Diffeomorphism invariance is sometimes taken to be a criterion of background independence. This claim is commonly accompanied by a second, that the genuine physical magnitudes (the ``observables'') of background-independent theories and those of background-dependent (non-diffeomorphism-invariant) theories are essentially different in nature. I argue against both claims. Background-dependent theories can be formulated in a diffeomorphism-invariant manner. This suggests that the nature of the physical magnitudes of relevantly analogous theories (one background free, the other background dependent) is essentially the same. The (...) temptation to think otherwise stems from a misunderstanding of the meaning of spacetime coordinates in background-dependent theories. (shrink)

In this paper, I consider particular attempts by E. J. Lowe and Michael Gorman at providing an independence criterion of substancehood and argue that the stipulative exclusion of non-particulars and proper parts (or constituents) from such accounts raises difficult issues for their proponents. The results of the present discussion seem to indicate that, at least for the case of composite entities, a unity criterion of substancehood might have at least as much, and perhaps more, to offer than an (...) class='Hi'>independence criterion and therefore ought to be explored further by neo-Aristotelians in search of a defensible notion of substancehood. I indicated briefly how such a unity criterion might be used by neo-Aristotelians to support the inclusion of hylomorphic compounds in the category of substance, given the traditional role of form as the principle of unity within the compound. (shrink)

This chapter contains sections titled: Two Dichotomies The Existential Mind‐Independence of Moral Principles The Strong Observational Mind‐Independence of Moral Principles Appendix.

An important appeal of strategy-proofness is the robustness that it implies. Under a strategy-proof voting rule, every individual has an optimal strategy independently of the behavior of all other voters, namely truth-telling. In particular, optimal play is robust with respect to the beliefs voters may have about the type and the behavior of the other voters. Following Blin and Satterthwaite (Economet J Economet Soc 45(4):881–888, 1977), we call this logically weaker property “belief-independence.” In this paper, we give a number (...) of examples of voting rules that are belief-independent but not strategy-proof. However, we also show that belief-independence implies strategy-proofness under a few natural additional conditions. The notion of belief-independence naturally leads to a the strengthening of strategy-proofness to “robust” strategy-proofness which requires that no voter whose true preference may come from a restricted domain can benefit by submitting any unrestricted preference ordering given any unrestricted preference profile for all other voters. There are examples of strategy-proof voting rules (on a restricted domain) that are not robustly strategy-proof, but under natural additional conditions the two properties are shown to be equivalent. (shrink)

A systematic introduction suitable for readers who have little familiarity with logic. Provides numerous examples and complete proofs.

In the latter half of the twentieth century, philosophers of science have argued (implicitly and explicitly) that epistemically rational individuals might compose epistemically irrational groups and that, conversely, epistemically rational groups might be composed of epistemically irrational individuals. We call the conjunction of these two claims the Independence Thesis, as they together imply that methodological prescriptions for scientific communities and those for individual scientists might be logically independent of one another. We develop a formal model of scientific inquiry, define (...) four criteria for individual and group epistemic rationality, and then prove that the four definitions diverge, in the sense that individuals will be judged rational when groups are not and vice versa. We conclude by explaining implications of the inconsistency thesis for (i) descriptive history and sociology of science and (ii) normative prescriptions for scientific communities. (shrink)

Background independence begins life as an informal property that a physical theory might have, often glossed as 'doesn't posit a fixed spacetime background'. Interest in trying to offer a precise account of background independence has been sparked by the pronouncements of several theorists working on quantum gravity that background independence embodies in some sense an essential discovery of the General Theory of Relativity, and a feature we should strive to carry forward to future physical theories. This paper (...) has two goals. The first is to investigate what a world must be like in order to be truly described by a background independent theory given extant accounts of background independence. The second is to argue that there are no non-empirical reasons to be more confident in theories that satisfy extant accounts of background independence than in theories that don't. The paper concludes by drawing a general moral about a way in which focussing primarily on mathematical formulations of our physical theories can adversely affect debates in the metaphysics of physics. (shrink)

