We investigate, within the framework of Zermelo-Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals.

We work with symmetric extensions based on Lévy collapse and extend a few results of Apter, Cody, and Koepke. We prove a conjecture of Dimitriou from her Ph.D. thesis. We also observe that if V is a model of $$\textsf {ZFC}$$ ZFC, then $$\textsf {DC}_{<\kappa }$$ DC < κ can be preserved in the symmetric extension of V in terms of symmetric system $$\langle {\mathbb {P}},{\mathcal {G}},{\mathcal {F}}\rangle $$ ⟨ P, G, F ⟩, if $${\mathbb {P}}$$ P is $$\kappa $$ (...) κ -distributive and $${\mathcal {F}}$$ F is $$\kappa $$ κ -complete. Further we observe that if $$\delta <\kappa $$ δ < κ and V is a model of $$\textsf {ZF}+\textsf {DC}_{\delta }$$ ZF + DC δ, then $$\textsf {DC}_{\delta }$$ DC δ can be preserved in the symmetric extension of V in terms of symmetric system $$\langle {\mathbb {P}},{\mathcal {G}},{\mathcal {F}}\rangle $$ ⟨ P, G, F ⟩, if $${\mathbb {P}}$$ P is ($$\delta +1$$ δ + 1 )-strategically closed and $${\mathcal {F}}$$ F is $$\kappa $$ κ -complete. (shrink)

We establish the choice property, a weak analogue of definable choice, for certain tame expansions of o‐minimal structures. Most noteworthily, this property holds for dense pairs of real closed fields, as well as for expansions of o‐minimal structures by a dense independent set.

We work in set theory ZF without axiom of choice. Though the Hahn-Banach theorem cannot be proved in ZF, we prove that every Gateaux-differentiable uniformly convex Banach space E satisfies the following continuous Hahn-Banach property: if p is a continuous sublinear functional on E, if F is a subspace of E, and if f: F → ℝ is a linear functional such that f ≤ p|F then there exists a linear functional g : E → ℝ such that (...) g extends f and g ≤ p. We also prove that the continuous Hahn-Banach property on a topological vector space E is equivalent to the classical geometrical forms of the Hahn-Banach theorem on E. We then prove that the axiom of Dependent choices DC is equivalent to Ekeland's variational principle, and that it implies the continuous Hahn-Banach property on Gateaux-differentiable Banach spaces. Finally, we prove that, though separable normed spaces satisfy the continuous Hahn-Banach property, they do not satisfy the whole Hahn-Banach property in ZF+DC. (shrink)

This dissertation argues that we have no good reason to accept any one theory of properties as correct. To show this, I present three possible bases for theory-choice in the properties debate: coherence, explanatory adequacy, and explanatory value. Then I argue that none of these bases resolve the underdetermination of our choice between theories of properties. First, I argue considerations about coherence cannot resolve the underdetermination, because no traditional theory of properties is obviously incoherent. Second, I argue considerations (...) of explanatory adequacy cannot resolve the underdetermination, because every traditional theory of properties lacks the theoretical resources to adequately explain resemblance, causal powers, and predication. However, these inadequacies are easily remedied with theoretical modifications. But this results in an overabundance of modified, but adequate, theories of properties. Third, I argue explanatory virtues cannot resolve the underdetermination, because we have no reason to think explanatory virtues make theories of properties more likely to be true. I reject the common argument that explanatory virtues are truth-conducive in theories of properties because they are truth-conducive in scientific theories. Since none of the three bases for theory choice can resolve the underdetermination, I conclude that we have no good reason to accept any one theory of properties as correct. Finally, I consider the possibility of choosing one theory over the others on pragmatic grounds. But I argue that pragmatic grounds cannot resolve the underdetermination either. Instead, I suggest we accept the view I call 'instrumental pluralism,' which allows practitioners to use whatever theory of properties they find useful. Adviser: Jennifer McKitrick. (shrink)

