After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning probably will not lead to AGI. We (...) indicate two possible ways traditional reinforcement learning could be altered to remove this roadblock. (shrink)

We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability (...) is replaced by a different type of infinite additivity. (shrink)

Many philosophers have claimed that extensive or additive measurement is incompatible with the existence of "higher values", any amount of which is better than any amount of some other value. In this paper, it is shown that higher values can be incorporated in a non-standard model of extensive measurement, with values represented by sets of ordered pairs of real numbers, rather than by single reals. The suggested model is mathematically fairly simple, and it applies to structures including negative as well (...) as positive values. (shrink)

Abstract: We sometimes say our moral claims are "objectively true," or are "right, even if nobody believes it." These additional claims are often taken to be staking out metaethical positions, representative of a certain kind of theorizing about morality that "steps outside" the practice in order to comment on its status. Ronald Dworkin has argued that skepticism about these claims so understood is not tenable because it is impossible to step outside such practices. I show that externally skeptical metaethical theory (...) can withstand his attacks, thereby defending the possibility of this kind of metatheoretical method and showing that the additional objectivity claims still make sense as external claims. Four interpretations of the additional objectivity claims can still be understood externally: as secondary properties, as arguing for some form of causal correspondence, as explaining error, and under Blackburn's expressivism. In the end, Dworkin's argument can be turned against itself. (shrink)

According to the orthodox account of meaning and translation in the literature, meaning is a property of expressions of a language, and translation is a matching of synonymous expressions across languages. This linguistic account of translation gives rise to well-known skeptical conclusions about translation, objectivity, meaning and truth, but it does not conform to our best translational practices. In contrast, I argue for a textual account of meaning based on the concept of a TEXT-TYPE that does conform to our (...) best translational practices. With their semantic function in view, text-types are Archimedean points for their respective disciplines. The text-type of philosophy is no exception. Culture-transcendent conceptual analysis can proceed on firm footing without having to deny the reality of radical cultural and linguistic difference by treating components of text-types as the concepts to be analyzed. Analyses of central philosophical concepts are provided as a means of adjudicating philosophical controversy. (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.

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive measurement, in the (...) sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom. (shrink)

We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any nonsemilinear expansion (...) of R. Combining these results, we obtain several restrictions on possible o-minimal expansions of arbitrary Archimedean ordered groups and in particular of the rational ordered group. (shrink)

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure M, Polish group G of permutations of M, and \, G has a comeager n-diagonal conjugacy class iff the family of all n-tuples of G-extendable bijections between finitely generated substructures of M, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not (...) homogenizable. Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom (...) of NAP _3.4_ Infinite sums _3.5_ Definition of NAP functions via infinite sums _3.6_ Relation to numerosity theory _4_ Objections and Replies _4.1_ Cantor and the Archimedean property _4.2_ Ticket missing from an infinite lottery _4.3_ Williamson’s infinite sequence of coin tosses _4.4_ Point sets on a circle _4.5_ Easwaran and Pruss _5_ Dividends _5.1_ Measure and utility _5.2_ Regularity and uniformity _5.3_ Credence and chance _5.4_ Conditional probability _6_ General Considerations _6.1_ Non-uniqueness _6.2_ Invariance Appendix. (shrink)

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, (...) to undermine Ishiguro’s interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions. (shrink)

We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, thereby demonstrating the independence (...) of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. (shrink)

We study properties of definable sets and functions in power-bounded T -convex fields, proving that the latter have the multidimensional Jacobian property and that the theory of T -convex fields is b -minimal with centers. Through these results and work of I. Halupczok we ensure that a certain kind of geometrical stratifications exist for definable objects in said fields. We then discuss a number of applications of those stratifications, including applications to Archimedean o-minimal geometry.

We discover geometric properties of certain definable sets over non-Archimedean valued fields with analytic structures. Results include a parameterized smooth stratification theorem and the existence of a bound on the piece number of fibers for these sets. In addition, we develop a dimension theory for these sets and also for the formulas which define them.