We often get evidence that bears on the reliability of some of our own first-order reasoning. The rational response to such “higher-order” evidence would seem to depend on a rational assessment of how reliable we can expect that reasoning to be, in light of the higher-order evidence. “Independence” principles are intended to constrain this reliability-assessment, so as to prevent question-begging reliance on the very reasoning being assessed. However, extant formulations of Independence principles tend to be vague or ambiguous, (...) and coming up with a tolerably precise formulation turns out to be tricky. This paper aims to make some progress toward developing a more precise Independence principle, and also to highlight some of the difficulties the project entails. The hope is to take a step toward understanding how rational belief is informed by evidence bearing on agents’ cognitive reliability. (shrink)

Kant’s theory of citizenship replaces the French revolutionary triptych of liberty, equality and fraternity with freedom (Freiheit), equality (Gleichheit) and civil self-sufficiency (Selbständigkeit). The interpretative question is what the third attribute adds to the first two: what does self-sufficiency add to free consent by juridical equals? This article argues that Selbständigkeit adds the idea of interdependent independence: the independent possession and use of citizens’ interdependent rightful powers. Kant thinks of the modern state as an organism whose members are agents (...) possessed of rightful (productive) powers, whose interdependent mode of exercise independently of unilateral permission matters for right. The empirical form of that ideal, according to Kant, is a republic of independent commodity producers. I will show that this reading of Selbständigkeit can consistently explain Kant’s disenfranchisement of women, wage labourers and landless farmers; that it offers a robust alternative to influential republican, libertarian and proprietarian interpretations of the Kantian state; and that it can buttress an original account of community as productive interdependence. (shrink)

An important principle in the epistemology of disagreement is Independence, which states, “In evaluating the epistemic credentials of another’s expressed belief about P, in order to determine how (or whether) to modify my own belief about P, I should do so in a way that doesn’t rely on the reasoning behind my initial belief about P” (Christensen 2011, 1-2). I present a series of new counterexamples to both Independence and also a revised, more widely applicable, version of it. (...) I then formulate and endorse a third version of Independence that avoids those counterexamples. Lastly, I show how this third version of Independence reveals two new ways one may remain steadfast in the face of two real life disagreements: one about God’s existence and one about moral realism. (shrink)

Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an (...) interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails. (shrink)

We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types.

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative (...) Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

The value of optimality modeling has long been a source of contention amongst population biologists. Here I present a view of the optimality approach as at once playing a crucial explanatory role and yet also depending on external sources of confirmation. Optimality models are not alone in facing this tension between their explanatory value and their dependence on other approaches; I suspect that the scenario is quite common in science. This investigation of the optimality approach thus serves as a case (...) study, on the basis of which I suggest that there is a widely felt tension in science between explanatory independence and broad epistemic interdependence, and that this tension influences scientific methodology. (shrink)

Mary Wollstonecraft argues that women must be independent citizens, but that they cannot be that unless they fulfill certain duties as mothers. This is problematic in a number of ways, as argued by Laura Brace in a 2000 article. However, I argue that if we understand Wollstonecraft's concept of independence in a republican, rather than a liberal context, and at the same time pay close attention to her discussion of motherhood, a feminist reading of Wollstonecraft is not only possible (...) but enriching. I will attempt to show, in particular, that the seeds of a feminist argument for co-parenting are to be found in the Vindication of the Rights of Woman. (shrink)

In cognitive science, the concept of dissociation has been central to the functional individuation and decomposition of cognitive systems. Setting aside debates about the legitimacy of inferring the existence of dissociable systems from ‘behavioural’ dissociation data, the main idea behind the dissociation approach is that two cognitive systems are dissociable, and thus viewed as distinct, if each can be damaged, or impaired, without affecting the other system’s functions. In this article, I propose a notion of functional independence that does (...) not require dissociability, and describe an approach to the functional decomposition and modelling of cognitive systems that complements the dissociation approach. I show that highly integrated cognitive and neurocognitive systems can be decomposed into non-dissociable but functionally independent components, and argue that this approach can provide a general account of cognitive specialization in terms of a stable structure–function relationship. 1 Introduction2 Functional Independence without Dissociability3 FI Systems and Cognitive Architecture4 FI Systems and Cognitive Specialization. (shrink)

