We introduce an analogue of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time computable functions. Many basic aspects of the classical theory remain intact, with the added bonus that it becomes sensible to study some special equivalence relations whose complexity is beyond Borel or even analytic. We also introduce an infinite time generalization of the (...) countable Borel equivalence relations, a key subclass of the Borel equivalence relations, and again show that several key properties carry over to the larger class. Lastly, we collect together several results from the literature regarding Borel reducibility which apply also to absolutely $\Delta^1_2$ reductions, and hence to the infinite time computable reductions. (shrink)

We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.

Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number. We analyze some of the basic behavior of these properties, showing, e.g., that the property corresponding to (...) the splitting number coincides with smoothness. We then settle many of the implication relationships between the properties; these relationships turn out to be closely related to (but not the same as) the Borel Tukey ordering on cardinal characteristics. (shrink)

We show that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is Borel complete. In fact we establish that each such G satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of G is Borel reducible to the conjugacy relation on automorphisms of G.

We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel; we investigate the precise complexity of each of these. Finally, we show that the classification problem for pairs of recursively saturated models and for automorphisms of a fixed recursively saturated model are Borel complete.

We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group [Formula: see text] we introduce the [Formula: see text]-jump. We study the elementary properties of the [Formula: see text]-jumps and compare them with other previously studied jump operators. One of our main results is to establish that for many groups [Formula: see text], the [Formula: see text]-jump is proper in the sense that for any Borel equivalence relation [Formula: see text] the [Formula: see (...) text]-jump of [Formula: see text] is strictly higher than [Formula: see text] in the Borel reducibility hierarchy. On the other hand, there are examples of groups [Formula: see text] for which the [Formula: see text]-jump is not proper. To establish properness, we produce an analysis of Borel equivalence relations induced by continuous actions of the automorphism group of what we denote the full [Formula: see text]-tree, and relate these to iterates of the [Formula: see text]-jump. We also produce several new examples of equivalence relations that arise from applying the [Formula: see text]-jump to classically studied equivalence relations and derive generic ergodicity results related to these. We apply our results to show that the complexity of the isomorphism problem for countable scattered linear orders properly increases with the rank. (shrink)

We introduce the computable FS-jump, an analog of the classical Friedman–Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

We study the complexity of the classification problem for countable models of set theory (). We prove that the classification of arbitrary countable models of is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well‐founded models of.

We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above \ in complexity.

We normally take it for granted that other people will live on after we ourselves have died. Even if we do not believe in a personal afterlife in which we survive our own deaths, we assume that there will be a "collective afterlife" in which humanity survives long after we are gone. Samuel Scheffler maintains that this assumption plays a surprising - indeed astonishing - role in our lives.

Mintz examines seventeenth-century reactions to the political philosophy of Thomas Hobbes.

“There is no world of thought that is not a world of language,” Walter Benjamin remarked, “and one only sees in the world what is preconditioned by ...

In light of Jewish tradition and the metaphysics of time, we argue that God can and will change the past. The argument makes for a new answer to the problem of evil and a new theory of atonement.

I argue that the social dimension of alienation, as discussed by Williams and Railton, has been underappreciated. The lesson typically drawn from their exchange is that moral theory poses a threat to the internal integrity of the agent, but there is a parallel risk that moral theory will implicitly construe agents as constitutively alienated from one another. I argue that a satisfying account of agency will need to make room for what I call ‘genuine ethical contact’ with others, both as (...) concrete objects in the world external to ourselves and as subjects who can recognize us reciprocally. (shrink)

