The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

Textual and historical subtleties aside, let's call the idea that numbers are properties of equinumerous sets ‘the Fregean thesis.’ In a recent paper, Palle Yourgrau claims to have found a decisive refutation of this thesis. More surprising still, he claims in addition that the essence of this refutation is found in the Grundlagen itself – the very masterpiece in which Frege first proffered his thesis. My intention in this note is to evaluate these claims, and along the way to (...) shed some light on relevant passages of the Grundlagen. I will argue that Yourgrau does not make his case.The arguments with which we are concerned are found in the last three sections of Yourgrau's paper. A pervasive difficulty in these sections is that it is not clear exactly what Yourgrau is arguing against. The stated object of his attack is the Fregean thesis, a thesis about what numbers are; however, instead of a frontal assault, his strategy is to embark on a foray into the ill-defined issue of what it is that numbers number, where, roughly speaking, a number n numbers an object x just in case n can be legitimately assigned to x. The reason for this shift in emphasis appears to be rooted in a misconception. As we’ll see in more detail shortly, Yourgrau's argument against the Fregean thesis is based on an extension of a well known argument of Frege's found in §§22-3 of the Grundlagen, which Glenn Kessler has tagged the ‘relativity argument,’. According to Yourgrau, this is an argument ‘to the effect that what is literally numbered cannot simply be concrete objects’. This is incorrect. Frege himself clarifies the point of the argument in §21 with the following preface:In language, numbers (i.e., numerals] most commonly appear in adjectival form and attributive construction in the same sort of way as the words "hard" or "heavy" or "red," which have for their meanings properties of external things. It is natural to ask whether we must think of the individual numbers too as such properties, and whether, accordingly, the concept of number can be classed along with that, say, of color. (shrink)

I argue for the consistency of frege's treatments of identity and number. Specifically, I argue that geach is wrong in suggesting that frege's insights about number should have led him to the doctrine of relative identity.

Relativists maintain that identity is always relative to a general term. According to them, the notion of absolute identity has to be abandoned and replaced by a multiplicity of relative identity relations for which Leibniz’s Law does not hold. For relativists RI is at least as good as the Fregean cardinality thesis, which contends that an ascription of cardinality is always relative to a concept specifying what, in any specific case, counts as a unit. The same train (...) of thought on cardinality and identity is apparent among those – Artifactualists – who take relative identity sentences for artifacts as the norm. The aim of this paper is to criticize the thesis thatfrom FC it is possible to derive RI, and to explain why Artifactualists mistakenly believe that RI can be derived from FC. The misunderstanding derives from their assumption that the concept of artifact – like the concept of object – is not a sortal concept. (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...) if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

In recent work on context­dependency, it has been argued that certain types of sentences give rise to a notion of relative truth. In particular, sentences containing predicates of personal taste and moral or aesthetic evaluation as well as epistemic modals are held to express a proposition (relative to a context of use) which is true or false not only relative to a world of evaluation, but other parameters as well, such as standards of taste or knowledge or (...) an agent. Thus, a sentence like chocolate tastes good would express a proposition p that is true or false not only at a world of evaluation, but relative to the additional parameter as well, such as a parameter of taste or an agent. I will argue that the sentences that apparently give rise to relative truth should be understood by relating them in a certain way to the first person. More precisely, such sentences express what I will call first­person­based genericity, a form of generalization that is based on or directed toward an essential first­person application of the predicate. The account differs from standard relative truth account in crucial respects: it is not the truth of the proposition expressed that is relative to the first person; the proposition expressed by a sentence with a predicate of taste rather has absolute truth conditions. Instead it is the propositional content itself that requires a first­personal cognitive access whenever it is entertained. This account, I will argue, avoids a range of problems that standard relative truth theories of the sentences in question face and explains a number of further peculiarities that such sentences display. (shrink)

Mach's principle is discussed as a fundamental statement on kinematics, and an apparent contradiction is identified in the Lorentz-Minkowski form of the inertial metric. To resolve the incompatibility, length is redefined so that the speed of light is a field-dependent variable, although still constant for all inertial observers at a point in space-time. Gravitational theories with variableG are considered, and it is shown that a redefinition of length and time results in constantG and variablec.

