We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support increasing limitwise monotonic on various computable domains. As applications, we provide a characterization of the sets S with computable increasing η-representations using support increasing limitwise monotonic sets on ℚ and note relationships between the class of order-computable sets and the class of support increasing limitwise monotonic sets on certain domains.

We show that the fact that the first player wins every instance of Galvin’s “racing pawns” game is equivalent to arithmetic transfinite recursion. Along the way we analyze the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.

LetEbe a computably enumerable equivalence relation on the setωof natural numbers. We say that the quotient set$\omega /E$realizesa linearly ordered set${\cal L}$if there exists a c.e. relation ⊴ respectingEsuch that the induced structure is isomorphic to${\cal L}$. Thus, one can consider the class of all linearly ordered sets that are realized by$\omega /E$; formally,${\cal K}\left = \left\{ {{\cal L}\,|\,{\rm{the}}\,{\rm{order}}\, - \,{\rm{type}}\,{\cal L}\,{\rm{is}}\,{\rm{realized}}\,{\rm{by}}\,E} \right\}$. In this paper we study the relationship between computability-theoretic properties ofEand algebraic properties of linearly ordered sets realized (...) byE. One can also define the following pre-order$ \le _{lo} $on the class of all c.e. equivalence relations:$E_1 \le _{lo} E_2 $if every linear order realized byE1is also realized byE2. Following the tradition of computability theory, thelo-degrees are the classes of equivalence relations induced by the pre-order$ \le _{lo} $. We study the partially ordered set oflo-degrees. For instance, we construct various chains and anti-chains and show the existence of a maximal element among thelo-degrees. (shrink)

We examine the sequences A that are low for dimension, i.e. those for which the effective dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, that every Martin-Löf random sequence has effective dimension (...) 1 relative to A, and lowishness for K, namely, that the limit of KA/K is 1. We show that there is a perfect [Formula: see text]-class of low for dimension sequences. Since there are only countably many low for random sequences, many more sequences are low for dimension. Finally, we prove that every low for dimension is jump-traceable in order nε, for any ε > 0. (shrink)

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex (...) automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability. (shrink)

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, so (...) we have the second characterization of K-triviality.The proof of the first characterization uses a new cupping result. We prove that if A≰LRB, then for every set X there is a B-random set Y such that X is computable from Y⊕A. (shrink)

It is common to hear talk of the aim of belief and to find philosophers appealing to that aim for numerous explanatory purposes. What belief 's aim explains depends, of course, on what that aim is. Many hold that it is somehow related to truth, but there are various ways in which one might specify belief 's aim using the notion of truth. In this article, by considering whether they can account for belief 's standard of correctness and the epistemic (...) norms governing belief, I argue against certain prominent specifications of belief 's aim given in terms of truth, and advance a neglected alternative. (shrink)

Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimullin and Yamaleev. Using the same techniques, we construct a computably categorical structure of non-computable Scott rank.

The _Physics_ is a foundational work of western philosophy, and the crucial one for understanding Aristotle's views on matter, form, essence, causation, movement, space, and time. This richly annotated, scrupulously accurate, and consistent translation makes it available to a contemporary English reader as no other does—in part because it fits together seamlessly with other closely associated works in the New Hackett Aristotle series, such as the _Metaphysics_, _De Anima_, and forthcoming _De Caelo_ and _On Coming to Be and Passing Away_. (...) Eventually the series will include all of Aristotle's works. Sequentially numbered endnotes provide the information most needed at each juncture, while a detailed Index of Terms indicates places where focused discussion of key notions occurs. An illuminating general Introduction describes the book that lies ahead, explaining what sort of work it is and what sorts of evidence it relies on. (shrink)

Infallibilism is the view that a belief cannot be at once warranted and false. In this essay we assess three nonpartisan arguments for infallibilism, arguments that do not depend on a prior commitment to some substantive theory of warrant. Three premises, one from each argument, are most significant: if a belief can be at once warranted and false, then the Gettier Problem cannot be solved; if a belief can be at once warranted and false, then its warrant can be transferred (...) to an accidentally true belief; if a belief can be at once warranted and false, then it can be warranted and accidentally true. We argue that each of these is either false or no more plausible than its denial. Along the way, we offer a solution to the Gettier Problem that is compatible with fallibilism. (shrink)

1. Happiness, then and now -- Happiness, eudaimonia, and practical reasoning -- Happiness as eudaimonia -- Happiness and virtuous activity -- New directions from old debates -- 2. Happiness then: the sufficiency debate -- Aristotle's case against the sufficiency thesis -- 3. Happiness now: rethinking the self -- Socrates' case for the sufficiency thesis -- Epictetus and the stoic self -- The Stoics' case for the sufficiency thesis -- The embodied conception of the self -- The embodied conception and psychological (...) well-being -- The Stoics' case against the embodied conception. (shrink)

