A recursively enumerable splitting of an r.e. setAis a pair of r.e. setsBandCsuch thatA=B∪CandB∩C= ⊘. Since for such a splitting degA= degB∪ degC, r.e. splittings proved to be a quite useful notion for investigations into the structure of the r.e. degrees. Important splitting theorems, like Sacks splitting [S1], Robinson splitting [R1] and Lachlan splitting [L3], use r.e. splittings.Since each r.e. splitting of a set induces a splitting of its degree, it is natural to study the relation between the degrees (...) of r.e. splittings and the degree splittings of a set. We say a setAhas thestrong universal splitting property if each splitting of its degree is represented by an r.e. splitting of itself, i.e., if for degA=b∪cthere is an r.e. splittingB, CofAsuch that degB=band degC=c. The goal of this paper is the study of this splitting property.In the literature some weaker splitting properties have been studied as well as splitting properties which imply failure of the SUSP. (shrink)

In 1987, Crispin Wright argued that degree-theoretic solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.

In 1987, Crispin Wright argued that degree-theoretic (fuzzy) solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.

In lieu of an abstract, here is a brief excerpt of the content:Theoretical Remarks on Combined Creative and Scholarly PhD Degrees in the Visual ArtsJames Elkins (bio)The PhD in visual arts is inescapable: it is on the horizon. In just a few years, there will be a number of such programs in the United States, and if the trend mirrors the expansion of MFAs after the mid-1960s, then in a few decades the PhD will be the consensus "terminal" degree (...) for artists. Given that, it is pressing to consider how the degree might be theorized. In Australia and the United Kingdom, where the degrees already exist, their growth has been dictated in large measure by the existing educational structures and by the inevitable quest for funding. (In the United Kingdom, university departments get a disproportionate increase in their funding if they offer doctorate programs, and the same pattern occurs in state schools in America.) As a result, existing programs simply grow by exonomic necessity or opportunity, and so far they have not been well theorized apart from models already in use elsewhere in the university. Private universities and art schools in the United States are therefore well positioned to rethink the conceptual foundations of combined studio and scholarly PhDs, because they are largely freed of the temptation of increased funding and the obligation to fit the new programs into existing structures. In this essay, I propose eight configurations that such degrees might take. I close with three general observations about the future of such programs.Three pieces of background are necessary as introduction. First, the School of the Art Institute, Chicago, where I teach, is currently running an four-year undergraduate major in visual studies. Soon we will be expanding it into an MA and, in a few years, a PhD. At the BA level our program already has a large studio component. For that reason we have been looking at programs that offer comparable combinations of creative and scholarly work at the PhD level. Our own program, we hope, will be a place [End Page 22] where the possibilities of other programs can be kept open and continuously questioned.Second, this essay was originally a reader's report for a creative-arts PhD thesis called "Beyond the Surface: The Contemporary Experience of the Italian Renaissance," written by Jo-Anne Duggan for the University of Technology, Sydney. In fall 2003 Duggan was a candidate for the "DCA," Doctorate of Creative Arts." She is a photographer, and her special interest is photographing inside museums; her thesis explores the history and theory of that practice. The report I wrote for her was the basis of this essay, because I found that her thesis is a mixture of what I think are the eight principal possibilities for combining PhD-level scholarship and creative work.Third, this essay is the outgrowth of several colloquia that have been held at the College Art Association and at the Association of Independent Colleges of Art and Design/National Association of Schools of Art and Design (AICAD/NASAD) conferences (organizations of art school administrators). These ad hoc forums have been, so far, the only places where the new programs have been debated. I hope this essay can contribute to a more detailed discussion.Here are the eight configurations. The first five are (or will be) common, and the last two are rare but preferable.1. The thesis is art history, intended to inform the art practice. The most obvious relation between scholarship and creative work is that the former informs the latter. The artist positions her scholarship so that it supports her art practice. Within this possibility, perhaps the most common option would be to write an art historical thesis, covering the history of practices that lead up to the writer's own practice. Among the advantages would be that, in theory, the candidate would be able to go on to teach in a department of art history. In terms of her practice, the idea would be that historical knowledge strengthens art practice: a debatable point, if only because so many artists have done so well by ignoring or distorting the relevant history. In Canberra in summer 2003, I met a recent PhD whose thesis was on... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Theoretical Remarks on Combined Creative and Scholarly PhD Degrees in the Visual ArtsJames Elkins (bio)The PhD in visual arts is inescapable: it is on the horizon. In just a few years, there will be a number of such programs in the United States, and if the trend mirrors the expansion of MFAs after the mid-1960s, then in a few decades the PhD will be the consensus "terminal" degree (...) for artists. Given that, it is pressing to consider how the degree might be theorized. In Australia and the United Kingdom, where the degrees already exist, their growth has been dictated in large measure by the existing educational structures and by the inevitable quest for funding. (In the United Kingdom, university departments get a disproportionate increase in their funding if they offer doctorate programs, and the same pattern occurs in state schools in America.) As a result, existing programs simply grow by exonomic necessity or opportunity, and so far they have not been well theorized apart from models already in use elsewhere in the university. Private universities and art schools in the United States are therefore well positioned to rethink the conceptual foundations of combined studio and scholarly PhDs, because they are largely freed of the temptation of increased funding and the obligation to fit the new programs into existing structures. In this essay, I propose eight configurations that such degrees might take. I close with three general observations about the future of such programs.Three pieces of background are necessary as introduction. First, the School of the Art Institute, Chicago, where I teach, is currently running an four-year undergraduate major in visual studies. Soon we will be expanding it into an MA and, in a few years, a PhD. At the BA level our program already has a large studio component. For that reason we have been looking at programs that offer comparable combinations of creative and scholarly work at the PhD level. Our own program, we hope, will be a place [End Page 22] where the possibilities of other programs can be kept open and continuously questioned.Second, this essay was originally a reader's report for a creative-arts PhD thesis called "Beyond the Surface: The Contemporary Experience of the Italian Renaissance," written by Jo-Anne Duggan for the University of Technology, Sydney. In fall 2003 Duggan was a candidate for the "DCA," Doctorate of Creative Arts." She is a photographer, and her special interest is photographing inside museums; her thesis explores the history and theory of that practice. The report I wrote for her was the basis of this essay, because I found that her thesis is a mixture of what I think are the eight principal possibilities for combining PhD-level scholarship and creative work.Third, this essay is the outgrowth of several colloquia that have been held at the College Art Association and at the Association of Independent Colleges of Art and Design/National Association of Schools of Art and Design (AICAD/NASAD) conferences (organizations of art school administrators). These ad hoc forums have been, so far, the only places where the new programs have been debated. I hope this essay can contribute to a more detailed discussion.Here are the eight configurations. The first five are (or will be) common, and the last two are rare but preferable.1. The thesis is art history, intended to inform the art practice. The most obvious relation between scholarship and creative work is that the former informs the latter. The artist positions her scholarship so that it supports her art practice. Within this possibility, perhaps the most common option would be to write an art historical thesis, covering the history of practices that lead up to the writer's own practice. Among the advantages would be that, in theory, the candidate would be able to go on to teach in a department of art history. In terms of her practice, the idea would be that historical knowledge strengthens art practice: a debatable point, if only because so many artists have done so well by ignoring or distorting the relevant history. In Canberra in summer 2003, I met a recent PhD whose thesis was on... (shrink)