In many voting systems, voters’ preferences on a set of candidates are represented by linear orderings. In this context, scoring rules are well-known procedures to aggregate the preferences of the voters. Under these rules, each candidate obtains a fixed number of points, sk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_k$$\end{document}, each time he/she is ranked k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}th by one voter and the candidates are ordered according to the total number of (...) points they receive. In order to identify the best scoring rule to use in each situation, we need to know which properties are met by each of these procedures. Although some properties have been analyzed extensively, there are other properties that have not been studied for all scoring rules. In this paper, we consider two desirable social choice properties, the Pareto-optimality and the immunity to the absolute loser paradox, and establish characterizations of the scoring rules that satisfy each of these specific axioms. Moreover, we also provide a proof of a result given by Saari and Barney, where the scoring rules meeting reversal symmetry are characterized. From the results of characterization, we establish some relationships among these properties. Finally, we give a characterization of the scoring rules satisfying the three properties. (shrink)

Property rights are the rules governing ownership in society. This Element offers an analytical framework to understand the origins and consequences of property rights. It conceptualizes of the political economy of property rights as a concern with the follow questions: What explains the origins of economic and legal property rights? What are the consequences of different property rights institutions for wealth creation, conservation, and political order? Why do property institutions change? Why do legal reforms (...) relating to property rights such as land redistribution and legal titling improve livelihoods in some contexts but not others? In analyzing property rights, the authors emphasize the complementarity of insights from a diversity of disciplinary perspectives, including Austrian economics, public choice, and institutional economics, including the Bloomington School of institutional analysis and political economy. (shrink)

Discrete choice experiments (DCE) are often used to elicit preferences, for instance, in health preference research. However, DCEs only provide binary responses, whilst real-life choices are made with varying degrees of conviction. We aimed to verify whether eliciting self-reported convictions on a 0–100 scale adds meaningful information to the binary choice. Eighty three respondents stated their preferences for health states using DCE and the time trade-off method (TTO). In TTO, utility ranges were also elicited to account for preference (...) imprecision. We verified the properties of the conviction across three areas: (1) response to various choice task modifications (e.g. dominance, increase in complexity, distance from the status quo) and association with rationality violations (e.g. intransitivity); (2) association with test–retest results; (3) relation to the utility difference and imprecision estimated in TTO. Regarding (1), conviction increased in choice tasks with lower complexity, larger relative attractiveness, and lower distance to the status quo. Regarding (2), choices made with above-median conviction were sustained in 90% of the cases, compared to 68% for below-median conviction. Regarding (3), the conviction increases with utility difference and it decreases with utility imprecision; overconfidence seems to prevail: non-zero conviction is reported even for identical utilities. Self-reported conviction in DCE is associated in an intuitive way with the observed choices. It may, therefore, be useful in explaining or predicting behaviour or bridging the gap between the results of various elicitation tasks. (shrink)

Social choice theory is the study of collective decision processes and procedures. It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare). Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options? What are the properties of different voting systems? When is a voting (...) system democratic? How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members' individual preferences or judgments? How can we rank different social alternatives in an order of social welfare? Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems. (shrink)

There has been a significant interest in the recent literature in developing a solution to the problem of theory choice which is both normative and descriptive, but agent-based rather than rule-based, originating from Pierre Duhem’s notion of ‘good sense’. In this paper we present the properties Duhem attributes to good sense in different contexts, before examining its current reconstructions advanced in the literature and their limitations. We propose an alternative account of good sense, seen as promoting social consensus in (...) science, and show that it is superior to its rivals in two respects: it is more faithful to Duhemian good sense, and it cashes out the effect that virtues have on scientific progress. We then defend the social consensus account against objections that highlight the positive role of diversity and division of labour in science. (shrink)

The rationalization of a choice function, in terms of assumptions that involve expansion or contraction properties of the feasible set, over non-finite sets is analyzed. Schwartz's results, stated in the finite case, are extended to this more general framework. Moreover, a characterization result when continuity conditions are imposed on the choice function, as well as on the binary relation that rationalizes it, is presented.

