Philosophy should not try to assimilate itself to the aims of the sciences. Scientism stems from the false assumption that a representation of the world minimally based on local perspectives is what best serves self-understanding. Philosophy must concern itself with the history of our conceptions, and we must overcome the need to think that this history should ideally be vindicatory. There is no basic conflict between arguing within the framework of our ideas, reflectively making better sense of them, and understanding (...) their highly contingent history. The third of these activities is an inescapable part of the second. (shrink)

I outline some of my work and results on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system’s matter-gravity entanglement entropy. The main arguments presented are: that this hypothesis is capable of resolving what I call the second-law puzzle, i.e. the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; that the black hole information loss puzzle may be (...) regarded as a special case of this second law puzzle and that therefore the same resolution applies to it; that the black hole thermal atmosphere puzzle can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity in such a way that the partial states of matter and gravity are each approximately thermal equilibrium states ; that the Susskind–Horowitz–Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string cannot be quite correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which ) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in is based on a general result, which I also describe, which concerns the likely state of a quantum system when it is weakly coupled to an energy-bath and the total state is a random pure state with a given energy. This result generalizes Goldstein et al.’s ‘canonical typicality’ result to systems which are not necessarily small. (shrink)

A computable structure $\mathcal {A}$ is $\mathbf {x}$-computably categorical for some Turing degree $\mathbf {x}$ if for every computable structure $\mathcal {B}\cong\mathcal {A}$ there is an isomorphism $f:\mathcal {B}\to\mathcal {A}$ with $f\leq_{T}\mathbf {x}$. A degree $\mathbf {x}$ is a degree of categoricity if there is a computable structure $\mathcal {A}$ such that $\mathcal {A}$ is $\mathbf {x}$-computably categorical, and for all $\mathbf {y}$, if $\mathcal {A}$ is $\mathbf {y}$-computably categorical, then $\mathbf {x}\leq_{T}\mathbf {y}$. We construct a $\Sigma^{0}_{2}$ set whose degree (...) is not a degree of categoricity. We also demonstrate a large class of degrees that are not degrees of categoricity by showing that every degree of a set which is 2-generic relative to some perfect tree is not a degree of categoricity. Finally, we prove that every noncomputable hyperimmune-free degree is not a degree of categoricity. (shrink)

This essay asks why Aristotle, certainly no friend to unlimited democracy, seems so much more comfortable with unconstrained rhetoric in political deliberation than current defenders of deliberative democracy. It answers this question by reconstructing and defending a distinctly Aristotelian understanding of political deliberation, one that can be pieced together out of a series of separate arguments made in the Rhetoric, the Politics, and the Nicomachean Ethics.

Abstract The idea of a purely civic nationalism has attracted Western scholars, most of whom rightly disdain the myths that sustain ethnonationalist theories of political community. Civic nationalism is particularly attractive to many Americans, whose peculiar national heritage encourages the delusion that their mutual association is based solely on consciously chosen principles. But this idea misrepresents political reality as surely as the ethnonationalist myths it is designed to combat. And propagating a new political myth is an especially inappropriate way of (...) defending the legacy of Enlightenment liberalism from the dangers posed by the growth of nationalist political passions. (shrink)

No understanding of morality has more zealous or influential defenders among academic philosophers than Kant’s. Yet as Michael Rosen demonstrates in The Shadow of God, there is a sense in which Kant’s critics take his conception of freedom more seriously nowadays than his defenders. As a result, contemporary versions of “Kantian ethics” often end up challenging what Rosen calls “the ethics of Kant,” not just the claims of rival moral theories. Rosen supports this surprising conclusion with some powerful arguments, showing (...) that we cannot make sense of Kantian moral philosophy or its extraordinary impact on modern philosophy while detaching it from Kant’s conception of transcendental freedom. But Rosen overstates the continuity between Kant and the Idealist philosophers that he inspired. Thinkers like Schiller, Schelling, and Hegel took Kant’s concept of transcendental freedom far more seriously than defenders of Kantian ethics do today. But precisely because they did so, they felt compelled to address a whole new set of problems, which could be solved only by radically transforming the conception of freedom that they received from Kant. (shrink)