The social sciences playa variety of multifaceted roles in the policymaking process. So varied are these roles, indeed, that it is futile to talk in the singular about the use of social science in policymaking, as if there were one constant relationship between two fixed and stable entities. Instead, to address this issue sensibly one must talk in the plural about uses of dif ferent modes of social scientific inquiry for different kinds of policies under various circumstances. In some cases, (...) the influence of social scientific research is direct and tangible, and the connection between the find ings and the policy is easy to see. In other cases, perhaps most, its influence is indirect-one small piece in a larger mosaic of politics, bargaining, and compromise. Occasionally the findings of social scientific studies are explicitly drawn upon by policymakers in the formation, implementation, or evaluation of particular policies. More often, the categories and theoretical models of social science provide a general background orientation within which policymakers concep tualize problems and frame policy options. At times, the in fluence of social scientific work is cognitive and informational in nature; in other instances, policymakers use social science primarily for symbolic and political purposes in order to le gitimate preestablished goals and strategies. Nonetheless, amid this diversity and variety, troubling general questions persistently arise. (shrink)

Sometimes it takes years of debate for philosophers to discover what it is they really disagree about. Sometimes they talk past each other in long series of books and articles, never guessing at the root disagreement that divides them. But occasionally a day comes when something happens to coax the cat out of the bag. "Aha!" one philosopher exclaims to another, "so that's why you've been disagreeing with me, misunderstanding me, resisting my conclusions, puzzling me all these years!".

Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, or indeed objects at all. Instead, I argue (...) that realists should follow Prior (1971) and others in treating higher-order quantification (e.g. quantification into predicate or sentence position) as a genuine form of quantification in its own right, and so in particular, not to be analysed in terms of first-order quantification over abstract objects. I argue that from this ‘higher-orderist’ perspective, there is a relatively straightforward answer to the question of how possible worlds-as-propositions succeed in representing possibilities. (shrink)

Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, or indeed objects at all. Instead, I argue (...) that realists should follow Prior (1971) and others in treating higher-order quantification (e.g. quantification into predicate or sentence position) as a genuine form of quantification in its own right, and so in particular, not to be analysed in terms of first-order quantification over abstract objects. I argue that from this ‘higher-orderist’ perspective, there is a relatively straightforward answer to the question of how possible worlds-as-propositions succeed in representing possibilities. (shrink)

Western philosophers have made significant contributions to the establishment of government around the world. Philosophers like Plato, Locke, Hobbes, and Machiavelli dramatically influenced the government system not just in foreign countries but also in the Philippines. Hence, this seminar paper explored the political notions of four Western philosophers and positioned them in Duterte’s six years of presidency. In pursuit of this study, the researcher employed a systematic literature review. A systematic review process is used to collect articles, and then a (...) qualitative approach is used to assess them. The researcher came up with four major themes in this study particularly (1) Duterte is a Dictator, not a Philosopher-King, (2) Violators of natural rights, (3) the Sea-monster of Davao, and lastly (4) Love, fear, cruelty, and Duterte. Thus, the researcher concurred that all of the philosophical ideas of the four Western philosophers did not fit or even violated during Duterte’s six years of presidency in the Philippines. (shrink)

This paper will attempt to assess the primary differences between what I take to be the two primary philosophical "traditions" in contemporary French philosophy, using Derrida (transcendence) and Deleuze (immanence) as exemplary representatives. The body of the paper will examine the use of these terms in three different areas of philosophy on which Derrida and Deleuze have both written: subjectivity, ontology, and epistemology. (1) In the field of subjectivity, the notion of the subject has been critiqued in two manners, either (...) by appealing either to the transcendence of the other (Levinas, Derrida) or to the immanent jlux of experience itself, in relation to which the Ego itself is trancendent (Deleuze, Foucault, Sartre, James). (2) In the field of ontology, a purely "immanent" ontology would be an ontology in which there is neither a "beyond" or an "otherwise" Being, nor "interruptions" in Being, both of which would require an appeal to a formal element of transcendence (Deleuze). Such a "transcendent" and aporetic structure, which can never appear or be present as such within Being, is what lies at the basis of the project of deconstruction, with its attendant aporias (Derrida). (3) This distinction, finally, finds parallels in Kant's epistemology, for whom the possible experience is conditioned by purely immanent criteria (Deleuze), whereas what goes beyond the limits of possible experience is transcendent (Derrida). Drawing on these three thread of analysis, the paper concludes with an assessment of what is at stake in the ethical differences between the two traditions. The question of "transcendence" is "What mast I do?", which is the question of morality (a duty or obligation that is beyond being, an "ought" beyond the "is"). The question of "immanence" is "What can I do?" (my power or capacity as an existing individual within being). For Levinas and Derrida, ethics precedes ontology because it is derived from an element of transcendence (the Other); for Deleuze, ethics is ontology because it is derived from the immanent relation of beings to Being at the level of their existence (Spinoza). (shrink)

In this groundbreaking book, Daniel D. Novotny explores one of the most controversial topics of Suarez's philosophy: "beings of reason." Beings of reason are impossible intentional objects, such as blindness and square-circle.

