We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of finite structures with μ (C)=1 (...) and such that L and L ′ define the same queries on C. We carry out a systematic investigation of $\equiv _{\text{a.e.}}$ with respect to the uniform measure and analyze the $\equiv _{\text{a.e.}}$ -equivalence classes of several logics that have been studied extensively in finite model theory. Moreover, we explore connections with descriptive complexity theory and examine the status of certain classical results of model theory in the context of this new framework. (shrink)

Currently there are at least four sizeable projects going on to establish the gravitational acceleration of massive antiparticles on earth. While general relativity and modern quantum theories strictly forbid any repulsive gravity, it has not yet been established experimentally that gravity is attraction only. With that in mind, the Elementary Process Theory (EPT) is a rather abstract theory that has been developed from the hypothesis that massive antiparticles are repulsed by the gravitational field of a body of ordinary matter: (...) the EPT essentially describes the elementary processes by which the smallest massive systems have to interact with their environments for repulsive gravity to exist. In this paper we model a nonrelativistic, one-component massive system that evolves in time by the processes as described by the EPT in an environment described by classical fields: the main result is a semi-classical model of a process at Planck scale by which a non-relativistic onecomponent system interacts with its environment, such that the interaction has both gravitational and electromagnetic aspects. Some worked-out examples are provided, among which the repulsion of an antineutron by the gravitational field of the earth. The general conclusion is that the semi-classical model of the EPT corresponds to non-relativistic classical mechanics. Further research is aimed at demonstrating that the EPT has a model that reproduces the successful predictions of general relativity. (shrink)

Supporters of the de Broglie-Bohm interpretation of quantum theory argue that because the theory, like classical mechanics, concerns the motions of point particles in 3D space, it is specially suited to recover classical behavior. I offer a novel account of classicality in dBB theory, if only to show that such an account falls out almost trivially from results developed in the largely interpretation-neutral context of decoherence theory. I then argue that this undermines any special claim that dBB theory is purported (...) to have on the unification of the quantum and classical realms. (shrink)

On the one hand, theories of modern physics are very successful in their areas of application. But on the other hand, the irreconcilability of General Relativity (GR) and Quantum Electrodynamics (QED) suggests that these theories of modern physics are not the final answer regarding the fundamental workings of the universe. This monograph takes the position that the key to advances in the foundations of physics lies in the hypothesis that massive systems made up of antimatter are repulsed by (...) the gravitational field of a body of ordinary matter: this hypothesis takes us to an uncharted territory where GR and QED do not hold up. From there the Elementary Process Theory (EPT) is developed: this is a collection of seven generalized process-physical principles that do hold up if the hypothesis is a fact of nature. Using four-dimensionalistic terminology, the EPT abstractly describes an elementary process in the temporal evolution of a massive system that interacts with its environment. The idea is that these elementary processes take place at Planck scale and are essentially all the same, regardless of the type of interaction that takes place: the EPT is thus intended as a candidate for a unifying scheme that applies to all four basic interactions. By mathematical modeling, the relation is explored between the EPT and classical mechanics, quantum mechanics, special relativity and GR. (shrink)

We study the notion of [Formula: see text]-MAD families where [Formula: see text] is a Borel ideal on [Formula: see text]. We show that if [Formula: see text] is any finite or countably iterated Fubini product of the ideal of finite sets [Formula: see text], then there are no analytic infinite [Formula: see text]-MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective [Formula: see text]-MAD families; and under the full Axiom of Determinacy [Formula: see text][Formula: (...) see text] or under [Formula: see text] there are no infinite [Formula: see text]-mad families. Similar results are obtained in Solovay’s model. These results apply in particular to the ideal [Formula: see text], which corresponds to the classical notion of MAD families, as well as to the ideal [Formula: see text]. The proofs combine ideas from invariant descriptive set theory and forcing. (shrink)

This book offers an ideal first reader in ancient Greek. It presents a selection of extracts from a comprehensive range of Greek authors, from Homer to Plutarch, together with generous help with vocabulary and grammar. The passages have been chosen for their intrinsic interest and variety, and brief introductions set them in context. All but the commonest Greek words are glossed as they occur and a general vocabulary is included at the back. Although the book is designed to be used (...) by students who have only completed a beginner's course in Greek, students of all ages will find that it helps them to improve their ability and confidence in reading a wide range of prose and verse texts, while at the same time providing a fascinating and copiously illustrated introduction to the riches and variety of ancient Greek literature over a period of almost a thousand years. (shrink)

We lay down the groundwork for the treatment of almost hyperdefinable groups: notions from [5] are put into a natural hierarchy, and new notions, essential to the study to such groups, fit elegantly into this hierarchy. We show that "classical" properties of definable and hyperdefinable groups in simple theories can be generalised to this context. In particular, we prove the existence of stabilisers of Lascar strong types and of the connected and locally connected components of subgroups, and that in (...) a simple one-based theory an almost hyperdefinable group is bounded-by-abelian-by-bounded. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question of whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: (...) I state and sketch proofs of two technical results—inspired by simple physical arguments about the generic properties of classical systems—to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none provided by Hamiltonian. The argument not only clarifies the conceptual structure of the two systems of mechanics, but also their relations to each other and their respective mechanisms for representing physical systems. It also shows why naïvely structural approaches to the representational content of physical theories cannot work. [Lagrange] grasped that he had gained a method of stating dynamical truths in a way, which is perfectly indifferent to the particular methods of measurement employed in fixing the positions of the various parts of the system. Accordingly, he went on to deduce equations of motion, which are equally applicable whatever quantitative measurements have been made, provided that they are adequate to fix positions. The beauty and almost divine simplicity of these equations is such that these formulae are worthy to rank with those mysterious symbols which in ancient times were held directly to indicate the Supreme Reason at the base of all things. (Whitehead [1948], p. 63)1. Introduction2.Classical Systems3. The Possible Interactions of a Classical System and the Structure of Its Space of States4. Classical Systems Are Lagrangian5. Classical Systems Are Not Hamiltonian6. How Lagrangian and Hamiltonian Mechanics Represent Classical Systems7. The Conceptual Structure of Classical Mechanics. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various methods of extracting computational information from proofs in classical first-order arithmetic, and reflects on some of the relationships between them. Variants of the Godel-Gentzen double-negation translation, some not so well known, serve to provide canonical and efficient computational interpretations of that theory.