Given the success of the formal approach, within contemporary epistemology, to understanding degreed belief, some philosophers have recently considered its extension to the challenge of understanding intention. According to them, (1) intentions can also admit of degrees, as beliefs do, and (2) these degreed states are all governed by the norms of the probability calculus, such that the rational norms for belief and for intention exhibit certain structural similarity. This paper, however, raises some worries about (2). It considers two schemes (...) for representing degreed intention, and casts some doubt on applying probabilistic norms to degreed intention on each scheme. And it argues that the norms of Intention–Belief Consistency and Enkrasia cannot plausibly be turned into norms prescribing a simple correspondence relation between one’s degrees of belief and intention. The results suggest a potential structural discrepancy between the norms of theoretical and practical rationality—at least for degreed belief and intention. This potential discrepancy not only raises interesting questions about the intention–belief relation and rational norms for degreed intention. It also poses a new challenge for intention-based expressivism about normative judgment and cognitivism about practical rationality. (shrink)

In this paper we argue that reflection on the patterns of practical concern that agents like us exhibit strongly suggests that the same person relation comes in continuous degrees rather than being an all or nothing matter. We call this the SP-degree thesis. Though the SP-degree thesis is consistent with a range of views about personal-identity, we argue that combining desire-first approaches to personal-identity with the SP-degree thesis better explains our patterns of practical concern, and hence gives (...) us reason to endorse such an approach. We then argue that the combination of the SP-degree thesis and the desire-first approach are best modelled by a stage-theoretic view of persistence according to which temporal counterpart relations are non-symmetric relations that come in continuous degrees. Ultimately, we think that the overall appeal of this package of views provides reason to accept the package: reasons that outstrip the reasons we have to endorse any particular member of the package. (shrink)

