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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 primenumbers, 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)

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Textual and historical subtleties aside, let's call the idea thatnumbers 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 whatnumbers are; however, instead of a frontal assault, his strategy is to embark on a foray into the ill-defined issue of what it is thatnumbers number, where, roughly speaking, a number nnumbers 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 individualnumbers too as such properties, and whether, accordingly, the concept of number can be classed along with that, say, of color. (shrink)

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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 ofrelative identity.

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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.

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Relativists maintain that identity is alwaysrelative to a general term. According to them, the notion of absolute identity has to be abandoned and replaced by a multiplicity ofrelative 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 alwaysrelative 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 takerelative 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)

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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)

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In recent work on context­dependency, it has been argued that certain types of sentences give rise to a notion ofrelative 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 onlyrelative 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, butrelative 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 torelative 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 standardrelative truth account in crucial respects: it is not the truth of the proposition expressed that isrelative 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 standardrelative truth theories of the sentences in question face and explains a number of further peculiarities that such sentences display. (shrink)

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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 therelative 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)

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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)

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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)

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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)

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Results from two self-paced reading experiments in English are reported in which subject- and object-extractedrelative clauses (SRCs and ORCs, respectively) were presented in contexts that support both types ofrelative 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)

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Therelative 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)

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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.

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Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. A corollary to this is that there is a Δn+10 basic sequence with respect to which no Δn0 real is distribution-normal. As a special case, there is a limit computable sequencerelative to which no computable real is distribution-normal.

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In this paper, we argue that there are more kinds ofrelative clause constructions between the linguistic heaven and earth than are dreamed of in the classical lore, which distinguishes just restrictiverelative 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 otherrelative clause constructions. We propose that the operation of maximalization takes place inrelative 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 ofrelative 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 restrictiverelative clauses and from appositives. We discuss free relatives, internally-headed relatives, and correlatives. (shrink)

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Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...) perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures. (shrink)

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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 domesticrelative increasingly circulated as a pet in urban spaces, thenumbers 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 thenumbers of non-human animals. (shrink)

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Revisiting the history of relativity Content Type Journal Article DOI 10.1007/s11016-010-9466-4 Authors Lewis Pyenson, Department of History, Western Michigan University, Kalamazoo, MI 49008-5242, USA Sean F. Johnston, School of Interdisciplinary Studies, University of Glasgow, Rutherford-McCowan Building, Dumfries, Glasgow, Scotland G2 0RB, UK Alberto A. Martínez, Department of History, University of Texas at Austin, 1 University Station B7000, Austin, TX 78712-0220, USA Richard Staley, Department of the History of Science, University of Wisconsin-Madison, 226 Bradley Memorial Building, 1225 Linden Drive, Madison, WI (...) 53706-1528, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796 Journal Volume Volume 20 Journal Issue Volume 20, Number 1. (shrink)

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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.

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The thesis thatnumbers are ratios of quantities has recently been advanced by a number of philosophers. While adequate as a definition of the naturalnumbers, it is not clear that this view suffices for our understanding of the reals. These require continuous quantity andrelative 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 realnumbers, 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)

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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)

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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)

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It is proved to be consistentrelative to a measurable cardinal that there is a uniform ultrafilter on the realnumbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistentrelative to a supercompact cardinal that there is a uniform ultrafilter on \ which is generated by fewer than \ sets.

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Doubling unconditionals are exemplified by the Spanish example Venga quien venga, estaré contento ‘Whoever comes, I’ll be happy’. This curious and little studied construction is attested in various forms in a number of Romance and Slavic languages. In this paper, I provide a basic description of these constructions, focusing especially on Spanish, Czech, and Slovenian, and argue that they can be brought in line with analyses of run-of-the-mill unconditionals if one recognizes that the wh-structure within the unconditional antecedent is a (...) freerelative and that the freerelative is focused. The focused freerelative introduces alternatives and thus gives rise to the denotation proposed by Rawlins :111–178, 2013) for English unconditionals. In the last part of the paper, I hypothesize that at least some non-doubling unconditionals could in fact have a doubling underlying structure, which is disguised byrelative sluicing—clausal ellipsis with arelative pronoun remnant. (shrink)