Studies in Wilfrid Sellars' philosophy: Aune, B. Sellars on practical reason.--Castañeda, H.-N. Some reflections on Wilfrid Sellars' theory of intentions.--Donagan, A. Determinism and freedom: Sellars and the reconciliationist thesis.--Robinson, W. S. The legend of the given.--Clark, R. The sensuous content of perception.--Grossmann, R. Perceptual objects, elementary particles, and emergent properties.--Rosenberg, J. F. The elusiveness of categories, the Archimedean dilemma, and the nature of man: a study in Sellarsian metaphysics.--Turnbull, R. G. Things, natures, and properties.--Wells, R. The indispensable word "now."--Van (...) Fraassen, B. C. Theories and counterfactuals.--Harman, G. H. Wilfrid Sellars' Theory of induction.--Sellarsiana: Sellars, W. Autobiographical reflections.--Sellars, W. The structure of knowledge. Lecture I, perception. Lecture II, minds. Lecture III, epistemic principles.--Wilfrid Sellars' Philosophical bibliography. (p. 349-353). (shrink)

This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture) with those of solvability (restricted, unrestricted) under the completeness and transitivity of a binary relation. Theorem 2 uses the primitive notion of a separately continuous function to answer the question when an analogous property on a relation is fully continuous. Theorem (...) 3 provides a portmanteau theorem on the equivalence between restricted solvability and various notions of continuity under weak monotonicity. Finally, Theorem 4 presents a variant of Theorem 3 that follows Theorem 1 in dispensing with the dimensionality requirement and in providing partial equivalences between solvability and continuity notions. These theorems are motivated for their potential use in representation theorems. (shrink)

Matti Eklund (2017) has argued that ardent realists face a serious dilemma. Ardent realists believe that there is a mind-independent fact as to which normative concepts we are to use. Eklund claims that the ardent realist cannot explain why this is so without plumping in favor of their own normative concepts or changing the topic. The paper first advances the discussion by clarifying two ways of understanding the question of which normative concepts to choose: a theoretical question about which concepts (...) have the abstract property of being normatively privileged and a further practical question of which concepts we are to choose even granting some concepts are thus privileged. I argue that the ardent realist’s best bet for answering the theoretical question while avoiding Eklund’s dilemma is to provide a real definition of this property. I point out the difficulties for providing such a definition. I then argue that even with an answer to the theoretical question, the ardent realist faces a further dilemma in answering the practical question. In sum, though I see no knock-down argument against ardent realism, it may nonetheless die a death by a thousand cuts. I close by considering a deeper reason for why ardent realism is so difficult to defend: every argument starts somewhere. It is unclear how there can be an Archimedean point that makes no reference to any normative concepts that can nonetheless be employed to convince everyone to adopt ours. I then briefly propose two options for someone still inclined towards realism: (i) accept that our normative concepts are normatively privileged without attempting to explain why this is so, or (ii) be less ardent and accept a perspective-dependent account of normativity. (shrink)

The central aim of this paper is to present a Boolean algebraic approach to the classical Aristotelian Relations of Opposition, namely Contradiction and (Sub)contrariety, and to provide a 3D visualisation of those relations based on the geometrical properties of Platonic and Archimedean solids. In the first part we start from the standard Generalized Quantifier analysis of expressions for comparative quantification to build the Comparative Quantifier Algebra CQA. The underlying scalar structure allows us to define the Aristotelian relations in Boolean (...) terms and to propose a 3D visualisation by transforming a cube into an octahedron. In part two, the architecture of the CQA is shown to carry over, both to the classical quantifiers of Predicate Calculus and to the modal operators—which are given a Generalized Quantifier style re-interpretation. In this way we provide an algebraic foundation for Blanché’s Aristotelian hexagon as well as a 3D alternative to his 2D star-like visualisation. In a final part, a richer scalar structure is argued to underly the realm of Modality, thus generalizing the 3D algebra with eight (2 3 ) operators to a 4D algebra with sixteen (2 4 ) operators. The visual representation of the latter structure involves a transformation of the hypercube to a rhombic dodecahedron. The resulting 3D visualisation allows a straightforward embedding, not only of the classical Blanché star of Aristotelian relations or the paracomplete and paraconsistent stars of Béziau (Log Investig 10, 218–232, 2003) but also of three additional isomorphic Aristotelian constellations. (shrink)

Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. This is interpreted as (...) involving arelational theory of quantity which contrasts in certain respects with thequalitative theory of quantity implicit in standard representational extensive measurement theory. The representational properties of extensiver-scales are investigated, and found to coincide withweak extensive measurement in the sense of Holman. This provides support for the thesis (developed in a separate paper) that weak extensive measurement is a more natural model of actual physical extensive scales than is the standard model using strong extensive measurement. Finally, the present apparatus is applied to slightly simplify the existing necessary and sufficient conditions for strong extensive measurement. (shrink)

This work adopts the perspective of plural logic and measurement theory in order first to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantifier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the first to examine comparatives within plural logic, a step which appears necessary, but which also harbors specific analytical problems examined here.Since nominal comparatives involve (...) plural and mass reference, we begin with a domain of discourse upon which a lattice structure (Link's) is imposed, and which maps (via abstract dimensions such asweight in kilograms) to concrete measures (in N,R+). The mapping must be homomorphic and Archimedean. Comparisons begin as simple predicates on dimensions or measures; from these we derive classes of predicates on the domain, i.e., generalized determiners (quantifiers), and show, e.g., how monotonicity properties follow in the derivation. This results in a proposal for a logical language which includes derived determiners, and which is an attractive target for semantics interpretation; it also turns out that some interesting comparative determiners are first order, at least when restricted to nonparametric and noncollective predications. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 43.4 (2005) 490-491 [Access article in PDF] Husain Sarkar. Descartes' Cogito: Saved from the Great Shipwreck. New York: Cambridge University Press, 2003. Pp. xviii + 305. Cloth, $65.00. Descartes's first critics attacked his cogito, ergo sum as deficient; his present critics attack it as excessive. Either way, it is an Archimedean point in Descartes's world and merits a book-length study. In this (...) book, Husain Sarkar makes a powerful case that the cogito is not an argument, but rather an "experiment," generating an intuition enabling Descartes to retrieve a timber from what Bourdin called the "great shipwreck" of the hyperbolic doubt.Sarkar places the experiment within his own fresh readings of Descartes's philosophy. They will be illuminating to new Descartes scholars. Some readings will seem perverse or cryptic. Constructive passages illuminate more, polemic passages less, as when Sarkar finds seven flaws in Hintikka's cogito interpretation. Despite the polemic excesses, Sarkar writes with modesty, epitomized by his slogan, "Reason with them in the most courteous manner."With verve and imagination Sarkar presents the cogito as an experiment which can be carried out in any world at all and yields an intuition that qualifies as a Cartesian first principle. He suggests various implications of his interpretation—for example, for the epistemic role of will: "The will initially learns the limits that it must recognize only at the foot of the cogito... It is in the state of the cogito that the will learns what it means to be ineluctably inclined toward affirming a proposition, and what it is to be free" (256).What is the content of the intuited 'I exist'? Sarkar calls upon Robert Adams's notion of a "primitive thisness," entirely distinct from a substance's properties or "suchnesses," and upon David Lewis's thesis that besides knowing propositions a person can know a self-ascription of a property. Still, he makes no headway at all. True, the question is extraordinarily [End Page 490] difficult. It has not yielded appreciably to brilliant phenomenologists or brilliant students of direct reference and indexicality or, for that matter, me. The content of 'I' statements is a topic for another book, and no one I know of is writing it.In the book's centerpiece, Sarkar marshals a series of attacks on the cogito as argument. Sometimes they miss—more polemic overkill. Usually they hit home. Their cumulative effect is persuasive.Descartes says that "I think, therefore I exist" is the first principle of his philosophy (VI, 32; VIIIA, 7; V, 147: references are to the Adam and Tannery edition). But if the cogito were an argument, one of its premises would become his first principle.An argument requires movement of thought and that requires reliance on memory (X, 370 and 408), and in the cogito Descartes strips memory of its credentials (VII, 24, superseding the assurances of X, 368).An argument relies on logical principles, but Descartes suspects these and reasoning generally. In the First Meditation he calls into doubt the simplest mathematics; elsewhere he generalizes from mathematics to "self-evident principles" and to "all the arguments I had previously taken as demonstrative proofs" (VI, 32; IXB, 6; similar aspersions are cast in V, 137 and 139). (But see also Mark Olson, "Descartes' First Meditation: Mathematics and the Laws of Logic" JHP 26 [1988]: 407–438.)I'll add a wrinkle. Descartes's mouthpiece Eudoxus says you can use your own doubt to deduce facts that are even more certain than those commonly built upon the great principle that it is impossible that a thing should both exist and at the same time not exist (X, 522). The conclusion of any argument rests on such logical principles. If the cogito were an argument, its certainty could not exceed theirs. Descartes suggests here that it does.Sarkar also cites Descartes's denigrations of "logic," but these often pertain not to reasoning generally but to syllogistic logic. Thus Margaret Wilson took the cogito to be a nonsyllogistic argument. Still, Sarkar effectively deploys... (shrink)