We give some new examples of possible degree spectra of invariant relations on Δ 0 2 -categorical computable structures, which demonstrate that such spectra can be fairly complicated. On the other hand, we show that there are nontrivial restrictions on the sets of degrees that can be realized as degree spectra of such relations. In particular, we give a sufficient condition for a relation to have infinite degree spectrum that implies that every invariant computable relation on a (...) Δ 0 2 -categorical computable structure is either intrinsically computable or has infinite degree spectrum. This condition also allows us to use the proof of a result of Moses [23] to establish the same result for computable relations on computable linear orderings. We also place our results in the context of the study of what types of degree-theoretic constructions can be carried out within the degree spectrum of a relation on a computable structure, given some restrictions on the relation or the structure. From this point of view we consider the cases of Δ 0 2 -categorical structures, linear orderings, and 1-decidable structures, in the last case using the proof of a result of Ash and Nerode [3] to extend results of Harizanov [14]. (shrink)

In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a new theory of vagueness: fuzzy plurivaluationism. -/- A predicate is said to be VAGUE if there is no sharply defined boundary between the things to which it applies and the things to which it does not apply. For example, 'heavy' is vague in a way that 'weighs over 20 kilograms' is not. A great many predicates -- both in everyday talk, and in a wide array of theoretical vocabularies, from law (...) to psychology to engineering -- are vague. -/- Smith argues, based on a detailed account of the defining features of vagueness, that an accurate theory of vagueness must involve the idea that truth comes in degrees. The core idea of degrees of truth is that while some sentences are true and some are false, others possess intermediate truth values: they are truer than the false sentences, but not as true as the true ones. Degree-theoretic treatments of vagueness have been proposed in the past, but all have encountered significant objections. In light of these, Smith develops a new type of degree theory. Its innovations include a definition of logical consequence that allows the derivation of a classical consequence relation from the degree-theoretic semantics, a unified account of degrees of belief and their relationships with degrees of truth and subjective probabilities, and the incorporation of semantic indeterminacy -- the view that vague statements need not have unique meanings -- into the degree-theoretic framework. -/- As well as being essential reading for those working on vagueness, Smith's book provides an excellent entry-point for newcomers to the area -- both from elsewhere in philosophy, and from computer science, logic and engineering. It contains a thorough introduction to existing theories of vagueness and to the requisite logical background. (shrink)

Based on the theory of dialectical structures, I review the concept of degree of justification of a partial position a proponent may hold in a controversial debate. The formal concept of degree of justification dovetails with our pre-theoretic intuitions about a thesis' strength of justification. The central claim I'm going to defend in this paper maintains that degrees of justification, as defined within the theory of dialectical structures, correlate with a proponent position's verisimilitude. I vindicate this thesis (...) with the results of simulations of controversial argumentation. (shrink)

The primary aim of this paper is to analyze the concept of degrees of causal contribution for actual events and examine the way in which it can be formally defined. This should go some way to filling out a gap in the legal and philosophical literature on causation. By adopting the conception of a cause as a necessary element of a sufficient set (the so-called NESS test) we show that the concept of degrees of causation can be given clear and (...) even empirical meaning. We then apply a game theoretical framework to derive a measure of causal contribution. Our favoured measure turns out to be a generalised version of the normalized Penrose-Banzhaf index of voting power. (shrink)

There are many classical connections between the proof-theoretic strength of systems of arithmetic and the provable totality of recursive functions. In this paper we study the provability strength of the totality of recursive functions by investigating the degree structure induced by the relative provability order of recursive algorithms. We prove several results about this proof-theoretic degree structure using recursion-theoretic techniques such as diagonalization and the Recursion Theorem.