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Although the form of the metric is invariant for arbitrary coordinate transformations, the magnitudes of the elements of the metric are not invariant. For Cartesian coordinates these elements are equal to one and are on the diagonal. Such a unitary metric can also apply to arbitrary coordinates, but only for a coordinate system inhabitant (CSI), to whom these coordinates would appear to be Cartesian. The meaning for a non-Euclidean metric consequently appears to be a simple coordinate system transformation for the (...) appropriate CSI. The conversion of arbitrary coordinates to the flat Cartesian ones can be accomplished by a sequence of isomorphic mappings linking the arbitrary coordinates to the flat Cartesian ones. This is shown for two, three, and four-dimensional spaces. It is also applied to toroidal metrics and fluidfilled spaces for toroidal vortices that are discontinuous, half-wavelength, electromagnetic dipole field distributions. A number of other applications are discussed. (shrink)

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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. Inrelative 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 attributivenumbers-meanings. This method of the meaning describing is called therelative 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 attributenumbers 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 therelative method and the vast majority of methods using information technologies for text processing is that therelative method, firstly, is not statistical, and secondly, conveys the meaning of the text fully and most adequately. Therelative 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)

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Therelative 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!

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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)

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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., telephonenumbers, playernumbers). Many studies that have cited number frequencies in support of claims about numerical cognition and mathematical cognition hinge on the assumption that mostnumbers analyzed are cardinal. This paper is the (...) first to investigate therelative frequencies of different number types, presenting a corpus analysis of morphologically unmarkednumbers (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 roundnumbers, 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 hownumbers 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)

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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)

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Borowski ("identity and personal identity," "mind", Volume lxxxv, Number 340, October 1976, Pages 481-502) claims that if x's brain were successfully transplanted into y's body, Our judgment of who the survivor z really is would berelative to our interest in z: for example, If the body y is that of an athlete or film actor, We would say it is y if we are athletic coaches or film directors. This view completely overlooks that acting talents and athletic skills (...) are also stored in the brain. If my brain controlled pele's body, Or laurence olivier's, I could not play football or act well. (shrink)

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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 inrelative 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)

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We say that a real X is n-genericrelative to a perfect tree T if X is a path through T and for all $\Sigma _{n}^{0}(T)$ sets S, there exists a number k such that either X|k ∈ S or for all σ ∈ T extending X|k we have σ ∉ S. A real X is n-genericrelative to some perfect tree if there exists such a T. We first show that for every number n all but countably (...) many reals are n-genericrelative to some perfect tree. Second, we show that proving this statement requires ZFC− + "∃ infinitely many iterates of the power set of ω". Third, we prove that every finite iterate of the hyperjump. ${\cal O}^{(n)}$ , is not 2-genericrelative to any perfect tree and for every ordinal α below the least λ such that supβ<i (βth admissible) = λ, the iterated hyperjump ${\cal O}^{(\alpha)}$ is not 5-genericrelative to any perfect tree. Finally, we demonstrate some necessary conditions for reals to be 1-genericrelative to some perfect tree. (shrink)

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The paper is an examination of Michael Friedman’s analysis of the conceptual structure of Einstein’s theory of gravitation, with a particular focus on a number of critical reactions to it. Friedman argues that conceptual frameworks in physics are stratified, and that a satisfactory analysis of a framework requires us to recognize the differences in epistemological character of its components. He distinguishes first-level principles that define a framework of empirical investigation from second-level principles that are formulable in that framework. On his (...) account, the theory of Riemannian manifolds and the equivalence principle define the framework of empirical investigation in which Einstein’s field equations are an intellectual and empirical possibility. Friedman is a major interpreter of relativity and his view has provoked a number of critical reactions, nearly all of which miss the mark. I aim to free Friedman’s analysis of Einsteinian gravitation from a baggage of misconceptions and to defend the notion that physical theories are stratified. But I, too, am a critic and I criticize Friedman’s view on several counts, notably his account of a constitutive principle and that of the principle of equivalence. (shrink)

