The vital status of patients who are a part of controlled donation after circulatory death (cDCD) is widely debated in bioethical literature. Opponents to currently applied cDCD protocols argue that they violate the dead donor rule, while proponents of the protocols advocate compatibility. In this article, we argue that both parties often misinterpret the moral implications of the dead donor rule. The rule as such does not require an assessment of a donor’s vital status, we contend, but rather an assessment (...) of whether procurement of organs in cDCD cause the death of the donor or not. We then argue that commonly practiced cDCD protocols do not violate the dead donor rule, since the donation does not trigger or cause the death of the donors. (shrink)

We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.

Alienation is among the most influential terms in Marxist theory, but also one of the most ambiguous and controversial. Unlike previous literature, which has tended to focus on Marx’ early philosophical writings, this offers a novel reinterpretation of the theory of alienation found in Marx’s later works. Rather than conceiving alienation as a subjective experience or an inherent feature of social organization, I contend that alienation in the Marxist sense can be understood as an objective process arising from the appropriation (...) of the results of production and their transformation into capital. This interpretation resolves the main theoretical problems conventionally associated with alienation theory, for example the tendency towards essentialism and moral paternalism. In particular, a Marxist theory of alienation explains the paradox of social power and isolation that characterizes contemporary capitalist societies, in which feelings of powerlessness and loneliness are intensified despite objective increases in humanity’s social power and interdependence. (shrink)

We show that IPC, K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules.

We show that \, the basic theory of bounded arithmetic corresponding to the complexity class \, proves the \ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the \ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, \ can also prove the integer division axiom, and the \-translation of induction and minimization for sharply bounded formulas. Similar consequences hold for the related theories \ and \. As a side (...) result, we also prove that there is a well-behaved \ definition of modular powering in \\). (shrink)

We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most (...) nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal. (shrink)

We study the extension 123) of the theory S21 by instances of the dual weak pigeonhole principle for p-time functions, dWPHPx2x. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie's witnessing theorem for S21+dWPHP. We construct a propositional proof system WF , which captures the Π1b-consequences of S21+dWPHP. We also show that WF p-simulates the Unstructured Extended Nullstellensatz proof system of Buss et al. 256). We prove that (...) dWPHP is equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity. Building on this result, we formalize the Nisan–Wigderson construction in a conservative extension of S21+dWPHP. (shrink)

Excerpt from Die Lehre vom Urteil Windelband hat in seinen "präludien und in dem Aufsatz der Festschrift für Zeller "beiträge zur Lehre vom nega tiven Urteil gerade vermittelst der Urteilslehre den ent scheidenden Schritt zu tun vermocht, der Logik wieder ihre sachliche Heimat im Ganzen der Philos0phie zu bestimmen. Rickerts "gegenstand der Erkenntnis ist sodann das Grund buch für alle logischen Untersuchungen der Werttheorie geworden und geblieben. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. (...) Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

According to John Rawls’s famous Liberal Principle of Legitimacy, the exercise of political power is legitimate only if it is justifiable to all citizens. The currently dominant interpretation of what is justifiable to persons in this sense is an internalist one. On this view, what is justifiable to persons depends on their beliefs and commitments. In this paper I challenge this reading of Rawls’s principle, and instead suggest that it is most plausibly interpreted in externalist terms. On this alternative view, (...) what is justifiable to persons is not in any way dependent on, or relativized to, their beliefs and commitments. Instead, what is justifiable to all in the relevant sense is what all could accept as free and equal. I defend this reinterpretation of the view by showing how it is supported by Rawls’s account of the freedom and equality of persons. In addition, a considerable advantage of this suggestion is that it allows for an inclusive account of to whom the exercise of political power must be made justifiable. (shrink)

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...) existential theories in the process. (shrink)

There have been few attempts thus far to read Rorty through a humanistic lens. This paper is an attempt at making explicit some of the key features of his conception. My main objective is to show that humanism is integral to his philosophy and to explain what it consists in. I focus on Rorty’s secular humanism, which I believe lies at the center of his thought. In sections 2 and 3, I provide an account of key humanist sources, both pragmatist (...) and non-pragmatist. Section 4 examines recent interpretations of Rorty as a humanist. In section 5, I focus on the distinction between the human and nonhuman as the central feature of his humanism. Section 6 outlines Rorty’s project to humanize humanity. In the concluding section, I summarize the key features of his humanism. (shrink)

We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all logics (...) of finite depth and width, and typical examples of logics of finite width and infinite depth. In most cases, we actually show an equivalence with the usual system for classical logic with respect to a naturally defined translation.On the other hand, we establish exponential speed-up of over for all modal and si logics of infinite branching, extending recent lower bounds by P. Hrubeš. We develop a model-theoretical characterization of maximal logics of infinite branching to prove this result. (shrink)

In Beyond the Limits of Thought [2002], Graham Priest argues that logical and semantic paradoxes have the same underlying structure (which he calls the Inclosure Schema ). He also argues that, in conjunction with the Principle of Uniform Solution (same kind of paradox, same kind of solution), this is sufficient to 'sink virtually all orthodox solutions to the paradoxes', because the orthodox solutions to the paradoxes are not uniform. I argue that Priest fails to provide a non-question-begging method to 'sink (...) virtually all orthodox solutions', and that the Inclosure Schema cannot be the structure that underlies the Liar paradox. Moreover, Ramsey was right in thinking that logical and semantic paradoxes are paradoxes of different kinds. (shrink)

We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in PV₁ + dWPHP(PV).