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)

The purpose of this paper is to investigate the relationship between collective rationality and permissible collective choice rules using a unified approach inspired by Bossert and Suzumura (J Econ Theory 138:311–320, 2008). We consider collective choice rules satisfying four axioms: unrestricted domain, strong Pareto, anonymity, and neutrality. A number of new classes of collective choice rules as well as the Pareto and Pareto extension rules are characterized under various concepts of collective rationality: acyclicity, transitivity, quasi-transitivity, semi-transitivity, and (...) the interval order property. Further, new concepts of collective rationality, K-term acyclicity and K-term consistency, are proposed and the corresponding characterizations are provided. (shrink)

The defense of necessity, also known as the “choice of evils,” reflects popular moral intuitions and common sense: sometimes, breaking the rules is the right—indeed, the only—thing to do in order to avoid a greater evil. Citing a classic example, mountain climbers may break into a cabin to wait out a deadly snow storm and appropriate the owner’s provisions because their property violations are a lesser evil compared to the loss of life. At the same time, this defense (...) contradicts the fundamental principles of criminal responsibility in that it authorizes violation of rights of innocent bystanders. By allowing the mountain climbers to override the property rights of the cabin owner, the defense effectively forbids the cabin owner to use force in response—a different rule would perpetuate violence. This outcome is at odds with the basic criminal law doctrines. There is no general duty to rescue in Anglo-American law. Yet, by forbidding the cabin owner to use force, the defense of necessity essentially imposes on him the duty to forego his interests in favor of those of the mountain climbers. The paper explores the origins and boundaries of the defense of necessity. It argues that the existing public and private theories of necessity are unsatisfactory and concludes that a viable theory of necessity should be able to explain why it is sometimes permissible to override individual rights of citizens without their consent or fault. (shrink)

In this paper it is argued that Hintikka's game theoreticalsemantics for Independence Friendly logic does not formalize theintuitions about independent choices; it rather is aformalization of imperfect information. Furthermore it is shownthat the logic has several remarkable properties (e.g.,renaming of bound variables is not allowed). An alternativesemantics is proposed which formalizes intuitions aboutindependence.

This article provides a systematic analysis of social choice theory without the Pareto principle, by revisiting the method of Murakami Yasusuke. This article consists of two parts. The first part investigates the relationship between rationality of social preference and the axioms that make a collective choice rule either Paretian or anti-Paretian. In the second part, the results in the first part are applied to obtain impossibility results under various rationality requirements of social preference, such as S-consistency, quasi-transitivity, semi-transitivity, (...) the interval-order property, and acyclicity. (shrink)

We propose a modification of the exhaustivity operator from Fox Presupposition and implicature in compositional semantics, Palgrave Macmillan, London, pp 71–120, 2007. https://doi.org/10.1057/9780230210752_4) that on top of negating all the Innocently Excludable alternatives affirms all the ‘Innocently Includable’ ones. The main result of supplementing the notion of Innocent Exclusion with that of Innocent Inclusion is that it allows the exhaustivity operator to identify cells in the partition induced by the set of alternatives whenever possible. We argue for this property (...) of ‘cell identification’ based on the simplification of disjunctive antecedents and the effects on free choice that arise as the result of the introduction of universal quantifiers. We further argue for our proposal based on the interaction of only with free choice disjunction. (shrink)

The Nash axiom is a basic property of consistency in choice. This paper proposes weaker versions of the axiom and examines their logical implications. In particular, we demonstrate that weak Nash axioms are useful to understand the relationship between the Nash axiom and the path independence axiom. We provide an application of weak Nash axioms to the no-envy approach. We present a possibility result and an impossibility result.

This paper contributes to the semantic typology of dependent indefinites, by accounting for the distribution and interpretation of the Romanian indefinite vreun. It is shown that its occurrences are restricted to negative polarity and a subset of modal contexts. More specifically, the study of its behavior in intensional environments reveals that vreun is systematically incompatible with non-epistemic operators, a restriction we capture by proposing a novel empirical generalization (‘the epistemic constraint’). To account for the observed pattern, we adopt the unitary (...) approach to polarity in Chierchia (Logic in Grammar: polarity, free choice and intervention, 2013a; in: Fălăuş (ed.) Alternatives in semantics, 2013b) and derive the properties of vreun from its obligatory association with alternatives. Its distributional restrictions are argued to follow from the interplay between the types of alternatives it activates (scalar and subdomain alternatives), the way these alternatives are factored into meaning (via an independently motivated mechanism of exhaustification) and the lexical semantics of the operators in the context of occurrence. We propose that the epistemic constraint arises from the lexicalization of an inference (anti-total variation) that non-epistemic operators can never satisfy. (shrink)

