A reassessment of Aquinas’s doctrine of divine infinity, particularly in the light of the previous history of the concept within Western philosophy and theology. From the critical perspective provided by this history the central place which has been claimed for it in Aquinas’s thinking is questioned, as are also its originality and coherence. The notion that the doctrine of divine infinity was introduced to Western thought by Judaeo‐Christianity is rejected; from Anaximander onwards it had been a central concept in Greek (...) philosophy. Aristotle however had rejected it so effectively that, for several centuries afterwards, it seems to have led an ‘underground’ existence until it finally surfaces again in ‘Gnostic’ and related currents of thought. It is from these circles that it finally, and after some resistance, patchily entered orthodox Christian thinking. Likewise Plotinus was not the source of the doctrine, as some have claimed; historical precedence must be given to the Gnostics. Neoplatonism never, despite the prestige of Plotinus, fully accepted the doctrine; in Proclus it is a subordinate emanation from the One, which is beyond Infinity and Infinitude. Nor, because of the influence of Aristotle, does Islamic Neoplatonized Aristotelianism endorse the doctrine. Aquinas’s commitment to it seems to stem from the impact of John of Damascus’s stress upon the doctrine, the translation of whose work greatly influenced Western theology from the late twelfth century onward, together with his need to distance himself from the restrictions of the divine power and freedom found in the Arabic Aristotelian philosophers, whom, in general, he regarded as philosophical authorities. But his position on the doctrine is flawed by equivocation and self‐contradiction, flowing from his attempt to reconcile Christian personalist theism with Neoplatonized Aristotleain necessitarian monism. (shrink)

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these (...) papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

As technology redefines relationships, new assumptions are emerging about the ethics of persuasion. In an increasingly global economy, technology is forcing greater transparency onto businesses and governments as the moral context of their communications is inseparable from the competitive nature of the business world. This article suggests that moral boundaries will be set naturally, that consumers have a moral obligation to excercise "due diligence" in their acceptance of messages, and that no one is in charge of the global economy's conventions (...) and morality. The system ultimately depends on participants to keep their own self-interested boat in the race. (shrink)

In June 21, 1990, the Joneses, an African-American family living in the mainly white and working-class neighbourhood of St. Paul in Minnesota, saw a small white cross burning in their yard. By placing the burning cross on the yard, the Minnesota Supreme Court argued that one of the accused, Robert A Viktora, had engaged in ‘fighting words’. However, the US Supreme Court reversed this decision, arguing that the local authority in St Paul only legally banned certain ‘fighting words’, but (...) not others. Judith Butler explores this legal case, R.A.V. v. St. Paul. Judith Butler argues in her earlier work that the Supreme Court in effect represented the burning cross as being non-performative and simply a vehicle of expression rather than a historical symbol of hate speech towards African-Americans. In this paper, I look again at the R.A.V. case. But I do so by both drawing on what Butler explicitly says about the case in her early work and integrating this with her later work on the ethics of grief, state hegemony and public assemblies. Furthermore, I also incorporate some of the insights of the Bakhtin Circle into Butler’s work to strengthen her arguments. The paper then revisits R.A.V. v. St. Paul and shows how Reaganite state hegemony effectively transformed issues of racism surrounding this free speech case into ‘monologic’ and ‘ungrievable’ public matters of concern. The paper concludes by briefly discussing counter-hegemonic politics of free speech. (shrink)

Emotion processing is known to be impaired in psychopathy, but less is known about the cognitive mechanisms that drive this. Our study examined experiencing and suppression of emotion processing in psychopathy. Participants, violent offenders with varying levels of psychopathy, viewed positive and negative images under conditions of passive viewing, experiencing and suppressing. Higher scoring psychopathics were more cardiovascularly responsive when processing negative information than positive, possibly reflecting an anomalously rewarding aspect of processing normally unpleasant material. When required to experience emotional (...) response, by ‘getting into the feeling’ of the emotion conveyed by a negative image, higher factor 1 psychopathic individuals showed reduced responsiveness, suggesting that they were less able to do this. These data, together with the absence of corresponding differences in subjective self-report might be used to inform clinical strategies for normalising emotion processing in psychopathic offenders to improve treatment outcome, and reduce risk amongst this client group. (shrink)

We consider the informal concept of "computability" or "effective calculability" and two of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness". We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. After a careful (...) historical and conceptual analysis of computability and recursion we make several recommendations in section §7 about preserving the intensional differences between the concepts of "computability" and "recursion." Specifically we recommend that: the term "recursive" should no longer carry the additional meaning of "computable" or "decidable;" functions defined using Turing machines, register machines, or their variants should be called "computable" rather than "recursive;" we should distinguish the intensional difference between Church's Thesis and Turing's Thesis, and use the latter particularly in dealing with mechanistic questions; the name of the subject should be "Computability Theory" or simply Computability rather than "Recursive Function Theory.". (shrink)

This article is an accompaniment to Anthony Freeman’s review of Views into the Chinese Room, reflecting on some pertinent outstanding questions about the Chinese room argument. Although there is general agreement in the artificial intelligence community that the CRA is somehow wrong, debate continues on exactly why and how it is wrong. Is there a killer counter-argument and, if so, what is it? One remarkable fact is that the CRA is prototypically a thought experiment, yet it has been very little (...) discussed from the perspective of thought experiments in general. Here, I argue that the CRA fails as a thought experiment because it commits the fallacy of undersupposing, i.e., it leaves too many details to be filled in by the audience. Since different commentators will often fill in details differently, leading to different opinions of what constitutes a decisive counter, the result is 21-plus years of inconclusive debate. (shrink)

This important new text establishes a framework for discussing, understanding, and ultimately making sound decisions on meeting these ethical challenges.