The primary aim of this paper is to analyze the concept of degrees of causal contribution for actual events and examine the way in which it can be formally defined. This should go some way to filling out a gap in the legal and philosophical literature on causation. By adopting the conception of a cause as a necessary element of a sufficient set (the so-called NESS test) we show that the concept of degrees of causation can be given clear and (...) even empirical meaning. We then apply a game theoretical framework to derive a measure of causal contribution. Our favoured measure turns out to be a generalised version of the normalized Penrose–Banzhaf index of voting power. (shrink)

This paper gives an explication of our intuitive notion of strength of justification in a controversial debate. It defines a thesis' degree of justification within the bipolar argumentation framework of the theory of dialectical structures as the ratio of coherently adoptable positions according to which that thesis is true over all coherently adoptable positions. Broadening this definition, the notion of conditional degree of justification, i.e.\ degree of partial entailment, is introduced. Thus defined degrees of justification correspond to (...) our pre-theoretic intuitions in the sense that supporting and defending a thesis t increases, whereas attacking it decreases, t's degree of justification. Moreover, it is shown that (conditional) degrees of justification are (conditional) probabilities. Eventually, the paper explains that it is rational to believe theses with a high degree of justification insofar as this strengthens the robustness of one's position. (shrink)

We study degree-theoretic properties of reals that are not random with respect to any continuous probability measure (NCR). To this end, we introduce a family of generalized Hausdorff measures based on the iterates of the “dissipation” function of a continuous measure and study the effective nullsets given by the corresponding Solovay tests. We introduce two constructions that preserve non-randomness with respect to a given continuous measure. This enables us to prove the existence of NCR reals in a number (...) of Turing degrees. In particular, we show that every \(\Delta ^0_2\) -degree contains an NCR element. (shrink)

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the (...) given class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings ; integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. This allows us to show that several theorems about degree spectra of relations on computable structures, nonpreservation of computable categoricity, and degree spectra of structures remain true when we restrict our attention to structures in any of the classes on this list. The codings we present are general enough to be viewed as establishing that the theories mentioned above are computably complete in the sense that, for a wide range of computability-theoretic nonstructure type properties, if there are any examples of structures with such properties then there are such examples that are models of each of these theories. (shrink)

The lecture starts by considering analytic philosophy as a tradition, and its global spread over recent years, of which Disputatio’s success is itself evidence. The costs and benefits of the role of English as the international language of analytic philosophy are briefly assessed. The spread of analytic philosophy is welcomed as the best hope for scientific philosophy, in a sense of ‘science’ on which mathematics, history, and philosophy can all count as sciences, though not as natural sciences. Arguably, experimental philosophy (...) provides no plausible alternative methodology for philosophy, only a way of psychologizing it. However, it serves a useful purpose by highlighting the inadequacy of current methods for detecting errors in judgments on possible cases, which may result from reliance on possibly universal but imperfectly reliable cognitive heuristics. The problem is exacerbated by analytic philosophers’ tendency to regard increased flexibility in a theoretical framework as progress, where natural scientists would treat it as methodologically vicious profligacy with degrees of freedom. The result is a familiar type of bad science, overfitting theory to uncritically accepted data. The recent ‘hyperintensional revolution’ may be an example of such overfitting, it is suggested. The lecture ends with a call for a more miserly attitude to degrees of freedom. (shrink)

We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it is (...) possible to capture proof-theoretically not only the entailment relation of the standard four-valued Belnap’s logic, but also its dual version, as well as some of their interesting extensions. The proof systems we propose are, in a sense, of a hybrid Hilbert–Gentzen nature. We examine some important properties of these systems and establish their completeness with respect to the corresponding entailment relations. (shrink)

There has been much discussion about whether traditional epistemology's doxastic attitudes are reducible to degrees of belief. In this paper I argue that what I call the Straightforward Reduction - the reduction of all three of believing p, disbelieving p, and suspending judgment about p, not-p to precise degrees of belief for p and not-p that ought to obey the standard axioms of the probability calculus - cannot succeed. By focusing on suspension of judgment (agnosticism) rather than belief, we can (...) see why the Straightforward Reduction is bound to fail. I argue that, in general, suspending about p is not just a matter of having some specified standard credence for p, and in the end I suggest some ways to extend the arguments that will put pressure on other credence-theoretic accounts of belief and suspension of judgment as well. (shrink)

F.A. Hayek argued that the sciences of complex phenomena, including (perhaps especially) economics, are limited to incomplete “explanations of the principle” and “pattern predictions.” According to Hayek, these disciplines suffer from (what I call) a data problem, i.e., the hopelessness of populating theoretical models with data adequate to full explanations and precise predictions. In Hayek’s terms, explanations in these fields are always a matter of “degree.” However, Hayek’s methodology implies a distinct theory problem: theoretical models of complex phenomena may (...) be underspecified so that, even were all the data available, a full explanation could not be inferred from the model. Where the sciences of complex phenomena are subject to both the data and theory problems, explanations and predictions will be of even lesser “predictive degree.” The paper also considers how to interpret Hayek’s claim that pattern predictions are falsifiable. (shrink)

