence for three flavorsbetween these two models is shown to be incorrectly given in the literature, and the properly equivalent extended three-flavor large-N c quark model is constructed and discussed.

Neo-Darwinism is based on the same principles as the Walrasian analysis of equilibrium. This may be surprising for evolutionary economists who resort to neo-Darwinism as a result of their dissatisfaction with Walrasian economics. As it is well-known, the principle of rationality does not play a role in neo-Darwinism. In fact, the whole (neo-)Darwinian agenda became popular exactly because it expunged the idea of rationality from nature, and hence, from equilibrium. It is less known, however, that the rationality principle is also (...) not central in Walrasian equilibrium analysis. Therefore, if we find that the rationality principle must be central to the analysis of decision making of human and nonhuman organisms, we must advance organomics . Organomics is bioeconomics understood as the use of rational choice to the study of the behavior of human and nonhuman organisms. Organomics offers a different starting point than the one offered by neo-Darwinism. (shrink)

In Baire space N = ω ω we define a sequence of equivalence relations $\langle E_\nu| \nu , each E v being Σ 1 1 with classes in Π 0 1 + ν + 1 and such that (i) E ν does not have perfectly many classes, and (ii) N/E ν is countable iff $\omega^L_\nu . This construction can be extended cofinally in (δ 1 3 ) L . A new proof is given of a theorem of Hausdorff on partitions (...) of R into ω 1 many Π 0 3 sets. (shrink)

We prove that the observational equivalence of third-order finitary Idealized Algol is decidable using Game Semantics. By modelling the state explicitly in our games, we show that the denotation of a term M of this fragment of IA is a compactly innocent strategy-with-state, i.e. the strategy is generated by a finite view function fM. Given any such fM, we construct a real-time deterministic pushdown automaton that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational (...) equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding the observational equivalence of third-order finitary IA. Restricted to second-order terms, the DPDA representation cuts down to a deterministic finite automaton; thus our approach gives a new proof of Ghica and McCusker’s regular-expression characterization for this fragment. Our algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns second-order IA with full recursion: we show that observational equivalence for this fragment is undecidable. (shrink)

The paper is devoted to applications of algebraic logic to databases. In databases a query is represented by a formula of first order logic. The same query can be associated with different formulas. Thus, a query is a class of equivalent formulae: equivalence here being similar to that in the transition to the Lindenbaum-Tarski algebra. An algebra of queries is identified with the corresponding algebra of logic. An algebra of replies to the queries is also associated with algebraic logic. (...) These relations lie at the core of the applications.In this paper it is shown how the theory of Halmos (polyadic) algebras (a notion introduced by Halmos as a tool in the algebraization of the first order predicate calculus) is used to create the algebraic model of a relational data base. The model allows us, in particular, to solve the problem of databases equivalence as well as develop a formal algebraic definition of a database's state description. In this paper we use the term "state description" for the logical description of the model. This description is based on the notion of filters in Halmos algebras. When speaking of a state description, we mean the description of a function which realizes the symbols of relations as real relations in the given system of data. (shrink)

Two new intuitionistic equivalents to Zarn’s Lemma are stated and proved.

Alsatian engineer Gustave-Adolphe Hirn is best known to historians of science for his experimental determination of the mechanical equivalent of heat, first published in 1855. Since the 1840s, that equivalent has been closely associated with the conservation of energy, indeed often conflated with it. Hirn was one of Thomas Kuhn’s twelve ‘pioneers’ whose work he deemed relevant to the ostensible ‘simultaneous discovery’ of energy conservation. Yet Hirn never wholeheartedly embraced energy conservation. After reviewing his experimental work, his philosophical (...) reflections, and his response to developments in heat theory, this article identifies three factors as having played central roles in this regard: Hirn’s deepest concerns were ontological, not energetic; none of the concepts basic to his natural philosophy were appropriate stand-ins for a quantitatively conserved energy; and, accurately reflecting the most common interpretation of the principle of the conservation of energy from the 1860s on – as exemplified already by Helmholtz in 1847 – Hirn associated its corpuscular-mechanical underpinning with the despiritualizing materialism he saw as dominating contemporary science. Hence although Hirn’s natural philosophy embraced sentiments quite in the spirit of the conservation of energy, he never explicitly subscribed to that principle. (shrink)