We begin with the history of the discovery of computability in the 1930’s, the roles of Gödel, Church, and Turing, and the formalisms of recursive functions and Turing automatic machines . To whom did Gödel credit the definition of a computable function? We present Turing’s notion [1939, §4] of an oracle machine and Post’s development of it in [1944, §11], [1948], and finally Kleene-Post [1954] into its present form. A number of topics arose from Turing functionals including continuous functionals on (...) Cantor space and online computations. Almost all the results in theoretical computability use relative reducibility and o-machines rather than a-machines and most computing processes in the real world are potentially online or interactive. Therefore, we argue that Turing o-machines, relative computability, and online computing are the most important concepts in the subject, more so than Turing a-machines and standard computable functions since they are special cases of the former and are presented first only for pedagogical clarity to beginning students. At the end in §10–§13 we consider three displacements in computability theory, and the historical reasons they occurred. Several brief conclusions are drawn in §14. (shrink)

In this essay I will discuss and appraise two conflicting answers to the question of whether there was a crisis in Ptolemaic astronomy prior to the Copernican revolution. I will begin by giving a brief account of why anybody should be interested in this question. I will discuss the two conflicting answers of Kuhn (1962, 1970), who claims to present evidence which shows that Ptolemaic astronomy was anomaly-ridden at the time of Copernicus, and of Gingerich (1975), who claims that the (...) supposed anomalies, which have been passed down in the historical literature due to poor scholarship, are fictitious. Finally I will appraise Gingerich’s criticism of Kuhn, giving my own evaluation of Gingerich’s arguments. I conclude that Gingerich’s arguments against the existence of a technical crisis in Ptolemaic astronomy prior to Copernicus appear to be, either arguments against the efficacy of the Copernican system, or arguments based on definitions of complexity which are not directly attributable to Kuhn. (shrink)

Let M be a smooth, compact manifold of dimension n ≥ 5 and sectional curvature | K | ≤ 1. Let Met (M) = Riem(M)/Diff(M) be the space of Riemannian metrics on M modulo isometries. Nabutovsky and Weinberger studied the connected components of sublevel sets (and local minima) for certain functions on Met (M) such as the diameter. They showed that for every Turing machine T e , e ∈ ω, there is a sequence (uniformly effective in e) of homology (...) n-spheres {P k e } k ∈ ω which are also hypersurfaces, such that P k e is diffeomorphic to the standard n-sphere S n (denoted P k e ≈ diff S n ) iff T e halts on input k, and in this case the connected sum N k e =M ♯ P k e ≈ diff M , so N k e ∈ Met(M), and N k e is associated with a local minimum of the diameter function on Met(M) whose depth is roughly equal to the settling time σ e (k) of T e on inputs y i } ∈ ω of c.e. sets so that for all i the settling time of the associated Turing machine for A i dominates that for A i + 1 , even when the latter is composed with an arbitrary computable function. From this, Nabutovsky and Weinberger showed that the basins exhibit a "fractal" like behavior with extremely big basins, and very much smaller basins coming off them, and so on. This reveals what Nabutovsky and Weinberger describe in their paper on fractals as "the astonishing richness of the space of Riemannian metrics on a smooth manifold, up to reparametrization." From the point of view of logic and computability, the Nabutovsky-Weinberger results are especially interesting because: (1) they use c.e. sets to prove structural complexity of the geometry and topology, not merely undecidability results as in the word problem for groups, Hilbert's Tenth Problem, or most other applications; (2) they use nontrivial information about c.e. sets, the Soare sequence {A i } i ∈ ω above, not merely G öodel's c.e. noncomputable set K of the 1930's; and (3) without using computability theory there is no known proof that local minima exist even for simple manifolds like the torus T 5 (see §). (shrink)

"This book discusses the vast and complex range of choices in between blanket amnesty and total accountability through criminal justice, and does so with ...

Debates over vaccine mandates raise intense emotions, as reflected in the current controversy over whether to mandate the vaccine against human papilloma virus (HPV), the virus that can cause cervical cancer. Public health ethics so far has failed to facilitate meaningful dialogue between the opposing sides. When stripped of its emotional charge, the debate can be framed as a contest between competing ethical values. This framework can be conceptualized graphically as a conflict between autonomy on the one hand, which militates (...) against government intrusion, and beneficence, utilitarianism, justice, and nonmaleficence on the other, which may lend support to intervention. When applied to the HPV vaccine, this framework would support a mandate based on utilitarianism, if certain conditions are met and if herd immunity is a realistic objective. (shrink)

In developing a framework for assessing privacy risks, Dupras and Bunnik’s “Toward a framework for assessing privacy risks in multi-omic research and databases” considers the question of whe...

John Searle’s Chinese room argument is a celebrated thought experiment designed to refute the hypothesis, popular among artificial intelligence scientists and philosophers of mind, that “the appropriately programmed computer really is a mind”. Since its publication in 1980, the CRA has evoked an enormous amount of debate about its implications for machine intelligence, the functionalist philosophy of mind, theories of consciousness, etc. Although the general consensus among commentators is that the CRA is flawed, and not withstanding the popularity of the (...) systems reply in some quarters, there is remarkably little agreement on exactly how and why it is flawed. A newcomer to the controversy could be forgiven for thinking that the bewildering collection of diverse replies to Searle betrays a tendency to unprincipled, ad hoc argumentation and, thereby, a weakness in the opposition’s case. In this paper, treating the CRA as a prototypical example of a ‘destructive’ thought experiment, I attempt to set it in a logical framework, which allows us to systematise and classify the various objections. Since thought experiments are always posed in narrative form, formal logic by itself cannot fully capture the controversy. On the contrary, much also hinges on how one translates between the informal everyday language in which the CRA was initially framed and formal logic and, in particular, on the specific conception of possibility that one reads into the logical formalism. (shrink)