The set-theoretic axiom WISC states that for every set there is a set of surjections to it cofinal in all such surjections. By constructing an unbounded topos over the category of sets and using an extension of the internal logic of a topos due to Shulman, we show that WISC is independent of the rest of the axioms of the set theory given by a well-pointed topos. This also gives an example of a topos that is not a predicative topos (...) as defined by van den Berg. (shrink)

The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom of choice nor provable in Zermelo-Fraenkel set theory without the axiom of choice. Thus, it is a new weak choice principle. Nevertheless, the restriction of the principle to sets of reals is provable without the axiom of (...) choice. (shrink)

We shall investigate certain set-theoretic pigeonhole principles which arise as generalizations of the usual pigeonhole principle; and we shall show that many of them are equivalent to full AC. We discuss also several restricted cases and variations of those principles and relate them to restricted choice principles. In this sense the pigeonhole principle is a rich source of weak choice principles. It is shown that certain sequences of restricted pigeonhole principles form implicational (...) hierarchies with respect to ZF. We state also several open problems in order to indicate the extent to which the whole subject of pigeonhole principles requires further exploration. (shrink)

Assume. Let κ be a cardinal. A ‐ground is a transitive proper class W modelling such that V is a generic extension of W via a forcing of cardinality. The κ‐mantle is the intersection of all ‐grounds. We prove that certain partial choice principles in are the consequence of κ being inaccessible/weakly compact, and some other related facts.

In the context of [Formula: see text], we analyze a version of Hindman’s finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the [Formula: see text].

For every$n\in \omega \setminus \{0,1\}$we introduce the following weak choice principle:$\operatorname {nC}_{<\aleph _0}^-:$For every infinite family$\mathcal {F}$of finite sets of size at least n there is an infinite subfamily$\mathcal {G}\subseteq \mathcal {F}$with a selection function$f:\mathcal {G}\to \left [\bigcup \mathcal {G}\right ]^n$such that$f(F)\in [F]^n$for all$F\in \mathcal {G}$.Moreover, we consider the following choice principle:$\operatorname {KWF}^-:$For every infinite family$\mathcal {F}$of finite sets of size at least$2$there is an infinite subfamily$\mathcal {G}\subseteq \mathcal {F}$with a Kinna–Wagner selection function. That is, there is (...) a function$g\colon \mathcal {G}\to \mathcal {P}\left (\bigcup \mathcal {G}\right )$with$\emptyset \not =f(F)\subsetneq F$for every$F\in \mathcal {G}$.We will discuss the relations between these two choice principles and their relations to other well-known weak choice principles. Moreover, we will discuss what happens when we replace$\mathcal {F}$by a linearly ordered or a well-ordered family. (shrink)

We study the role the axiom of choice plays in the existence of some special subsets of ℝ and its power set ℘.

Especially nice models of intuitionistic set theories are realizability models $V$, where $\mathcal A$ is an applicative structure or partial combinatory algebra. This paper is concerned with the preservation of various choice principles in $V$ if assumed in the underlying universe $V$, adopting Constructive Zermelo–Fraenkel as background theory for all of these investigations. Examples of choice principles are the axiom schemes of countable choice, dependent choice, relativized dependent choice and the presentation axiom. It (...) is shown that any of these axioms holds in $V$ for every applicative structure $\mathcal A$ if it holds in the background universe.1 It is also shown that a weak form of the countable axiom of choice, $\textbf{AC}^{\boldsymbol{\omega, \omega }}$, is rendered true in any $V$ regardless of whether it holds in the background universe. The paper extends work by McCarty and Rathjen. (shrink)

