This paper gives a formalization of general topology in second-order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF denote the set of maximal filters on P endowed with the topology generated by {Np | p ∈ P}, where Np = {F ∈ MF | p ∈ F}. We define a countably based MF space to be a space of the form MF for some (...) countable poset P. The class of countably based MF spaces includes all complete separable metric spaces as well as many nonmetrizable spaces. The following reverse mathematics results are obtained. The proposition that every nonempty Gδ subset of a countably based MF space is homeomorphic to a countably based MF space is equivalent to [Formula: see text] over ACA0. The proposition that every uncountable closed subset of a countably based MF space contains a perfect set is equivalent over [Formula: see text] to the proposition that [Formula: see text] is countable for all A ⊆ ℕ. The proposition that every regular countably based MF space is homeomorphic to a complete separable metric space is equivalent to [Formula: see text] over [Formula: see text]. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π2 1 comprehension. An MF space is defined to be a topological space of the form MF(P) with the topology generated by $\lbrace N_p \mid p \in P \rbrace$ . Here P is a poset, MF(P) is the set of maximal filters on P, and $N_p = \lbrace F \in MF(P) \mid p \in F \rbrace$ . If the poset P is countable, (...) the space MF(P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, "every countably based MF space which is regular is homeomorphic to a complete separable metric space," is equivalent to Π2 1-CA0. The equivalence is proved in the weaker system Π1 1-CA0. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π2 1 comprehension. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π12 comprehension. An MF space is defined to be a topological space of the form MF with the topology generated by {Np ∣ p ϵ P}. Here P is a poset, MF is the set of maximal filters on P, and Np = {F ϵ MF ∣ p ϵ F }. If the poset P is countable, the space MF is said to (...) be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, “every countably based MF space which is regular is homeomorphic to a complete separable metric space,” is equivalent to. The equivalence is proved in the weaker system. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π12 comprehension. (shrink)

Let n be a positive integer. By a $\beta_{n}-model$ we mean an $\omega-model$ which is elementary with respect to $\sigma_{n}^{1}$ formulas. We prove the following $\beta_{n}-model$ version of $G\ddot{o}del's$ Second Incompleteness Theorem. For any recursively axiomatized theory S in the language of second order arithmetic, if there exists a $\beta_{n}-model$ of S, then there exists a $\beta_{n}-model$ of S + "there is no countable $\beta_{n}-model$ of S". We also prove a $\beta_{n}-model$ version of $L\ddot{o}b's$ Theorem. As a corollary, we obtain (...) a $\beta_{n}-model$ which is not a $\beta_{n+1}-model$. (shrink)

We study the Lindenbaum algebra ${\fancyscript{A}}$ (WKL o, RCA o) of sentences in the language of second-order arithmetic that imply RCA o and are provable from WKL o. We explore the relationship between ${\Sigma^1_1}$ sentences in ${\fancyscript{A}}$ (WKL o, RCA o) and ${\Pi^0_1}$ classes of subsets of ω. By applying a result of Binns and Simpson (Arch. Math. Logic 43(3), 399–414, 2004) about ${\Pi^0_1}$ classes, we give a specific embedding of the free distributive lattice with countably many generators into ${\fancyscript{A}}$ (...) (WKL o, RCA o). (shrink)

The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic. We argue that s-logic captures precisely the “logical” content of the implication and nonimplication relations between subsystems in Reverse Mathematics. We present a sound, complete, decidable, and compact tableau-style deductive system (...) for s-logic, and explore in detail two fragments that are particularly relevant to Reverse Mathematics practice and automated theorem proving of Reverse Mathematics results. (shrink)

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing complete. We obtain the reverse mathematics result that the principle (...) "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets. (shrink)

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a certain form is provable using E-HA ${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. (...) These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis. (shrink)

We show that \\) cannot be proved with one typical application of \\) in an intuitionistic extension of \ to higher types, but that this does not remain true when the law of the excluded middle is added. The argument uses Kohlenbach’s axiomatization of higher order reverse mathematics, results related to modified reducibility, and a formalization of Weihrauch reducibility.

Remembering seems, to philosophers and scientists, one of the most mystifying of human activities. Yet natural language users have no problem understanding what is meant by ‘memory’. Memory is simply the ability to recall personally experienced events and certain kinds of information such as facts, names, or faces; or how to perform certain actions, like riding a bike or playing chess. It is on this basis that people sometimes make claims about themselves or others having a good or bad memory, (...) especially for things like names, numbers, or faces. Why then is memory such a mystery? Because, firstly, of its diversity: memory enables us to perform a plethora of different tasks, including the continuous interpretation of every moment of consciousness. Secondly, different forms of memory have different standards of accuracy, and often dramatically different criteria for success. (shrink)

This remarkable book presents a rich and up-to-date view of evolution that explores the far-reaching implications of Darwin's theory and emphasizes the power, significance, and relevance of evolution to our lives today. After all, we ourselves are the product of evolution, and we can tackle many of our gravest challenges -- from lethal resurgence of antiobiotic-resistant diseases to the wave of extinctions that looms before us -- with a sound understanding of the science.

Carl Craver investigates what we are doing when we sue neuroscience to explain what's going on in the brain.

Carl F. Craver investigates what we are doing when we use neuroscience to explain what's going on in the brain. When does an explanation succeed and when does it fail? Craver offers explicit standards for successful explanation of the workings of the brain, on the basis of a systematic view about what neuroscientific explanations are.