We can classify the (truth-theoretic) paradoxes according to their degrees of paradoxicality. Roughly speaking, two paradoxes have the same degrees of paradoxicality, if they lead to a contradiction under the same conditions, and one paradox has a (non-strictly) lower degree of paradoxicality than another, if whenever the former leads to a contradiction under a condition, the latter does so under the same condition. In this paper, we outline some results and questions around the degrees of paradoxicality and summarize (...) recent progress. (shrink)

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and (...) prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values. (shrink)

To provide a theoretical basis for the common view that moral status comes in degrees, many philosophers endorse ‘two-factor’ accounts of the foundations of moral status. These accounts postulate one or more properties which endow individuals with moral status, and one or more other properties which increase the moral status of those who possess them. Critical assessment of two-factor accounts has focused on their implications, especially for humans who lack the properties thought to increase individuals’ moral status. Unfortunately, this approach (...) has led to an impasse. To try to break it, the present manuscript instead assesses the assumption on which two-factor accounts are based, namely, possession of one or more properties, what I call ‘moral status enhancing’ properties, increases their possessors’ moral status. I argue that two challenges, the problem of relevance and the need for a threshold, reveal that there are no moral status enhancing properties, hence, no degrees of moral status among those who matter morally. (shrink)

There has been increasing interest over the last few decades in the study of the effective content of Mathematics. One field whose effective content has been the subject of a large body of work, dating back at least to the early 1960s, is model theory. Several different notions of effectiveness of model-theoretic structures have been investigated. This communication is concerned withcomputablestructures, that is, structures with computable domains whose constants, functions, and relations are uniformly computable.In model theory, we identify isomorphic (...) structures. From the point of view of computable model theory, however, two isomorphic structures might be very different. For example, under the standard ordering of ω the success or relation is computable, but it is not hard to construct a computable linear ordering of type ω in which the successor relation is not computable. In fact, for every computably enumerable degree a, we can construct a computable linear ordering of type ω in which the successor relation has degree a. It is also possible to build two isomorphic computable groups, only one of which has a computable center, or two isomorphic Boolean algebras, only one of which has a computable set of atoms. Thus, for the purposes of computable model theory, studying structures up to isomorphism is not enough. (shrink)

In this survey we discuss work of Levin and V’yugin on collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. More precisely, Levin and V’yugin introduced an ordering on collections of sequences that are closed under Turing equivalence. Roughly speaking, given two such collections $\mathcal {A}$ and $\mathcal {B}$, $\mathcal {A}$ is below $\mathcal {B}$ in this ordering if $\mathcal {A}\setminus \mathcal {B}$ is negligible. The degree structure (...) associated with this ordering, the Levin–V’yugin degrees, can be shown to be a Boolean algebra, and in fact a measure algebra. We demonstrate the interactions of this work with recent results in computability theory and algorithmic randomness: First, we recall the definition of the Levin–V’yugin algebra and identify connections between its properties and classical properties from computability theory. In particular, we apply results on the interactions between notions of randomness and Turing reducibility to establish new facts about specific LV-degrees, such as the LV-degree of the collection of 1-generic sequences, that of the collection of sequences of hyperimmune degree, and those collections corresponding to various notions of effective randomness. Next, we provide a detailed explanation of a complex technique developed by V’yugin that allows the construction of semi-measures into which computability-theoretic properties can be encoded. We provide two examples of the use of this technique by explicating a result of V’yugin’s about the LV-degree of the collection of Martin-Löf random sequences and extending the result to the LV-degree of the collection of sequences of DNC degree. (shrink)