In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified certain (...) class='Hi'>choice principles such as co-finite choice, discrete choice, interval choice, compact choice and closed choice, which are cornerstones among Weihrauch degrees and it turns out that certain core theorems in analysis can be classified naturally in this structure. In particular, we study theorems such as the Intermediate Value Theorem, the Baire Category Theorem, the Banach Inverse Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem. We also explore how existing classifications of the Hahn—Banach Theorem and Weak Kőnig's Lemma fit into this picture. Well-known omniscience principles from constructive mathematics such as LPO and LLPO can also naturally be considered as Weihrauch degrees and they play an important role in our classification. Based on this we compare the results of our classification with existing classifications in constructive and reverse mathematics and we claim that in a certain sense our classification is finer and sheds some new light on the computational content of the respective theorems. Our classification scheme does not require any particular logical framework or axiomatic setting, but it can be carried out in the framework of classical mathematics using tools of topology, computability theory and computable analysis. We develop a number of separation techniques based on a new parallelization principle, on certain invariance properties of Weihrauch reducibility, on the Low Basis Theorem of Jockusch and Soare and based on the Baire Category Theorem. Finally, we present a number of metatheorems that allow to derive upper bounds for the classification of the Weihrauch degree of many theorems and we discuss the Brouwer Fixed Point Theorem as an example. (shrink)

We study theorems from Functional Analysis with regard to their relationship with various weak choice principles and prove several results about them: “Every infinite‐dimensional Banach space has a well‐orderable Hamel basis” is equivalent to ; “ can be well‐ordered” implies “no infinite‐dimensional Banach space has a Hamel basis of cardinality ”, thus the latter statement is true in every Fraenkel‐Mostowski model of ; “No infinite‐dimensional Banach space has a Hamel basis of cardinality ” is not provable in (...) ; “No infinite‐dimensional Banach space has a well‐orderable Hamel basis of cardinality ” is provable in ; (the Axiom of Choice for denumerable families of non‐empty finite sets) is equivalent to “no infinite‐dimensional Banach space has a Hamel basis which can be written as a denumerable union of finite sets”; Mazur's Lemma (“If X is an infinite‐dimensional Banach space, Y is a finite‐dimensional vector subspace of X, and, then there is a unit vector such that for all and all scalars α”) is provable in ; “A real normed vector space X is finite‐dimensional if and only if its closed unit ball is compact” is provable in ; (Principle of Dependent Choices) + “ can be well‐ordered” does not imply the Hahn‐Banach Theorem () in ; and “no infinite‐dimensional Banach space has a Hamel basis of cardinality ” are independent from each other in ; “No infinite‐dimensional Banach space can be written as a denumerable union of finite‐dimensional subspaces” lies in strength between (the Axiom of Countable Choice) and ; implies “No infinite‐dimensional Banach space can be written as a denumerable union of closed proper subspaces” which in turn implies ; “Every infinite‐dimensional Banach space has a denumerable linearly independent subset” is a theorem of, but not a theorem of ; and “Every infinite‐dimensional Banach space has a linearly independent subset of cardinality ” implies “every Dedekind‐finite set is finite”. (shrink)

A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through.

In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.

We study the relationship between various properties of the real numbers and weak choice principles.

For \(n\in \omega \), the weak choice principle \(\textrm{RC}_n\) is defined as follows: _For every infinite set_ _X_ _there is an infinite subset_ \(Y\subseteq X\) _with a choice function on_ \([Y]^n:=\{z\subseteq Y:|z|=n\}\). The choice principle \(\textrm{C}_n^-\) states the following: _For every infinite family of_ _n_-_element sets, there is an infinite subfamily_ \({\mathcal {G}}\subseteq {\mathcal {F}}\) _with a choice function._ The choice principles \(\textrm{LOC}_n^-\) and \(\textrm{WOC}_n^-\) are the same as \(\textrm{C}_n^-\), but we assume that (...) the family \({\mathcal {F}}\) is linearly orderable (for \(\textrm{LOC}_n^-\) ) or well-orderable (for \(\textrm{WOC}_n^-\) ). In the first part of this paper, for \(m,n\in \omega \) we will give a full characterization of when the implication \(\textrm{RC}_m\Rightarrow \textrm{WOC}_n^-\) holds in \({\textsf {ZF}}\). We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that \(\textrm{RC}_5\Rightarrow \textrm{LOC}_5^-\) and that \(\textrm{RC}_6\Rightarrow \textrm{C}_3^-\), answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that \(\textrm{RC}_6\Rightarrow \textrm{C}_9^-\) and that \(\textrm{RC}_7\Rightarrow \textrm{LOC}_7^-\). (shrink)