The problem known as Buridan’s Ass says that a hungry donkey equipoised between two identical bales of hay will starve to death. Indecision kills the ass. Some philosophers worry about human analogs. Computer scientists since the 1960s have known about the computer versions of such cases. From what Leslie Lamport calls ‘Buridan’s Principle’—a discrete decision based on a continuous range of input-values cannot be made in a bounded time—it follows that the possibilities for human analogs of Buridan’s Ass are far (...) more wide-ranging and securely provable than has been acknowledged in philosophy. We are never necessarily decisive. This is mathematically provable. I explore four consequences: first, increased interest of the literature’s solutions to Buridan’s Ass; second, a new asymmetry between responsibility for omissions and responsibility for actions; third, clarification of the standard account of akrasia; and, fourth, clarification of the role of credences in normative decision-theory. (shrink)

The Jewish Philosophy Reader is the first comprehensive anthology of classic writings on Jewish philosophy from the Bible to postmodernism. The Reader is clearly divided into four separate parts: Foundations and First Principles, Medieval and Renaissance Jewish Philosophy, Modern Jewish Thought, and Contemporary Jewish Philosophy. Each part is clearly introduced by the editors. The readings featured are representative writings of each era listed above and are from the following major thinkers: Abrabanel, Baeck, Bergman, Borowitz, Buber, Cohen, Crescas, Fackenheim, Geiger, Gersonides, (...) Goodman, Graetz, Halevi, Hartman, Heschel, Hess, Hirsch, Ibn Ezra, Ibn Gabirol, Ibn Paquda, Kellner, Kook, Krochmal, Leibowitz, Levinas, Maimonides, Maybaum, Mendelssohn, Novak, Philo, Plaskow, Rosenzweig, Saadia, Scholem, Seeskin, Soloveitchik, Spinoza, Strauss, Wolf, Zunz. (shrink)

Deleuze’s philosophy of immanence, because it vigorously rejects every appeal to the beyond, is often presumed to be indifferent to the concerns of religion. This book argues against such a presumption. It does so, first of all, by emphasising how both Deleuze’s thought and the notion of religion are motivated by a demand to create new modes of existence, or to imagine and enact a future that would substantively break with the present configuration of being. If Deleuze’s thought and the (...) notion of religion intersect in this regard, then their divergence must be located elsewhere, namely in the distinction between immanence and transcendence. The book thus argues that the enemy of Deleuze’s thought is not religion in general but instead the specific operation of transcendence. Furthermore, it argues that since Deleuze’s thought is not simply anti-religious, it cannot be identified with secularism. Along these lines, the book shows how Deleuzian immanence is able both to oppose religious transcendence and to enter an allliance with immanent accounts of the name of God. The effect of this is to suspend the paralysing debate between religion and the secular in order to attend to the ways in which immanence – whether “religious” or “secular” – is able to break with the present and to create the future. (shrink)

Both new and seasoned psychotherapists wrestle with the relationship between psychological distress and inequality across race, class, gender, and sexuality. How does one address this organically in psychotherapy? What role does it play in therapeutic action? Who brings it up, the therapist or the patient? Daniel José Gaztambide addresses these questions by offering a rigorous decolonial approach that rethinks theory and technique from the ground up, providing an accessible, evidence-informed reintroduction to psychoanalytic practice. He re-examines foundational thinkers from three (...) traditions—Freudian, relational-interpersonal, and Lacanian—through the lens of revolutionary psychiatrist Frantz Fanon, and offers a detailed analysis of Fanon’s psychoanalytic practice. Drawing on rich yet grounded discussions of theory and research, Gaztambide presents a clinical model that facilitates exploration of the social in the clinical space in a manner intimately related to the patient’s presenting problem. In doing so, this book demonstrates that clinicians no longer have to choose between attending to the personal, interpersonal, or sociopolitical. It is a guide to therapeutic action “on the couch,” which envisions political action “off the couch” and in the streets. Decolonizing Psychoanalytic Technique provides a comprehensive, practice-oriented and compelling guide for students, practitioners, and scholars of critical, multicultural and decolonial approaches to psychotherapy. (shrink)