There are three main types of number used in modern, industrialized societies. Cardinals count sets (e.g., people, objects) and quantify elements of conventional scales (e.g., money, distance), ordinals index positions in ordered sequences (e.g., years, pages), and nominals serve as unique identifiers (e.g., telephone numbers, player numbers). Many studies that have cited number frequencies in support of claims about numerical cognition and mathematical cognition hinge on the assumption that most numbers analyzed are cardinal. This paper is the (...) first to investigate the relative frequencies of different number types, presenting a corpus analysis of morphologically unmarked numbers (not, e.g., “eighth” or “21st”) in which we manually annotated 3,600 concordances in the Corpus of Contemporary American English. Overall, cardinals are dominant—both pure cardinals (sets) and measurements (scales)—except in the range 1,000–10,000, which is dominated by ordinal years, like 1996 and 2004. Ordinals occur less often overall, and nominals even less so. Only for cardinals do round numbers, associated with approximation, dominate overall and increase with magnitude. In comparison with other registers, academic writing contains a lower proportion of measurements as well as a higher proportion of ordinals and, to some extent, nominals. In writing, pure cardinals and measurements are usually represented as number words, but measurements—especially larger, unround ones—are more likely to be numerals. Ordinals and nominals are mostly represented as numerals. Altogether, this paper reveals how numbers are used in American English, establishing an initial baseline for any analyses of number frequencies and shedding new light on the cognitive and psychological study of number. (shrink)

In the processing of subject-verb agreement, non-subject plural nouns following a singular subject sometimes “attract” the agreement with the verb, despite not being grammatically licensed to do so. This phenomenon generates agreement errors in production and an increased tendency to fail to notice such errors in comprehension, thereby providing a window into the representation of grammatical number in working memory during sentence processing. Research in this topic, however, is primarily done in related languages with similar agreement systems. In order to (...) increase the cross-linguistic coverage of the processing of agreement, we conducted a self-paced reading study in Modern Standard Arabic. We report robust agreement attraction errors in relative clauses, a configuration not particularly conducive to the generation of such errors for all possible lexicalizations. In particular, we examined the speed with which readers retrieve a subject controller for both grammatical and ungrammatical agreeing verbs in sentences where verbs are preceded by two NPs, one of which is a local non-subject NP that can act as a distractor for the successful resolution of subject-verb agreement. Our results suggest that the frequency of errors is modulated by the kind of plural formation strategy used on the attractor noun: nouns which form plurals by suffixation condition high rates of attraction, whereas nouns which form their plurals by internal vowel change (ablaut) generate lower rates of errors and reading-time attraction effects of smaller magnitudes. Furthermore, we show some evidence that these agreement attraction effects are mostly contained in the right tail of reaction time distributions. We also present modeling data in the ACT-R framework which supports a view of these ablauting patterns wherein they are differentially specified for number and evaluate the consequences of possible representations for theories of grammar and parsing. (shrink)

I defend interest-relative invariantism from a number of recent attacks. One common thread to my response is that interest-relative invariantism is a muchweaker thesis than is often acknowledged, and a number of the attacks only challenge very specific, and I think implausible, versions of it. Another is that a number of the attacks fail to acknowledge how many things we have independent reason to believe knowledge is sensitive to. Whether there is a defeater for someone's knowledge can be (...) sensitive to all manner of features of their environment, as the host of examples from the post-Gettier literature shows. Adding in interest-sensitive defeaters is a much less radical move than most critics claim it is. (shrink)

Results from two self-paced reading experiments in English are reported in which subject- and object-extracted relative clauses (SRCs and ORCs, respectively) were presented in contexts that support both types of relative clauses (RCs). Object-extracted versions were read more slowly than subject-extracted versions across both experiments. These results are not consistent with a decay-based working memory account of dependency formation where the amount of decay is a function of the number of new discourse referents that intervene between the dependents (...) (Gibson, 1998; Warren & Gibson, 2002). Rather, these results support interference-based accounts and decay-based accounts where the amount of decay depends on the number of words or on the type of noun phrases that intervene between the dependents. In Experiment 2, presentation in supportive contexts was directly contrasted with presentation in null contexts. Whereas in the null context the extraction effect was only observed during the RC region, in a supportive context the extraction effect was numerically larger and persisted into the following region, thus showing that extraction effects are enhanced in supportive contexts. A sentence completion study demonstrated that the rate of SRCs versus ORCs was similar across null and supportive contexts (with most completions being subject-extractions), ruling out the possibility that an enhanced extraction effect in supportive contexts is due to ORCs being less expected in such contexts. However, the content of the RCs differed between contexts in the completions, such that the RCs produced in supportive contexts were more constrained, reflecting the lexical and semantic content of the preceding context. This effect, which we discuss in terms of expectations/lexico-syntactic priming, suggests that the enhancement of the extraction effect in supportive contexts is due to the facilitation of the subject-extracted condition. (shrink)

In a recent paper, Howard Stein makes a number of criticisms of an earlier paper of mine ('Are Probabilism and Special Relativity Incompatible?', Phil. Sci., 1985), which explored the question of whether the idea that the future is genuinely 'open' in a probabilistic universe is compatible with special relativity. I disagree with almost all of Stein's criticisms.

The relative clause specifies the amount/number of books referred to. It functions as a cardinality modifier. It denotes the number of books on the table. The noun books moves from the RC-internal position into the external head position. We will see that it is semantically active in both positions!