For an integer \, Ramsey Choice\ is the weak choice principle “every infinite setxhas an infinite subset y such that\ has a choice function”, and \ is the weak choice principle “every infinite family of n-element sets has an infinite subfamily with a choice function”. In 1995, Montenegro showed that for \, \. However, the question of whether or not \ for \ is still open. In general, for distinct \, not even the (...) status of “\” or “\” is known. In this paper, we provide partial answers to the above open problems and among other results, we establish the following:1.For every integer \, if \ is true for all integers i with \, then \ is true for all integers i with \.2.If \ are any integers such that for some prime p we have \ and \, then in \: \ and \.3.For \, \\\ implies \, and \ implies neither \ nor \ in \.4.For every integer \, \ implies “every infinite linearly orderable family of k-element sets has a partial Kinna–Wagner selection function” and the latter implication is not reversible in \ ). In particular, \ strictly implies “every infinite linearly orderable family of 3-element sets has a partial choice function”.5.The Chain-AntiChain Principle implies neither \ nor \ in \, for every integer \. (shrink)

We work in set theory without the Axiom of Choice ZF. We prove that the Principle of Dependent Choices (DC) implies that the closed unit ball of a uniformly convex Banach space is weakly compact and, in particular, that the closed unit ball of a Hilbert space is weakly compact. These statements are not provable in ZF and the latter statement does not imply DC. Furthermore, DC does not imply that the closed unit ball of a reflexive space is (...) weakly compact. (shrink)

In this paper, the independence of irrelevant alternatives and the Pareto principle are simultaneously weakened in the Arrovian framework of social choice. Moreover, we also relax transitivity of social preferences. We show that impossibility remains under weaker versions of Arrow’s original conditions. Our results complement the recent work by Coban and Sanver (Soc Choice Welf 43(4):953–961, 2014).

This article investigates the relationship among the weak Pareto principle, the strong Pareto principle, and positive responsiveness in the context of voting. First, it is shown that under a mild domain condition, if an anonymous and neutral collective choice rule (CCR) is complete and transitive, then the weak Pareto principle and the strong Pareto principle are equivalent. Next, it is shown that under another mild domain condition, if a neutral CCR is transitive, then the strong Pareto principle (...) and positive responsiveness are equivalent. By applying these results, we obtain a new characterization of the method of majority decision. (shrink)

Should weak forms of the axiom of choice really be accepted within constructive mathematics? A critical view of the Brouwer-Heyting-Kolmogorov interpretation, accompanied by the intention to include nondeterministic algorithms, leads us to subscribe to Richman's appeal for dropping countable choice. As an alternative interpretation of intuitionistic logic, we propose to renew dialogue semantics.

We study within the framework of Zermelo-Fraenkel set theory ZF the role that the axiom of choice plays in the theory of Lindelöf metric spaces. We show that in ZF the weak choice principles: Every Lindelöf metric space is separable and Every Lindelöf metric space is second countable are equivalent. We also prove that a Lindelöf metric space is hereditarily separable iff it is hereditarily Lindelöf iff it hold as well the axiom of choice restricted (...) to countable sets and to topologies of Lindelöf metric spaces as the countable union theorem restricted to Lindelöf metric spaces. (shrink)

In set theory without the Axiom of Choice (), we investigate the problem of the placement of Łoś's Theorem () in the hierarchy of weak choice principles, and answer several open questions from the book Consequences of the Axiom of Choice by Howard and Rubin, as well as an open question by Brunner. We prove a number of results summarised in § 3.

I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering what useful mathematical work is done by weak counterexamples; whether they are rigorous mathematical proofs or just plausibility arguments; the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; what axioms for the creative subject are needed; what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of (...) Brouwer’s claims with a weak counterexample of my own. I also examine Brouwer’s 1927 proof of the negative continuity theorem, which appears to be a weak counterexample reliant on both the creative subject and the concept of choice sequence; I argue that it provides a good justification for the weak continuity principle, but it is not a weak counterexample and it does not depend essentially on the creative subject. (shrink)

We investigate certain statements about factors of unary functions which have connections with weak forms of the axiom of choice. We discuss more extensively the fine structure of Howard and Rubin's Form 314 from [4]. Some of our set-theoretic results have also interesting recursive versions.