Recently, new types of independence of a pair of C *- or W *-subalgebras (1,2) of a C *- or W *-algebra have been introduced: operational C *- and W *-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C *- and W *-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C *-independence is equivalent to operational C *-separability and that operational W *- (...) class='Hi'>independence is equivalent to operational W *-separability. Specific further sub-types of both operational C *- and W *-separability and operational C *- and W *-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised. (shrink)

This paper investigates the plausibility of Witmer, Butchard and Trogdon’s proposal to distinguish intrinsic properties from extrinsic ones in terms of independence from accompaniment and grounding. I argue that the proposed criterion is not adequate to determine intrinsicality, since according to it some intuitively extrinsic properties turn out to be intrinsic. I suggest and evaluate two responses: first, one could characterize a conception of independence which is specific to the individual instantiating the property; and second, one could justify (...) two assumptions about properties which entail that counterexample properties of the kinds I present do not exist, most importantly that there are no fundamental properties which are instantiated in an intrinsic fashion by some individuals and an extrinsic fashion by others. Although the latter seems prima facie plausible, I present some potential counterexamples to it from current physical theory. I conclude that the grounding- and independence-based criterion of intrinsicality can be defended from my objections, although the cost of doing so might make it more attractive to characterize intrinsicality in terms of independence, or in terms of grounding, alone. (shrink)

In this paper we extend to non-classical set theories the standard strategy of proving independence using Boolean-valued models. This extension is provided by means of a new technique that, combining algebras (by taking their product), is able to provide product-algebra-valued models of set theories. In this paper we also provide applications of this new technique by showing that: (1) we can import the classical independence results to non-classical set theory (as an example we prove the independence of (...) $\mathsf {CH}$ ); and (2) we can provide new independence results. We end by discussing the role of non-classical algebra-valued models for the debate between universists and multiversists and by arguing that non-classical models should be included as legitimate members of the multiverse. (shrink)

Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally affected by (...) environmental factors such as commonly perceived evidence. In a general theorem, we identify causal conditions guaranteeing each kind of opinion independence. These results have implications for whether and how ‘wisdom of crowds’ arguments are possible, and how truth-conducive institutions can be designed. (shrink)

In epistemology and in ordinary life, we make many normative claims about beliefs. As with all normative claims, philosophical questions arise about what – if anything – underwrites these kinds of normative claims. On one view, epistemic instrumentalism, facts about what we (epistemically) ought to believe, or about what is an (epistemic, normative) reason to believe what, obtain at least partly in virtue of our goals (or aims, ends, intentions, desires, etc.). The converse view, anti-instrumentalism, denies this, and holds that (...) the facts about what we ought or have reasons to believe are independent of our goals. In this chapter, I present the case for anti-instrumentalism. I lay out a well-known problem for instrumentalism, which is to say exactly what goal (or goals) grounds our epistemic reasons. For each possible answer, the view seems to generate problematic results. I consider some ways of trying to make the instrumentalist view more sophisticated to solve the problem and reject them. I then note a further problem for instrumentalism that applies regardless of what goal the instrumentalist says grounds our epistemic reasons. Finally, I sketch my preferred positive anti-instrumentalist view and argue that it is more theoretically virtuous than instrumentalism in several respects. (shrink)

We present a family of counter-examples to David Christensen's Independence Criterion, which is central to the epistemology of disagreement. Roughly, independence requires that, when you assess whether to revise your credence in P upon discovering that someone disagrees with you, you shouldn't rely on the reasoning that lead you to your initial credence in P. To do so would beg the question against your interlocutor. Our counter-examples involve questions where, in the course of your reasoning, you almost fall (...) for an easy-to-miss trick. We argue that you can use the step in your reasoning where you caught the trick as evidence that someone of your general competence level likely fell for it. Our cases show that it's permissible to use your reasoning about disputed matters to disregard an interlocutor's disagreement, so long as that reasoning is embedded in the right sort of explanation of why she finds the disputed conclusion plausible, even though it's false. (shrink)