In a number of works, we have suggested that whereas the ordered field R of real numbers should merely be regarded as constituting an arithmetic continuum (modulo the Archimedean axiom), the ordered field No of surreal numbers may be regarded as a sort of absolute arithmetic continuum (modulo NBG). In the present chapter, as part of a more general exposition of the absolute arithmetic continuum, we will outline some of the properties of the system of surreal numbers that we (...) believe lend credence to this mathematico-philosophical thesis. We will also provide an overview of No’s rich structure as a simplicity-hierarchical (or s-hierarchical) ordered field that recursively emerges from the interplay between its structure as an ordered field and its structure as a lexicographically ordered full binary tree. Finally, we will draw attention to how properties of the system of surreal numbers considered as an s-hierarchical ordered algebraic structure can be appealed to in conjunction with classical relations between ordered algebraic and geometric systems to help resolve, for the surreal case, one of the purported difficulties that lies at the heart of attempts to bridge the gap between the domains of number and of geometrical magnitude. In particular, we will explain how it is possible that despite the fact that every surreal number, considered as a member of an s-hierarchical ordered field, differs from every other in characteristic individual properties, the absolute (Euclidean) geometrical continuum, which is modeled by the Cartesian space over the ordered field No of surreal numbers, appears as an amorphous pulp of points that display little individuality. (shrink)

The book critically analyses the nature and scope of intellectual property rights using three different approaches: the philosophical, the empirical, and the theoretical. It studies the different justifications usually put forward in favour of protecting intellectual property rights, and shows how such rights come into conflict with other rights in society. The volume also discusses their benefits and drawbacks with the help of case studies. The author contends that rights can and should be 'structured in a lexical order (...) of priority where rights which are linked to survival strategies ought to have enough legal teeth to trump rights which are more in the nature of economic entitlements, like intellectual property rights are'. (shrink)

Veit suggests that the challenge of coordinating movement in multicellular organisms led to the evolution of a prioritizing value system, which rendered organisms complex enough to be sentient and drove the Cambrian explosion, while the absence of this evaluation system led to the demise of Ediacaran animals. In this commentary we criticize Veit’s terminology and evolutionary proposals, arguing that his terminology and evolutionary scenarios are problematic, and put forward alternative proposals. We suggest that sentience is a system property, and (...) that the evolution of sentience was the outcome of the evolution of open-ended associative learning, which included the coevolution of sensory, motor, memory, and value subsystems. We suggest that these coevolutionary system dynamics were a factor in the Cambrian explosion and contributed to the extinction of the Ediacaran biota. (shrink)