The Axiom of Choice implies the Partition Principle and the existence, uniqueness, and monotonicity of (possibly infinite) sums of cardinal numbers. We establish several deductive relations among those principles and their variants: the monotonicity follows from the existence plus uniqueness; the uniqueness implies the Partition Principle; the Weak Partition Principle is strictly stronger than the Well-Ordered Choice.

We shall investigate certain statements concerning the rigidity of unary functions which have connections with forms of the axiom of choice.

In a recent article, Gauthier rejects orthodox rational choice contractarianism in favor of a revisionist approach to the social contract that, according to him, justifies his principle of maximin proportionate gain as a principle of distributive justice. I agree with Gauthier that his principle of maximin proportionate gain cannot be justified by orthodox rational choice contractarianism. I argue, however, that orthodox rational choice contractarianism, before and after Gauthier, is still a viable approach to the social contract, although (...) the scope of this approach is limited. Orthodox rational choice contractarianism can be applied fruitfully to moral philosophy only in situations of deep moral pluralism in which moral reasoning is reduced to instrumental reasoning, because the members of society do not share, as assumed by traditional moral theories, a consensus on moral ideals as traditionally conceived as a starting point for the derivation of moral rules but only an overarching end that they aim to reach. If orthodox rational choice contractarianism is applied adequately, then it offers a viable approach to the social contract that, in contrast to Gauthier’s theory, justifies a rival principle for distributive conflicts that is valid for deeply morally pluralistic societies. (shrink)

The one-page 1978 informal proof of Goodman and Myhill is regimented in a weak constructive set theory in free logic. The decidability of identities in general (⁠|$a\!=\!b\vee\neg a\!=\!b$|⁠) is derived; then, of sentences in general (⁠|$\psi\vee\neg\psi$|⁠). Martin-Löf’s and Bell’s receptions of the latter result are discussed. Regimentation reveals the form of Choice used in deriving Excluded Middle. It also reveals an abstraction principle that the proof employs. It will be argued that the Goodman–Myhill result does not provide the (...) constructive set theorist with a dispositive reason for not adopting (full) Choice. (shrink)

Classically, any structure for a signature ${\rm{\Sigma }}$ may be completed to a model of a desired regular theory ${T}}$ by means of the chase construction or small object argument. Moreover, this exhibits ${\rm{Mod}}\left$ as weakly reflective in ${\rm{Str}}\left$.We investigate this in the constructive setting. The basic construction is unproblematic; however, it is no longer a weak reflection. Indeed, we show that various reflectivity principles for models of regular theories are equivalent to choice principles in the (...) ambient set theory. However, the embedding of a structure into its chase-completion still satisfies a conservativity property, which suffices for applications such as the completeness of regular logic with respect to Tarski models.Unlike most constructive developments of predicate logic, we do not assume that equality between symbols in the signature is decidable. While in this setting, we also give a version of one classical lemma which is trivial over discrete signatures but more interesting here: the abstraction of constants in a proof to variables. (shrink)

The difficulty in discovering a difference between killing and letting die has led many philosophers to deny the distinction. This paper seeks to develop an argument defending the distinction between killing and letting die. In relation to Rachels’ cases, the argument is that (a) even accepting that Smith and Jones may select equally heinous options from the choices they have available to them, (b) the fact that the choices available to them are different is morally relevant, and (c) this difference (...) in available choices can be used to distinguish between the agents in certain circumstances. It is the principle of justice, as espoused by Aristotle, which requires that equal things are treated equally and that unequal things are treated unequally that creates a presumption that Smith and Jones should be treated differently. The magnitude of this difference can be amplified by other premises, making the distinction morally relevant in practical reality. (shrink)

In the realm of metric spaces the role of choice principles is investigated.