An old question, still much discussed in moral philosophy, is whether there is any ethical knowledge. It is closely related, by simple etymology, to the question of cognitivism in ethics. Despite the fact that the terms ‘cognitivism’ and ‘objectivism’ seem sometimes to be used interchangeably, I take it that the question whether there can be ethical knowledge is not the same as the question whether ethical outlooks can be objective. A sufficient reason for this is that an ethical outlook might (...) be taken to consist of rules or principles, which do not admit of truth or falsehood and so cannot be objects of knowledge, but which can be seen as having an objective basis. (shrink)

The Prague Philosopher Bernard Bolzano (1781-1848) has long been admired for his groundbreaking work in mathematics: his rigorous proofs of fundamental theorems in analysis, his construction of a continuous, nowhere-differentiable function, his investigations of the infinite, and his anticipations of Cantor's set theory. He made equally outstanding contributions in philosophy, most notably in logic and methodology. One of the greatest mathematician-philosophers since Leibniz, Bolzano is now widely recognised as a major figure of nineteenth-century philosophy. Praised by Husserl as “one (...) of the greatest logicians of all times,” he has also been recognised by Michael Dummett as one of the first modern analytic philosophers and by Alberto Coffa as the founder of the “semantic tradition.” This volume contains English translations of the essay “On the Mathematical Method,” a concise introduction to Bolzano’s logic and philosophy of mathematics, as well as substantial selections from his correspondence with Franz Exner, Professor of Philosophy at the Charles University in Prague in the 1830s and 40s. It will be of interest to students of Austrian philosophy, the development of analytic philosophy, the philosophy of language, and the history and philosophy of logic and mathematics. (shrink)

ABSTRACT This paper reconsiders the arguments of my book, The Longing for Total Revolution, in response to the thoughtful analyses collected in this symposium. It restates the book’s main genealogical and critical arguments about the philosophical sources of uniquely modern forms of social discontent, while distinguishing those arguments from recent attempts to uncover the deeper, theological sources of discontent. It focuses, in particular, on the role played in modern social discontent by the group of thinkers I describe as the “Kantian (...) left”: a long line of social critics who sought to “realize” Kant’s understanding of human autonomy in society, thereby gaining what Marx called “control and conscious mastery” over our social world, not just over our wills. (shrink)

We provide a suitable theoretical foundation for the notion of the quantum coherent state which describes the electrostatic field due to a static external macroscopic charge distribution introduced by the author in 1998 and use it to rederive the formulae obtained in 1998 for the inner product of a pair of such states. (We also correct an incorrect factor of 4π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\pi$$\end{document} in some of those formulae.) Contrary to what one might expect, (...) this inner product is usually non-zero whenever the total charges of the two charge distributions are equal, even if the charge distributions themselves are different. We actually display two different frameworks that lead to the same inner-product formulae, in the second of which Gauss’s law only holds in expectation value. We propose an experiment capable of ruling out the latter framework. We then address the problem of finding a product picture for QED—i.e. a reformulation in which it has a total Hamiltonian, arising as a sum of a free electromagnetic Hamiltonian, a free charged-matter Hamiltonian and an interaction term, acting on a Hilbert space which is a subspace (the physical subspace) of the full tensor product of a charged-matter Hilbert space and an electromagnetic-field Hilbert space. (The traditional Coulomb gauge formulation of QED isn’t a product picture in this sense because, in it, the longitudinal part of the electric field is a function of the charged matter operators.) Motivated by the first framework for our coherent-state construction, we find such a product picture and exhibit its equivalence with Coulomb gauge QED both for a charged Dirac field and also for a system of non-relativistic charged balls. For each of these systems, in all states in the physical subspace (including the vacuum in the case of the Dirac field) the charged matter is entangled with longitudinal photons and Gauss’s law holds as an operator equation; albeit the electric field operator (and therefore also the full Hamiltonian) while self-adjoint on the physical subspace, fails to be self-adjoint on the full tensor-product Hilbert space. The inner products of our electrostatic coherent states and the product picture for QED are relevant as analogues to quantities that play a rôle in the author’s matter-gravity entanglement hypothesis. Also, the product picture provides a temporal gauge quantization of QED which appears to be free from the difficulties which plagued previous approaches to temporal-gauge quantization. (shrink)

This paper uses E. M. Forster’s novel Howards End to help articulate what I describe as a moral pluralist approach to moral conflict. Moral pluralism, I argue here, represents a way of responding to the moral conflicts we encounter in our lives, rather than the mere acknowledgment of their inevitability, as suggested by value pluralists like Isaiah Berlin. The tragic view of moral conflict epitomized by Sophocles’ Antigone and endorsed by most theories of value pluralism, tells us that we must (...) choose between moral commitments and reconcile ourselves to the moral regrets that inevitably follow from moral choice. The moral pluralist view, in contrast, suggests that we should seek means, however imperfect, of satisfying conflicting moral commitments and minimizing causes for moral regret. That view, I argue, drives the words and actions of Forster’s heroine in Howards End, Margaret Schlegel. Confronted with a battle between a willful patriarch and a self-righteous sister, a conflict that maps neatly onto the central conflict in Sophocles’ tragedy, Margaret refuses to take sides without refusing to make moral choices. And in doing so, she comes to exemplify an unexpected kind of moral heroism. (shrink)

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and weak updating (...) axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability. (shrink)

The scholastic philosopher is interested in definition for a different reason than the lexicographer and linguist. The philosopher is trying to learn things. Fe defines, after investigating reality, in an attempt to describe reality clearly and to sum up some aspect of his understanding of reality. Hence, we find our scholastic philosophers adopting as a main feature of their method this insistence on defining, on precise and detailed explanation of their definitions, and on proving that their definitions da correctly express (...) what a nature or activity is. A dictionary of the language of scholastic philosophy fitted to the needs of beginners and of undergraduate students of the subject is not available in English. (shrink)

We define the bounded jump of $A$ by $A^{b}=\{x\in \omega \mid \exists i\leq x[\varphi_{i}\downarrow \wedge\Phi_{x}^{A\upharpoonright \!\!\!\upharpoonright \varphi_{i}}\downarrow ]\}$ and let $A^{nb}$ denote the $n$th bounded jump. We demonstrate several properties of the bounded jump, including the fact that it is strictly increasing and order-preserving on the bounded Turing degrees. We show that the bounded jump is related to the Ershov hierarchy. Indeed, for $n\geq2$ we have $X\leq_{bT}\emptyset ^{nb}\iff X$ is $\omega^{n}$-c.e. $\iff X\leq_{1}\emptyset ^{nb}$, extending the classical result that $X\leq_{bT}\emptyset '\iff (...) X$ is $\omega$-c.e. Finally, we prove that the analogue of Shoenfield inversion holds for the bounded jump on the bounded Turing degrees. That is, for every $X$ such that $\emptyset ^{b}\leq_{bT}X\leq_{bT}\emptyset ^{2b}$, there is a $Y\leq_{bT}\emptyset ^{b}$ such that $Y^{b}\equiv_{bT}X$. (shrink)

Cet article étudie les principales classifications grecques anciennes des sciences mathématiques. Je souligne le rôle joué par Platon dans cette topique.

The scholastic philosopher is interested in definition for a different reason than the lexicographer and linguist. The philosopher is trying to learn things. Fe defines, after investigating reality, in an attempt to describe reality clearly and to sum up some aspect of his understanding of reality. Hence, we find our scholastic philosophers adopting as a main feature of their method this insistence on defining, on precise and detailed explanation of their definitions, and on proving that their definitions da correctly express (...) what a nature or activity is. A dictionary of the language of scholastic philosophy fitted to the needs of beginners and of undergraduate students of the subject is not available in English. (shrink)

Abduction was first introduced in the epistemological context of scientific discovery. It was more recently analyzed in artificial intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from events E if H is a good explanation of E. The paper surveys four known schemes for abduction (...) that can be used in both fields. Its first contribution is a taxonomy of these schemes according to a common semantic framework based on belief revision. Its second contribution is to produce, for each non-trivial scheme, a representation theorem linking its semantic framework to a set of postulates. Its third contribution is to present semantic and axiomatic arguments in favor of one of these schemes, ordered abduction, which has never been vindicated in the literature. (shrink)