In this book, Phillips gives an overview of the contribution of Nyaya--the classical Indian school that defends an externalist position about knowledge as well as an internalist position about justification. Nyaya literature extends almost two thousand years and comprises hundreds of texts, and in this book, Phillips presents a useful overview of the under-studied system of thought. For the philosopher rather than the scholar of Sanskrit, the book makes a whole range of Nyaya positions and arguments accessible to students of (...) epistemology who are unfamiliar with classical Indian systems. (shrink)

Excluding only pure nominalists and "imagists" he includes in the classical theory "almost everyone who lived before the second decade of the twentieth century." This of course covers most of the other general types of theory found in the epistemology textbooks: that concepts are in the mind, that they are also in the thing, and finally that they are fundamentally prior to the thing. These types may be exemplified by Locke, Aristotle, and Plato, respectively. The controversy between these three schools (...) Price feels can for his purposes be regarded as a "domestic difference within the classical tradition." His subsidiary discussions of these differences he confines almost entirely to the first two. The Platonic theory he handles very lightly and gingerly; "it is a sufficiently difficult task in these days to convince people that there is any sense in talking of universals at all, even in the mild and moderate Aristotelian way". (shrink)

The theory of beauty has always rested on the representation of the infinite, understood in its finite expression and perceptible through the senses. The relationship of beauty to truth, of art to science, is inevitably modified with the new way of treating the infinite in the modern conception of the world. Non-classical science works with the notions of “infinitely large” and “infinitely small,” modifying their meanings in terms of experimental observations. We put these words in quotation marks because the Whole (...) may be considered as finite or infinite according to the angle from which it is viewed: the “infinitely small” only becomes so in determined circumstances, for example, when we consider the extended and discrete elements of space and time in a macroscopic approximation, as infinitely small elements of perpetual motion. Modern science studies these two poles of being—the Whole and its parts—in their interaction, admitting the dependence of macroscopic and even cosmic processes with regard to the processes being created in infinitely small spheres (or, according to another interpretation, finite but extremely small). However, as characteristic of our time as these concepts are—most often hypothetical—they nonetheless express a very old historical tradition that contemporary retrospection, turned toward classical science and the past of science in general, allows us to discern very clearly. All the culture of the past was dominated by the principle of the authority of the Whole over its parts. In peripatetic cosmology and physics, individual processes depended on the cosmic harmony of the center and frontiers of the universe, on the spheres and places toward which bodies tend. This authority of the general law, of universal harmony, of the system hinging on individual processes, is confirmed in Aristotle's Physics, but not only there: we find it in almost all the thinkers of antiquity. On the plane of general logic, it received expression in the Hegelian concept of the true infinite, a concept constituting to a high degree the philosophical equivalent of classical science. In Hegel's time, this last was already drawing away somewhat from the idea of an absolute and strict subordination of elementary processes to integrating systems and general laws, laws being realized through the probability of microprocesses, thus statistical laws, and whose exact application ignored individual acts, for example, the mechanism of molecules in thermodynamics. The statistical theory of heat has rendered continual a discrete microcosm—for the movement of individual molecules it substituted the average speed of the molecules—and continual laws became supreme points determining macroscopic processes. These laws had a differential nature. In other words, they prescribed the defined relationships between the infinitely small increases in size. Also, the schema of the classic law consisted in defining infinitely small processes by an infinitely large integral legality because of the number of processes. The infinitely true of Hegel is the actual infinite being realized in each of its finite elements; it is the subjection of the finite element to the infinite. (shrink)

Pierre le Pesant Boisguilbert was considered by Marx as one of the founders of classical political economy. His writings contain a large number of concepts and ideas that reappear in the writings of Quesnay, Cantillon and Adam Smith. George Berkeley - a major figure in the history of philosophical idealism - was the author of 'The Querist', a treatise on the nature of Irish under-development and cures for Irish poverty. Baron de Montesquieu - one of the great 18th century polymaths (...) - is author of the masterpiece 'The Spirit of the Laws' (1748) which, while ostensibly a treatise on law, is actually a study of political organization, types of government, national character and the determining ethos of different societies. It enjoyed enormous success in the 18th century and was almost certainly read and studied by Adam Smith. Ferdinando Galiani was a leading critic of physiocracy and a major 18th century proponent of the subjective theory of value. In 1751 he published 'Della Moneta' which contains some notable chapters on monetary theory, and some brilliant pages on the utility theory of value. James Anderson was a Scottish farmer and a prolific author of tracts on the agricultural development of Scotland and the outstanding policy issues of the last quarter of the 18th century. Dugald Stewart was author of 'Account of the Life and Writings of Adam Smith LLD' (1793) which is one of the earliest, extended commentaries on the works of Adam Smith by one who knew him well. (shrink)