We provide a detailed history of the concepts of atomic number and isotopy before the discovery of protons and neutrons that draws attention to the role of evolving interplays of multiple aims and criteria in chemical and physical research. Focusing on research by Frederick Soddy and Ernest Rutherford, we show that, in the context of differentiating disciplinary projects, the adoption of a complex and shifting concept of elemental identity and the ordering role of the periodic table led to a relatively (...) coherent notion of atomic number. Subsequent attention to valency, still neglected in the secondary literature, and to nuclear charge led to a decoupling of the concepts of elemental identity and weight and allowed for a coherent concept of isotopy. This concept received motivation from empirical investigations on the decomposition series of radioelements and their unstable chemical identity. A new model of chemical order was the result of an ongoing collaboration between chemical and physical research projects with evolving aims and standards. After key concepts were considered resolved and their territories were clarified, chemistry and physics resumed autonomous projects, yet remained bound by newly accepted explanatory relations. It is an episode of scientific collaboration and partial integration without simple, wholesale gestalt switches or chemical revolutions. (shrink)

The relative age effect is associated with advantages in competitive sports. While the RAE in elite male soccer reveals a skewed birthdate distribution in relation to a certain cut-off date, research of RAE in elite female soccer is affected by small number of samples and conflicting results. The purpose of this study was to investigate the RAE in elite adult German soccer regarding gender and competition level. The sample comprised 680 female and 1,083 male players of the two top (...) German leagues during the 2019/20 season and German national teams. Differences between the observed and expected birthdate distributions were analyzed using chi-square statistics and effect sizes followed by calculating odds ratios. Results showed a statistically significant RAE with small effect size across all players included for both genders. The identified RAE was based on an over-representation of players born at the beginning of the year. According to gender and competition level, RAEs were more pronounced in German male soccer. While significant RAEs were found among males in the first two leagues, the RAE of females was more pronounced in the second league. The analysis of RAE regarding the national teams revealed a statistically significant RAE with large effect size for only the youngest investigated age group of male players. Our data show an RAE in female and male German adult soccer, which could be accompanied by a loss of valuable elite players during the youth phase of the career. Consequently, the pool of talented players at the adult level would be limited. (shrink)

Gilbert Harman, Indeterminacy, Relativity, and Behaviorism: The indeterminacy of radical translation is comparable to the various ways of representing number theory in set theory. Transcendent notions of reference and meaning, which are subject to indeterminacy, can be distinguished from immanent notions that are trivially not subject to indeterminacy. Although Quine's discussions of these issues emphasize behavioral dispositions, he appeals to dispositions as place‐holders for currently unknown underlying physical or functional bases. His discussion in The Roots of Reference shows that considerable (...) understanding can be achieved even at that behavioral level. (shrink)

The thesis that numbers are ratios of quantities has recently been advanced by a number of philosophers. While adequate as a definition of the natural numbers, it is not clear that this view suffices for our understanding of the reals. These require continuous quantity and relative to any such quantity an infinite number of additive relations exist. Hence, for any two magnitudes of a continuous quantity there exists no unique ratio. This problem is overcome by defining ratios, (...) and hence real numbers, as binary relations between infinite standard sequences. This definition leads smoothly into a new definition of measurement consonant with the traditional view of measurement as the discovery or estimation of numerical relations. The traditional view is further strengthened by allowing that the additive relations internal to a quantity are distinct from relations observed in the behaviour of objects manifesting quantities. In this way the traditional theory can accommodate the theory of conjoint measurement. This is worth doing because the traditional theory has one great strength lacked by its rivals: measurement statements and quantitative laws are able to be understood literally. 1 This paper was completed in 1990-1. while the author was a visiting scholar at the Irvine Research Unit in Mathematical Behavioral Sciences. University of California. Irvine. The author wishes to thank the Director. Professor R. D. Luce, for the generous provision of space and facilities within the Unit and for his critical comments upon some of the ideas expressed herein: Professor L. Narens. for his trenchant criticisms: and the University of Sydney, for granting Special Study Leave and financial assistance to make the visit possible. (shrink)

In this paper, we argue that there are more kinds of relative clause constructions between the linguistic heaven and earth than are dreamed of in the classical lore, which distinguishes just restrictive relative clauses and appositives. We start with degree relatives. Degree, or amount, relatives show restrictions in the relativizers they allow, in the determiners that can combine with them, and in their stacking possibilities. To account for these facts, we propose an analysis with two central, and novel, (...) features: First, we argue that the standard notion of degree (a number on a measuring scale) needs to be replaced by a notion of structured degree, which keeps track of the object measured. Second, we argue that at the CP-level of degree relatives an operation of (degree) maximalization takes place. We show that the observed facts concerning degree relatives follow from these assumptions. We then broaden the discussion to other relative clause constructions. We propose that the operation of maximalization takes place in relative clauses when the head noun is semantically interpreted CP-internally, while syntactically the CP is part of a DP that also contains CP-external material. Based on this, we argue that degree relatives form part of a linguistically coherent class of relative clause constructions -- we call them maximalizing relatives -- which all show restrictions similar to those observed for degree relatives, and which differ semantically (and often also syntactically) both from restrictive relative clauses and from appositives. We discuss free relatives, internally-headed relatives, and correlatives. (shrink)