Two recent and influential papers, van Rooij 2007 and Lassiter 2012, propose solutions to the proviso problem that make central use of related notions of independence—qualitative in the first case, probabilistic in the second. We argue here that, if these solutions are to work, they must incorporate an implicit assumption about presupposition accommodation, namely that accommodation does not interfere with existing qualitative or probabilistic independencies. We show, however, that this assumption is implausible, as updating beliefs with conditional information does (...) not in general preserve independencies. We conclude that the approach taken by van Rooij and Lassiter does not succeed in resolving the proviso problem. (shrink)

Philosophers often claim that humility is a dependent virtue: a virtue that depends on another virtue for its value. I consider three views about this relation: Specific Dependence, Unspecific Dependence, and Fittingness. I argue that, since humility cannot uniquely depend on another virtue, and since this uniqueness is desirable, we should reject Specific and Unspecific Dependence. I defend a Fittingness view, according to which the humble person possesses some objectively good quality fitting for humility. I show beyond Slote’s original characterization (...) of the dependence relation that, even if humility’s value depends on having objectively good qualities, humility itself can be one such quality. So, humility can depend on itself. I call this view Bootstrapped Fittingness. (shrink)

On an increasingly popular view of rationality, rationality is fundamentally about responding correctly to reasons and there is no independent rational requirement to avoid incoherence: having an incoherent combination of attitudes is irrational not because there is a fundamental requirement of rationality that prohibits it, but rather because you are guaranteed to fail to respond correctly to reasons in having it. This paper argues that any such attempt to explain the irrationality of incoherence in terms of responsiveness to reasons fails. (...) For there is something distinctively irrational about incoherence that is not explained in terms of the guaranteed failure to respond to reasons. Any adequate account of the nature of coherence requirements on belief and intention should take into account the distinctive kind of commitments involved in each type of attitude. (*published with open access). (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.

Conciliationists about peer disagreement hold that when one disagrees with an epistemic peer about some proposition p, one should significantly change one's view about p. Many arguments for conciliationism appeal to a principle Christensen [2011] dubs Independence. Independence says that evaluations of the beliefs of those with whom one disagrees should not be made on the basis of one's initial reasoning about p. In this paper, I show that this principle is false. I also show that two weaker (...) principles that vindicate conciliationism are either false, unmotivated, or both. (shrink)

Traditionally, independence accounts of substance have held pride of place. Aristotle, Aquinas, Descartes and Spinoza—among many others—accepted independence accounts in one form or another. The general thrust of such views is that substances are those things that are apt to exist in themselves. In this paper, I argue that several contemporary independence theories of substance—including those of Kit Fine, E.J. Lowe and Michael Gorman—include an ad hoc element that renders them unacceptable. I'll also consider the theories of (...) Hoffman and Rosenkrantz. (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 paper presents a comprehensive solution to the new riddle of induction. Gruesome induction is blocked because “grue” is not independent of our sampling and observation methods. Before presenting my theory, I critically survey previous versions of what I call the “independence strategy”, tracing the strategy to three different papers from the 1970s by (respectively) Wilkerson, Moreland, and Jackson. Next I critically examine recent approaches by Okasha, Godfrey-Smith, Schramm, and Freitag. All of these approaches have their virtues, but none (...) of them rules out every problem case. Nor do any of them alone explain exactly what goes wrong in all types of gruesome reasoning. My account aims to do both. Learning lessons from my criticisms of previous theories, I argue that there are several crucial types of independence. All of them are needed to rule out every problem case. I close by suggesting that the independence solution can also be adopted by proponents of other approaches—Bayesians, fans of natural kinds, and pragmatists. (shrink)

We study higher analogues of the classical independence number on $\omega $. For $\kappa $ regular uncountable, we denote by $i(\kappa )$ the minimal size of a maximal $\kappa $ -independent family. We establish ZFC relations between $i(\kappa )$ and the standard higher analogues of some of the classical cardinal characteristics, e.g., $\mathfrak {r}(\kappa )\leq \mathfrak {i}(\kappa )$ and $\mathfrak {d}(\kappa )\leq \mathfrak {i}(\kappa )$. For $\kappa $ measurable, assuming that $2^{\kappa }=\kappa ^{+}$ we construct a maximal $\kappa $ (...) -independent family which remains maximal after the $\kappa $ -support product of $\lambda $ many copies of $\kappa $ -Sacks forcing. Thus, we show the consistency of $\kappa ^{+}=\mathfrak {d}(\kappa )=\mathfrak {i}(\kappa )<2^{\kappa }$. We conclude the paper with interesting open questions and discuss difficulties regarding other natural approaches to higher independence. (shrink)

We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics and statistics.

