We present a method for rejecting competing models from noisy time-course data that does not rely on parameter inference. First we characterize ordinary differential equation models in only measurable variables using differential-algebra elimination. This procedure gives input-output equations, which serve as invariants for time series data. We develop a model comparison test using linear algebra and statistics to reject incorrect models from their invariants. This algorithm exploits the dynamic properties that are encoded in the structure of the model equations without (...) recourse to parameter values, and, in this sense, the approach is parameter-free. We demonstrate this method by discriminating between different models from mathematical biology. (shrink)

For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size $\beth_n$ with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least $\beth_\omega$ . (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly $\beth_\omega$ ). If T ≠ true arithmetic, then $H(T) = \beth_{\omega1}$ . If $\delta \not\rightarrow (\rho)^{ , then any completion of (...) Peano Arithmetic has a model of size δ with no set of indiscernibles of size ρ. There are similar results for theories strongly resembling Peano Arithmetic, e.g., ZF + V = L. (shrink)

The luminaries of late thirteenth-century Europe took great interest in the mysterious fifth-century author known as Dionysius the Areopagite. They typically read Dionysius not in the original Greek, but in a Latin edition prepared sometime in the middle of the thirteenth century. This edition, which appeared first in Paris and later circulated all over Western Europe, was no mere translation. In addition to the famous translation made by Eriugena in the ninth century, it contained translations of scholia on the Dionysian (...) texts made by Anastasius the Librarian, alternative readings provided by Anastasius and other Latin readers, as well as excerpts from Eriugena's own theological masterwork, the Periphyseon. University scholars such as Albert the Great and Thomas Aquinas thus learned Dionysian mystical theology not only from his text, but from the seven-hundred year interpretive tradition that literally surrounded it on the page. (shrink)

The Dionysian corpus makes virtually no statement about the authority of kings or the structure of nations, but it has nevertheless repeatedly been the subjectof political analysis. Several scholars have recently sketched out a Dionysian politics by drawing analogies between the Dionysian church and the city, and between the Dionysian bishop and the emperor. These analogies are of limited usefulness. They show that Dionysius does employ Platonic political language to describe the ecclesiastical hierarchy, but they risk overlooking or downplaying the (...) hierarchy’s non-temporal, and therefore non-political, activity. A more fruitful ground for developing a Dionysian politics may be found in his brief discussion of the legal hierarchy, which provides practical instruction for action in the temporal realm without direct reference to the contemplative activity of the church. (shrink)

Apparently alone among medieval Christians, Eriugena argues that all life is immortal. He relies on Plato’s Timaeus as his primary source for this claim, but he modifies the argument of the Timaeus considerably. He turns Plato’s cosmic soul into the genus of life, thereby taking a treatise that originally dealt with cosmology and using it to explore the ontological significance of definition. All species that fall under the genus of life must be immortal, because a mortal species would contradict the (...) genus. No later medieval author would take up Eriugena’s arguments explicitly, although Aquinas comes close. The two thirteenth-century thinkers to address universal immortality seriously—Aquinas and Bonaventure—argue against it, but they are more faithful than Eriugena himself to a literal reading of the Timaeus. (shrink)

