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)

We provide a general theorem implying that for a (strongly) dependent theory T the theory of sufficiently well-behaved pairs of models of T is again (strongly) dependent. We apply the theorem to the case of lovely pairs of thorn-rank one theories as well as to a setting of dense pairs of first-order topological theories.

In continuation of [JOH04, OH07], we prove that existentially closed CSA-groups have the independence property. This is done by showing that there exist words having the independence property relative to the class of torsion-free hyperbolic groups.

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class (...) of basic formulas provided it can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)

A theory is stable up to Δ if any Δ-type over a model has a few extensions up to complete types. We prove that a theory has no the independence property iff it is stable up to some Δ, where each equation image has no the independence property.

We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.

A class K of structures is controlled if for all cardinals λ, the relation of L∞,λ-equivalence partitions K into a set of equivalence classes . We prove that no pseudo-elementary class with the independence property is controlled. By contrast, there is a pseudo-elementary class with the strict order property that is controlled 69–88).

No theory of a partially ordered set of finite width has the independence property, generalizing Poizat's corresponding result for linearly ordered sets. In fact, a question of Poizat concerning linearly ordered sets is answered by showing, moreover, that no theory of a partially ordered set of finite width has the multi-order property. It then follows that a distributive lattice is not finite-dimensional $\operatorname{iff}$ its theory has the independence property $\operatorname{iff}$ its theory has the multi-order (...) class='Hi'>property. (shrink)

We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of M which are invariant under the natural action of $\operatorname{Aut}(M)$ . This pursuit requires a generalization of Shelah's forking formulas [8] to "essentially measure zero" sets and an application of Myer's "rank diagram" [5] of the Boolean algebra under consideration. The classification is completed for a large class of ℵ 0 -categorical structures without the independence property including those which are (...) stable. (shrink)

We develop a new notion of independence (þ-independence, read "thorn"-independence) that arises from a family of ranks suggested by Scanlon (þ-ranks). We prove that in a large class of theories (including simple theories and o-minimal theories) this notion has many of the properties needed for an adequate geometric structure. We prove that þ-independence agrees with the usual independence notions in stable, supersimple and o-minimal theories. Furthermore, we give some evidence that the equivalence between forking and (...) þ-forking in simple theories might be closely related to one of the main open conjectures in simplicity theory, the stable forking conjecture. In particular, we prove that in any simple theory where the stable forking conjecture holds. þ-independence and forking independence agree. (shrink)

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)

I first show how one might argue for a mind-independent conception of beauty and artistic merit. I then discuss whether this makes aesthetic judgements suitable to undermine skeptical worries about the existence of mind-independent moral value and categorical reasons.

We study a class of 0-categorical simple structures such that every M in has uncomplicated forking behavior and such that definable relations in M which do not cause forking are independent in a sense that is made precise; we call structures in independent. The SU-rank of such M may be n for any natural number n>0. The most well-known unstable member of is the random graph, which has SU-rank one. The main result is that for every strongly independent structure M (...) in , if a sentence φ is true in M then φ is true in a finite substructure of M. The same conclusion holds for every structure in with SU-rank one; so in this case the word ‘strongly’ can be removed. A probability theoretic argument is involved and it requires sufficient independence between relations which do not cause forking. A stable structure M belongs to if and only if it is 0-categorical, 0-stable and every definable strictly minimal subset of is indiscernible. (shrink)

As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations.

We define a formula φ in a first-order language L , to be an equation in a category of L -structures K if for any H in K , and set p = {φ;i ϵI, a i ϵ H} there is a finite set I 0 ⊂ I such that for any f : H → F in K , ▪. We say that an elementary first-order theory T which has the amalgamation property over substructures is equational if every (...) quantifier-free formula is equivalent in T to a boolean combination of equations in Mod, the category of models of T with embeddings for morphisms. Thus, we develop a theory of independence with respect to equations in general categories of structures, which is similar to the one introduced in stability but which, in our context, has an algebraic character. (shrink)

While it is a point of agreement in contemporary republican political theory that property ownership is closely connected to freedom as non-domination, surprisingly little work has been done to elucidate the nature of this connection or the constraints on property regimes that might be required as a result. In this paper, I provide a systematic model of the boundaries within which republican property systems must sit and explore some of the wider implications that thinking of property (...) in these terms may have for republicans. The boundaries I focus on relate to the distribution of property and the application of types of property claims over particular kinds of goods. I develop this model from those elements of non-domination most directly related to the operation of a property regime: (a) economic independence, (b) limiting material inequalities, and (c) the promotion of common goods. The limits that emerge from this analysis support intuitive judgments that animate much republican discussion of property distribution. My account diverges from much orthodox republican theory, though, in challenging the primacy of private property rights in the realization of economic independence. The value of property on republican terms can be realized without private ownership of the means of production. (shrink)