Endurantism is not inconsistent with the theory of special relativity, or so I shall argue. Endurantism is not committed to presentism, and thus not committed to a metaphysics that is at least prima facie inconsistent with special relativity. Nor is special relativity inconsistent with the idea that objects are wholly present at a time just if all of their parts co-exist at that time. For the endurantist notion of co-existence in terms of which “wholly present” is defined, is not, I (...) will argue, a notion according to which co-existence is transitive. Although an absence of absolute simultaneity presents some problems for the endurantist claim that objects are wholly present whenever they exist, there are a number of ways that the endurantist can respond to this difficulty. Thus, I conclude, considerations pertaining to the theory of special relativity certainly do not rule out endurantism as a metaphysics of persistence. (shrink)

We show that for any real number, the class of real numbers less random than it, in the sense of rK-reducibility, forms a countable real closed subfield of the real ordered field. This generalizes the well-known fact that the computable reals form a real closed field. With the same technique we show that the class of differences of computably enumerable reals (d.c.e. reals) and the class of computably approximable reals (c.a. reals) form real closed fields. The d.c.e. result was (...) also proved nearly simultaneously and independently by Ng (Keng Meng Ng. Master's Thesis. National University of Singapore, in preparation). Lastly, we show that the class of d.c.e. reals is properly contained in the class or reals less random than Ω (the halting probability), which in turn is properly contained in the class of c.a. reals, and that neither the first nor last class is a randomness class (as captured by rK-reducibility). (shrink)

Dominic Wilkinson’s defence of identity-relative paternalism raises many important issues that are well worth considering. In this short paper, I will argue that there could be two important differences between the first-party and third-party cases that Wilkinson discusses, namely, a difference in associative duties and how the decision relates to the decision maker’s own autonomous life. This could mean that identity-relative paternalism is impermissible in a greater number of cases than he suggests.

A set of natural numbers B is computably enumerable in and strictly above (or c.e.a. for short) another set C if C < T B and B is computably enumerable in C. A Turing degree b is c.e.a. c if b and c respectively contain B and C as above. In this paper, it is shown that if b is c.e.a. c then b is c.e.a. some 1-generic g.

In lieu of an abstract, here is a brief excerpt of the content:158. RELATIVE IDEAS REVISITED: A REPLY TO THOMAS In "Hume's Relative Ideas" I argued that what Hume called a "relative idea" is the cognitive analogue of a definite description, that relative ideas are nonimagistic, and that recognizing the distinction between positive ideas (images) and relative ideas sheds light on various issues that remain opaque apart from that distinction. Thomas has recently taken exception to (...) my position, contending that I have "produced a 2 theory without application in Hume's framework." In reply I shall present the three cornerstones of my view and then turn to Thomas's criticisms. I. On Relative Ideas 1.What relative ideas are: In claiming that a relative idea is the cognitive analogue of a definite description, I mean only that a relative idea functions in the cognitive realm (realm of ideas) in the same way that a definite description functions in the linguistic realm. Just as the statement expressing the contextual definition of a definite description specifies the truth conditions for a statement containing that description, the statement expressing the contextual definition of a definite description corresponding to a relative idea indicates the (factual) conditions that must obtain if that relative idea succeeds in singling out an entity, i.e., it specifies the "truth conditions" for a relative idea (see T 448, T 458, and T 84 for Hume's use of 'truth'). 2.The intellectual milieu: The expressions 'relative idea' and 'relative notion' seem to have at least two uses in eighteenth century philosophy. Some philosophers used such expressions to refer to an idea 4 or a conception of a relation. Nonetheless, since no 159. substance theorist held that a substance is a relation, this can hardly be the sense in which Locke used the expression when he claimed that one has an "obscure and relative idea of substance in general." Further, Locke's discussion of the relationship between positive ideas (images) and the relative idea of substance clearly indicates that relative ideas provide an indirect means of allowing one to know what something is on the basis of its relation to something known directly, i.e., on the basis of its relation to a C positive idea. Locke also claimed that one's idea of 7 infinity is a relative idea, he seems to have held that the idea of power is a relative idea, and given his account of perception, it is at least reasonable to suggest that relative ideas are found in perceptual contexts. Similarly, Berkeley maintained that one has a relative notion of immaterial substance, but no relative notion of material substance, since in the former case, but not in the latter, one has a notion 9 of the relation between: a substance and its attributes. Outside the "way of ideas" one finds the distinction between direct and relative "conception" clearly spelled out in Reid' s Essays on the Active Powers of the Human Mind. Reid wrote: Of some things, we know what they are in themselves; our conception of such things I call direct. Of other things, we do not know what they are in themselves, but only that they have certain properties or attributes, or certain relations to other things; of these our conception is only relative. 10 Reid contended that our conceptions of mind, of body, of powers, and of secondary qualities are relative conceptions, that at least some of our conceptions of large numbers of things and of polygons are relative conceptions, and that relative conceptions are operative in memory. Now given that there seems to have been a fairly 160. widely recognized doctrine of relative conception in the eighteenth century, given that the contexts in which Hume used the term 'relative idea' are contexts in which proponents of relative conception employed that term, and given that Hume stated philosophical issues in terms of the conceptual system of his time, I consider it reasonable to suggest that Hume recognized and held a doctrine of relative conception even though he did not devote so much as a paragraph to stating that doctrine. 3. The relation of images to relative ideas: A relative idea is inherently complex: it includes a positive idea (or ideas) and a relation... (shrink)