Preface. I. BASICS OF LOGIC. Introduction. The Structure of Simple Statements. The Structure of Complex Statements. Simple and Complex Properties. Validity. 2. PROBABILITY AND INDUCTIVE LOGIC. Introduction. Arguments. Logic. Inductive versus Deductive Logic. Epistemic Probability. Probability and the Problems of Inductive Logic. 3. THE TRADITIONAL PROBLEM OF INDUCTION. Introduction. Hume’s Argument. The Inductive Justification of Induction. The Pragmatic Justification of Induction. Summary. IV. THE GOODMAN PARADOX AND THE NEW RIDDLE OF INDUCTION. Introduction. Regularities and Projection. The Goodman Paradox. The Goodman (...) Paradox, Regularity, and the Principle of the Uniformity of Nature. Summary. 5. MILL’S METHODS OF EXPERIMENTAL INQUIRY AND THE NATURE OF CAUSALITY. Introduction. Causality and Necessary and Sufficient Conditions. Mill’s Methods. The Direct Method of Agreement. The Inverse Method of Agreement. The Method of Difference. The Combined Methods. The Application of Mill’s Methods. Sufficient Conditions and Functional Relationships. Lawlike and Accidental Conditions. 6. THE PROBABILITY CALCULUS. Introduction. Probability, Arguments, Statements, and Properties. Disjunction and Negation Rules. Conjunction Rules and Conditional Probability. Expected Value of a Gamble. Bayes’ Theorem. Probability and Causality. 7. KINDS OF PROBABILITY. Introduction. Rational Degree of Belief. Utility. Ramsey. Relative Frequency. Chance. 8. PROBABILITY AND SCIENTIFIC INDUCTIVE LOGIC. Introduction. Hypothesis and Deduction. Quantity and Variety of Evidence. Total Evidence. Convergence to the Truth. ANSWERS TO SELECTED EXERCISES. INDEX. (shrink)

. Fresh evidence from Free Choice Items (FCIs) in French question the current perception of the class. The role of some standard distinctions found in the literature is weakened or put in a new perspective. The distinction between universal and existential is no longer an intrinsic property of FCIs. Similarly, the opposition between variation-based vs intension-based analyses is relativized. We show that the regime of free choiceness can be characterized by an abstract constraint, that we call Non-Individuation (NI), (...) and which can be satisfied in different ways that match current distinctions. NI says that the information conveyed by a sentence containing a FCI should not be reducible to a referential situation, that is a situation in which particular individuals satisfy the sentence in the current world. The widely used resource of modal variation becomes a particular scenario of free-choiceness, not its essence. In fact, we show that under certain conditions, FCIs can occur in episodic, non-modal sentences, a fact that NI can accommodate. We also discuss more fine-grained aspects of the semantics of FCIs, such as their emotional colour. (. . .) the tripod fell spontaneously, because, though it stood on its feet so as to serve for a seat, it did not fall so as to serve for a seat. Aristotle, Physics II,6. (shrink)

With the Axiom of Choice, for any infinite cardinal but, without, we cannot conclude any relationship between and for an arbitrary infinite cardinal. In this paper, we give some properties of in the absence of and compare them to those of for an infinite cardinal. Among our results, we show that “ for any infinite cardinal and any natural number n” is provable in although “ for any infinite cardinal ” is not.