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable (...) fan theorem is not equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

I argue that in "en", Aristotle allows not only for weak akrasia but also for "strong akrasia". In weak akrasia, The agent makes only a "nominal" choice according to the right principle, While in strong akrasia he/she makes a "real" choice, But still acts against it. I show that, Although aristotle does not give a detailed account of strong akrasia, Such an account can be reconstructed on the basis of the analyses and examples of choice (...) and akratic behaviour provided by him in "en" and "de motu". (shrink)

I. INTRODUCTION: THE PROBLEMAkrasia (or, weakness of the will), often defined as “the moral state of agents who act against their better judgment”—a definition first given by Aristotle in the Nicomachean Ethics, depicts one of the most human of predicaments.Risto Sarrinen, Weakness of the Will in Medieval Thought: From Augustine to Buridan (New York: E. J. Brill, 1994), p. 1. Similar definitions can be found in, e.g., Aristotle, Nicomachean Ethics VII, 1045b10–15; Donald Davidson, “How is Weakness of the Will Possible?” (...) in Moral Concepts, ed. J. Feinberg (Oxford: Oxford University Press, 1970) p. 93; William Charlton, Weakness of Will (Oxford: Basil Blackwell, 1988), p. 1. We know what we ought to do, and we try. But, for one reason or other, we sometimes choose to act contrary to our better judgment.Being influenced by Socratic reasoning, some philosophers have argued that, in principle, one cannot freely and intentionally choose to act against one’s better judgment, if (1) one rationally judges what is best for oneself, (2) one prefers to act according to one’s rational judgment, and (3) one is free to make one’s own choice. See, e.g., Davidson, “How is Weakness,” pp. 93–113; and R. M. Hare, Freedom and Reason (Oxford: Oxford University Press, 1963), pp. 78–79. Despite the logical difficulty, many believe that weakness of the will is a fact. (shrink)

The value of rational choice theory for the social sciences has long been contested. It is argued here that, in the debate over its role, it is necessary to distinguish between claims that people maximise manifest payoffs, and claims that people maximise their utility. The former version has been falsified. The latter is unfalsifiable, because utility cannot be observed. In principle, utility maximisation can be adapted to fit any form of behaviour, including the behaviour of non-human organisms. Allegedly 'inconsistent' (...) behaviour is also impossible to establish without qualification. This utility-maximising version of rational choice theory has the character of a universal 'explanation' that can be made to 'fit' any set of events. This is a sign of weakness rather than strength. In its excessive quest for generality, utility-maximising rational choice theory fails to focus on the historically and geographically specific features of socio-economic systems. As long as such theory is confined to ahistorical generalities, then it will remain highly limited in dealing with the real world. Instead we have to consider the real social and psychological determinants of human behaviour. (shrink)

In 1970 Amartya Sen exposed an apparent antinomy that has come to be known as the Paradox of the Paretian Libertarian. Sen introduced his paradox by establishing a simple but startling theorem. Roughly put, what he proved was that if a mechanism for selecting social choice functions satisfies two standard adequacy conditions, there are possible situations in which it will violate either the very weak libertarian precept that every individual has at least some rights or the seemingly innocuous (...) Paretian principle that an option should be judged unacceptable if there is an available alternative that everyone prefers to it. Many economists and philosophers have proposed solutions to Sen's problem, but there is no general consensus on what solution is correct. In the present paper I argue that Sen's original theorem fails to establish the existence of any conflict between libertarianism and Paretianism. Furthermore, I contend that Sen has misinterpreted certain other theorems which he has used to defend the existence of a paradoxical conflict between these two doctrines. In general, I try to show that whenever Sen posits a Paretian-libertarian conflict to explain an apparently troubling result in social choice theory, the difficulty can be better dealt with either by claiming that the theorem in question imposes overly strong background constraints on the form of social choice functions or by claiming that it relies on an unacceptable construal of individual rights. (shrink)