Let T 0?T 1 denote that each computable function, which is provable total in the first order theory T 0, is also provable total in the first order theory T 1. Te relation ? induces a degree structure on the sound finite Π2 extensions of EA (Elementary Arithmetic). This paper is devoted to the study of this structure. However we do not study the structure directly. Rather we define an isomorphic subrecursive degree structure <≤,?>, and then we study (...) <≤,?> by ubrecursive and computability-theoretic means. Furthermore, we introduce and investigate some operators on the degrees of <≤,?>. These operators corresponds to inferencerules in formal arithmetic. One operator corresponds to the Σ1 collection rule. Another operator corresponds to the Σ1 induction rule. (shrink)

to that goal, and it is hoped that it will incorporate further works dealing in an exact way with interesting philosophical issues. Zurich, April 1973 Mario Bunge Preface In this book I have investigated the logical and methodological role of the much debated theoretical concepts in scientific theories. The philosophical viewpoint underlying my argumentation is critical scientific realism. My method of exposition has been to express ideas first in general terms and then to develop and elaborate them within a specific (...) formal framework. It is assumed in the book that the reader has a relatively good knowledge of the basic techniques and results of modern symbolic logic, including model theory. Examples from actual science are mostly from the social sciences. I have deliberately omitted a treatment of a number of characteristic features which are particular to theoretical concepts in the more developed sciences, such as modern physics. This book owes very much to Professor Jaakko Hintikka, to whom I wish to express my deep gratitude. Especially at the begin ning of this project in 1968/69 when I was doing research for my doctoral degree at Stanford University I worked with him closely. (shrink)

Mereological nihilism (henceforth just "nihilism") is the thesis that composition never occurs. Nihilism has often been defended on the basis of its theoretical simplicity, including its ontological simplicity and its ideological simplicity (roughly, nihilism's ability to do without primitive mereological predicates). In this paper I defend nihilism on the basis of the theoretical unification conferred by nihilism, which is, roughly, nihilism's capacity to allow us to take fewer phenomena as brute and inexplicable. This represents a respect in which nihilism enjoys (...) greater theoretical simplicity than its rivals which has not yet been explored, and which is immune to many of the objections which have been leveled against previous arguments for nihilism from nihilism's theoretical simplicity. Composition as identity might be thought to confer a similar degree of theoretical unification as nihilism. I end the paper by arguing that this is not the case. (shrink)

Let be an infinite computable structure, and let R be an additional computable relation on its domain A. The syntactic notion of formal hypersimplicity of R on , first introduced and studied by Hird, is analogous to the computability-theoretic notion of hypersimplicity of R on A, given the definability of certain effective sequences of relations on A. Assuming that R is formally hypersimple on , we give general sufficient conditions for the existence of a computable isomorphic copy of on (...) whose domain the image of R is hypersimple and of arbitrary nonzero computably enumerable Turing degree. (shrink)

The University of Michigan conference “Where Religion, Policy, and Bioethics Meet: An Interdisciplinary Conference on Islamic Bioethics and End-of-Life Care” in April 2011 addressed the issue of brain death as the prototype for a discourse that would reflect the emergence of Islamic bioethics as a formal field of study. In considering the issue of brain death, various Muslim legal experts have raised concerns over the lack of certainty in the scientific criteria as applied to the definition and diagnosis of brain (...) death by the medical community. In contrast, the medical community at large has not required absolute certainty in its process, but has sought to eliminate doubt through cumulative diagnostic modalities and supportive scientific evidence. This has recently become a principal model, with increased interest in data analysis and evidence-based medicine with the intent to analyze and ultimately improve outcomes. Islamic law has also long employed a systematic methodology with the goal of eliminating doubt from rulings regarding the question of certainty. While ample criticism of the scientific criteria of brain death (Harvard criteria) by traditional legal sources now exists, an analysis of the legal process in assessing brain death, geared toward informing the clinician’s perspective on the issue, is lacking. In this article, we explore the role of certainty in the diagnostic modalities used to establish diagnoses of brain death in current medical practice. We further examine the Islamic jurisprudential approach vis-à-vis the concept of certainty (yaqīn). Finally, we contrast the two at times divergent philosophies and consider what each perspective may contribute to the global discourse on brain death, understanding that the interdependence that exists between the theological, juridical, ethical, and medical/scientific fields necessitates an open discussion and active collaboration between all parties. We hope that this article serves to continue the discourse that was successfully begun by this initial interdisciplinary endeavor at the University of Michigan. (shrink)

1. The problem. The concept of confirmation of an hypothesis by empirical evidence is of fundamental importance in the methodology of empirical science. For, first of all, a sentence cannot even be considered as expressing an empirical hypothesis at all unless it is theoretically capable of confirmation or disconfirmation, i.e. unless the kind of evidence can be characterized whose occurrence would confirm, or disconfirm, the sentence in question. And secondly, the acceptance or rejection of a sentence which does represent an (...) empirical hypothesis is determined, in scientific procedure, by the degree to which it is confirmed by relevant evidence. (shrink)