Goethe's objections to Newton's theory of light and colours are better than often acknowledged. You can accept the most important elements of these objections without disagreeing with Newton about light and colours. As I will argue, Goethe exposed a crucial weakness of Newton's methodological self-assessment. Newton believed that with the help of his prism experiments, he could prove that sunlight was composed of variously coloured rays of light. Goethe showed that this step from observation to theory is more problematic than (...) Newton wanted to admit. By insisting that the step to theory is not forced upon us by the phenomena, Goethe revealed our own free, creative contribution to theory construction. And Goethe's insight is surprisingly significant, because he correctly claimed that all of the results of Newton's prism experiments fit a theoretical alternative equally well. If this is correct, then by suggesting an alternative to a well-established physical theory, Goethe developed the problem of underdete... (shrink)

Le but de ce texte est de mettre en évidence les équi­valences entre la façon dont le concept de conatus résout, dans l'Éthique, le problème de l'unité modale complexe. en rendant consis­tant le concept de chose singulière en tant que celle-ci doit être consi­dérée comme un légitime sujet d'attribution d'états, et la façon dont ce même concept dessine le rapport cognitif de l'esprit avec lui-même, rapport par lequel l'esprit se saisit comme sujet de ses états et qui ca­ractérise la notion (...) moderne de subjectivité. Ainsi, en éclairant cet as­pect du concept spinoziste de chose singulière. on comprendra aussi, de façon indirecte, l'une des conditions par lesquelles les choses peuvent, dans la doctrine spinoziste, devenir des objets ou des signes pour la connaissance humaine. (shrink)

This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory. Here, we first show that there are two versions of Maxwell’s equations. The new version fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for all observers, but depends (...) on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. The theory provides a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group. This approach also provides a natural (and unique) definition of simultaneity for all observers.The corresponding particle theory is independent of particle number, noninvariant under time reversal (arrow of time), compatible with quantum mechanics and has a corresponding positive definite canonical Hamiltonian associated with the clock of the source.We also provide a brief review of our work on the foundational aspects of the corresponding relativistic quantum theory. Here, we show that the standard square-root and Dirac equations are actually two distinct spin- $\frac{1}{2}$ particle equations. (shrink)

J. L. Austin, in "Ifs and Cans," proclaimed the common hope that we soon "may see the birth, through the joint labors of philosophers, grammarians, and numerous other students of language, of a true and comprehensive science of language." The problem has always been with the "joint labors" part. Philosophers have always been willing to issue linguists dictums and linguists have been happy to teach philosophers "plain facts." Austin’s general view of language, and his particular notion of performative utterance, can (...) be found in the writing of J. R. Firth, the most commanding British linguist of Austin’s generation, but Austin never refers to Firth. In the present volume, however, we find clear and exciting evidence of genuinely joint labors on the part of philosophers and linguists. They stem from a summer conference in 1969 rounded out with contributions from notables. To two thick issues of Synthese the editors have added a dazzling piece by Saul Kripke, two substantial pieces by James McCawley and J. R. Ross, a short paper by Paul Ziff, and a reprint of P. F. Strawson’s "Grammar and Philosophy." This is an invaluable book and the best book among the many now available concerning the interaction of linguistics and philosophy: worth the cost, which the contributors attempted to reduce through foregoing royalties. The philosophers in this volume hold, or hold intriguing, the view that the semantics of a natural language can and must, in effect, be a theory of truth for a language in much the manner that Tarski suggested, and provided, for artificial language: the recursive specification of biconditionals in which the left hand gives the structural description of an object language sentence and the right hand, the truth conditions in the metalanguage. In "homophonic" translation this requirement can be trivially satisfied simply by mentioning the sentence on the left that one uses on the right: one makes the requirement non-trivial by forcing enough into the recursive specification so that one captures the native speaker’s implicit semantic competence. In this volume, the "orthodox" Davidsonian program, which takes the syntax of the metalanguage to be standard predicate logic, is ably argued by John Wallace ; Richard Montague, David Lewis, and Jaakko Hintikka would want an intensional logic covering modality and propositional attitudes. The linguists who find this philosophical climate most appealing are called "generative semanticists": McCawley, Ross, George Lakoff and others argue that any proposed semantic rule will eventually prove necessary to syntax too and that, hence, the deepest level of syntactical form will be equivalent to semantic form. Whatever the ultimate fate of this joint program, it leads here to much exciting interaction between linguists and philosophers: linguists who welcome the machinery and conceptual standards of modern logic, and philosophers who try to grasp the specifics of crucial issues in recent linguistic theory. Even if Quine’s doubts, here sketched, and Chomsky’s currently unpublished more technical objections should be well-founded, nonetheless the joint labor will have been very much worthwhile. Aside from this general debate about semantics, there are several papers covering more specific issues. The papers of J. A. Fodor, Terence Parsons, and Ross concern adverbs and the logical form of action sentences; several papers, particularly B. H. Partee’s, examine "Opacity, Coreference, and Pronouns." In all these papers one notes the fulfillment of Austin’s hope that philosophic and linguistic arguments should become intermixed, if not at times properly indistinguishable. Perhaps the most enjoyable and exciting paper stands aside from linguistics: Saul Kripke’s "Naming and Necessity." Kripke here argues quite informally for the separation of analytic, a priori, and necessary that is required for a Kripke style, S5, modal logic with de re modalities. "Gold is a yellow metal," for example, turns out to be contingent, while "Heat is the motion of particles" is necessary but a posteriori ; and that philosopher’s stone of stones, "The morning star is the evening star," is discovered to be necessary but a posteriori.—J. L. (shrink)