Because it consists of an entire family of specific theories derived from the same first principles, rational choice offers one approach to generate explanations that provide for micro-macro links, and to attack a wide variety of empirical problems in macrosociology. The aims of this paper are (1) to provide a bare skeleton of all rational choice arguments; (2) to demonstrate their applicability to a range of macrosociological concerns by reviewing a sample of both new and classic works; (...) and (3) to discuss the weaknesses of current rational choice theory and the possibilities for its future development. (shrink)

This paper focuses on Sen?s concept of contrapreferential choice. Sen has developed this concept in order to overcome weaknesses of the rational choice theory. According to rational choice theory a decision-maker can be always seen as someone who maximises utility, and each choice he makes as the one that brings to him the highest level of personal wellbeing. Sen argues that in some situations we chose alternatives that bring us lower level of wellbeing than we could (...) achieve if we had chosen some other alternative available to us. This happens when we base our decisions on moral principles, when we act out of duty. Sen calls such action a commitment-based action. When we act out of commitment we actually neglect our preferences and thus we make a contrapreferential choice, as Sen argues. This paper shows that, contrary to Sen, a commitment-based action can be explained within the framework of rational choice theory. However, when each choice we make can be explained within the framework of rational choice theory, when in everything we do maximisation principle can be loaded, then the variety of our motives and traits is lost, and the explanatory power of the rational choice theory is questionable. (shrink)

Effects of globalization have amplified the magnitude and frequency of corporate abuses, particularly in developing economies where weak or absent rules undermine social norms and principles. Improving multinational enterprises’ (MNEs) ethical conduct is a factor of both the ability of firms to change behaviors in the direction of the moral good, and their willingness to do so. Constraints and enablers of a firm’s ability to act ethically emanate from the external environment, including the industry environment of which the (...) firm is a resident, and the host country environment in which it operates. A firm’s willingness to engage in ethical conduct is determined by the effective bundling of internal resources and the commitment of those resources to social ends. The interaction of external and internal conditions carves out categories of expected firm behaviors and suggests interventions that would push these behaviors in a more positive ethical direction. With reference to integrative social contracts theory (ISCT), these categories of firms are examined, and a conceptual model for analysis is developed to explain the drivers of corporate choices in the adoption and implementation of codes of conduct, and the relative power of relevant communities to the process. (shrink)

We compare diverse degrees of compactness and finiteness in Boolean algebras with each other and investigate the influence of weak choice principles. Our arguments rely on a discussion of infinitary distributive laws and generalized prime elements in Boolean algebras. In ZF set theory without choice, a Boolean algebra is Dedekind finite if and only if it satisfies the ascending chain condition. The Denumerable Subset Axiom implies finiteness of Boolean algebras with compact top, whereas the converse fails (...) in ZF. Moreover, we derive from DS the atomicity of continuous Boolean algebras. Some of the results extend to more general structures like pseudocomplemented semilattices. (shrink)

Significant criticisms have been raised regarding the ethical and psychological basis of living wills. Various solutions to address these criticisms have been advanced, such as the use of surrogate decision makers alone or data science‐driven algorithms. These proposals share a fundamental weakness: they focus on resolving the problems of living wills, and, in the process, lose sight of the underlying ethical principle of advance care planning, autonomy. By suggesting that the same sweeping solutions, without opportunities for choice, be applied (...) to all, individual patients are treated as population‐level groups—as a theoretical patient who represents a population, not the specific patient crafting his or her individualized future care plans. Instead, advance care planning can be improved through a multimodal approach that both mitigates cognitive biases and allows for customization of the decision‐making process by allowing for the incorporation of a variety of methods of advance care planning. (shrink)

Effects of globalization have amplified the magnitude and frequency of corporate abuses, particularly in developing economies where weak or absent rules undermine social norms and principles. Improving multinational enterprises’ (MNEs) ethical conduct is a factor of both the ability of firms to change behaviors in the direction of the moral good, and their willingness to do so. Constraints and enablers of a firm’s ability to act ethically emanate from the external environment, including the industry environment of which the (...) firm is a resident, and the host country environment in which it operates. A firm’s willingness to engage in ethical conduct is determined by the effective bundling of internal resources and the commitment of those resources to social ends. The interaction of external and internal conditions carves out categories of expected firm behaviors and suggests interventions that would push these behaviors in a more positive ethical direction. With reference to integrative social contracts theory (ISCT), these categories of firms are examined, and a conceptual model for analysis is developed to explain the drivers of corporate choices in the adoption and implementation of codes of conduct, and the relative power of relevant communities to the process. (shrink)