Following the tradition of classical liberalism, Kant's political philosophy and theory of justice focus on the relation between individual freedom, as the central value of political life, and the state, whose primary normative function is both to restrain and protect individual liberty. In this accessible interpretation of Kant's political philosophy, Allen D. Rosen focuses on the relation among justice, political authority (the state), and individual liberty. He offers interpretations of the ethical bases of Kant's view of justice, of the structure (...) of his taxonomy of duties, and of his understanding of social welfare legislation. Arguing against the grain of much recent scholarly commentary, Rosen asserts that Kant's principles of justice are direct corollaries of the Categorical Imperative and that Kant does not support an absolute or even near-absolute duty of obedience to governments. He also maintains that Kant has principled and important reasons for repudiating a right of revolution and that Kant is not, as he is almost always taken to be, an advocate of the nightwatchman or minimal state. The Kant that emerges from Rosen's pages is an appealing and surprisingly modern philosopher, whose preoccupation with individual freedom still resonates in contemporary political and philosophical debates, and whose attempts to define the proper limits of individual liberty remain relevant even at the end of the twentieth century. (shrink)

: In the 1980s, the analysis of presupposition projection contributed to a ‘dynamic turn’ in semantics: the classical notion of meanings as truth conditions was replaced with a dynamic notion of meanings as Context Change Potentials. We argue that this move was misguided, and we offer an alternative in which presupposition projection follows from the combination of a fully classical semantics and a new pragmatic principle, which we call Be Articulate. This principle requires that a meaning pp’ conceptualized as involving (...) a pre-condition p should be articulated as … … rather than as … pp’ …, unless the full conjunction is ruled out because the first or the second conjunct is semantically idle. In particular, … … is infelicitous - and hence … pp’ … is acceptable - if one can determine as soon as p and is uttered that no matter how the sentence ends these words could be eliminated without affecting its contextual meaning. An equivalence theorem guarantees that this condition suffices to derive Heim’s results in almost all cases. Extensions of the condition lead to several new predictions, in particular concerning some ‘symmetric readings’, as well as presupposition projection in quantified structures, which displays a complex interaction between the nature of the trigger and the monotonicity of the quantifier. (shrink)

Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their (...) neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises the following six volumes : I. Classical Logic W. Rautenberg II. Non-classical Logics W. Rautenberg III. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. Proof Theory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. (shrink)

Due to the current availability of the English translation of almost all of Lesniewski's works it is now possible to give a clear and detailed picture of his ideas. Lesniewski's system of the foundation of mathematics is discussed. In abrief ouüine of his three systems Mereology, Ontology and Protothetics his positions conceming the problems of the forms of expression, proper names, synonymity, analytic and synthetic propositions, existential propositions, the concept of logic, and his views of theory of science and metaphysics (...) are sketched. The influence of Mill, Lukasiewicz, Austrian philosophy and especially Petrazycki on his thinking is evaluated and an interpretation is suggested setting him squarely in a tradition of classical Aristotelian logic. (shrink)

Due to the current availability of the English translation of almost all of Lesniewski's works it is now possible to give a clear and detailed picture of his ideas. Lesniewski's system of the foundation of mathematics is discussed. In abrief ouüine of his three systems Mereology, Ontology and Protothetics his positions conceming the problems of the forms of expression, proper names, synonymity, analytic and synthetic propositions, existential propositions, the concept of logic, and his views of theory of science and metaphysics (...) are sketched. The influence of Mill, Lukasiewicz, Austrian philosophy and especially Petrazycki on his thinking is evaluated and an interpretation is suggested setting him squarely in a tradition of classical Aristotelian logic. (shrink)

We introduce a quite natural Frege-style set theory, which we call Strong-Frege-2 equation image, a sort of simplification of the theory considered in 13 and 1 . We give a model of a weaker variant of equation image, called equation image, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Π11 sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of (...) 5 and 15. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

. The effort in providing constructive and predicative meaning to non-constructive modes of reasoning has almost without exception been applied to theories with full classical logic [4]. In this paper we show how to combine unrestricted countable choice, induction on infinite well-founded trees and restricted classical logic in constructively given models. These models are sheaf models over a $\sigma$ -complete Boolean algebra, whose topologies are generated by finite or countable covering relations. By a judicious choice of the Boolean algebra (...) we can directly extract effective content from $\Pi_2^0$ -statements true in the model. All the arguments of the present paper can be formalised in Martin-Löf's constructive type theory with generalised inductive definitions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Political Economy and Classical AntiquityNeville MorleyThe literature of the ancients, their legislation, their public treaties, and their administration of the conquered provinces, all proclaim their utter ignorance of the nature and origin of wealth, of the manner in which it is distributed, and of the effects of its consumption.... The steadily increasing progress of different branches of industry, the advancement of the sciences, whose influence upon wealth we shall (...) have occasion hereafter to notice, and the direction of public opinion, at length estimating national prosperity as being of some importance, caused the science of political economy to enter into the contemplation of a great number of writers.J.-B. Say 1I. The science of political economy offered an entirely new way of understanding human society. 2 Say’s account of its emergence is teleological and self-serving, figuring his own work as the logical culmination of earlier enquiries, but it accurately reflects the way in which political economy was perceived and presented as a modern innovation. The more that eighteenth- and nineteenth-century political economists turned their attention towards the economic rather than the political state of the nation, the more they became aware of their own originality in doing so. The writings of the ancients might still dominate discussions of political theory, but the moderns noted with satisfaction the failings and fumblings of classical authors in the study of the economy; they alone had discerned its significance and developed the tools with which to [End Page 95] analyze it. Moreover, there was no obvious reason why this new science should confine its attentions to the contemporary world; the economies of the past could be studied in the same manner, and thus political economy offered the possibility of understanding ancient society better than the ancients did themselves.Students of ancient society were slow to respond to this challenge. Neither Edward Gibbon nor George Grote had much to say about the ancient economy, despite their close relationships with economists of the Scottish Enlightenment and the Philosophic Radicals respectively. Gibbon was well aware of contemporary debates on luxury (see below), and he also disputed Montesquieu’s theory that taxes decrease according to the level of despotism in a state, but that was all. 3 A letter written by Grote’s wife suggests that his chapter on Greek colonization was intended to infuse useful doctrines on political economy and the principle of population, but in the published version this intent is limited to vague statements about the importance of agriculture in sustaining a colony. 4 Grote’s advocacy of comparative history—“not omitting the points of resemblance as well as of contrast with the better-known forms of modern society”—was in practice limited to politics and the history of ideas, above all in the debate on the merits of democracy. 5 The sole exception was a comparison of Solon’s legislation restricting Athenian exports with the British Corn Laws, to the advantage of the former. 6With the lone exception of Boeckh’s 1817 treatise on The Public Economy of Athens, the subject of the ancient economy was almost entirely ignored by historians until the middle of the nineteenth century. 7 Their own interests and those of the ancient sources on which they relied led them to conceive of history in terms of events, above all of events in the fields of politics and war. Economic matters were touched upon in their accounts of certain episodes—the reforms of Solon, for example, or the Roman agrarian laws—but never in detail or with much analytical sophistication, let alone drawing upon the theoretical insights of political economy. William Ramsay’s Manual of Roman Antiquities in 1851 devoted much more space to economic topics than had been customary, but was otherwise indistinguishable from its predecessors; the chapter on Roman agriculture was little more than a paraphrase of the writings [End Page 96] of Vergil and Varro, and his account of state revenues merely compiled information from the ancient sources as an end in itself. 8The drought was not ended until 1854, when Theodor Mommsen’s History of Rome not only devoted considerable attention to such subjects as agriculture, commerce, and... (shrink)

The main purpose of this dissertation is to apply and develop new forcing techniques to obtain models where several cardinal characteristics are pairwise different as well as force many (even more, continuum many) different values of cardinal characteristics that are parametrized by reals. In particular, we look at cardinal characteristics associated with strong measure zero, Yorioka ideals, and localization and anti-localization cardinals.In this thesis we introduce the property “F-linked” of subsets of posets for a given free filter F on the (...) natural numbers, and define the properties “ $\mu $ -F-linked” and “ $\theta $ -F-Knaster” for posets in a natural way. We show that $\theta $ -F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. These kinds of posets led to the development of a general technique to construct $\theta $ - $\textrm {Fr}$ -Knaster posets (where $\textrm {Fr}$ is the Frechet ideal) via matrix iterations of ${<}\theta $ -ultrafilter-linked posets (restricted to some level of the matrix). The latter technique allows proving consistency results about Cichoń’s diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal characteristics associated with it are pairwise different. Another important application is to show that three strongly compact cardinals are enough to force that Cichoń’s diagram can be separated into 10 different values. Later on, it was shown by Goldstern, Kellner, Mejía, and Shelah that no large cardinals are needed for Cichoń’s maximum (J. Eur. Math. Soc. 24 (2022), no. 11, p. 3951–3967).On the other hand, we deal with certain types of tree forcings including Sacks forcing, and show that these increase the covering of the strong measure zero ideal $\mathcal {SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal characteristics of the continuum. Even more, Sacks forcing can be used to force that $\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$, which is the first consistency result where more than two cardinal characteristics associated with $\mathcal {SN}$ are pairwise different. To obtain another result in this direction, we provide bounds for $\operatorname {\mathrm{cof}}(\mathcal {SN})$, which generalizes Yorioka’s characterization of $\mathcal {SN}$ (J. Symbolic Logic 67.4 (2002), p. 1373–1384). As a consequence, we get the consistency of $\operatorname {\mathrm{add}}(\mathcal {SN})=\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$ with ZFC (via a matrix iteration forcing construction).We conclude this thesis by combining creature forcing approaches by Kellner and Shelah (Arch. Math. Logic 51.1–2 (2012), p. 49–70) and by Fischer, Goldstern, Kellner, and Shelah (Arch. Math. Logic 56.7–8 (2017), p. 1045–1103) to show that, under CH, there is a proper $\omega ^\omega $ -bounding poset with $\aleph _2$ -cc that forces continuum many pairwise different cardinal characteristics, parametrized by reals, for each one of the following six types: uniformity and covering numbers of Yorioka ideals as well as both kinds of localization and anti-localization cardinals, respectively. This answers several open questions from Klausner and Mejía (Arch. Math. Logic 61 (2022), pp. 653–683).Abstract prepared by Miguel Antonio Cardona-MontoyaE-mail: [email protected]: https://repositum.tuwien.at/handle/20.500.12708/19629. (shrink)

The present book takes the discovery that quantum-like behaviour is not solely reserved to atomic particles one step further. If electrons are modelled as vibrating droplets instead of the usually assumed point objects, and if the classical laws of nature are applied, then exactly the same behaviour as in quantum theory is found, quantitatively correct! The world of atoms is strange and quantum mechanics, the theory of this world, is almost magic. Or is it? Tiny droplets of oil bouncing round (...) on a fluid surface can also mimic the world of quantum mechanics. For the layman - for whom the main part of this book is written - this is good news. If the everyday laws of nature can conspire to show up quantum-like phenomena, there is hope to form mental pictures how the atomic world works. The book is almost formula-free, and explains everything by using many sketches and diagrams. The mathematical derivations underlying the main text are kept separate in a -peer reviewed - appendix. The author, a retired professor of Flight Mechanics and Propulsion at the Delft University of Technology, chose to publish his findings in this mixed popular and scientific form, because he found that interested laymen more often than professional physicists feel the need to form visualisations of quantum phenomena. (shrink)

We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from previous research in paraconsistent set theory, which has almost exclusively been motivated by a desire to avoid Russell’s paradox and fulfil naive comprehension. Instead, we prioritise setting up a system with a clear ontology of non-classical sets, which can be used to (...) reason informally about incomplete and inconsistent phenomena, and is sufficiently similar to ${\mathrm {ZFC}}$ to enable the development of interesting mathematics. We propose an axiomatic system ${\mathrm {BZFC}}$, obtained by analysing the ${\mathrm {ZFC}}$ -axioms and translating them to a four-valued setting in a careful manner, avoiding many of the obstacles encountered by other attempted formalizations. We introduce the anti-classicality axiom postulating the existence of non-classical sets, and prove a surprising results stating that the existence of a single non-classical set is sufficient to produce any other type of non-classical set. Our theory is naturally bi-interpretable with ${\mathrm {ZFC}}$, and provides a philosophically satisfying view in which non-classical sets can be seen as a natural extension of classical ones, in a similar way to the non-well-founded sets of Peter Aczel [1]. Finally, we provide an interesting application concerning Tarski semantics, showing that the classical definition of the satisfaction relation yields a logic precisely reflecting the non-classicality in the meta-theory. (shrink)

Moral-theoretical categories have almost disappeared from the theoretical vocabulary of sociology. Neither perceptions of legitimacy nor perceptions of injustice, neither moral argument nor normative consensus now play a significant role in explaining the social order. Instead the object of sociological inquiry is understood either according to the pattern of anonymous self-organization processes or as the result of cooperation among strategically-oriented actors; accordingly, the disciplinary role models are biology or economics, whose conceptual models appear suited to explain such a complex process (...) as the reproduction of societies. One may easily get the impression that current sociology wishes to finally bid farewell to the generation of its founding fathers; since from Weber and Durkheim to Talcott Parsons, it was a settled matter that an adequate basic conception of the social world could only be derived using the concepts, models, or hypotheses of moral theory – practical philosophy was, so to speak, the foundation and guiding discipline for classical sociology. After the “Theory of Communicative Action”– the last grand sketch of a complete social theory based on the sources of practical philosophy – all this seems to have been forgotten. In any event, it could until recently appear that with Habermas’ book the tradition of a normatively oriented sociology has come to an end. It is mostly due to the efforts of a small group of researchers in France – which assembled around Luc Boltanski and Laurent Thévenot – that there continues to be a strand within social theory that employs sources of moral philosophy. Having emerged from an internal critique of Pierre Bourdieu's sociology, the works of this highly productive circle, probing ever new directions, seek to explain the integration of our societies through the interplay of different moral convictions.1 The foundational text of this sociological school is the study On Justification, originally published in 1991.2 This book, which has meanwhile also been published in German,3 deserves careful consideration not least because it represents the most interesting attempt of the more recent past to give sociology a basis in moral philosophy. (shrink)

Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in (...) their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg II. Non-classical Logics W. Rautenberg III. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. Proof Theory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. (shrink)

In 1824 Sadi Carnot published Réflexions sur la Puissance Motrice du Feu in which he founded almost the entire thermodynamics theory. Two years after his death, his friend Clapeyron introduced the famous diagram PV for analytically representing the famous Carnot’s cycle: one of the main and crucial ideas presented by Carnot in his booklet. Twenty-five years later, in order to achieve the modern version of the theory, Kelvin and Clausius had to reject the caloric hypothesis, which had influenced a few (...) of Carnot’s arguments. Relying on the possibility of studying the history of science by means of logical investigation, in this paper I shall propose an historical/epistemological research on Sadi Carnot’s original thermodynamics theory in which the French scientist presents more than two principles, all of which are expressed by double negated sentences (generally speaking) within non-classical logic. (shrink)

In a well-known passage Aristotle ascribes to Plato, or as some think to his followers, the dictum, γρ ριθμóς στιν κ νòς κα τς ορίστον , ‘Number is from the one and the undetermined dyad ’, but what this apparently simple statement means has remained a mystery until modern times. In other passages Aristotle expands it to explain that the indefinite duality is a duality of the great and small, e.g., ς μν ον λην τò μγα κα τò μικρòν εναι (...) ρχς, ς δ' οσίαν τò ν. ξ κείνων γρ κατ μθεξιν το νòς εναι τος ριθμος . ‘As the matter he posits the great and small for principles, as substance the one; for by the mixture of the one with them he says numbers .’ This identification of the dyad with the great and small, elsewhere called τò νισον and τò πειρον , gives a first clue to its nature. In a notable article in Mind 35 , 419–40, continued in vol. 36, , 12–33, and amplified by D' Arcy Wentworth Thompson in vol. 38 , 43–55, A. E. Taylor first suggested a connexion between the indefinite duality and the modern theory of continued fractions. In the light of subsequent research in the history of Greek mathematics it may now be asserted with a high degree of confidence that his conjecture was almost certainly correct; but it was then no more than a conjecture, and when he looked for confirmation he looked in the wrong direction. (shrink)

In a well-known passage Aristotle ascribes to Plato, or as some think to his followers, the dictum, γρ ριθμóς στιν κ νòς κα τς ορίστον, ‘Number is from the one and the undetermined dyad ’, but what this apparently simple statement means has remained a mystery until modern times. In other passages Aristotle expands it to explain that the indefinite duality is a duality of the great and small, e.g., ς μν ον λην τò μγα κα τò μικρòν εναι ρχς, (...) ς δ' οσίαν τò ν. ξ κείνων γρ κατ μθεξιν το νòς εναι τος ριθμος. ‘As the matter he posits the great and small for principles, as substance the one; for by the mixture of the one with them he says numbers.’ This identification of the dyad with the great and small, elsewhere called τò νισον and τò πειρον, gives a first clue to its nature. In a notable article in Mind 35, 419–40, continued in vol. 36,, 12–33, and amplified by D' Arcy Wentworth Thompson in vol. 38, 43–55, A. E. Taylor first suggested a connexion between the indefinite duality and the modern theory of continued fractions. In the light of subsequent research in the history of Greek mathematics it may now be asserted with a high degree of confidence that his conjecture was almost certainly correct; but it was then no more than a conjecture, and when he looked for confirmation he looked in the wrong direction. (shrink)

David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense in which the Principal Principle is (...) a theorem of quantum probability theory for any credence function satisfying a suitable additivity requirement. No additional principle of rationality is needed to bring credence into line with objective chance. (shrink)

David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. This paper develops an account of how chance works in quantum theory that reveals a connection between credence and quantum chance (...) quite unlike what is envisioned in the philosophical literature: as a theorem of quantum probability, updating a completely additive chance function on a knowledge of chance brings credence into line with chance. The account also suggests a way of construing the Humean supervenience of chance that has the virtue of dissolving some puzzles about the "undermining" of chances. A number of interpretative moves in quantum theory are needed to generate the account of quantum chance on offer here, and they can all be disputed. But engaging in these disputes is part and parcel of naturalized metaphysics, and as such it can be more productive than engaging in the battle of intuitions among analytical metaphysicians about how chance ought to work this and other possible worlds. -/- . (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.3 (2002) 219-227 [Access article in PDF] The Practical Kinds Model as a Pragmatist Theory of Classification Peter Zachar Pragmatist theories of scientific classification are intended to be pluralistic models that recognize different ways of cutting up the world as valuable, but do not require us to adopt whatever-goes relativism or metaphysical antirealism. How ironic that my application of pragmatism to psychopathology has been (...) charged with not being sufficiently pluralistic because it tries to fit all psychiatric disorders into the Procrustean bed of practical kinds. The Practical Kinds Model in General As a point of clarification, the practical kinds model is not a description of a type of category combined with an argument that all psychiatric disorders should be seen as belonging to that type. If it were that kind of model, I would fully agree with Haslam that practical kinds, fuzzy kinds, and discrete kinds are all potential types of psychiatric disorders. Like Nick Haslam, I believe that there are many different things in the DSM-IV and the ICD-10, and they cannot neatly be classified as the same type of thing.Rather than identifying a type of category, the practical kinds model is a general theory of scientific classification. It is a nonessentialistic theory. Essentialism is the view that things have real essences. In the Aristotelian version of essentialism, an essence is an internal structure, and it is the internal structure that makes anything be the kind of thing it really is. In this classical category model, category members either have the essence or they do not, and everything that has the appropriate essence is a member of that category. The world is supposed to therefore have a well-defined structure, and the job of the scientist is to discover that structure. Ian Hacking (1999) has termed this view of categorization inherent structurism.The practical kinds model does not deny that things have internal structures; it only denies that internal structure by itself determines category membership. Internal structure is an important consideration in identifying categories, but external criteria can always play a role. External or relational criteria play more important roles in some cases than they do in others, but they cannot be eliminated once and for all. Essentialistic theories, which favor an almost exclusive focus on inherent structures, have the advantage of being more parsimonious, but they do so by ignoring real complexity.The best way to illustrate this point is to examine a category whose identification is heavily weighted in terms of internal criteria, or an inherent structure, such as a chemical element. [End Page 219] For example, hydrogen is defined as the element that has an atomic number of 1. This means that it has one proton in its nucleus and normally one electron orbiting its nucleus. The atomic number reflects an internal property, and anything that has an atomic number of 1 is hydrogen. The same is true for the other elements. Anything that has an atomic number of 79 is gold; anything that has an atomic number of 19 is potassium, and so on. Also part of the essentialistic view is the notion that all the important properties of an element are systematically (or lawfully) related to its internal structure.It would be foolish to deny the practical utility of the atomic theory of chemistry. But even in this strongest of cases, external criteria can potentially play a role in how we decide to carve up the world and what we identify as the relevant categories. The point can be clearly illustrated with a Gedanken experiment based on the ideas of Donnellan (1983). Assume that we were to make contact with extraterrestrial life, and the result of that contact was our initiation into a larger galactic community like those portrayed on Star Trek or Babylon 5. Fortunately for us, it turns out that all planets in the community use a gold-based currency, just like we do on Earth. What we call gold, however, is too common to be the galactic basis of a currency, but a particular isotope... (shrink)

The comment deals with the relevance of Coleman’s Foundations of Social Theory for so called ‘sociological theory’. On the one hand Coleman’s work is an extraordinary contribution to the solution of some of the most important ‘classical’ questions of sociology. On the other hand it is to be expected that the enormous potential of the book probably has only limited effects within the wider sociological profession. One reason for that estimation is the unfamiliarity of many sociologists with Coleman’s instruments of (...) aggregation of collective effects. The other - more important - reason is that Coleman almost completely leaves out any discussion of the importance of ‘symbolic’ and ‘cultural’ processes. Insofar the book is indeed a ‘Foundation of Social Theory’ but not a foundation of ‘sociology’ in its past and present understanding. (shrink)

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard (...) classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

These are three welcome works on medieval logic. The Summa Logica of William of Ockham has long been a classic, and scholars have been waiting for this critical edition, begun almost a quarter of a century ago by Philotheus Boehner and finally brought to completion by the combined efforts of Stephen Brown and especially Gedeon Gal, now the general editor of the Opera Philosophica et Theologica being prepared at the Franciscan Institute at St. Bonaventure University. The editors date this work (...) after the Commentary on the Sentences, two volumes of which have already appeared in the above mentioned series. It also postdates Ockham’s commentaries on Porphyry, the Praedicamenta, Perihermenias, and Sophisticis Elenchis, as well as the first four books of Aristotle’s Physics. As a terminus ante quem the editors take the fifth book of this same Physics and see it as certainly prior to the Tractatus de praedestinatione, and to the De corpore Christi and De Sacramento Altaris. Parts of the Quodlibetal questions, however, precede it, and others follow. Loux’s translation, unfortunately, antedated this splendid edition of the Summa Logicae, being based on only the partial, earlier edition of Boehner. Nevertheless, it is a useful instrument providing a good and relatively complete introduction to the basic themes of Ockham’s philosophy of language as well as his ontology. A spot check reveals some misprints, e.g., on pp. 56, 192 and on page 38, lines 68-83 of the Latin edition he used have not been translated. The work is introduced by two essays: "The Ontology of William Ockham" and "Ockham on Generality"—the latter dealing with his theory of supposition. Nuchelmans’ interesting work, though it deals mostly with the medieval history of propositions as bearers of truth and falsity, contains some six chapters which trace the history of the term as early as Plato’s treatment in the Sophist, through Aristotle and the important Stoic lekton and axioma. He also concludes with a useful chapter on the significance of a true propositio, both as a mode of being of a thing and as the mental conception.—A.B.W. (shrink)

Gert H. Müller The growth of the number of publications in almost all scientific areas,· as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview ofthe existing literature, partic ularly if they do not have an extensive library available in their (...) neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg II. Non-c1assical Logics W. Rautenberg IH. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. ProofTheory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. (shrink)

For principled and substantially philosophical reasons, based largely on his reform of natural history by inverting the Paleyan notion of overarching and purposeful beneficence in the construction of organisms, Darwin built his theory of selection at the single causal level of individual bodies engaged in unconscious struggle for their own reproductive success. But the central logic of the theory allows selection to work effectively on entities at several levels of a genealogical hierarchy, provided that they embody a set of requisite (...) features for defining evolutionary individuality. Genes, cell lineages, demes, species, and clades-as well as Darwin’s favoured organisms-embody these requisite features in enough cases to form important levels of selection in the history of life. R. A. Fisher explicitly recognized the unassailable logic of species selection, but denied that thsi real process could be important in evolution because, compared with the production of new organisms within a species, the origin of new species is so rare, and the number of species within most clades so low. I review this and other classical arguments against higher-level selection, and conclude that they are invalid in practice for interdemic selection, and false in principle for species selection. Punctuated equilibrium defines the individuality of species and refutes Fisher’s classical argument based on cycle time. In the second part of the paper, I argue that we have failed to appreciate the range and power of selection at levels above and below the organismic because we falsely extrapolate the defining properties of organisms to these other levels, and then regard the other levels as impotent because their effective individuals differ so much from organisms. We would better appreciate the power and generality of hierarchical models of selection if we grasped two key principles: first, that levels can interact in all modes, and not only in the negative style that, for heuristic and operational reasons, has received almost exclusive attention in the existing literature; and second, that each hierarchical level differs from all others in substantial and interesting ways, both in the style and frequency of patterns in change and causal modes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Contemplative Foundations of Classical Daoism by Harold D. RothDerek Asaba Chi (bio)The Contemplative Foundations of Classical Daoism. By Harold D. Roth. Albany: State University of New York Press, 2021. Series: SUNY series in Chinese Philosophy and Culture. Pp. xiii+ 522. Hardcover ＄ 77.37, isbn 978-1-4384-8271-2. The Contemplative Foundations of Classical Daoism (hereafter Contemplative Foundations) is a compilation of articles and book chapters selected from Harold Roth's almost (...) 27 years of scholarly publications on the origins and early history of the classical Daoist tradition. The essays that constitute this collection seek to counter certain myths about Early China Studies and Daoist Studies that have previously prevented the field from identifying, in a historically plausible, contemplatively grounded, and textually justified fashion, some of the basic contours of classical Daoism. Roth begins by discussing prior studies of the early history of Daoism. In his view, these studies were hampered in their understanding of the contemplative foundations of Daoism by limits derived from a set of unreflective assumptions that restrict human cognitive possibilities to merely those that were deemed possible by European cultures. Some of the most deleterious of these assumptions were: "all human beings have a genetic predisposition to a belief in gods or other supernatural beings; veridical human cognition is restricted to either reason or emotion—categories established by the European Enlightenment" (p. 2). Roth argues that these products of unreflective Eurocentrism have largely contributed to a failure to recognize that early Daoist thinkers could possibly have derived their ideas about human psychology, human nature, and the nature of the cosmos through anything other than abstract rational thought or emotional responses (pp. 3-5). These unreflective thoughts have contributed to constructing the idea that contemplative experiences can never be epistemologically valid, and that, because of this non-veridicality, attempts to ascertain the contemplative foundations of classical Daoism are either unnecessary or deluded. The author also discusses the distinctive philosophical origins of classical Daoism. The first myth about the origins of classical Daoism revolves around beliefs that the Daoist tradition began with Lao Dan 老聃 in the sixth century BCE and his outstanding work the Daodejing 道德經. Further, Lao Dan founded a Daoist "school" that included Zhuang Zhou 莊周, the sole author of the Zhuangzi [End Page 1] 莊子, and other eponymous works created by later disciples such as Liezi 列子 and Wenzi 文子. Together they created and transmitted a Daoist school that developed a lofty mystical philosophy which accepted death as a natural transformation and maintained a cosmology of the Way Dao 道 and its Inner Power or Potency De 德. However, this tradition of "philosophical Daoism" or "Lao-Zhuang" 老 莊 became singularly corrupted through its contact with superstitious beliefs in longevity, immortality, and polytheistic deities to form the organized Daoist religion that emerged in the second century CE and that persists until today (p. 3). Roth argues that the contemplative foundations of classical Daoism are grounded in a distinctive form of practice that the author defines as "inner cultivation," neiye 內業, or "inward training" (p. 6). Roth provides a list of works that present surviving evidence for these practices. These include: the Laozi and the Zhuangzi, as well as other classical texts of mixed traditions, including the Lüshi Chunqiu 呂士春秋 and the Huainanzi 淮 南子. Contemplative Foundations is divided into two parts which present a more or less holistic view of the contemplative foundation of classical Daoism. Part I is dedicated to the careful textual analysis of the major surviving sources of classical Daoism to derive evidence for both its contemplative foundations and its historical and social context. First, the author examines the theories of the physiological basis of psychology and self-cultivation as discussed in three texts from the Guanzi 管子 and in the Huainanzi. Despite its apparent absence in the early Daoist tradition, the physiological basis of human psychology plays a major role in the theory and practice of neidan 內丹, or "physiological alchemy," which emerged somewhat later, when Daoism became institutionalized (p. 23). Roth tries to link the psychological experience to physiological conditions that make possible a whole range of neidan practices that seem to have preceded Daoist religion but became fully developed therein. Roth moves on to debunk the traditional... (shrink)