In my paper ‘A Logic for Evidential Support’ (this Journal, 17 (1966), 21 ff.) the argument on page 25 is illustrated by wrong and misleading examples.1 The argument proceeds by considering statements logically equivalent to a universal hypothesis U1 that are formed by generalising analogously not about the individual elements of U1's domain of discourse, but about pairs, trios, or n-membered classes of these elements, where the domain of U1 has at least n elements. But the generalisations must be (...) understood distributively : not collectively, as the examples in the original version suggested. Such an equivalent for ‘All ravens are black’ will not be ‘All pairs of ravens are pairs of black things’, but ‘All pairs are pairs of things each of which is a raven only if black’. Similarly, instead of ‘If the pair a, b is a pair of ravens it is a pair of black things’ on page 26,1 should have written ‘The pair a, b is a pair of things each of which is a raven only if black’. If these alterations are made, the argument is unobjectionable, and the qualification about truth-functional conditionals, on page 25, is no longer required. (A corresponding correction should be made in the argument of ‘What has Confirmation to do with Probabilities ?’, Mind, 75 (1966), 474.). (shrink)

Co-hyperintensionality, or hyperintensional equivalence, is a relation holding between two or more contents that can be substituted in a hyperintensional context salva veritate. I argue that two strategies used to provide criteria for co-hyperintensionality fail. I argue that there is no generalized notion of co-hyperintensionality that meets plausible desiderata, by showing that the opposite thesis leads to falsity. As a conclusion, I suggest to take co-hyperintensionality as a primitive and I provide a general criterion of co-hyperintensionality whose content depends on (...) each hyperintensional notion we aim to formalize. (shrink)

This commentary proposes keeping the bridge locus construct with a revised definition which requires the bridge locus to be dynamic, representation-independent and influenced by top-down processes. The denial of the uniformity of content thesis is equivalent to dualism. The active perception perspective is a valuable one.

La question platonicienne est traversée par une énigme qui défie les interprètes depuis les travaux de Léon Robin, qui datent de plus d'un siècle. Platon a-t-il élaboré une doctrine, ou sa pensée est-elle tout entière contenue dans les dialogues? Autrement dit, y a-t-il un enseignement secret de Platon qui n'apparaîtrait pas dans son oeuvre écrite? Le témoignage des doxographes, à commencer par Aristote, laisse entendre que Platon a bien enseigné une doctrine, mais comment expliquer le silence des dialogues? Analysant l'étrange (...) passage du Timée qui s'articule sur la gamme pythagoricienne, J.-J. Duhot, qui a aussi été musicien professionnel, en a décrypté la clef, qui avait échappé aux interprètes : le Même code l'octave, soit le rapport 2, et l'Autre code la quinte, soit le rapport 3/2. Cette clef, indiscutable en elle-même, comme le démontre J.-J. Duhot, permet d'établir la grille de lecture qui éclaire toutes les obscurités du passage. On a donc là une double équivalence, entre métaphysique (Un/Multiple), acoustique (octave et quinte), et mathématiques (construction arithmétique de la gamme). J.-J. Duhot montre que c'est la matrice sur laquelle Platon construit son oeuvre et met en place le postulat de mathématicité du monde, qui sera la base de toute la science moderne, à partir de Galilée. La gamme du Timée offre un modèle mathématique, la division de 2 en produits de facteurs dans un système logarithmique, qui résout (métaphoriquement) les problèmes de l'Un et du Multiple. On voit ainsi apparaître un "cycle éléatique" dans lequel, au fil des dialogues, Parménide, Théétète, Sophiste et Politique, se met en place une véritable doctrine platonicienne. Doctrine secrète qui s'offre au lecteur qui sait en décrypter le code. (shrink)