Consciousness is defined as operating with the meanings of representations, which are what arises in mind under the influence of a stimulus (primary representations) as well as what arises as a result of their transformation (secondary, combined representations). In a first approximation, a representation is expressed by words. The concept of “representation” is a special case of the concept of “information-certainty”, which is the result of distinction. Any distinction is a distinction by a specific attribute and representation is the value (...) of the attribute. In relative ontology, distinction is an essential condition of being that is formalized quantitatively through the operation of ontological subtraction, which is a quantitative expression of representation in relation to consciousness. The finite set of representations for one attribute can always be sorted in ascending order of this attribute values. In the order constructed, each representation corresponds to an attribute number, the only difference of which from a number in mathematics is that the one is always associated with a specific attribute, and the other is not associated with any attribute. The meaning of a representation expressed by an attribute number has a place in an ordered quantitative series of other representations of the same attribute, which is the basis of distinction. Operating with meanings is operating with attributive numbers-meanings. This method of the meaning describing is called the relative method. All operations with the meanings of representations are performed in a multidimensional cognitive space. Each axis of the cognitive space corresponds to an attribute by which representations differ. On each axis there are attribute numbers corresponding to the meanings of representations for the attribute. This approach is a quantitative method of describing of all experimental processes of consciousness, which allows to build a scientific, i.e. quantitative, theory of consciousness with laws written down in a quantitative way. Based on this, it is possible to construct a quantitative calculation of this theory predictions. Such a prediction allows to make an accurate (unambiguous) experimental verification. Due to the quantitative way of describing the operation of meanings, such a theory of consciousness is easily modeled in information technologies, since the latter are also based on the numerical nature of all their processes. The main difference between the relative method and the vast majority of methods using information technologies for text processing is that the relative method, firstly, is not statistical, and secondly, conveys the meaning of the text fully and most adequately. The relative method is effective in operating not only with text data, but also with any data of a different nature, for example, with video data, audio data. (shrink)

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such (...) later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism. (shrink)

In two earlier works (Balashov, 2000a: Philosophical Studies 99, 129–166; 2000b: Philosophy of Science 67 (Suppl), S549–S562), I have argued that considerations based on special relativity and the notion of coexistence favor the perdurance view of persistence over its endurance rival. Cody Gilmore (2002: Philosophical Studies 109, 241–263) has subjected my argument to an insightful three fold critique. In the first part of this paper I respond briefly to Gilmore’s first two objections. I then grant his observation that anyone who (...) can resist the first objection is liable to succumb to the third one. This, however, opens a way to other closely related relativistic arguments against endurantism that are immune to all three objections and, in addition, throw new light on a number of important issues in the ontology of persistence. I develop two such novel arguments in the second half of the paper. (shrink)

Scientific realism has three dimensions: a metaphysical commitment to the existence of a mind-independent world; a semantic commitment to a literal interpretation of scientific claims; and an epistemological commitment to scientific knowledge of both observable and unobservable entities. The semantic dimension is uncontroversial, and the epistemological dimension, though contested, is well articulated in a number of ways. The metaphysical dimension, however, is not even well articulated. In this paper, I elaborate a plausible understanding of mind independence for the realist – (...) plausible in conceding the force of sceptical arguments to the effect that there is no one correct way to carve nature at its joints, but realist in proposing an objective basis for carving nonetheless. Walking this line between implausible realism and full-blown constructivism leads down the path of three forms of relativism or pluralism: one concerning the ways in which scientists “package” properties into entities; another concerning the precise metaphysical natures of these entities; and another concerning the context relativity of their behaviour. (shrink)