The process dissociation procedure (PDP) of implicit sequence learning states that the correct inclusion-task response contains the incorrect exclusion-task response. However, there has been no research to test the hypothesis. The current study used a single variable (Stimulus Onset Asynchrony SOA: 850 ms vs. 1350 ms) between-subjects design, with pre-task resting-state fMRI, to test and improve the classical PDP to the mutually exclusive theory (MET). (1) Behavioral data and neuroimaging data demonstrated that the classical PDP has not been validated. In (...) the SOA = 850 ms group, the correct inclusion-task response was at chance, but the incorrect exclusion-task response occurred greater than chance. In the SOA = 850 ms group, the two responses were not correlated, but in the SOA = 1,350 ms group and putting the two groups together, the two responses were in contrast to each other. In each group, brain areas whose amplitude of low frequency fluctuations (ALFFs) in the resting-state related to the two responses were either completely different or opposite to one another. However, the results were perfectly consistent with the MET proposed by the present study which suggests that the correct inclusion-task response is equal to the correct exclusion-task response is equal toC+A1, and the incorrect exclusion-task response is equal toA2.Cdenotes the controlled response andA1andA2denote two different automatic responses. (2) The improved PDP was proposed to categorize the 12 kinds of triplets as delineating four knowledge types, namely non-acquisition of knowledge, uncontrollable knowledge, half-controllable knowledge, and controllable knowledge with the MET. ALFFs in the resting-state could predict the four knowledge types of the improved PDP among two groups. The participants’ control of the four knowledge types (degree of consciousness) gradually improved. Correspondingly, the brain areas in the resting-state positively related to the four knowledge types, gradually changed from the sensory and motor network to the somatic sensorimotor network, and then to the implicit learning network, and then to the consciousness network. The brain areas in the resting-state negatively related to the four knowledge types gradually changed from the consciousness network to the sensory and motor network. As SOA increased, the brain areas associated with almost all the four knowledge types changed. (3) The inhomogeneous hypothesis of the MET is best suited to interpret behavioral and neuroimaging data; it states that the same components among the four knowledge types are not homogeneous, and the same knowledge types are not homogeneous between the two SOA groups. (shrink)

Classical statistical mechanics has commanded a modest but steady amount of attention from philosophers of science. By contrast, there has been an almost total neglect of relativistic statistical mechanics, or more precisely, a neglect of the prospects and problems of producing a relativistic version of classical statistical mechanics. The neglect is undeserved, for this area offers a fascinating array of case studies for those concerned with the history and sociology of science, with the structure and dynamics of scientific theories, (...) or with foundations problems in physics. This paper is dedicated to the goal of ending the neglect. Towards this end, I will survey some of the issues which arise in attempting to marry statistical-thermodynamics with relativity theory. The choice of the issues to be discussed and their treatment naturally reflect my own preferences and prejudices, and I cannot hope for the reader’s agreement on all points. (shrink)