The author, a consultant psychotherapist who works with dying patients in a National Health Service (NHS) hospital, argues that the moral issue is not simply whether or not to tell cancer patients the truth, but more importantly how to do so. Lies and the bald unprepared-for truth may both be damaging. Time and trouble is needed to understand patients and help them understand their situation. Dr Goldie warns that putting oneself into the patient's shoes, as doctors so often do, is (...) the best way of not knowing what another feels. Such misunderstanding may lead to medical decisions based on `nothing more than fantasies - uninspired guesses about what other people think and feel. It is the equivalent of prescribing for patients without examination'. (shrink)

Kruskal proved that finite trees are well-quasi-ordered by hom(e)omorphic embeddability. Friedman observed that this statement is not provable in predicative analysis. Friedman also proposed (see in [Simpson]) some stronger variants of the Kruskal theorem dealing with finite labeled trees under home(e)omorphic embeddability with a certain gap-condition, where labels are arbitrary finite ordinals from a fixed initial segment of ω. The corresponding limit statement, expressing that for all initial segments of ω these labeled trees are well-quasi-ordered, is provable in Π 1 (...) 1 -CA, but not in the analogous theory Π 1 1 -CA 0 with induction restricted to sets. Schutte and Simpson proved that the one-dimensional case of Friedman's limit statement dealing with finite labeled intervals is not provable in Peano arithmetic. However, Friedman's gap-condition fails for finite trees labeled with transfinite ordinals. In [Gordeev 1] I proposed another gap-condition and proved the resulting one-dimensional modified statements for all (countable) transfinite ordinal-labels. The corresponding universal modified one-dimensional statement UM 1 is provable in (in fact, is equivalent to) the familiar theory ATR 0 whose proof-theoretic ordinal is Γ 0 . In [Gordeev 1] I also announced that, in the general case of arbitrarily-branching finite trees labeled with transfinite ordinals, in the proof-theoretic sense the hierarchy of the limit modified statements $\mathbf{M}_{ (which are denoted by LM λ in the present note) is as strong as the hierarchy of the familiar theories of iterated inductive definitions (more precisely, see [Gordeev 1, Concluding Remark 3]). In this note I present a "positive" proof of the full universal modified statement UM, together with a short proof of the crucial "reverse" results which is based on Okada's interpretation of the well-established ordinal notations of Buchholz corresponding to the theories of iterated inductive definitions. Formally the results are summarized in $\S5$ below. (shrink)

We analyze N. C. A. da Costa and F. A. Doria’s “exotic formalization” of the conjecture P = NP [3–7]. For any standard axiomatic PA extension T and any number-theoretic sentence ${\varphi }$ , we let ${\varphi ^{\star} := \varphi \vee \lnot \mathsf{Con}\left( \mathsf{T}\right)}$ and prove the following “exotic” inferences 1–3. 1. ${\mathsf{T}+\varphi ^{\star}}$ is consistent, if so is T, 2. ${\mathsf{T}+\varphi}$ is consistent, provided that ${\mathsf{T}+\varphi ^{\star}}$ is ω-consistent, 3. ${\mathsf{T}+\varphi}$ is consistent, provided that T is consistent and has (...) the same provably total recursive functions as ${\mathsf{T}+\left( \varphi \leftrightarrow \varphi ^{\star }\right) }$ . Furthermore we show that 1–3 continue to hold for ${\varphi ^{\star} := \varphi _{S} :=\varphi \vee \lnot S}$ , where ${S=\forall x\exists yR\left( x,y\right)}$ is any ${\Pi _{2}^{0}}$ sentence satisfying: 4. ${\left( \forall n\in \omega \right) \left( \mathsf{T}\vdash S_{x}\left[ \underline{n}\right] \right) }$ , 5. ${\mathsf{Con}\left( \mathsf{T}\right) \Rightarrow \mathsf{T}\nvdash S}$ . We observe that if ${\varphi :=\left[ \mathsf{P}=\mathsf{NP}\right] }$ and ${S:= \left[\digamma total\right] }$ , where ${\digamma=\digamma _{\mathsf{T}}}$ is da Costa-Doria “exotic” function with respect to T, then 4, 5 are satisfied for most familiar (presumably) consistent T in question, while ${\varphi _{S}}$ becomes equivalent to da Costa-Doria “exotic formalization” ${\left[ \mathsf{P}=\mathsf{NP}\right]^{\digamma}}$ . Moreover, the corresponding “exotic” inferences 1–3 generalize analogous da Costa-Doria results. Hence these “exotic” inferences are universal for all number-theoretic sentences and not characteristic to the conjecture P = NP. Nor do they infer relative consistency of P = NP (see Conclusion 15 in the text). (shrink)

The tripartite account of propositional, fallibilist knowledge that p as justified true belief can become adequate only if it can solve the Gettier Problem. However, the latter can be solved only if the problem of a successful coordination of the resources (at least truth and justification) necessary and sufficient to deliver propositional, fallibilist knowledge that p can be solved. In this paper, the coordination problem is proved to be insolvable by showing that it is equivalent to the ''''coordinated attack'''' (...) problem, which is demonstrably insolvable in epistemic logic. It follows that the tripartite account is not merely inadequate as it stands, as proved by Gettier-type counterexamples, but demonstrably irreparable in principle, so that efforts to improve it can never succeed. (shrink)

In this paper I argue that deontic modals are hyperintensional, i.e. logically equivalent contents cannot be substituted in their scope. I give two arguments, one deductive and the other abductive. First, I show that the contrary thesis leads to falsity; second, I argue that a hyperintensional theory of deontic modals fares better than its rivals in terms of elegance, theoretical simplicity and explanatory power. I then propose a philosophical analysis of this thesis and outline some consequences. In Section 1 (...) I introduce and define deontic modality and hyperintensionality. In Section 2 I give a reductio for the hyperintensionality of deontic modals. If the argument is sound, a useful corollary is that deontic modals are also non-intensional, and therefore possible-world semantics accounts are illfitted for them. I then show how the main result can be strengthened or weakened by varying the definition of logical validity. In Section 3 I give an abductive argument for the hyperintensionality of deontic modals, arguing that with a single move we are able to solve many paradoxes and puzzles traditionally troubling deontic logic. I present a version of a hyperintensional deontic logic in an appendix, which I prove is sound and complete with respect to a version of truthmaker semantics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Piety, Justice, and the Unity of VirtueMark L. McPherranNo doubt the Socrates of the Euthyphro would be delighted to encounter many of its readers, offering as they do an audience of piety-seeking interlocutors, eager to mend the dialogical breach created by Euthyphro’s sudden departure. Socrates’ enthusiasm for this pursuit is at least as intense and comprehensible as theirs. We are told, after all, that he will never abandon his (...) quest for knowledge of “what the pious is” (15c–16a), since not only is this enterprise both pious and “inconceivably happy” (cf. Ap. 41c3–4) in itself,1 but coming to understand piety would allow one to “live better the rest of one’s life,” (15e7–16a4), especially should its continuation be threatened by a charge of impiety (3b–d, 5a–c, 12e, 15e–16a).2 My own search here is no less happy and ambitious, since I wish to uncover Socrates’ own, implicit understanding of piety and its relation to his claim elsewhere that “the virtues are one.”3 The account of this I shall provide will also touch on Platonic piety, although this notion obviously rests on a tendentious distinction. Nevertheless, there do seem to be some interesting differences between the way piety is treated in elenctic dialogues such as the Euthyphro and Protagoras, and the more explicitly theory-laden, constructive works such as the Republic and Laws. I shall later characterize [End Page 299] these differences, primarily in terms of the more carefully articulated, internalist moral psychology of the Republic.42. SOCRATIC PIETYThe distinct phenomena the term “religion” popularly designates for us were for the Greeks seamlessly integrated into everyday life. Thus, it is natural that the term “piety”—εὐσέβεια—carried a wider sense than our English equivalent commonly does: it concerned not only one’s immediate relation to the gods—emphasizing proper religious conduct and carrying a sense of respect and fear towards divinity (concomitant with a grasp of one’s own mortal limits)—but also often designated appropriate behavior towards parents, native land, and the dead.5 It is to this rough, inclusive conception of piety that Euthyphro appeals when confronted by Socrates on the Porch of the King (2a–6a). Moreover, and despite his own shockingly irreverent attempt at father-bashing and the subsequent elenctic drubbing he then receives from Socrates, toward the close of the dialogue Euthyphro still manages to envision piety in the quasi-traditionalist fashion with which he began—as “a knowledge of how to ensure the preservation of families and states by gratifying the gods through proper prayer and sacrifice” (14b; cf. 14c–15c).6 It is, however, precisely [End Page 300] at this dramatic juncture (14a–c) that we find—arguably—the final elements of a Socratically-acceptable conception of piety; one that builds upon Euthyphro’s initial concession to Socrates that piety and “human justice” are to be distinguished from one another (11e–12e). This, in turn, is a move that in principle forces Euthyphro to disengage from those aspects of the traditional conception of piety which would—from Socrates’ perspective—conflate the two.7 Recent challenges to this reading, however, have seen in Euthyphro’s initial holism not the heterogeneous presumptions of popular thought, but a semi-sophisticated grasp of the Socratic unity of the virtues.8 And since it does appear that the character Euthyphro is designed to serve not only as a hubristically-inflated, Homeric “fundamentalist,” but as an odd and Sophistically-influenced doppelgänger of Socrates as well—a lesson, that is, in what Socrates both is and is not—it now seems worthwhile to reexamine the view that Socratic piety is but a part and not the whole of justice.9Turning to our text, then, we discover that following the failure of Euthyphro’s initial definitional attempts to specify the nature of pious action and the resulting aporetic interlude, Socrates is willing to offer Euthyphro renewed assistance (11e1–4). This he does by asking whether all the just is pious, or whether justice is broader than piety such that piety is then merely a “part” (μóϱιον) of justice (11e4–12e5). Subsequent to his explanation of these alternatives, Socrates... (shrink)

Since its inception in 1968, the concept of whole-brain death has been contentious, and four decades on, controversy concerning the validity and coherence of whole-brain death continues unabated. Although whole-brain death is legally recognized and medically entrenched in the United States and elsewhere, there is reasonable disagreement among physicians, philosophers, and the public concerning whether brain death is really equivalent to death as it has been traditionally understood. A handful of states have acknowledged this plurality of viewpoints and enacted (...) “conscience clauses” that require “reasonable accommodation” of religious and moral objections to the determination of death by neurological criteria. This paper argues for the universal adoption of “reasonable accommodation” policies using the New Jersey statute as a model, in light of both the ongoing controversy and the recent case of Jahi McMath, a child whose family raised religious objections to a declaration of brain death. Public policies that accommodate reasonable, divergent viewpoints concerning death provide a practical and compassionate way to resolve those conflicts that are the most urgent, painful, and difficult to reconcile. (shrink)

This paper examines the work of Nāgārjuna as interpreted by later Madhyamaka tradition, including the Tibetan Buddhist Tsongkhapa (1357–1419). It situates Madhyamaka skepticism in the context of Buddhist philosophy, Indian philosophy more generally, and Western equivalents. Find it broadly akin to Pyrrhonism, it argues that Madhyamaka skepticism still differs from its Greek equivalents in fundamental methodologies. Focusing on key hermeneutical principles like the two truths and those motivating the Svātantrika/Prāsaṅgika schism (i.e., whether followers of Nāgārjuna should offer positive arguments or (...) should proceed on a purely “negative” basis), it argues that the Svātantrika commitment to mere conventional practice is robust and allows for a skepticism consistent with the scientific practices we must take seriously in the modern world. These findings are put forth as an illustration of what the Western tradition might gain by better understanding of non-Western philosophy. (shrink)