Bertrand Russell and the Nature of Propositions offers the first book-length defence of the Multiple Relation Theory of Judgement (MRTJ). Although the theory was much maligned by Wittgenstein and ultimately rejected by Russell himself, Lebens shows that it provides a rich and insightful way to understand the nature of propositional content. In Part I, Lebens charts the trajectory of Russell’s thought before he adopted the MRTJ. Part II reviews the historical story of the theory: What led Russell to deny the (...) existence of propositions altogether? Why did the theory keep evolving throughout its short life? What role did G. F. Stout play in the evolution of the theory? What was Wittgenstein’s concern with the theory, and, if we can’t know what his concern was exactly, then what are the best contending hypotheses? And why did Russell give the theory up? In Part III, Lebens makes the case that Russell’s concerns with the theory weren’t worth its rejection. Moreover, he argues that the MRTJ does most of what we could want from an account of propositions at little philosophical cost. This book bridges the history of early analytic philosophy with work in contemporary philosophy of language. It advances a bold reading of the theory of descriptions and offers a new understanding of the role of Stout and the representation concern in the evolution of the MRTJ. It also makes a decisive contribution to philosophy of language by demonstrating the viability of a no-proposition theory of propositions. (shrink)

What if "liberal democracy" were a contradiction in terms? This book distinguishes liberalism from democracy to defend a Rancirean vision of impure politics. Disclosing Rancire's refusal of ontology as political, The Lessons of Rancire enacts a critical theory beyond unmasking and a democratic politics beyond liberalism.

Philosophical Investigations, Volume 45, Issue 3, Page 320-333, July 2022.

This paper is an attempt to lay out a meta‐ethical position that is inspired by the framework of Wittgenstein's later philosophy. To achieve this goal, this paper is divided into two parts. First, I explore recent attempts to tie Wittgenstein's epistemology in On Certainty to moral epistemology. I argue that there can be a meaningful parallel drawn between the epistemic certainties discussed in On Certainty and what I consider to be moral certainties. These moral certainties are unjustified fundamental moral attitudes (...) that underlie our moral practices. Then, I show how the debate over moral certainty has branched into two directions. One direction presents the concept of moral certainty as a naturalistic concept. On this reading, moral certainties transcend time and place since they are rooted in our natural tendencies to act or not act in certain ways. The other direction presents moral certainty as a distinctly relativistic concept. On this reading, we have our moral certainties because we belong to communities that agree on these certainties. In the second section, I argue that we have both natural, universal certainties and localized, relative certainties. I also argue that our localized certainties are constrained by non‐moral facts about ourselves and about the world. To make this argument, I rely on Wittgenstein's concept of “general facts of nature.” The result of the paper is a meta‐ethical position that can be located in between moral relativism and moral realism. (shrink)

Skepticism in epistemology refers to the supposedly irrational attitude of suspending judgment about all beliefs, particularly those taken for granted. The skeptical attitude presses philosophy to investigate the conditions under which knowledge and justification rather than accidental truths can be arrived at. In the first chapter, we will investigate how to construct a form of radical skepticism known as Pyrrhonian skepticism; we will see how Agrippa's Trilemma builds three ways of skeptical defense to object to three possible conditions in the (...) structuring of epistemic justification. In the second chapter, we will examine infinitism as a possible answer to the trilemma, as well as the conceptual bases that make possible the existence of this possible solution to the skeptical challenge. In the third, the main objection to infinitism known as the finite mind problem will be analyzed. In the fourth chapter, we will look at an alternative formulation of the trilemma, as well as the challenges this approach poses to the anti-skeptical response. (shrink)

In this rejoinder, we respond to two commentaries on the study by Greiff, S.; Stadler, M.; Sonnleitner, P.; Wolff, C.; Martin, R. Sometimes less is more: Comparing the validity of complex problem solving measures. Intelligence 2015, 50, 100–113. The study was the first to address the important comparison between a classical measure of complex problem solving (CPS) and the more recent multiple complex systems (MCS) approach regarding their validity. In the study, we investigated the relations between one classical microworld as (...) the initially developed method (here, the Tailorshop) with three more recently developed multiple complex systems (MCS; here, MicroDYN, Genetics Lab, and MicroFIN) tests. We found that the MCS tests showed higher levels of convergent validity with each other than with the Tailorshop even after reasoning was controlled for, thus empirically distinguishing between the two approaches. The commentary by Kretzschmar and the commentary by Funke, Fischer, and Holt expressed several concerns with how our study was conducted, our data was analyzed, and our results were interpreted. Whereas we acknowledge and agree with some of the more general statements made in these commentaries, we respectfully disagree with others, or we consider them to be at least partially in contrast with the existing literature and the currently available empirical evidence. (shrink)

Taking a thematic approach to Butler as a political thinker, this text develops Butler's theory of the political through an exploration of her politics of troubling.