An argument against treating our bodies as commodities No one wants to be treated like an object, regarded as an item of property, or put up for sale. Yet many people frame personal autonomy in terms of self-ownership, representing themselves as property owners with the right to do as they wish with their bodies. Others do not use the language of property, but are similarly insistent on the rights of free individuals to decide for themselves whether to (...) engage in commercial transactions for sex, reproduction, or organ sales. Drawing on analyses of rape, surrogacy, and markets in human organs, Our Bodies, Whose Property? challenges notions of freedom based on ownership of our bodies and argues against the normalization of markets in bodily services and parts. Anne Phillips explores the risks associated with metaphors of property and the reasons why the commodification of the body remains problematic. What, she asks, is wrong with thinking of oneself as the owner of one's body? What is wrong with making our bodies available for rent or sale? What, if anything, is the difference between markets in sex, reproduction, or human body parts, and the other markets we commonly applaud? Phillips contends that body markets occupy the outer edges of a continuum that is, in some way, a feature of all labor markets. But she also emphasizes that we all have bodies, and considers the implications of this otherwise banal fact for equality. Bodies remind us of shared vulnerability, alerting us to the common experience of living as embodied beings in the same world. Examining the complex issue of body exceptionalism, Our Bodies, Whose Property? demonstrates that treating the body as property makes human equality harder to comprehend. (shrink)

The dominant approach to environmental policy endorsed by conservative and libertarian policy thinkers, so-called “free market environmentalism”, is grounded in the recognition and protection of property rights in environmental resources. Despite this normative commitment to property rights, most self-described FME advocates adopt a utilitarian, welfare-maximization approach to climate change policy, arguing that the costs of mitigation measures could outweigh the costs of climate change itself. Yet even if anthropogenic climate change is decidedly less than catastrophic, human-induced climate change (...) is likely to contribute to environmental changes that violate traditional conceptions of property rights. Viewed globally, the actions of some countries—primarily industrialized nations—are likely to increase environmental harms suffered by other countries—less developed nations that have not made any significant contribution to climate change. It may well be that aggregate human welfare would be maximized in a warmer, wealthier world, or that the gains from climate change will offset environmental losses. Yet such claims, even if demonstrated, would not address the normative concern that the consequences of anthropogenic global warming would infringe upon the rights of people in less-developed nations. As a consequence, this paper calls for a rethinking of FME approaches to climate change policy. (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 the first part of the article, we show that if $\omega \le \kappa < \lambda$ are cardinals, ${\kappa ^{ < \kappa }} = \kappa$, and λ is weakly compact, then in $V\left[M {\left} \right]$ the tree property at $$\lambda = \left^{V\left[ {\left} \right]} $$ is indestructible under all ${\kappa ^ + }$-cc forcing notions which live in $V\left[ {{\rm{Add}}\left} \right]$, where ${\rm{Add}}\left$ is the Cohen forcing for adding λ-many subsets of κ and $\left$ is the standard Mitchell forcing (...) for obtaining the tree property at $\lambda = \left^{V\left[ {\left} \right]} $. This result has direct applications to Prikry-type forcing notions and generalized cardinal invariants. In the second part, we assume that λ is supercompact and generalize the construction and obtain a model ${V^{\rm{*}}}$, a generic extension of V, in which the tree property at ${\left^{{V^{\rm{*}}}}}$ is indestructible under all ${\kappa ^ + }$-cc forcing notions living in $V\left[ {{\rm{Add}}\left} \right]$, and in addition under all forcing notions living in ${V^{\rm{*}}}$ which are ${\kappa ^ + }$-closed and “liftable” in a prescribed sense. (shrink)

Tense logics in the bimodal propositional language are investigated with respect to the Finite Model Property. In order to prove positive results techniques from investigations of modal logics above K4 are extended to tense logic. General negative results show the limits of the transfer.