This book is a translation of a key commentary on the Book of Changes, or Yijing, perhaps the most broadly influential text of classical China. The Yijing first appeared as a divination text in Zhou-dynasty China and later became a work of cosmology, philosophy, and political theory as commentators supplied it with new meanings. While many English translations of the Yijing itself exist, none are paired with a historical commentary as thorough and methodical as that written by the Confucian scholar (...) Cheng Yi, who turned the original text into a coherent work of political theory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Clement of AlexandriaL. Michael HarringtonEric Osborn. Clement of Alexandria. Cambridge-New York: Cambridge University Press, 2005. Pp. xviii + 324. Cloth, $85.00.With Clement of Alexandria, Eric Osborn returns to the subject of his 1957 book, The Philosophy of Clement of Alexandria, but its style and themes more closely resemble his more recent studies of second-century Christian thinkers: Tertullian, First Theologian of the West (Cambridge, 1997) and Irenaeus of Lyons (...) (Cambridge, 2001). Osborn's Clement, Tertullian, and Irenaeus are bound together by more than the century in which they happened to live. They share an optimism—a confidence that the world is finally comprehensible—and an argumentative theology, developed in response to the Gnostics, who, Osborn says in his book on Irenaeus, "were strong on picture and myth but weak on argument" (xiii).Osborn's approach to Clement is, as he describes it, analytic or problematic, meaning that "we simply ask what problems forced Clement to write and where he found Christian teaching in need of elucidation" (xii-xiii). Three problems concern Clement: (1) "how can the narrative of the kerygma (what God does) be translated into a metaphysic (who God is)?"; (2) "how two distinct beings, father and son, constitute one God"; and (3) "an answer had to be found for those who divided faith and knowledge." Each problem is addressed by means of a theme—divine economy for the first, reciprocity for the second, and salvation by faith for the third—and each of the book's three major parts devotes itself to one of these themes.Having laid out this systematic division, Osborn generally follows the logic of Clement's own thought rather than an imposed structure, developing his argument by careful collation and paraphrase. As a result, by the end of the book, the reader will feel thoroughly and effortlessly initiated in Clement's major works: the Protrepticus, the Paedagogus, and the Stromateis. The book thus serves as a thorough introduction to Clement, without aiming so low that it is of no interest to the scholar.Osborn's central argument unfolds from his observation that "Clement, more than any other early Christian writer, knew and enjoyed Greek philosophy and literature" (2). Clement defends the rationality shared between Christians and Greeks against the irrationalists of his time: the theosophers, or Gnostics (215). Osborn, in turn, defends Clement against the irrationalists of our own time, represented in his book by Wolfhart Pannenberg. The "divine irrational freedom" praised by Pannenberg is replaced in Osborn's Irenaeus and Clement by "universal wisdom" (47). The universality of wisdom allows great and dispassionate natures to reach the truth—whether they are Christians or Greeks—though each is like one limb of the truth, severed from the rest. Convinced that Christ will reunite these disiecta membra, "Clement converses with them and joins their broken lights" (104).In footnotes and parenthetical references throughout the book, Osborn argues against the approaches to Clement in doxography and Discourse Power theory, precisely because they are unable to treat him as a philosopher (79). The doxographer can show Clement's dependence on earlier philosophers, but is unable to see how he differs from them (xii). The Discourse Power theorist can see that Clement's system differs from the Gnostic system, but is able to explain the difference only as a competition between two social structures, without seeing that only one of them aspires to logical coherence (215).This dismissal of doxography and Discourse Power theory may strike the reader as too thoroughgoing, especially if we distinguish, as Osborn himself does in his book on Tertullian, philosophy as "a matter of system and speculation" from philosophy as "a matter of argument" (198). Clement's optimism depends on his confidence in system and speculation, in so far as they can be defended by argument. But if argument can defend two different systems equally well, then we may wonder why Clement chooses the system he does. Here the doxographer, who can show the provenance of his thought, becomes essential, as does the Discourse Power theorist, who can set Clement's choice of system in the context of the contemporary social fabric that inevitably affects even the... (shrink)

This article asserts the need for the ethical analysis of regulatory policy. The article explores the conventional wisdom surrounding the proper role of government, the function of law, the role of lawmakers, the nature of business, and the relationship between business and government. It is the traditional thinking regarding these fundamental aspects of our social life which creates barriers to the ethical analysis of regulatory policy. It is argued that, in spite of the persistence of agency theories of the firm, (...) a stakeholder theory of the firm best approximates a true descriptive and normative view of business organizations. If the role of government is to maximize the full range of public — private relationships for any given series of inputs, and the role of the firms is to maximize the balance of diverse stakeholders' interests, then a stakeholders' interests paradigm becomes the natural foundation for the ethical analysis of policies which regulate business. (shrink)

I defend a one category ontology: an ontology that denies that we need more than one fundamental category to support the ontological structure of the world. Categorical fundamentality is understood in terms of the metaphysically prior, as that in which everything else in the world consists. One category ontologies are deeply appealing, because their ontological simplicity gives them an unmatched elegance and spareness. I’m a fan of a one category ontology that collapses the distinction between particular and property, replacing it (...) with a single fundamental category of intrinsic characters or qualities. We may describe the qualities as qualitative charactersor as modes, perhaps on the model of Aristotelian qualitative (nonsubstantial) kinds, and I will use the term “properties” interchangeably with “qualities”. The qualities are repeatable and reasonably sparse, although, as I discuss in section 2.6, there are empirical reasons that may suggest, depending on one’s preferred fundamental physical theory, that they include irreducibly intensive qualities. There are no uninstantiated qualities. I also assume that the fundamental qualitative natures are intrinsic, although physics may ultimately suggest that some of them are extrinsic. On my view, matter, concrete objects, abstract objects, and perhaps even spacetime are constructed from mereological fusions of qualities, so the world is simply a vast mixture of qualities, including polyadic properties (i.e., relations). This means that everything there is, including concrete objects like persons or stars, is a quality, a qualitative fusion, or a portion of the extended qualitative fusion that is the worldwhole. I call my view mereological bundle theory. (shrink)

Critics of contemporary metaphysics argue that it attempts to do the hard work of science from the ease of the armchair. Physics, not metaphysics, tells us about the fundamental facts of the world, and empirical psychology is best placed to reveal the content of our concepts about the world. Exploring and understanding the world through metaphysical reflection is obsolete. In this paper, I will show why this critique of metaphysics fails, arguing that metaphysical methods used to make claims about the (...) world are similar to scientific methods used to make claims about the world, but that the subjects of metaphysics are not the subjects of science. Those who argue that metaphysics uses a problematic methodology to make claims about subjects better covered by natural science get the situation exactly the wrong way around: metaphysics has a distinctive subject matter, not a distinctive methodology. The questions metaphysicians address are different from those of scientists, but the methods employed to develop and select theories are similar. In the first section of the paper, I will describe the sort of subject matter that metaphysics tends to engage with. In the second section of the paper, I will show how metaphysical theories are classes of models and discuss the roles of experience, common sense and thought experiments in the construction and evaluation of such models. Finally, in the last section I will discuss the way these methodological points help us to understand the metaphysical project. Getting the right account of the metaphysical method allows us to better understand the relationship between science and metaphysics, to explain why doing metaphysics successfully involves having a range of different theories, to understand the role of thought experiments involving fictional worlds, and to situate metaphysical realism in a scientifically realist context. (shrink)

I summarize the main argument of Transformative Experience (OUP 2014). The book develops familiar examples from classical philosophical debates, as well as original examples, to argue that an agent’s decision to undergo a transformative experience—an experience constituted by radical personal and epistemic change for the agent—must either be authentic or irrational, but not both. The Precis of Transformative Experience walks the reader through the main ideas involved in epistemically and personally transformative experiences, the problems they pose for rational decision-making, and (...) discusses a number of key original examples of transformative experiences. (shrink)

I address two related questions: first, what is the best theory of how objects have de re modal properties? Second, what is the best defence of essentialism given the variability of our modal intuitions? I critically discuss several theories of how objects have their de re modal properties and address the most threatening antiessentialist objection to essentialism: the variability of our modal intuitions. Drawing on linguistic treatments of vagueness and ambiguity, I show how essentialists can accommodate the variability of modal (...) intuitions while holding that objects have their modal properties independently of contexts. (shrink)

This chapter offers an overview of the phenomenological approach to delusions, emphasizing what Karl Jaspers called the "true delusions" of schizophrenia. Phenomenological psychopathology focuses on the experience of delusions and the delusional world. Several features of this approach are surveyed, including emphasis on formal qualities of subjective life and questioning of standard assumptions about delusions as erroneous belief. The altered modalities of world-oriented and self-oriented experience that precede and ground delusions in schizophrenia, especially the experiences of revelation that Klaus Conrad (...) termed the outer and inner apophany, are then discussed. The chapter first considers the famous "delusional mood", then the role of ipseity-disturbance. In both cases it is explained how delusions can develop out of these distinctive alterations of perception and feeling. The classic question of the understandability or comprehensibility of schizophrenic delusion, together with the related issues of wish-fulfillment and rationalizing motives are then considered. The chapter addresses the crucial but neglected issue of the felt reality-status of delusions or the delusional world, discussing derealization, "double bookkeeping", and "double exposure". The chapter concludes by discussing delusions typically found in paranoid and affective psychoses, and monothematic delusions found in certain organic conditions. (shrink)

Bundle theory takes objects to be bundles of properties. Some bundle theorists take objects to be bundles of instantiated universals, and some take objects to be bundles of tropes. Tropes are instances of properties: some take instantiated universals to be tropes, while others deny the existence of universals and take tropes to be ontologically fundamental. Historically, the bundling relation has been taken to be a primitive relation, not analyzable in terms of or ontologically reducible to some other relation, and has (...) been variously characterized as, e.g., “compresence,” “concurrence,” or “consubstantiation.” Bertrand Russell (1940) defends compresence of universals, and Hector-Neri Castañeda (1974) defends consubstantiation of universals. John Bacon (1995) defends concurrent tropes and Keith Campbell (1990) defends compresent tropes. Jonathan Schaffer (2001) bucks this trend, endorsing compresence understood as co-location in spacetime, but this brings with it undesireable consequences such as the impossibility of distinguishing between objects (such as electrons or other microentities) with the same location. Mereological bundle theory improves upon traditional bundle theory by taking the primitive relation of bundling to be the more familiar relation of fusing or composing, such that objects are fusions of properties or fusions of property instances. Hence, mereological bundle theorists endorse a property mereology: a mereology where properties or property instances can be parts of objects. An advantage of the approach derives from the fact that standard mereologies take composition to be primitive or define it using a different primitive mereological notion (such as primitive parthood). Thus, taking the basic primitive of bundle theory to be composition can reduce the need for.. (shrink)

We show that the double jump is definable in the computably enumerable sets. Our main result is as follows: let [Formula: see text] is the Turing degree of a [Formula: see text] set J ≥T0″}. Let [Formula: see text] such that [Formula: see text] is upward closed in [Formula: see text]. Then there is an ℒ property [Formula: see text] such that [Formula: see text] if and only if there is an A where A ≡T F and [Formula: see text]. (...) A corollary of this is that, for all n ≥ 2, the high n computably enumerable degrees are invariant in the computably enumerable sets. Our work resolves Martin's Invariance Conjecture. (shrink)

Involuntary civil commitment to treatment for opioid use disorder prevents imminent overdose, but also restricts autonomy and raises other ethical concerns. Using the Kass Public Health Ethics Framework, we identified ICC benefits and harms. Benefits include: protection of vulnerable, underserved patients; reduced legal consequences; resources for families; and “on-demand” treatment access. Harms include: stigmatizing and punitive experiences; heightened family conflict and social isolation; eroded patient self-determination; limited or no provision of OUD medications; and long-term overdose risk. To use ICC ethically, (...) it should be recognized as comprising vulnerable patients worthy of added protections; be a last resort option; utilize consensual, humanizing processes; provide medications and other evidence-based-treatment; integrate with existing healthcare systems; and demonstrate effective outcomes before diffusion. ICC to OUD treatment carries significant potential harms that, if unaddressed, may outweigh its benefits. Findings can inform innovations for ensuring that ICC is used in an ethically responsible way. (shrink)

The purpose of this communication is to announce some recent results on the computably enumerable sets. There are two disjoint sets of results; the first involves invariant classes and the second involves automorphisms of the computably enumerable sets. What these results have in common is that the guts of the proofs of these theorems uses a new form of definable coding for the computably enumerable sets.We will work in the structure of the computably enumerable sets. The language is just inclusion, (...) ⊆. This structure is called ε.All sets will be computably enumerable non-computable sets and all degrees will be computably enumerable and non-computable, unless otherwise noted. Our notation and definitions are standard and follow Soare [1987]; however we will warm up with some definitions and notation issues so the reader need not consult Soare [1987]. Some historical remarks follow in Section 2.1 and throughout Section 3.We will also consider the quotient structure ε modulo the ideal of finite sets, ε*. ε* is a definable quotient structure of ε since “Χ is finite” is definable in ε; “Χ is finite” iff all subsets of Χ are computable. We use A* to denote the equivalent class of A under the ideal of finite sets. (shrink)

The sports world has historically rejected the practice of tanking. I argue that this attitude is unwarranted. To do so, I introduce a concept called strategic suboptimal play (SSP), which is the practice of incurring the risk of a short-term competitive disadvantage to increase the chances of gaining a longer-term competitive advantage. Tanking is just an instance of SSP employed in higher-order games, i.e. games that are at least partially played by other games, like tournaments or seasons. Since SSP is (...) integral to every sport, there are currently no easy grounds for rejecting it outright. As such, the same is true of tanking. I will explore some possible reasons why tanking is wrongly thought objectionable, as well as some objections to and implications of my argument for competitive sports more broadly. (shrink)

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in as a (...) fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. (shrink)

We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.

Causation is at once familiar and mysterious. Neither common sense nor extensive philosophical debate has led us to anything like agreement on the correct analysis of the concept of causation, or an account of the metaphysical nature of the causal relation. Causation: A User's Guide cuts a clear path through this confusing but vital landscape. L. A. Paul and Ned Hall guide the reader through the most important philosophical treatments of causation, negotiating the terrain by taking a set of examples (...) as landmarks. They clarify the central themes of the debate about causation, and cover questions about causation involving omissions or absences, preemption and other species of redundant causation, and the possibility that causation is not transitive. Along the way, Paul and Hall examine several contemporary proposals for analyzing the nature of causation and assess their merits and overall methodological cogency.The book is designed to be of value both to trained specialists and those coming to the problem of causation for the first time. It provides the reader with a broad and sophisticated view of the metaphysics of the causal relation. (shrink)