This chapter contains sections titled: Property‐Owning Democracy Before Socialism: The Rise of Commercial Republicanism Property‐Owning Democracy at the Socialist High Tide (i): Progressive Conservative Origins Property‐Owning Democracy at the Socialist High Tide (ii): Liberals and Labour Revisionists Property‐Owning Democracy at the Socialist High Tide (iii): James Meade Property‐Owning Democracy After Socialism? Rawlsian and Neoliberal Lineages References.

In this paper, I will reconstruct Hume's argument for the ontological (in the sense of rigid existential) independence of simple properties in A Treatise of Human Nature , Book 1 (1739). According to my reconstruction, the main premises of the argument are the real distinctness of every perception of a simple property, Hume's Separability Principle and his Conceivability Principle. In my view, Hume grounds the real distinctness of every perception of a simple property in his atomistic theory (...) of sense perception and his Copy Principle. I will also show why Hume's argument should be seen as relevant nowadays. David Lewis and his followers in metaphysics continue Hume's line of thinking in this respect, which is opposed by power ontologists (Brian Ellis, Stephen Mumford), for example. (shrink)

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

While it is a point of agreement in contemporary republican political theory that property ownership is closely connected to freedom as non-domination, surprisingly little work has been done to elucidate the nature of this connection or the constraints on property regimes that might be required as a result. In this paper, I provide a systematic model of the boundaries within which republican property systems must sit and explore some of the wider implications that thinking of property (...) in these terms may have for republicans. The boundaries I focus on relate to the distribution of property and the application of types of property claims over particular kinds of goods. I develop this model from those elements of non-domination most directly related to the operation of a property regime: (a) economic independence, (b) limiting material inequalities, and (c) the promotion of common goods. The limits that emerge from this analysis support intuitive judgments that animate much republican discussion of property distribution. My account diverges from much orthodox republican theory, though, in challenging the primacy of private property rights in the realization of economic independence. The value of property on republican terms can be realized without private ownership of the means of production. (shrink)

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)

The article presents the metaethical discussion of moral properties with emphasis on the connection between metaphysical views on properties and theories on moral properties. Theories on moral properties vary along three dimensions: realism vs. anti-realism, naturalism vs. non-naturalism, and reductionism vs. non-reductionism. It is argued that realism should be understood in terms of Specific Mind-Independence which entails that moral properties are not arbitrarily dependent on the mental states of individuals agents. It is further noticed that theories on moral properties (...) should account for the practicality of morality. The article then considers different versions of naturalism and non-naturalism in reductionist and non-reductionist forms. It is discussed how these theories account for the practicality of morality and what metaphysical challenges they face. Moreover, it is suggested that Specific Mind-Independence offers plausible classifications of metaethical theories as ‘realist’ or ‘anti-realist’. (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)

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)

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)

Powers are popularly assumed to be distinct from, and dependent upon, inert qualities, mainly because it is believed that qualities have their nature independently of other properties while powers have their nature in virtue of a relation to distinct manifestation property. George Molnar and Alexander Bird, on the other hand, characterize powers as intrinsic and relational. The difficulties of reconciling the characteristics of being intrinsic and at the same time essentially related are illustrated in this paper and it is (...) argued that the reasons for thinking of powers as essentially relational are based on misguided epistemological consideration. Finally, I present a way of thinking of fundamental properties as primitive natures that we can only understand in virtue of what they do but which we should not think of as being ontologically constituted by these doings. According to this view, properties are both qualities and powers. (shrink)

Should property owners have a unique right to express their opinion just because they own property? While current law recognizes owners’ rights to express their voices in certain instances, it does not provide comprehensive and coherent answers to this question. This article provides an analytical framework for recognizing the owners’ right to voice as an independent property entitlement within the owners’ property bundle of rights and delineates its boundaries. Yet even when the owners’ voice is (...) class='Hi'>property-dependent, there is a difference between voice that facilitates the realization of another property entitlement (such as the right to exclude, use, or trade) and voice that is constitutive to ownership in and of itself. Only the latter instances justify recognition of the owners’ right to a voice as an independent property entitlement. By examining different branches of both tangible and intellectual property law, such as inheritance law, eminent domain, homeowners’ association law, zoning law, and copyright law, this article demonstrates the usefulness of the proposed analytical framework in explaining certain parts of the current law and suggests modifications of other parts. (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.