We develop an arithmetical theory and its variant , corresponding to “slightly nonuniform” . Our theories sit between and , and allow evaluation of log-depth bounded fan-in circuits under limited conditions. Propositional translations of -formulas provable in admit L-uniform polynomial-size Frege proofs.

The elementary arithmetic operations +,·,≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${+,\cdot,\le}$$\end{document} on integers are well-known to be computable in the weak complexity class TC0, and it is a basic question what properties of these operations can be proved using only TC0-computable objects, i.e., in a theory of bounded arithmetic corresponding to TC0. We will show that the theory VTC0 extended with an axiom postulating the totality of iterated multiplication proves induction for quantifier-free formulas in the language ⟨+,·,≤⟩\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle{+,\cdot,\le}\rangle}$$\end{document}, and more generally, minimization for Σ0b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma_{0}^{b}}$$\end{document} formulas in the language of Buss’s S2. (shrink)

We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.

We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the level of the substructural hierarchy.

We show that the universally axiomatized, induction-free theory equation image is a sequential theory in the sense of Pudlák's 5, in contrast to the closely related Robinson's arithmetic.

It has been argued that Hume's denial of infinite divisibility entails the falsity of most of the familiar theorems of Euclidean geometry, including the Pythagorean theorem and the bisection theorem. I argue that Hume's thesis that there are indivisibles is not incompatible with the Pythagorean theorem and other central theorems of Euclidean geometry, but only with those theorems that deal with matters of minuteness. The key to understanding Hume's view of geometry is the distinction he draws between a precise and (...) an imprecise standard of equality in extension. Hume's project is different from the attempt made by Berkeley in some of his later writings to save Euclidean geometry. Unlike Berkeley, who interprets the theorems of Euclidean geometry as false albeit useful approximations of geometrical facts, Hume is able to save most of the central theorems as true. (shrink)

D’Aquino et al. (J Symb Log 75(1):1–11, 2010) have recently shown that every real-closed field with an integer part satisfying the arithmetic theory IΣ4 is recursively saturated, and that this theorem fails if IΣ4 is replaced by IΔ0. We prove that the theorem holds if IΣ4 is replaced by weak subtheories of Buss’ bounded arithmetic: PV or $${\Sigma^b_1-IND^{|x|_k}}$$. It also holds for IΔ0 (and even its subtheory IE 2) under a rather mild assumption on cofinality. On the other hand, it (...) fails for the extension of IOpen by an axiom expressing the Bézout property, even under the same assumption on cofinality. (shrink)

We study variants of Buss’s theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on \ induction schemes, which were so far neglected in the literature. We present inclusions and conservation results between the systems and \ of a new form), results on numbers of instances of the axioms or rules, connections to reflection principles for quantified propositional calculi, and separations between the systems.

We investigate the provability of some properties of abelian groups and quadratic residues in variants of bounded arithmetic. Specifically, we show that the structure theorem for finite abelian groups is provable in S22 + iWPHP, and use it to derive Fermat's little theorem and Euler's criterion for the Legendre symbol in S22 + iWPHP extended by the pigeonhole principle PHP. We prove the quadratic reciprocity theorem in the arithmetic theories T20 + Count2 and I Δ0 + Count2 with modulo-2 counting (...) principles. (shrink)

Williamson and others have argued that contextualist theories of the semantics of ‘know’ have a special problem of accounting for our practices of ‘consuming’ knowledge attributions and denials made in other contexts. In what follows, I shall understand the objection as the idea that contextualism has a special problem of accounting for how we are able to acquire epistemically useful information from knowledge claims made in other contexts. I respond to the objection by arguing that the defeasibility of knowledge makes (...) it difficult for everyone to acquire epistemically useful information from knowledge claims made in other contexts, and that there is no special problem for contextualism when it comes to acquiring epistemically useful information from knowledge claims made in other contexts. (shrink)

1. Introduction The influence of Richard Rorty has not faded since his demise more than a decade ago. Some of his works have been published posthumously (Rorty 2010; Rorty 2016), others have been republished in valuable collections (Voparil & Bernstein 2010; Rorty 2014) and some of his unpublished work has already appeared too (Małecki & Voparil 2020). Important international symposia have been held around the world (see e.g. Penelas & Voparil 2014) and the Richard Rorty Society (RSS) was fou...

Mixed strategies have been used to show that Pascal’s Wager fails to offer sufficient pragmatic reasons for believing in God. Their proponents have argued that, in addition to outright belief in God, rational agents can follow alternatives strategies whose expected utility is infinite as well. One objection that has been raised against this way of blocking Pascal’s Wager is that applying a mixed strategy in Pascal’s case is tantamount to applying an iterated mixed strategy which, properly understood, collapses into the (...) pure strategy of becoming a theist. I argue that since the assumptions used to develop the iterated mixed strategies response are even more questionable than those the initial objection relies on, this type of response to the mixed strategy objection fails. (shrink)

The paper provides a philosophical insight into the contemporary critical trends in the university life, and an outline of possible solutions based on the historical overview of an idea of university. The particular section is devoted to the depiction of situation in Slovakia. The author suggests that the creative reconstruction of academic practices is the key to the future of university.