‘The independence of auditors is primarily an issue of perception and communication’. The author is Professor of Auditing at Maastricht Accounting and Auditing Research Center University of Limburg, and University of Amsterdam; and a partner of Coopers & Lybrand Dijker Van Dien Accountants, Amsterdam. He wishes to express his thanks to Gijs Bak, Tony Bingham, John Hegarty, Wim Moleveld, David Pimm and Arno de Schepper for their valuable comments.

Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to explain the full (...) range of data. Instead, I argue, modals with embedded disjunctions license ‘Independence’ inferences: from the truth of a modal with an embedded disjunction, hearers infer that each disjunct is an independent alternative among the relevant set of worlds. I then develop a bilateral inquisitive semantics for modals that predicts the validity of these Independence inferences. My account vindicates common intuitions about both Ross’s puzzle and the puzzle of free choice permission, and explains the full range of data. (shrink)

We introduce an independence notion for choice functions, which we call ‘epistemic independence’ following the work by De Cooman et al. [17] for lower previsions, and study it in a multivariate setting. This work is a continuation of earlier work of one of the authors [29], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [11]. We obtain the many-to-one independent natural extension (...) in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less expressive imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [28], which De Bock and De Cooman [2] have called S-independence. We show that neither is more general than the other. (shrink)

This paper examines whether independent directors who have social ties to management (inside directors) can effectively perform their fiduciary duty to monitor management on behalf of shareholders. Ex ante, it is not clear whether social ties will enhance or obstruct the quality of board performance. Theory suggests that directors who are socially tied to management are ineffective and would make decisions favoring management. However, social ties can increase trust and information sharing between management and independent directors, improving directors' ability and (...) effectiveness in governing the company (Westphal, J. D.: 1999, The Academy of Management Journal 42(1), 7-24). To examine these contradicting predictions I use social network analysis and construct proxies for social ties between management and independent board members. Using these proxies, I first demonstrate that social ties are associated with higher managerial compensation. Further analyses reveal that these results are driven by social ties that include members of the compensation committee. Conversely, I demonstrate that financial reporting quality is improved when social ties exist. Specifically, I find that the likelihood of material weaknesses in internal controls and the likelihood of financial restatements are lower in companies with social ties. I further observe that this improved quality of financial reporting holds only when social ties include members of the audit committee. I conclude that ethically, socially tied independent directors should disqualify themselves from serving on compensation committees where social independence is essential. However, in tasks where collaboration with management is essential, directors with social links to each other can be of added value to shareholders. (shrink)

To infer the state of a cause from the states of its effects, independent lines of evidence are preferable to dependent ones. This familiar idea is here investigated, the goal being to identify its presuppositions. Connections are drawn with Reichenbach's (1956) and Salmon's (1984) discussions of the principle of the common cause.

The aim of the paper is to explicate the concept of causal independence between sets of factors and Reichenbach's screening-off-relation in probabilistic terms along the lines of Suppes' probabilistic theory of causality (1970). The probabilistic concept central to this task is that of conditional stochastic independence. The adequacy of the explication is supported by proving some theorems about the explicata which correspond to our intuitions about the explicanda.

I argue that the freedom which is to coexist with the freedom of choice of others in accordance with a universal law mentioned in Kant's Rechtslehre is not itself freedom of choice. Rather, it is the independence which is a condition of being able to exercise genuine free choice by not having to act in accordance with the choices of others. Kant's distinction between active and passive citizenship appears, however, to undermine this idea of independence, because the possession (...) of a certain type of property right on the part of some citizens makes it possible for them to dominate others. Kant's account of property in this way turns out to be central to the question as to whether his Rechtslehre represents an internally consistent account of how freedom can be guaranteed within a legal and political community. I go on to argue that Kant's attempt to justify a pre-political right of property cannot be viewed as a successful justification of private property, and that he should have abandoned the notion of su... (shrink)