In this paper, we present a contest success function, which is homogeneous of degree zero and in which the probability of winning the prize depends on the relative difference of efforts. In a simultaneous game with two players, we present a necessary and sufficient condition for the existence of a pure strategy Nash equilibrium. This equilibrium is unique and interior. This condition does not depend on the size of the valuations as in an absolute difference CSF. We prove that (...) several properties of Nash equilibrium with the Tullock CSF still hold in our framework. Finally, we consider the case of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} players, generalize the previous condition and show that this condition is sufficient for the existence of a unique interior Nash equilibrium in pure strategies. For some parameter values of our CSF and when all players are identical, equilibrium entails full rent dissipation for any number of players. (shrink)

Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, (...) ). While about half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words “thousand, million, billion, trillion” constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. (shrink)

The purpose of the present paper is to develop kinematics of the special relativity with an anisotropy of the one-way speed of light. As distinct from a common approach, when the issue of anisotropy of the light propagation is placed into the context of conventionality of distant simultaneity, it is supposed that an anisotropy of the one-way speed of light is due to a real space anisotropy. In that situation, some assumptions used in developing the standard special relativity kinematics are (...) not valid so that the “anisotropic special relativity” kinematics should be developed based on the first principles, without refereeing to the relations of the standard relativity theory. In particular, using condition of invariance of the interval between two events becomes unfounded in the presence of anisotropy of space since the standard proofs drawing the interval invariance from the invariance of equation of light propagation are not valid in that situation. Instead, the invariance of the equation of light propagation, which is a physical law, should be taken as a first principle. A number of other physical requirements, associativity, reciprocity and so on are satisfied by the requirement that the transformations between the frames form a group. Finally, the correspondence principle is to be satisfied which implies that the coordinate transformations should turn into the Galilean transformations in the limit of small velocities. The above formulation based on the invariance and group property suggests applying the Lie group theory apparatus which includes the following steps: constructing determining equations for the infinitesimal group generators using the invariance condition; solving the determining equations; specifying the solutions using the correspondence principle; defining the finite transformations by solving the Lie equations; relating the group parameter to physical parameters. The transformations derived in such a way, as distinct from the transformations derived in the context of conventionality of distant simultaneity, cannot be converted into the standard Lorentz transformations by a coordinate change. The anisotropic nature of the presented transformations manifests itself in that they do not leave the interval invariant but only provide the conformal invariance of the interval. The relations that represent measurable effects include the conformal factor which depends on the relative velocity of the frames and the anisotropy degree. It is important to note the use of the correspondence principle as a heuristic principle which allows to relate the conformal factor to the anisotropy degree and thus completely specify the transformations and observable quantities. (shrink)

This article is concerned with two elementary propositions of English property law: in general, a person acquires a title in respect of a tangible chattel if and when he or she obtains possession of it; and titles are relative. Neither claim is as straightforward as it seems. Much hinges on the answer to one question: is a title a property right, or is it something else? A number of prominent property law scholars have claimed that, for the purposes of (...) and, a title is indeed a property right. This article claims that there is a plausible alternative, one that is committed to the view that in English law, having possession of a chattel is a condition of the law deeming a person to be its owner. It argues that this assertion is supported by an important line of cases. And it maintains that, if that assertion is kept in mind, one can make better sense of the otherwise obscure view that having possession of a chattel is a condition of a person acquiring a ‘claim’ to the ownership of it and hence a title that is not a property right. (shrink)