This exceptional anthology immerses students in such powerful ideas that they will find themselves not just reading about, but actually participating in, the kind of philosophical thinking that can change the way they look at their lives and the world around them. Now in a new edition, The Experience of Philosophy features eighty-five readings that challenge students' thinking about God, freedom, reality, nothingness, death, and their own identities. Provocative and accessible, these selections have been carefully chosen for their ability to (...) draw students out of an ordinary frame of reference into exciting new territory. Although the editors include many classic sources from philosophers such as Plato, Descartes, Locke, and Kant, the emphasis is on contemporary writings. Articles by Derek Parfit, Bertrand Russell, and others help students see philosophy's links to literature, the natural sciences, and the physical and social sciences. The sixth edition features twelve new essays--by Augustine, Alvin Plantinga and Daniel Kolak, Georges Rey, Fred Dretske, David Reisman, Paul Teller, Clea F. Rees, Padmasiri de Silva, Daniel Kolak, Karl Marx, Anand Chandavarkar, and Vincent Hendricks--as well as more text boxes offering excerpts from other relevant works. The Experience of Philosophy, Sixth Edition, integrates helpful pedagogical aids including section introductions, a brief introduction to each selection, biographical information on each author, and questions before and after each reading to reinforce main ideas and promote thinking. Further readings after each selection direct students to additional material on related issues. Ideal for introductory philosophy courses, The Experience of Philosophy, Sixth Edition, encourages students to "do" philosophy, rather than just read about its history. (shrink)

We are bombarded with more information each day than our brains can process especially in election season. It's raining bad data, half-truths, and even outright lies. Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and written reports revealing the ways lying weasels can use them.

Much has been written about medicine and the market in recent years. This book is the first to include an assessment of market influence in both developed and developing countries, and among the very few that have tried to evaluate the actual health and economic impact of market theory and practices in a wide range of national settings. Tracing the path that market practices have taken from Adam Smith in the eighteenth century into twenty-first-century health care, Daniel Callahan and (...) Angela A. Wasunna add a fresh dimension: they compare the different approaches taken in the market debate by health care economists, conservative market advocates, and liberal supporters of single-payer or government-regulated systems. In addition to laying out the market-versus-government struggle around the world -- from Canada and the United States to Western Europe, Latin America, and many African and Asian countries -- they assess the leading market practices, such as competition, physician incentives, and co-payments, for their economic and health efficacy to determine whether they work as advertised. This timely and necessary book engages new dimensions of a development that has urgent consequences for the delivery of health care worldwide. (shrink)

Three studies test eight hypotheses about (1) how judgment differs between people who ascribe greater vs. less moral relevance to choices, (2) how moral judgment is subject to task constraints that shift evaluative focus (to moral rules vs. to consequences), and (3) how differences in the propensity to rely on intuitive reactions affect judgment. In Study 1, judgments were affected by rated agreement with moral rules proscribing harm, whether the dilemma under consideration made moral rules versus consequences of choice salient, (...) and by thinking styles (intuitive vs. deliberative). In Studies 2 and 3, participants evaluated policy decisions to knowingly do harm to a resource to mitigate greater harm or to merely allow the greater harm to happen. When evaluated in isolation, approval for decisions to harm was affected by endorsement of moral rules and by thinking style. When both choices were evaluated simultaneously, total harm -- but not the do/allow distinction -- influenced rated approval. These studies suggest that moral rules play an important, but context-sensitive role in moral cognition, and offer an account of when emotional reactions to perceived moral violations receive less weight than consideration of costs and benefits in moral judgment and decision making. (shrink)

The experimental validity of research in the experimental philosophy of free will has been called into question. Several new, important studies (Murray et al. forthcoming; Nadelhoffer et al., Cognitive Science 44 (8): 1–28, 2020 ; Nadelhoffer et al., 2021; Rose et al., Cognitive Science 41 (2): 482–502, 2017 ) are interpreted as showing that the vignette-judgment model is defective because participants only exhibit a surface-level comprehension and not the deeper comprehension the model requires. Participants, it is argued, commit _bypassing_, _intrusion_, (...) and _fatalism_ errors. We respond in two ways: (1) we critique and improve existing methods for assessing deeper comprehension and (2) we develop videos to convey deterministic principles of change that succeed in significantly reducing participants’ bypassing, intrusion, and fatalism errors. Consequently, we have the best existing instrument for gauging folk intuitions about the relationship between free will and determinism. (shrink)

We review the current knowledge concerning strong jump-traceability. We cover the known results relating strong jump-traceability to randomness, and those relating it to degree theory. We also discuss the techniques used in working with strongly jump-traceable sets. We end with a section of open questions.