Abstract: Contemporary analytic philosophers of the “reactive attitudes” tend to share a simple conception of guilt as “self-directed blame”—roughly, an “unpleasant affect” felt in combination with, or in response to, the thought that one has violated a moral requirement, evinced substandard “quality of will,” or is blameworthy. I believe that this simple conception is inadequate. As an alternative, I offer my own theory of guilt’s logic and its connection to morality. In doing so, I attempt to articulate guilt’s defining thought (...) or proposition through an extended investigation and analysis of guilt’s many competing metaphors, which I trace from the Hebrew Bible to the New Testament to Shakespeare to contemporary vernacular. My interpretation of this literary genealogy offers a way to understand guilt’s seemingly disparate metaphors in terms of a single master-image that illuminates our self-conceptions and our relationship to morality. I conclude by making a very brief start toward a moral vindication of guilt against the backdrop of Nietzschean and Freudian analyses that explicitly call guilt’s place in a healthy social and personal life into question. I suggest that once guilt’s logic is made explicit, we can see that it makes sense of, honors, and addresses some of our deepest aspirations and needs. (shrink)

Recently there has been a growing literature on the concept of moral certainty. This concept, which is inspired by Wittgenstein’s reflections in On Certainty, is most prominently argued for by Nigel Pleasants. Pleasants contends that there is a meaningful parallel to be drawn between the epistemic certainties discussed by Wittgenstein and moral certainties. These moral certainties are unreflective, non-propositional, and show in the ways that we act. In addition, these certainties cannot be doubted by a reasonable moral agent. In a (...) recently published article, Fairhurst is critical of Pleasants’ account. Fairhurst argues that there are problems with Pleasants’ example of a moral certainty, 'it is wrong to kill innocent non-threatening people'. Fairhurst appeals to euthanasia as an example of when a reasonable person could meaningfully doubt that it is wrong to kill innocent, non-threatening people. If this is a certainty, then a doubt such as this should not be possible. In addition, he argues that Pleasants’ claim that moral certainties are natural is not well substantiated. In this article, I attempt to defend an account of moral certainty against Fairhurst’s criticisms. I divide his criticisms into two parts. His first set of criticisms deal with Pleasants’ example of a moral certainty. I argue that some of his criticisms are inconsistent while others can be addressed by making a small amendment to Pleasants’ account. His second criticism deals with Pleasants’ claim that moral certainties are natural. In order to address this criticism, I appeal to Machery’s Nomological Account of human nature and use it as a basis that allows us to consistently make the claim that there are natural moral certainties. (shrink)

Bearing Society in Mind disrupts the disciplinary boundaries of economic, political and cultural theory by exploring the theory and politics of the social formation.

Much contemporary metaphysics, moved by an apparent necessity to take reality to consist of given beings and properties, presents us with what appear to be deep problems requiring radical changes in the common sense conception of persons and the world. Contemporary meta-ethics ignores questions about logical form and formulates questions in ways that make the possibility of correct value judgments mysterious. In this book, Wheeler argues that given a Davidsonian understanding of truth, predication, and interpretation, and given a relativised version (...) of Aristotelian essentialism compatible with Davidson’s basic thinking, many metaphysical problems are not very deep. Likewise, many philosophers' claims that common sense needs to be modified are unfounded. He argues further that a proper consideration of questions of logical form clarifies and illuminates meta-ethical questions. Although the analyses and arguments he gives are often at odds with those at which Davidson arrived, they apply the central Davidsonian insights about semantics, understanding, and interpretation. (shrink)