The quantum Zeno effect (QZE) is often associated with the ironic maxim, “a watched pot never boils”, although the notion of “watching” suggests a continuous activity at odds with the usual (pulsed measurement) presentation of the QZE. We show how continuous watching can provide the same halting of decay as the usual QZE, and, for incomplete hindrance, we provide a precise connection between the interval between projections and the response time of the continuous observer. Thus, watching closely, but not so (...) closely as to halt the “boiling”, is equivalent to—gives the same degree of partial hindrance as—pulsed measurements with a particular pulsing rate. Our demonstration is accomplished by treating the apparatus for the continuous watching as a fully quantum object. This in turn allows us a second perspective on the QZE, in which it is the modified level structure of the combined system/apparatus Hamiltonian that slows the decay. This and other considerations favor the characterization “dominated time evolution” for the QZE. (shrink)

We can think about the use of controlled substances in the treatment of anxiety disorders in two simple but diametrically opposed ways. First, we can say that anxiety disorders are trivial and require only acts of willpower, or, if anxiety disorders do require treatment, they are better treated without the use of benzodiazepines. When BZs are used to treat anxiety, they pose grave risks of addiction to the patients to whom these medicines are prescribed; they relieve patients’ symptoms, but are (...) the equivalent of a pharmacological “roach motel,” a haven into which many unsuspecting patients enter, but from which few emerge without becoming addicted. Patients must then face terrible struggles to free themselves of dependence on BZs, and this compounds the problem for which they sought treatment. Furthermore, the large number of prescriptions for BZs are a threat to the public health because these drugs are widely abused by alcoholics and drug addicts. (shrink)

We critically revisit the definition of thermal equilibrium, in its operational formulation, provided by standard thermodynamics. We show that it refers to experimental conditions which break the covariance of the theory at a fundamental level and that, therefore, it cannot be applied to the case of moving bodies. We propose an extension of this definition which is manifestly covariant and can be applied to the study of isolated systems in special relativity. The zeroth law of thermodynamics is, then, proven to (...) establish an equivalence relation among bodies which have not only the same temperature, but also the same center of mass four-velocity. (shrink)

Peter Kosso discusses the weak gravitational lensing observations of the Bullet Cluster and argues that dark matter can be detected in this system solely through the equivalence principle without the need to specify a full theory of gravity. This paper argues that Kosso gets some of the details wrong in his analysis of the implications of the Bullet Cluster observations for the Dark Matter Double Bind and the possibility of constructing robust tests of theories of gravity at galactic and greater (...) scales. Even the Bullet Cluster evidence is not sufficiently detailed to allow precision tests of General Relativity that would distinguish it from its rivals at galactic and greater scales. Taking into account the total evidence available, we cannot rule out “ugly” solutions to the dynamical discrepancy in astrophysics that involve both a large quantity of dark matter and a theory of gravity whose predictions differ significantly from those of General Relativity for interactions taking place at galactic and greater scales. (shrink)

"Human beings are a part of nature and apart from it." The argument of Natural Law and Justice is that the philosophy of natural law and contemporary theories about the nature of justice are both efforts to make sense of the fundamental paradox of human experience: individual freedom and responsibility in a causally determined universe. Professor Weinreb restores the original understanding of natural law as a philosophy about the place of humankind in nature. He traces the natural law tradition from (...) its origins in Greek speculation through its classic Christian statement by Thomas Aquinas. He goes on to show how the social contract theorists adapted the idea of natural law to provide for political obligation in civil society and how the idea was transformed in Kant's account of human freedom. He brings the historical narrative down to the present with a discussion of the contemporary debate between natural law and legal positivism, including particularly the natural law theories of Finnis, Richards, and Dworkin. Professor Weinreb then adopts the approach of modern political philosophy to develop the idea of justice as a union of the distinct ideas of desert and entitlement. He shows liberty and equality to be the political analogues of desert and entitlement and both pairs to be the normative equivalents of freedom and cause. In this part of the book, Weinreb considers the theories of justice of Rawls and Nozick as well as the communitarian theory of Maclntyre and Sandel. The conclusion brings the debates about natural law and justice together, as parallel efforts to understand the human condition. This original contribution to legal philosophy will be especially appreciated by scholars, teachers, and students in the fields of political philosophy, legal philosophy, and the law generally. (shrink)