This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability (...) classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${\mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${\mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language. (shrink)

This paper explores some issues about the choice of variables for causal representation and explanation. Depending on which variables a researcher employs, many causal inference procedures and many treatments of causation will reach different conclusions about which causal relationships are present in some system of interest. The assumption of this paper is that some choices of variables are superior to other choices for the purpose of causal analysis. A number of possible criteria for variable choice are described and (...) defended within a broadly interventionist approach to causation. (shrink)

A detailed theoretical analysis is presented of what five utility representations – subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU – say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about the descriptive aspects of the representations from data (...) concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models. (shrink)

The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also from “residual” (...) consumption in the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one). (shrink)

In this paper, we investigate the semantics and logic of choice-driven counterfactuals, that is, of counterfactuals whose evaluation relies on auxiliary premises about how agents are expected to act, i.e., about their default choice behavior. To do this, we merge one of the most prominent logics of agency in the philosophical literature, namely stit logic, with the well-known logic of counterfactuals due to Stalnaker and Lewis. A key component of our semantics for counterfactuals is to distinguish between deviant (...) and non-deviant actions at a moment, where an action available to an agent at a moment is deviant when its performance does not agree with the agent’s default choice behavior at that moment. After developing and axiomatizing a stit logic with action types, instants, and deviant actions, we study the philosophical implications and logical properties of two candidate semantics for choice-driven counterfactuals, one called rewind models inspired by Lewis, 455–476 1979) and the other called independence models motivated by well-known counterexamples to Lewis’s proposal Slote, 3–27 1978). In the last part of the paper we consider how to evaluate choice-driven counterfactuals at moments arrived at by some agents performing a deviant action. (shrink)

We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the options, but also “context-related” properties. Our framework can accommodate (...) boundedly rational and sophisticatedly rational choice. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts. (shrink)

John Rawls says: “The main problem of distributive justice is the choice of a social system.” Property-owning democracy is the social system that Rawls thought best realized the requirements of his principles of justice. This article discusses Rawls’s conception of property-owning democracy and how it is related to his difference principle. I explain why Rawls thought that welfare-state capitalism could not fulfill his principles: it is mainly because of the connection he perceived between capitalism and utilitarianism.

In considering the nature of properties four controversial decisions must be made. (1) Are properties universals or tropes? (2) Are properties attributes of particulars, or are particulars just bundles of properties? (3) Are properties categorical (qualitative) in nature, or are they powers? (4) If a property attaches to a particular, is this predication contingent, or is it necessary? These choices seem to be in a great degree independent of each other. The author indicates his own choices.

In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$ used in the Andersonian–Kangerian approach to deontic (...) logic with respect to prohibition and obligation. Consequently, we define a permission operator on the basis of the $\texttt {permit}$ constant and a relation of legitimization. The general idea is that $P \varphi $ is true if and only if $\texttt {permit}$ is true, which means that a permission is actually issued and $\varphi $ is legitimized by $\texttt {permit}$. The intuitive notion of legitimization is formally represented by an operator of relating implication: a non-classical implication that is semantically defined by adding a constraint to the classical meaning of implication to the effect that arguments are related by a special relation. The properties of this relation are based on an informal, intuitive meaning of legitimization and determine the properties of the permission operator. We show that the resulting permission operator possesses the free choice property and avoids certain unwanted consequences that follow from alternative approaches. (shrink)

: Our paper discusses the epistemic attitudes of particle physicists on the discovery of the Higgs boson at the Large Hadron Collider. It is based on questionnaires and interviews made shortly before and shortly after the discovery in 2012. We show, to begin with, that the discovery of a Standard Model Higgs boson was less expected than is sometimes assumed. Once the new particle was shown to have properties consistent with SM expectations – albeit with significant experimental uncertainties –, there (...) was a broad agreement that ‘a’ Higgs boson had been found. Physicists adopted a two-pronged strategy. On the one hand, they treated the particle as a SM Higgs boson and tried to establish its properties with higher precision; on the other hand, they searched for any hints of physics beyond the SM. This motivates our first philosophical thesis: the Higgs discovery, being of fundamental importance and establishing a new kind of particle, represented a crucial experiment if one interprets this notion in an appropriate sense. By embedding the LHC into the tradition of previous precision experiments and the experimental strategies thus established, underdetermination and confirmational holism are kept at bay. Second, our case study suggests that criteria of theory preference should be understood as epistemic and pragmatic values that have to be weighed in factual research practice. The Higgs discovery led to a shift from pragmatic to epistemic values as regards the mechanisms of electroweak symmetry breaking. Complex criteria, such as naturalness, combine epistemic and pragmatic different values, but are coherently applied by the community. (shrink)