Relative essentialism, the view that multiple objects about which there are distinct de re modal truths can occupy the same space at the same time, is a metaphysical view that dissolves a number of metaphysical issues. The present essay constructs and defends relative essentialism and argues that it is implicit in some of the ideas of W. V. Quine and Donald Davidson. Davidson’s published views about individuation and sameness can accommodate the common-sense insights about change and persistence of (...) Aristotle and Kripke. Aristotle and Kripke have to give up unmediated direct reference resting on a unique correct articulation of reality into entities. Davidson has to acknowledge a distinction between descriptions giving accidental and those giving essential features of an object. Quine and Davidson were in a position to be a relative essentialist, but were over-impressed by supervenience. The relative essentialist view of beings developed from Quine and Davidson strongly suggests the Heideggerian distinction between beings and Being, and is the perspective from which analytic philosophy can engage that topic. Relative essentialism also connects analytic philosophy to Derrida’s thinking about differance. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:158. RELATIVE IDEAS REVISITED: A REPLY TO THOMAS In "Hume's Relative Ideas" I argued that what Hume called a "relative idea" is the cognitive analogue of a definite description, that relative ideas are nonimagistic, and that recognizing the distinction between positive ideas (images) and relative ideas sheds light on various issues that remain opaque apart from that distinction. Thomas has recently taken exception to (...) my position, contending that I have "produced a 2 theory without application in Hume's framework." In reply I shall present the three cornerstones of my view and then turn to Thomas's criticisms. I. On Relative Ideas 1.What relative ideas are: In claiming that a relative idea is the cognitive analogue of a definite description, I mean only that a relative idea functions in the cognitive realm (realm of ideas) in the same way that a definite description functions in the linguistic realm. Just as the statement expressing the contextual definition of a definite description specifies the truth conditions for a statement containing that description, the statement expressing the contextual definition of a definite description corresponding to a relative idea indicates the (factual) conditions that must obtain if that relative idea succeeds in singling out an entity, i.e., it specifies the "truth conditions" for a relative idea (see T 448, T 458, and T 84 for Hume's use of 'truth'). 2.The intellectual milieu: The expressions 'relative idea' and 'relative notion' seem to have at least two uses in eighteenth century philosophy. Some philosophers used such expressions to refer to an idea 4 or a conception of a relation. Nonetheless, since no 159. substance theorist held that a substance is a relation, this can hardly be the sense in which Locke used the expression when he claimed that one has an "obscure and relative idea of substance in general." Further, Locke's discussion of the relationship between positive ideas (images) and the relative idea of substance clearly indicates that relative ideas provide an indirect means of allowing one to know what something is on the basis of its relation to something known directly, i.e., on the basis of its relation to a C positive idea. Locke also claimed that one's idea of 7 infinity is a relative idea, he seems to have held that the idea of power is a relative idea, and given his account of perception, it is at least reasonable to suggest that relative ideas are found in perceptual contexts. Similarly, Berkeley maintained that one has a relative notion of immaterial substance, but no relative notion of material substance, since in the former case, but not in the latter, one has a notion 9 of the relation between: a substance and its attributes. Outside the "way of ideas" one finds the distinction between direct and relative "conception" clearly spelled out in Reid' s Essays on the Active Powers of the Human Mind. Reid wrote: Of some things, we know what they are in themselves; our conception of such things I call direct. Of other things, we do not know what they are in themselves, but only that they have certain properties or attributes, or certain relations to other things; of these our conception is only relative. 10 Reid contended that our conceptions of mind, of body, of powers, and of secondary qualities are relative conceptions, that at least some of our conceptions of large numbers of things and of polygons are relative conceptions, and that relative conceptions are operative in memory. Now given that there seems to have been a fairly 160. widely recognized doctrine of relative conception in the eighteenth century, given that the contexts in which Hume used the term 'relative idea' are contexts in which proponents of relative conception employed that term, and given that Hume stated philosophical issues in terms of the conceptual system of his time, I consider it reasonable to suggest that Hume recognized and held a doctrine of relative conception even though he did not devote so much as a paragraph to stating that doctrine. 3. The relation of images to relative ideas: A relative idea is inherently complex: it includes a positive idea (or ideas) and a relation... (shrink)

In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper "Relativität und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham" in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague (...) centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: "Relativity and Gravitation, 100 Years after Einstein in Prague". The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation, and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume "General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague", editions. J. Bičák and T. Ledvinka, published also by Springer Verlag. (shrink)

Biological kin share up to half of their genetic material, including predisposition to disease. Thus, variants of clinical significance identified in each individual’s genome can implicate an exponential number of relatives at potential risk. This has renewed the dilemma over family access to research participant’s genetic results, since prevailing US practices treat these as private, controlled by the individual. These individual-based ethics contrast with the family-based ethics – in which genetic information, privacy, and autonomy are considered to be familial – (...) endorsed in UK genomic medicine and by participants in a multi-method study of US research participants presented here. The dilemma reflects a conflict between US legal and ethical frameworks that privilege “the individual” and exclude “the family” versus actual human genetics that are simultaneously individual and familial. Can human genetics succeed in challenging bioethics’ hegemonic individualism to recognize and place the family at the center of the room where bioethics happens? (shrink)

This paper aims to shed light on the terminological and conceptual area around linguistic relativity (nowadays a mostly empirically conceived problem), namely the relations with relativism as a philosophical position. Throughout history and up to now there has been a degree of confusion in handling the terms ‘linguistic relativity’, ‘linguistic relativism’, ‘linguistic determinism’ and the like, all in a more or less conscious fashion. Here it is clarified that linguistic relativity, at least as construed by the recent Neo-Whorfian literature (but (...) also in some important sense, from Whorf ’s own point of view as well) is not, by definition, the same as linguistic determinism, but neither is a form or relativism. On the other hand, relativism, maintains the recent philosophical literature, is a family of theses that share a number of common features even though a single defining core is not easily identifiable. While linguistic relativity does have some connections with some of those features, to make it collapse into an easily dismissible kind of relativism is a crucial misconception of the nature and scopes of such an idea, i.e., that different languages have a different bearing on speakers’ cognition and actions. (shrink)