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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 therelative 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)

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Readingnumbers aloud involves visual processes that analyze the digit string and verbal processes that produce the number words. Cognitive models of number reading assume that information flows from the visual input to the verbal production processes—a feed‐forward processing mode in which the verbal production depends on the visual input but not vice versa. Here, I show that information flows also in the opposite direction, from verbal production to the visual input processes. Participants read aloud briefly presented multi‐digit strings (...) in Hebrew, in which the order of words is congruent with the order of digits (21 = twenty‐and‐one), and in Arabic, in which the ones word precedes the tens word (one‐and‐twenty). The error‐by‐digit‐position curve was affected by language:relative to Hebrew, in Arabic the error rate was slightly lower for the unit digit and slightly higher for the decade digit, indicating that in Arabic the unit digit was processed earlier and the decade digit later, in accord with the Arabic word order. This language‐dependent processing order originated in the visual level and was not a verbal confound, because it persisted even when I controlled for the serial position of the decade/unit word in the verbal number by usingnumbers with 0 (two hundred three/two hundred thirty). I conclude that the visual analyzer's digit scanning order, decade‐first or unit‐first, is not fixed but affected by the language in which the number is produced—a top‐down, verbal‐to‐visual information flow. (shrink)

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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)

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Supposing that one is already familiar with special relativistic physics, what constitutes the best route via which to arrive at the architecture of the general theory of relativity? Although the later Einstein would stress the significance of mathematical and theoretical principles in answering this question, in this article we follow the lead of the earlier Einstein (circa 1916) and stress instead how one can go a long way to arriving at the general theory via inductive and empirical principles, without invoking (...) presumptions concerning the geometrical structure of the final theory. We focus on the construction of the kinematical structure and the terms describing the coupling of matter to gravity. General covariance, understood and employed as a straightforward extrapolation of empirical considerations, is central to our derivation, together with what we dub the `Methodological Equivalence Principle'. We argue that our approach has a number of virtues, both for one's understanding of the general theory of relativity, but also for pedagogy, since it stresses---to the greatest extent possible (a lesson which we inherit from Bell, [1976])---both the methodological precedence of dynamical considerations to interpretative issues and the theoretical continuity between general relativity and its precursors. We conclude by comparing our approach to other philosophical approaches to general relativity and discussing the significance of empirically motivated methodological principles in the philosophy of science. (shrink)

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Visual experience is shaped by a number of factors that are independent of the external objects that we perceive—factors like lighting, angle of view, and the sensitivities of photoreceptors in the retina. This paper seeks to catalog, analyze, and explain the fluctuations in visual phenomenology that are due to such factors.

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NPs with intensionalrelative 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)

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The number of books at home is commonly used as a proxy for socioeconomic status in educational studies. While both parents’ and students’ reports of the number of books at home are relatively strong predictors of student achievement, they often disagree with each other. When interpreting findings of analyses that measure socioeconomic status using books at home, it is important to understand how findings may be biased by the imperfect reliability of the data. For example, it was recently suggested that (...) especially low-achieving students tend to underestimate the number of books at home, so that use of such data would lead researchers to overestimate the association between books at home and achievement. Here we take a closer look at how students’ and parents’ reports of the number of books at home relate to literacy among fourth grade students, by analyzing data from more than 250,000 students in 47 countries participating in 2011 PIRLS. Contrary to prior claims, we find more downward bias in estimates of books at home among high-achieving students than among low-achieving students, but unsystematic errors appear to be larger among low-achieving students. This holds within almost every country. It also holds between countries, that is, errors in estimates of books at home are larger in low-achieving countries. This has implications for studies of the association between books at home and achievement: the strength of the association will generally be underestimated, and this problem is exacerbated in low-achieving countries and among low-achieving students. (shrink)

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