Our regimentation of Goodman and Myhill’s proof of Excluded Middle revealed among its premises a form of Choice and an instance of Separation.Here we revisit Zermelo’s requirement that the separating property be definite. The instance that Goodman and Myhill used is not constructively warranted. It is that principle, and not Choice alone, that precipitates Excluded Middle.Separation in various axiomatizations of constructive set theory is examined. We conclude that insufficient critical attention has been paid to how those forms (...) of Separation fail, in light of the Goodman–Myhill result, to capture a genuinely constructive notion of set. (shrink)

In this article, we model FPTP systems as social preference rules and give two characterizations. We show that a social preference rule is an FPTP system if, and only if, it satisfies the axioms of subset consistency, district consistency, subset cancellation, and district cancellation. The second characterization consists of the axioms of subset consistency, subset anonymity, neutrality, topsonlyness, Pareto optimality, district consistency and district cancellation. The characterizations give us an opportunity to compare the characteristic properties of FPTP systems to the (...) characteristic properties that we found for list systems of proportional representation (list PR systems) in Hout et al. (Social Choice and Welfare, 27:459–475, 2006), where we modelled those systems also as social preference rules. We find that consistency and anonymity distinguish list PR systems from FPTP systems. On the other hand, it is district cancellation that distinguishes FPTP systems from list PR systems. (shrink)

This paper examines social choice theory with the strong Pareto principle. The notion of conditional decisiveness is introduced to clarify the underlying power structure behind strongly Paretian aggregation rules satisfying binary independence. We discuss the various degrees of social rationality: transitivity, semi-transitivity, the interval-order property, quasi-transitivity, and acyclicity.

To nudge is to design choice contexts in order to improve choice outcomes. Richard Thaler and Cass Sunstein emphatically endorse nudging but reject more restrictive means. In contrast, I argue that the behavioral psychology that motivates nudging also motivates what may be called jolting — i.e. the design of choice content. I defend nudging and jolting by distinguishing them from the sometimes oppressive means with which they can be implemented, by responding to some common arguments against nudging, (...) and by showing how respect for preferences over option sets and their aggregate properties may require the trimming of option sets, as well as helpful choice contexts. (shrink)

Rawls defended the model of a property‐owning democracy; critically reflected on the US constitutional history of free speech; and argued that “both Hiroshima and the fire‐bombing of Japanese cities were great evils.” What ties these and many other disparate concerns together is the idea of the original position. “Justice as Fairness,” published in 1958, included several crucial developments. Rawls proposes his “two principles of justice,” which, through various revisions, he would defend for the rest of his career: a principle (...) of equal liberty and a principle encompassing fair equality of opportunity and the difference principle. Rawls argues that parties would accept his two principles in two stages: first, by a comparison with average utilitarianism, which focuses on his first principle, and then by a comparison with so‐called “mixed conceptions,” which focuses on the second principle. Rawls continues to claim that the original position establishes a form of objectivity. (shrink)

According to the experience property framework qualia are properties of experiences the subject undergoing the experience is aware of. A phenomenological argument against this framework is developed and a few mistakes invited by the framework are described. An alternative to the framework, the framework of experiential properties is presented and defended as preferable. It is argued that the choice between these two frameworks makes a substantial difference for theoretical purposes.

Property and Practical Reason makes a moral argument for common law property institutions and norms, and challenges the prevailing dichotomy between individual rights and state interests and its assumption that individual preferences and the good of communities must be in conflict. One can understand competing intuitions about private property rights by considering how private property enables owners and their collaborators to exercise practical reason consistent with the requirements of reason, and thereby to become practically reasonable agents (...) of deliberation and choice who promote various aspects of the common good. The plural and mediated domains of property ownership, though imperfect, have moral benefits for all members of the community. They enable communities and institutions of private ordering to pursue plural and incommensurable good ends while specifying the boundaries of property rights consistent with basic moral requirements. (shrink)

We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom.