We locate winning strategies for various ${\mathrm{\Sigma }}_{3}^{0}$ -games in the L-hierarchy in order to prove the following: Theorem 1. KP+Σ₂-Comprehension $\vdash \exists \alpha L_{\alpha}\ models"\Sigma _{2}-{\bf KP}+\Sigma _{3}^{0}-\text{Determinacy}."$ Alternatively: ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ "there is a β-model of ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17 em}}{\mathrm{\Sigma }}_{3}^{0}$ -Determinacy." The implication is not reversible. (The antecedent here may be replaced with ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left({\mathrm{\Pi }}_{3}^{1}\right)-{\mathrm{C}\mathrm{A}}_{0}:\text{\hspace{0.17em}}{\mathrm{\Pi }}_{3}^{1}$ instances of Comprehension with only ${\mathrm{\Pi }}_{3}^{1}$ -lightface definable parameters—or even weaker theories.) Theorem 2. KP +Δ₂-Comprehension +Σ₂-Replacement + ${\mathrm{\Sigma }}_{3}^{0}\phantom{\rule{0ex}{0ex}}$ -Determinacy. (Here AQI (...) is the assertion that every arithmetical quasi-inductive definition converges.) Alternatively: $\Delta _{3}^{1}{\rm CA}_{0}+{\rm AQI}\nvdash \Sigma _{3}^{0}$ -Determinacy. Hence the theories: ${\mathrm{\Pi }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0},\text{\hspace{0.17em}}{\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\text{\hspace{0.17em}}{\mathrm{\Sigma }}_{3}^{0}-\mathrm{D}\mathrm{e}\mathrm{t}\phantom{\rule{0ex}{0ex}}$ -Det, ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\mathrm{A}\mathrm{Q}\mathrm{I}$ , and ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ are in strictly descending order of strength. (shrink)

Anna Wexler and Laura Specker Sullivan (2023) draw on their positionality as Global North early career neuroethics scholars to initiate a meaningful and timely conversation on Translational Neuroet...

This essay presents a critique of current views of Hugo Grotius which erroneously see him as a major theorist of natural rights and a formative influence upon the rights theory of Thomas Hobbes. Especially singled out for criticism are the misconceptions due to Richard Tuck in a number of writings that discuss the political ideas of Grotius and Hobbes and the relationship between them. In an examination of Hobbes's conception of natural rights, the essay reaffirms its originality and notes its (...) revolutionary potential contrary to the main intention of Hobbes's own political doctrine. (shrink)

Hempel's Dilemma is the claim that physicalism is an ill-formed thesis because it can offer no account of the physics that it refers to: current physics will be discarded in the future, and we don't yet know the nature of future physics. This article confronts the first horn of the dilemma, and argues that our knowledge of current physics is sufficient for offering a physicalist ontology of the mind. We have good scientific evidence that future physics will be irrelevant to (...) the mind-body problem because mental processes lie safely within the well-understood domains of applicability of current physical theories. (shrink)

Ideal interpretation is understanding a text in the best possible way. It is usually used when the text has a canonical status, such as the Bible or the U.S. Constitution. We argue that Zhu Xi’s view about interpreting the Four Books and Ronald Dworkin’s view about constitutional interpretation are examples of ideal interpretation and that their basic principles are similar. Each holds, roughly, that their target text contains moral truth; that the author’s mind requires the mediation of learning; that the (...) purpose of interpretation is not only to lead the reader to the moral truth but to become a better person; that all propositions are about the same moral truth or about political justice; that the interpretation ultimately must come from oneself, purged of prejudices; and that the only correct interpretation is one that captures the original meaning. (shrink)

It is widely accepted that EinstcinRi7;s general theory of relativity is an satisfactory description of gravity 0nly in the macroscopic limit, where quantum eiTcc1;s may be neglected. Presumably this theory is inapplicable at the Planck length, but recently much attention has been devoted to gravitational theory at intermediate length scales where quantum affects 0f matter are inescapable, but where there is an general assumption that the gravitational Held may bc treated as a classical background, augmented if necessary by quamtizcd linearized (...) pertur-. (shrink)

Wiggins recently proposed construing frege's 'unsaturated expressions' as containing two elements, Viz., (1) a copula and (2) a general term standing for a concept; but he argued that concepts, So understood, Were not to be identified with properties. While accepting the above division of 'unsaturated expressions', I argue, Contra wiggins, That concepts, So understood, Were precisely to be identified with properties.

Rid and Wendler propose the development of a Patient Preference Predictor (PPP), an actuarial model for predicting incapacitated patient’s life-sustaining treatment preferences across a wide range of end-of-life scenarios. An actuarial approach to end-of-life decision making has enormous potential, but transferring the logic of actuarial prediction to end-of-life decision making raises several conceptual complexities and logistical problems that need further consideration. Actuarial models have proven effective in targeted prediction tasks, but no evidence supports their effectiveness in the kind of broad (...) spectrum prediction task that is the proposed goal of the PPP. We argue that a more focused approach, targeting specific medical conditions and generating treatment predictions based on the preferences of individuals with actual disease experience, is both more firmly grounded in past research and is a more prudent initial strategy for exploring the efficacy of actuarial prediction in end-of-life decision making. (shrink)

We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

Using covariant derivatives and the operator definitions of quantum mechanics, gauge invariant Proca and Lehnert equations are derived and the Lorenz condition is eliminated in U(1) invariant electrodynamics. It is shown that the structure of the gauge invariant Lehnert equation is the same in an O(3) invariant theory of electrodynamics.

Equipoise is advocated as a means of achieving high scientific and ethical standards in randomised trials. As used in the context of research the word describes a state of uncertainty characterised by the belief that in a trial no arm is known to offer greater harm or benefit than any other arm. Clinicians who lack personal equipoise are advised to accept clinical or communal equipoise, based on current unresolved disagreement among the medical profession. Equipoise is mainly discussed in the literature (...) as an issue for senior doctors and research directors. Limitations of professional equipoise are reviewed, and data on the neglected topic of patients' equipoise are reported using the example of breast cancer trials. In theory, a patient who gives informed and voluntary consent to enter a randomised trial has achieved the equilibrium of equipoise. In practice, equipoise among patients ranges from personal to proxy acceptance. (shrink)

In this paper we introduce a poset of subvarieties of BL-algebras, whose completion is the entire lattice of subvarietes; we exhibit also a description of this poset in terms of finite sequences of functions on the natural numbers.

This book brings together both new and previously published essays on the Greek political history of the fifth century BC and historiography. It examines the relationship between philosophy and social/political conditions, and includes a new analysis of Aristotle's views on slavery and a discussion of the practicality of Plato's political theories.

We present in this article a new logical system inspired from linear logic. This system is designed in order to express causality and dynamism. The cut elimination theorem holds for this logic. Examples of applications are given.

Open peer commentary on the article “Social Autopoiesis?” by Hugo Urrestarazu. Upshot: Hugo Urrestarazu’s social theoretical concept is reduced to the material reality. These suggestions exclude the essential constructivist character of the social and thereby important social phenomena by definition. The systems theoretical approach by Niklas Luhmann offers an adequate alternative.