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and (...) response time are expected near the boundaries between categories. In contrast to previous work that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers. (shrink)

NPs with intensional relative clauses such as 'the book John needs to write' pose a significant challenge for semantic theory. Such NPs act like referential terms, yet they do not stand for a particular actual object. This paper will develop a semantic analysis of such NPs on the basis of the notion of a variable object. The analysis avoids a range of difficulties that a more standard analysis based on the notion of an individual concept would face. Most importantly, (...) unlike the latter, the proposed analysis can be carried over NPs such as 'the number of people that fit into the bus', which describe tropes (particularized properties). (shrink)

Numbers of European hamsters in the Dutch Province of Limburg have been subject to much scrutiny and controversy. In the late nineteenth century, policymakers who considered them too numerous set up eradication programs. In the second half of the twentieth century, even when its domestic relative increasingly circulated as a pet in urban spaces, the numbers of European hamsters in the rural areas collapsed. Large-scale preservation campaigns and reintroduction programs ensued. According to some media, all this has (...) turned the European hamster into the most expensive undomesticated animal of the Netherlands. A whole network of institutions became involved to save the species – ranging from local activist organizations, over zoos and universities, to federal ministries and international organizations. The interactions between the Dutch and ‘their’ hamsters, this article argues, were inscribed in various forms of biopolitics. The article highlights the changing discursive framings and spatial practices that have shaped the management of Cricetus cricetus over time and calls attention to the diversity of living and non-living agents that produced the multispecies choreographies of the present-day Limburg landscape. Finally, it alerts us to the kinds of agency that reside in the numbers of non-human animals. (shrink)

Concerns that cash payments to people who inject drugs (PWID) to reimburse research participation will facilitate illicit drug purchases have led some ethical authorities to mandate department store/supermarket vouchers as research reimbursement. To examine the relative efficacy of the two forms of reimbursement in engaging PWID in research, clients of two public opioid substitution therapy clinics were invited to participate in a 20–30 min, anonymous and confidential interview about alcohol consumption on two separate occasions, 4 months apart. Under the (...) crossover design, at Time 1, clients of Clinic 1 were offered $A20 cash as reimbursement, while clients of Clinic 2 were offered an $A20 voucher; at Time 2, the form of reimbursement was reversed. Using clinic records to determine the denominator (number of clients dosed), we found that compared with clients offered a voucher, a significantly higher proportion of clients who were offered cash participated in the survey (58% (139/241) vs 74% (186/252); χ2=14.27; p=0.0002). At first participation, respondents most commonly reported planning to purchase food/drinks/groceries (68%), cigarettes (21%) and transport/fuel (11%) with their payments, with those reimbursed in cash more likely to report planning to fund transport/fuel (19% vs 1%; p<.01) and less likely to report planning to purchase food/drinks/groceries (62% vs 76%; p=0.02). Just three out of 155 cash participants reported planning to purchase illicit drugs with their payment. Results demonstrate that modest cash payments enhanced recruitment of this group, an important consideration given the challenges of delineating the parameters of a population defined by illegal activity, seemingly without promoting excessive additional drug use. (shrink)

Appositive relative clauses differ from restrictive relative clauses in a number of ways. The fundamental distinction is semantically based: an appositive relative like that in (1a) conveys an independent assertion about the referent of its associated head; the reference of the head is established independently of the appositive relative. In contrast, a restrictive relative like that in (1b) is interpreted as an intersective predicate modifier, restricting the reference of its head.

An extended scale relativity theory, actively developed by one of the authors, incorporates Nottale's scale relativity principle where the Planck scale is the minimum impassible invariant scale in Nature, and the use of polyvector-valued coordinates in C-spaces (Clifford manifolds) where all lengths, areas, volumes⋅ are treated on equal footing. We study the generalization of the ordinary point-particle quantum mechanical oscillator to the p-loop (a closed p-brane) case in C-spaces. Its solution exhibits some novel features: an emergence of two explicit scales (...) delineating the asymptotic regimes (Planck scale region and a smooth region of a quantum point oscillator). In the most interesting Planck scale regime, the solution recovers in an elementary fashion some basic relations of string theory (including string tension quantization and string uncertainty relation). It is shown that the degeneracy of the first collective excited state of the p-loop oscillator yields not only the well-known Bekenstein–Hawking area-entropy linear relation but also the logarithmic corrections therein. In addition we obtain for any number of dimensions the Hawking temperature, the Schwarschild radius, and the inequalities governing the area of a black hole formed in a fusion of two black holes. One of the interesting results is a demonstration that the evaporation of a black hole is limited by the upper bound on its temperature, the Planck temperature. (shrink)