Nicholas Smith argues that an adequate account of vagueness must involve\ndegrees of truth. The basic idea of degrees of truth is that while\nsome sentences are true and some are false, others possess intermediate\ntruth values: they are truer than the false sentences, but not as\ntrue as the true ones. This idea is immediately appealing in the\ncontext of vagueness--yet it has fallen on hard times in the philosophical\nliterature, with existing degree-theoretic treatments of vagueness\nfacing apparently insuperable objections. Smith seeks to turn (...) the\ntide in favor of a degree-theoretic treatment of vagueness, by motivating\nand defending the basic idea that truth can come in degrees, by arguing\nthat no theory of vagueness that does not countenance degrees of\ntruth can be correct, and by developing a new degree-theoretic treatment\nof vagueness--fuzzy plurivaluationism--that solves the problems plaguing\nearlier degree theories. (shrink)

This essay seeks a new approach between philosophy and neuroscience inspired by the recent ontological turn to think about one of the affects modulations across the contemporary sociopolitical scenario. In this regard, it theoretically triangulates the appropriation of Spinoza's philosophy by neuroscientist Antonio Damasio and the reception of Damasio's neuroscience by philosopher Catherine Malabou, taking Gilles Deleuze as a connecting point between these perspectives. It proposes to think the concept of destructive plasticity as a metamorphosis in the organism that, shocked (...) by some traumatic event, turns to a new configuration that deactivates its somatic markers and ends up taking a form of disaffection. Finally, it concludes by bringing this figure closer to what Achille Mbembe, taking the death drive as central concept for thinking necropolitics, names as "lumpenradical". (shrink)

On any speedometer, there are two kinds of what might very loosely be called ‘zones of indifference’. The first kind is found between any two marked speeds. If your speed is in fact 61 mph, it probably falls in one kind of zone of indifference. A normal speedometer is simply not designed to distinguish speeds between 60 and 65 mph, and if asked, we would probably report such a speed as ‘about 60’. There is, however, another kind of zone of (...) indifference. It is the one that extends beyond the highest marked speed, and includes all speeds that are too fast for the speedometer to register them—all the speeds that are literally off the scale. The big-picture theoretical aim of this paper is to explore the possibility that natural languages work in more or less the same way, with both kinds of zones of indifference. (shrink)

What does it mean to say that a scientific theory is unified? Prominent attempts by John Watkins, Philip Kitcher, and Margaret Morrison to answer this question face serious difficulties, and many analysts of science remain pessimistic about the possibility of ever rendering precise or explaining what theoretical unity consists in. This paper gives grounds for optimism, offering a novel account of the concept of unification. This account is tested against a detailed study of the standard model in contemporary high-energy physics, (...) a theory for which a high degree of unity has repeatedly been claimed. (shrink)

This paper is discusses some central points in a dissertation for the degree of dr. phil., "Regulation as Productive Tool Use - a Participatory Observation in the Control Room of a District Heating System." An earlier version of the paper was presented by the author as part of the defense of the dissertation at Roskilde University Center June 14 2002. As suggested by the title, the dissertation was an empirical study of regulation in a control room. The object of (...) the authors participatory observation was how the operators in the control room followed rules when they regulated a highly automated plant. When I was shown the plant I was told that the technology ran smoothly and without error. Its control structures are based on formal logic and mechanical principles, all the same human beings are required in the control room to take care of anomalies. Among other things, the observations provide an opportunity to discuss the limitations of psychologies that study human beings on the basis of formal principles. The present paper focuses on two characteristic aspects of this discussion in the dissertation. First, it takes its point of departure in some practical problems of the control structures of the control room. It will demonstrate that the practical problems are problems of principle, and that formal principles are not adequate to study the object of human sciences, namely, human beings. Second, it sketches out what is required of a conception of human beings. As human beings are trusted to handle anomalies, we must explain how they are able to act on an incomplete understanding of the situation. And since they are able to identify what is wrong, we must explain how they develop new knowledge. The paper presented at the defense summarized the main arguments of the dissertation and alluded to an expansion of the main point using a particular instance. Here the weight is shifted to the latter expansion. (shrink)