We characterize þ-independence in a variety of structures, focusing on the field of real numbers expanded by predicate defining a dense multiplicative subgroup, G, satisfying the Mann property and whose pth powers are of finite index in G. We also show such structures are super-rosy and eliminate imaginaries up to codes for small sets.

This chapter defends the property dualism argument. The term “semantic premise” mentioned is used to refers to an assumption identified by Brian Loar that antiphysicalist arguments, such as the property dualism argument, tacitly assume that a statement of property identity that links conceptually independent concepts is true only if at least one concept picks out the property it refers to by connoting a contingent property of that property. It is argued that, the property (...) that does the work in explaining the possibility of a posteriori identities need not be a first-order property of the referent in question. On his view, the property dualism argument requires only a weaker semantic premise, which allows that the property in question be a higher order property. A refined version of the property dualism argument is formulated, which uses the weaker premise, and defends the argument against various objections. (shrink)

Can we employ the property of rationality in establishing what rationality requires? According to a central and formal thesis of John Broome’s work on rational requirements, the answer is ‘no’ – at least if we expect a precise answer. In particular, Broome argues that (i) the property of full rationality (i.e. whether or not you are fully rational) is independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. That is, (...) (ii) by replacing a wide-scope requirement with a corresponding narrow-scope requirement (or vice versa), we do not alter the situations in which a person is fully rational. As a consequence, (iii) the property of full rationality is unable to guide us in determining whether a rational requirement has a wide or a narrow logical scope. We cannot resolve the wide/narrow scope debate by appealing to a theory of fully rational attitudes. This paper argues that (i), (ii) and (iii) are incorrect. Replacing a wide- with a corresponding narrow-scope requirement (or vice versa) can alter the set of circumstances in which a person is fully rational. The property of full rationality is therefore not independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. As a consequence, the property of full rationality can guide us in determining what rationality requires – even in cases where we expect a precise answer. (shrink)

In this paper we study a specific subclass of abstract elementary classes. We construct a notion of independence for these AEC’s and show that under simplicity the notion has all the usual properties of first order non-forking over complete types. Our approach generalizes the context of 0-stable homogeneous classes and excellent classes. Our set of assumptions follow from disjoint amalgamation, existence of a prime model over 0/, Löwenheim–Skolem number being ω, -tameness and a property we call finite character. (...) We also start the studies of these classes from the 0-stable case. Stability in 0 and -tameness can be replaced by categoricity above the Hanf number. Finite character is the main novelty of this paper. Almost all examples of AEC’s have this property and it allows us to use weak types, as we call them, in place of Galois types. (shrink)

This paper defends the case against (sparse) disjunctive properties by means of four Armstrongian arguments. The first of these is a logical atomist argument from truthmaking, which is, broadly speaking, ‘Armstrongian’ (Armstrong 1997). This argument is strong – although it stands or falls with the relevant notion of truthmaking, as it were. However, three arguments, which are prima facie independent of truthmaking, can be found explicitly early in Armstrong’s middle period. Two of these early arguments face a serious objection put (...) forward forcefully by Louise Antony (2003) and Alan Penczek (1997), respectively. I consider these objections and argue that they fail. Thus, even if the argument from truthmaking is indecisive, disjunctive properties should be rejected. (shrink)

David Lewis may be regarded as an antiessentialist. The reason is that he is said to believe that individuals do not have essential properties independent of the ways they are represented. According to him, indeed, the properties that are determined to be essential to individuals are a matter of which similarity relations among individuals are salient, and salience, in turn, is a contextual matter also determined to some extent by the ways individuals are represented. Todd Buras argues that the acknowledgment (...) of natural properties in counterpart theoretic ontology affects Lewis’s theory with regard to essentialism. Buras’s reasoning is appealing. He claims that, since natural properties determine the existence of similarity relations among individuals that are salient independent of context, Lewis can no longer be claimed to be an antiessentialist. The aim of this paper is to argue, against Buras, that if counterpart theory was antiessentialist before natural properties were taken into account, then it remains so afterwards. (shrink)