This book gives an account of a full spectrum of property rights and their relationship to individual liberty. It shows that a purely deontological approach to justice can deal with the most complex questions regarding the property system. Moreover, the author considers the economic, ecological, and technological complexities of our real-world property systems. The result is a more conceptually sound account of natural rights and the property system they demand. If we think that liberty should be (...) at the centre of justice, what does that mean for the property system? Economists and lawyers widely agree that a property system must be composed of many different types of property: the kind of private ownership one has over one's person and immediate possessions, as well as the kinds of common ownership we each have in our local streets, as well as many more. However, theories of property and justice have not given anything approaching an adequate account of the relationship between liberty and any other form of property other than private ownership. It is often thought that a basic commitment to liberty cannot really tell us how to arrange the major complexities of the property system, which diverge from simple private ownership. Property and Justice demonstrates how philosophical rigour coupled with interdisciplinary engagement enables us to think clearly about how to deal with real-world problems. It will be of interest to political philosophers, political theorists, and legal theorists working on property rights and justice. (shrink)

New developments in biotechnology radically alter our relationship with our bodies. Body tissues can now be used for commercial purposes, while external objects, such as pacemakers, can become part of the body. Property in the Body: Feminist Perspectives transcends the everyday responses to such developments, suggesting that what we most fear is the feminisation of the body. We fear our bodies are becoming objects of property, turning us into things rather than persons. This book evaluates how well-grounded this (...) fear is, and suggests innovative models of regulating what has been called 'the new Gold Rush' in human tissue. This is an up-to-date and wide-ranging synthesis of market developments in body tissue, bringing together bioethics, feminist theory and lessons from countries that have resisted commercialisation of the body, in a theoretically sophisticated and practically significant approach. (shrink)

This paper is about the relation between two metaphysical topics: the nature of properties, and way the instantiation of a property is sometimes “realized in” something more fundamental. It is partly an attempt to develop further, but also to correct, my earlier treatments of these topics. In my published work on realization, including my book Physical Realization, I was at pains to insist that acceptance of my view about this does not commit one to the causal theory of properties (...) I have defended in several places. I held that it commits one to the claim that within any given world, properties with the same causal profile are identical, but not to the requirement that a property must have the same causal profile in any world in which it can be instantiated. I now think that this was a mistake. There is an argument from the account of realization I have offered to the conclusion that, if physicalism is true, properties of macroscopic objects have their causal profiles essentially. In what follows I will present that argument.Along the way I will correct what now seem to me mistakes in my earlier presentationsof the account of realization. And I will conclude with an additional argument for the causal theory of properties, one that does not tie it to the assumption that physicalism is true or to my account of realization. (shrink)

Because law, policy, and ethics are multiply intertwined, developments in any one of these areas can affect what happens in each of the others. Thus those interested in African information ethics will find it valuable to examine trends in law and policy – and those concerned about legal trends should acknowledge effective leadership when it comes from the direction of ethical practices. Though African societies are almost always pictured as receivers of social, informational, and technological innovations that come from other (...) sources, today many Africans are providing global leadership by developing innovative techniques for approaching the problem of information access. This article describes the context within which this is taking place, including a brief introduction to innovations in a number of areas, before looking in particular at innovations involving intellectual property rights that blend law, policy, and ethics. (shrink)

The article discusses an idea of how to extend the notion of rigidity to predicates, namely the idea that predicates stand in a certain systematic semantic relation to properties, such that this relation may hold rigidly or nonrigidly. The relation (which I call signification) can be characterised by recourse to canonical property designators which are derived from predicates (or general terms) by means of nominalization: a predicate signifies that property which the derived property designator designates. Whether signification (...) divides into rigid and non-rigid cases will then depend uponwhether canonical property designators divide into rigid and non-rigid ones. But, I shall argue, they do not, and so the only notion of rigidity gained this way is trivial. To show this, I first focus on the kind of canonical property designators which could be thought to be nonrigid, canonical designators such as having the colour of ripe tomatoes which themselves contain non-rigid property designators. An argument to the effect that such complex canonical designators are non-rigid is rebutted, five arguments to the effect that they are rigid are formulated, and finally an explanation of their rigidity based on the general nature of canonical property designators is presented. (shrink)

It is widely thought that mind–body substance dualism is implausible at best, though mere “property” dualism is defensible and even flourishing. This paper argues that substance dualism is no less plausible than property dualism and even has two advantages over it.