White lies, lies that are beneficial to the addressee and uttered out of concern for them, are pervasive in daily life. This raises a prima facie question: if white lies are so common, are they still lies? I tackle this question from the perspective of speech act theory, using the case of white lies to shed light on the broader question of whether lying itself can be considered a type of speech act. Adopting Sbisà’s (Uptake and Conventionality in Illocution. Lodz (...) Papers in Pragmatics 5 33–52. Reprinted in Marina Sbisà (forthcoming), Essays on Speech Acts and Other Topics in Pragmatics. Oxford: Oxford University Press, 2009) neo-Austinian approach that places the emphasis on the achievement of certain conventional effects, I claim that malicious lying cannot be a type of speech act. However, white lies are a type of speech act, a claim which finds support in three types of evidence: the conventionality of means by which white lies are performed, their online processing, and their acquisition. Moreover, the existence of a continuum between white (harmless) lies (which are a type of speech act) and malicious (harmful) lies (which are not) suggests that whether an utterance performs a certain type of speech act or not can be a matter of degree. In other words, the property itself of being a speech act of a certain kind, an utterance’s speech-act-hood, so to speak, may be graded. This is an interesting result, which applies to speech acts more generally, beyond lying. (shrink)

An important advance in normativity research over the last decade is an increased understanding of the distinction, and difference, between normativity and rationality. Normativity concerns or picks out a broad set of concepts that have in common that they are, put loosely, guiding. For example, consider two commonly used normative concepts: that of a normative reason and that of ought. To have a normative reason to perform some action is for there to be something that counts in favour of performing (...) that action. Likewise with ought, when there is sufficient evidence for something, one ought to believe it (at least under normal circumstances). Not all guidance need be directed towards a specific state or a specific action. Subject to the requirements of normativity, too, are relations. It is commonly believed, for example, that we ought not to hold contradictory beliefs.1 At least some of the requirements that concern relations amongst an agent’s mental states are, or seem, distinctive. Agents who fail to satisfy these requirements are considered, at least to some degree, irrational. On many current views, being irrational is distinct in some way from not being how one ought to be; rationality is a concept distinct from normativity. Much of the literature on this topic over the last decade stems from attempts to capture the characteristic features of the requirements of rationality. Two influential views in particular did much to set the agenda. The first of these two was put forward John Broome.2 His view, the particulars of which I shall discuss in more detail below, is that the requirements of rationality could be expressed using a normative relation, which he calls a ‘normative requirement’. Normative requirements are conditionals governed by an all-thingsconsidered ought. In the case of rationality, the conditional is made up entirely of mental states.. (shrink)

In 2004 Csima, Hirschfeldt, Knight, and Soare [1] showed that a set A ≤T 0' is nonlow₂ if and only if A is prime bounding, i.e., for every complete atomic decidable theory T, there is a prime model M computable in A. The authors presented nine seemingly unrelated predicates of a set A, and showed that they are equivalent $\Delta _{2}^{0}$ sets. Some of these predicates, such as prime bounding, and others involving equivalence structures and abelian p-groups come from model (...) theory, while others involving meeting dense sets in trees and escaping a given function come from pure computability theory. As predicates of A, the original nine properties are equivalent for $\Delta _{2}^{0}$ sets; however, they are not equivalent in general. This articale examines the (degree-theoretic) relationship between the nine properties. We show that the nine properties fall into three classes, each of which consists of several equivalent properties. We also investigate the relationship between the three classes, by determining whether or not any of the predicates in one class implies a predicate in another class. (shrink)

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings (...) via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs. (shrink)

The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. (...) This is the first example of an exact estimation of the degree of natural complex logics, i.e. logics whose deducibility relation cannot be represented by a single matrix. The remaining examples of complex logics are more artificial, having been constructed for the purpose of checking some theoretical possibilities. (shrink)

The semantic view of theoriesis one according to which theoriesare construed as models of their linguisticformulations. The implications of thisview for scientific realism have been little discussed. Contraryto the suggestion of various champions of the semantic view,it is argued that this approach does not makesupport for a plausible scientific realism anyless problematic than it might otherwise be.Though a degree of independence of theory fromlanguage may ensure safety frompitfalls associated with logical empiricism, realism cannot be entertained unless models or (abstractedand/or (...) idealized) aspects thereof are spelled out in terms of linguistic formulations (such as mathematical equations),which can be interpreted in terms of correspondencewith the world. The putative advantage of thesemantic approach – its linguistic independence – isthus of no help to the realist. I consider recent treatmentsof the model-theoretic view (Suppe, Giere, Smith), and find that although some of these accounts harbour the promiseof realism, this promise is deceptive. (shrink)