John Rawls famously argued that the Difference Principle would be chosen by any rational agent in the original position. Derek Parfit and Philippe Van Parijs have claimed, contra Rawls, that it is not the Difference Principle which is implied by Rawls’ original position argument, but rather the more refined Lexical Difference Principle. In this paper, we study both principles in the context of social choice under ignorance. First, we present a general format for evaluating original position arguments in (...) this context. We argue that in this format, the Difference Principle can be specified in three conceptually distinct ways. We show that these three specifications give the same choice recommendations, and can be grounded in an original position argument in combination with the well-known maximin rule. Analogously, we argue that one can give at least four plausible specifications of the Lexical Difference Principle, which however turn out to give different recommendations in concrete choice scenarios. We prove that only one of these four specifications can be grounded in an original position argument. Moreover, this one specification seems the least appealing from the viewpoint of distributive justice. This insight points towards a general weakness of original position arguments. (shrink)

Parfit (2017) proposed a novel principle for outcome betterness in different people and different number choices. It is claimed to solve the Non-Identity Problem while avoiding the Repugnant Conclusion, and it shall do so in person-affecting rather than in impersonal terms. According to this Wide Dual Person-Affecting Principle, one of two outcomes would be (i) in one way better if this outcome would together benefit people more, and (ii) in another way better if this outcome would benefit each person more. (...) I argue that a plausible construal of this principle has two features that make it vulnerable to objections. First, the most plausible interpretation of the second part of the principle turns out to incorporate an average function. Although this helps to avoid the Repugnant Conclusion, it implausibly implies that it can be better to add further people with less bad but still miserable lives to populations consisting only of lives full of suffering. Second, the principle is not based on a comparative but on an intrinsic notion of benefit. This allows to solve the Non-Identity Problem, yet it accounts only for a weak sense of person-affecting rather than for the more substantive person-affecting intuition that it is morally significant that particular people are made better (or worse) off. Eventually, I highlight what we can, nevertheless, learn from Parfit’s idea of combining different ways in which outcomes might be better. (shrink)

This chapter argues that from a particularly weak recombination principle and plausible assumptions about the nature of parthood and location, it follows that it is possible that the mereological structure of the material world and that of space-time fail to correspond to one another in very radical ways. The chapter suggests, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of no less unappealing alternatives. It also discusses a few ways in which (...) their possibility is relevant to various important debates in metaphysics. (shrink)

The context-free weak ordering principle is viewed by many as a cornerstone of rational choice theory. McClennen, for example, claims that this principle is one of a pair on which '[t]he theory of rational choice and preference, as it has been developed in the past few decades by economists and decision theorists, rests', and Sen characterizes a version of context freedom as ‘a very basic requirement of rational choice’. But this principle is certainly not uncontroversial: there (...) are examples of principle is certainly not apper irrational. (shrink)

I argue that from a very weak recombination principle and plausible assumptions about the nature of parthood and location it follows that it's possible that the mereological structure of the material world and that of spacetime fail to correspond to one another in very radical ways. I defend, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of equally radical alternatives. I also discuss a few ways in which their possibility is relevant (...) to various debates in metaphysics. (shrink)

It is well known that the extensional axiom of choice implies the law of excluded middle . We here prove that the converse holds as well if we have the intensional axiom of choice ACint, which is provable in Martin-Löf's type theory, and a weak extensionality principle , which is provable in Martin-Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory.

It is well known that the extensional axiom of choice implies the law of excluded middle. We here prove that the converse holds as well if we have the intensional axiom of choice ACint, which is provable in Martin-Löf's type theory, and a weak extensionality principle, which is provable in Martin-Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory.

Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.