Anderson and Csima :245–264, 2014) defined a jump operator, the bounded jump, with respect to bounded Turing reducibility. They showed that the bounded jump is closely related to the Ershov hierarchy and that it satisfies an analogue of Shoenfield jump inversion. We show that there are high bounded low sets and low bounded high sets. Thus, the information coded in the bounded jump is quite different from that of the standard jump. We also consider whether the analogue of the Jump (...) Theorem holds for the bounded jump: do we have A≤bTB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \le _{bT}B$$\end{document} if and only if Ab≤1Bb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^b \le _1 B^b$$\end{document}? We show the forward direction holds but not the reverse. (shrink)

This critical notice of Stephen Neale's "Descriptions", (MIT Press, 1990) summarizes the content of the book and presents several objections to its arguments, as well as praising Neale for showing just how close the linguistic notion of L F is to the analytic philosopher's notion of "logical form". It is claimed that Neale's use of generalized quantifiers to represent definite descriptions from Russell's account by which descriptions are "incomplete symbols". I also argue that his assessment of the Quine/Smullyan exchange about (...) "Necessarily the number of the planets is greater than seven" is incorrect. (shrink)

Two main schemes explain how a system adapts to its environment. Evolutionary models are grounded on three usual processes (variation, transmission, selection) acting at the population level. Learning models are concerned with the endogenous search for a better performance at the individual level. The first ones were initially favored by biology and the second well illustrated by game theory. The article examines first how game theory went to evolution and how biology later considered learning. It shows some examples of a (...) hybrid use of models of each type. It finally proposes a common framework for both types of models. (shrink)

The common ancestor of modern humans and the great apes is estimated to have lived between 5 and 8 Myrs ago, but the earliest evidence in the human, or hominid, fossil record is Ardipithecus ramidus, from a 4.5 Myr Ethiopian site. This genus was succeeded by Australopithecus, within which four species are presently recognised. All combine a relatively primitive postcranial skeleton, a dentition with expanded chewing teeth and a small brain. The most primitive species in our own genus, Homo habilis (...) and Homo rudolfensis, are little advanced over the australopithecines and with hindsight their inclusion in Homo may not be appropriate. The first species to share a substantial number of features with later Homo is Homo ergaster, or ‘early African Homo erectus’, which appears in the fossil record around 2.0 Myr. Outside Africa, fossil hominids appear as Homo erectus‐like hominids, in mainland Asia and in Indonesia close to 2 Myr ago; the earliest good evidence of ‘archaic Homo’ in Europe is dated at between 600–700 Kyr before the present. Anatomically modern human, or Homo sapiens, fossils are seen first in the fossil record in Africa around 150 Kyr ago. Taken together with molecular evidence on the extent of DNA variation, this suggests that the transition from ‘archiac’ to ‘modern’ Homo may have taken place in Africa. (shrink)

States are in the process of creating controversial legislation aimed at subjecting ‘harmful’ online communication on social media and search engines to new regulatory regimes. Critics argue that these measures are serious threats to the right to freedom of expression and freedom from surveillance. This article first draws on elements of systems theory to reframe the right to freedom of expression in democracy as a means of protecting the value of generalised second-order observation. Taking the UK’s Online Safety bill as (...) the paradigm example of the new laws, the article analyses the concept of harmful communication at three levels: society, organisation, and subject. It identifies a shift in the law’s epistemic approach to communication, by which individuals are reconfigured from agential subjects into contingent users, whose capacities are determined by the structure of online communication platforms. In this configuration, norms previously considered indispensible are relegated to second-order effects of the affordances of media. Arguing that it is insufficient to merely reaffirm subjective rights in light of this shift, the article suggests systems theoretical analysis as a means of identifying lines of critique. (shrink)

A correspondence theory of truth involves at least three constituents; the truth bearer, propositions, which stand in a relation of correspondence to the third element, the truth maker, some objects or fact with which the truth maker must correspond. Correspondence theories differ about the nature of truth makers, over whether one needs to include properties, and in particular over whether facts must be assumed in addition in order to give a correct account not merely of the conditions under which propositions (...) are true, but also what makes them true. Simple modal propositions state that objects necessarily or possibly have certain properties. What makes such propositions true? In this paper I want to consider various candidates for an account of the truth makers of modal propositions. After rejecting several alternatives that rely only on objects and properties, i.e., truth conditions, I will present several refinements of a fact based theory culminating in the view that truth makers for modal propositions are actual or non-actual facts which have facts and possible worlds as constituents. (shrink)