Hermann von Helmholtz’s work on perceptual science had a fundamental impact on Neo-Kantian movements in the late nineteenth century, and his influence continues to be felt in psychology and analytic philosophy of perception. As is widely acknowledged, Helmholtz denied that we can perceive mind-independent properties of external objects, a view I label Ignorance. Given his commitment to Ignorance, Helmholtz might seem to be committed to a subjectivism according to which we only perceive properties of our own representations. Against this, I (...) argue that for Helmholtz, the properties we perceive are not monadic properties of either the subject or the object. Rather, Helmholtz endorsed a relationalism about the properties we perceive: the properties of objects we perceive are all relational properties. I then suggest that once we take into account oft-neglected terminological distinctions in Helmholtz’s corpus, we are better able to make sense of his commitment to relationalism. (shrink)

We obtain some new results on the topology of unary definable sets in expansions of densely ordered Abelian groups of burden 2. In the special case in which the structure has dp‐rank 2, we show that the existence of an infinite definable discrete set precludes the definability of a set which is dense and codense in an interval, or of a set which is topologically like the Cantor middle‐third set (Theorem 2.9). If it has burden 2 and both an infinite (...) discrete set D and a dense‐codense set X are definable, then translates of X must witness the Independence Property (Theorem 2.26). In the last section, an explicit example of an ordered Abelian group of burden 2 is given in which both an infinite discrete set and a dense‐codense set are definable. (shrink)

There have been many attempts to determine what makes a natural kind real, chief among them is the criterion according to which natural kinds must be mind-independent. But it is difficult to specify this criterion: many supposed natural kinds have an element of mind-dependence. I will argue that the mind-independence criterion is nevertheless a good one, if correctly understood: the mind-independence criterion concerns the unification principles for natural kinds. Unification principles determine how natural kinds unify their properties, and (...) only those natural kinds that have a mind-independent unification principle should be considered real. (shrink)

I. Vague Properties and the Problem of Vagueness The philosophical problem of vagueness is to say what vagueness is in a way that helps to resolve the sorites paradox. Saying what vagueness is requires saying what kinds of things can be vague and in what the vagueness of each kind consists. Philosophers dispute whether things of this, that, or the other kind can be vague, but no one disputes that there are vague linguistic expressions. Among vague expressions, predicates hold a (...) special place in the problem of vagueness, for it’s their vagueness that is soritesgenerating. That puts the vagueness of predicates at the hub of the problem of vagueness, and there can be little doubt that we’ll be a short step from home if we can account for it. Any account of vagueness will of course require commitment to theses that are themselves foci of philosophical debate, but one can’t expect to get anywhere without taking on some as working hypotheses and then striving to say something that will be plausible if those hypotheses are plausible. One of the working hypotheses of this paper is that propositional attitudes and propositional speech acts are relations to propositions of some stripe or other, in the generic sense in which a proposition is an abstract, mind- and language-independent entity that has a truth condition, and has that truth condition both essentially and absolutely (i.e. without relativization to anything).1 The existence of propositions requires the existence of properties, in the generic sense in which a property is an abstract, mind- and language-independent entity that has an instantiation condition, and has that instantiation condition both essentially and absolutely. For present purposes it will be harmless to pretend that the propositions we believe and assert are Russellian propositions---structured entities whose basic constituents are the objects and properties our beliefs and speech acts are about. When a propositionalist speaks in loosey-goosey mode, she is apt to say that a sentence token is true just in case the proposition expressed in its utterance is true. (shrink)

The projection latticesP(ℳ1),P(ℳ2) of two von Neumann subalgebras ℳ1, ℳ2 of the von Neumann algebra ℳ are defined to be logically independent if A ∧ B≠0 for any 0≠AεP(ℳ1), 0≠BP(ℳ2). After motivating this notion in independence, it is shown thatP(ℳ1),P(ℳ2) are logically independent if ℳ1 is a subfactor in a finite factor ℳ andP(ℳ1),P(ℳ2 commute. Also, logical independence is related to the statistical independence conditions called C*-independence W*-independence, and strict locality. Logical independence ofP(ℳ1,P(ℳ2 turns (...) out to be equivalent to the C*-independence of (ℳ1,ℳ2) for mutually commuting ℳ1,ℳ2 and it is shown that if (ℳ1,ℳ2) is a pair of (not necessarily commuting) von Neumann subalgebras, thenP(ℳ1,P(ℳ2 are logically independent in the following cases: ℳ is a finite-dimensional full-matrix algebra and ℳ1,ℳ2 are C*-independent; (ℳ1,ℳ2) is a W*-independent pair; ℳ1,ℳ2 have the property of strict locality. (shrink)