The title of this book echoes a phrase used by the Washington Post to describethe American attempt to kill Saddam Hussein at the start of the war againstIraq. Its theme is the notion of targeting (skopos) as the name of an intentionalstructure in which the subject tries to confirm its invulnerability by aiming todestroy a target. At the center of the first chapter is Odysseus’s killing of the suitors;the second concerns Carl Schmitt’s Roman Catholicism and Political Form; thethird and fourth (...) treat Freud’s “Thoughts for the Times on War and Death” and“The Man Moses and Monotheistic Religion.” Weber then traces the emergenceof an alternative to targeting, first within military and strategic thinking itself(“Network Centered Warfare”), and then in Walter Benjamin’s readings of“Capitalism as Religion” and “Two Poems of Friedrich Hölderlin.”. (shrink)

We have good reason to believe that Nicomachean Ethics VI. 2 is a Nicomachean revision of an originally Eudemian text. Aristotle seems to have inserted lines 1139a31-b11 by means of a marginal note, which the first editor then mistakenly added in the wrong place, and I propose that we move these lines so that they follow the word κοινωνεῖν at 1139a20. The suggested note appears to be Nicomachean for several reasons but most importantly because it contains a desire-based account of (...) the practical intellect as teleologically oriented to action. The NE articulates consequences of this account regarding practical philosophy’s methodology and teleological orientation to action. The EE does not articulate such consequences, and instead seems to assume an object-based account of the practical intellect. Consequently, it would seem that, between the EE and the NE, Aristotle revised his conception of the practical intellect and consequently his conception of practical philosophy. (shrink)

I argue that the paradoxes attributed to the Megarians, namely the Liar, the Sorites, presupposition ("Have you stopped beating your father,") and failure of substitution of co-referential terms in psychological verbs ("The Electra") were intended to be reasons to accept Parmenides view that non-being is an incoherent notion and that there is exactly One Being. That is, Eubulides and others were akin to Zeno, in indirectly supporting Parmenidean monism.

Dasgupta poses a serious challenge to realism about natural properties. He argues that there is no acceptable explanation of why natural properties deserve the value realists assign to them and are consequently absent of value. In response, this paper defines and defends an alternative non-explanatory account of normativity compatible with realism. Unlike Lewis and Sider, who believe it is sufficient to defend realism solely on realist terms, I engage with the challenge on unfriendly grounds by revealing a tu quoque. Dasgupta (...) and anti-realists face a similar challenge to that directed against realism: one that not only undermines the objection to realism by legitimising non-explanatory normativity but leaves them facing a significant dilemma. (shrink)

This is the text of The Lindley Lecture for 1994, given by Samuel Scheffler, an American philosopher.

What is Leibniz’s argument for simple substances? I propose that it is an extension of his prior argument for incorporeal forms as principles of unity for individual corporeal substances. The extension involves seeing the hylomorphic analysis of corporeal substances as implying a resolution of matter into forms, and this seems to demand that forms, which are themselves simple, be the only elements of things. The argument for simples thus presupposes the existence of corporeal substances as a key premise. Yet a (...) theory of simple substances as the elements of things threatens to preclude the existence of corporeal substances for Leibniz, and the extension of the argument for forms into an argument for simples is not cogent. If nothing else rides on the simplicity of individual substances, then perhaps instead of being its most fundamental tenet, the doctrine of simples—the monadology—is something that over-extends and destabilizes Leibniz’s metaphysics. (shrink)

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.

Samuel Sandmel's book: Philo of Alexandria: An Introduction, is a basic introductory, supplementing his own teacher' Goodenough: 'An Introduction to Philo Judaeus, ' and foundation to more recent works on Philo.

In this paper I argue that what has been called Leibniz’s “aggregate argument” for unities in things in fact comprises three quite distinct lines of argument, with different concepts being advanced under the name ‘unity’ and meriting quite different conceptual treatment. Two of those arguments, what I call the Borrowed Reality Argument and the Multitude Argument, also appear in later writings to be further elaborated into arguments not just for unities but for simples. I consider the arguments in detail. I (...) suggest that one of the two, the Borrowed Reality Argument, is philosophically more promising and has the stronger evidence for being central in Leibniz’s thought as he argues for the existence of simple substances. (shrink)