In this systematic introduction to the philosophy of Charles S. Peirce, the author focuses on four of Peirce's fundamental conceptions: pragmatism and Peirce's development of it into what he called 'pragmaticism'; his theory of signs; his phenomenology; and his theory that continuity is of prime importance for philosophy. He argues that at the centre of Peirce's philosophical project is a unique form of metaphysical realism, whereby continuity and evolutionary change are both necessary for our understanding of experience. In his final (...) chapter Professor Hausman applies this version of realism to contemporary controversies between anti-realists and anti-idealists. Peirce's views are compared to those of such contemporary figures as Davidson, Putnam, and Rorty. The book will be of particular interest to philosophers concerned with American philosophy and current debates on realism as well as linguists working in semiotics. (shrink)

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections (...) in the preservation process, and hope you enjoy this valuable book. ++++ The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Uber Den Psychologischen Ursprung Der Raumvorstellung Carl Stumpf S. Hirzel, 1873 Space perception. (shrink)

Carl Schmitt (1888–1985), Professor für Staats- und Völkerrecht, bewegt nach wie vor die Gemüter. Die Reaktion auf seine Schriften, Handlungen und Ausstrahlungen ist vielfältig; die Spanne reicht von entrüsteten, für die er der Teufel in Person bleibt, über viele Zwischenstufen bis zu jenen Lesern, die ihn für einen der subtilsten, noch keineswegs ausgeloteten Geistern dieses Jahrhunderts halten. Sein Leben lang war Carl Schmitt ein passionierter Schreiber von Briefen. Meist handelte es sich um handschriftlich verfasste, die für den Schreibenden (...) die Fortsetzung eines konkreten Gespräches mit anderen Mitteln war. Das macht das authentische und die Spontanität der Schmitt-Briefe aus. Als erste Edition einer umfangreichen Korrespondenz wird in dem Buch die Korrespondenz zwischen Carl Schmitt und Armin Mohler veröffentlicht. Der Briefwechsel umfasst die Zeit von 1947 bis 1980 und enthält 280 Briefe und Karten von Carl Schmitt an Armin Mohler. Von dem Briefpartner und Herausgeber wird in der Regel aus den eigenen Briefen nur auszugsweise zitiert, sofern es für das von Carl Schmitt Geschriebene notwendig ist. Armin Mohler (1920 bis 2003), ist einer der bekanntesten rechtskonservativen Schriftsteller, Kritiker und Historiker in Deutschland. Sein Handbuch zur Konservativen Revolution ist ein Standardwerk. In der Zeit des Briefwechsels war Mohler von 1949 bis 1953 Sekretär Ernst Jüngers, danach Korrespondent großer Zeitungen in Paris und von 1964 an Geschäftsführer der Carl Friedrich von Siemens Stiftung, in der er sehr beachtete Symposien zu aktuellen wissenschaftlichen Themen organisierte. Der Briefwechsel ist für die Deutung Carl Schmitts in der Nachkriegszeit in seinem Sauerländer "Exil" grundlegend, gleichzeitig enthält er pointierte Schlaglichter auf das politische und kulturelle Geschehen der frühen und mittleren Bundesrepublik sowie auf Werk und Leben von Ernst Jünger. (shrink)

This study investigated the attitudinal responses of 403 undergraduate students with respect to nine hypothetical marketing moral dilemmas. Participants varied by gender, major, and age.It was found that undergraduate women responded more ethically on the hypothetical marketing moral dilemmas, as hypothesized. Secondly, chosen major did not make a difference on cognitive, affective, or behavioral responses. Further, the overall means for each scenario were in the morally correct direction in every case. Also, all intercorrelations for each story were significant. Finally, whenever (...) there was a nonchance finding for age, the oldest participants answered more morally than the youngest subjects. (shrink)

The Proliferation of Rights explores how the assertion of rights has expanded dramatically since World War II. Carl Wellman illuminates for the reader the historical developments in each of the major categories of rights, including human rights, civil rights, women’s rights, patient rights, and animal rights. He concludes by assessing where this proliferation has been legitimate and helpful, cases where it has been illusory and unproductive, and alternatives to the appeal to rights.

In this paper I argue against one variety of contextualism about aesthetic predicates such as “beautiful.” Contextualist analyses of these and other predicates have been subject to several challenges surrounding disagreement. Focusing on one kind of contextualism— individualized indexical contextualism —I unpack these various challenges and consider the responses available to the contextualist. The three responses I consider are as follows: giving an alternative analysis of the concept of disagreement ; claiming that speakers suffer from semantic blindness; and claiming that (...) attributions of beauty carry presuppositions of commonality. I will argue that none of the available strategies gives a response which both satisfactorily explains all of the disagreement -data and is plausible independent of significant evidence in favor of contextualism. I conclude that individualized indexical contextualism about the aesthetic is untenable, although this does not rule out alternative contextualist approaches to the aesthetic. (shrink)

This collection of articles and associated discussion papers focuses on a problem that has attracted increasing attention from linguists and psychologists throughout the world during the past several years. Reduced to essentials, the problem is that of discovering the character of the mental capacities that make it possible for human beings to attain knowledge of their language on the basis of fragmentary and haphazard early linguistic experience. A fundamental assumption running through all of these contributions is that people possess strong (...) innate predispositions that are critical for success in this task. (shrink)

Some philosophers writing on the possibility of faultless disagreement have argued that the only way to account for the intuition that there could be disagreements which are faultless in every sense is to accept a relativistic semantics. In this article we demonstrate that this view is mistaken by constructing an absolutist semantics for a particular domain – aesthetic discourse – which allows for the possibility of genuinely faultless disagreements. We argue that this position is an improvement over previous absolutist responses (...) to the relativist's challenge and that it presents an independently plausible account of the semantics of aesthetic discourse. (shrink)

A mutual fund family incubates a fund when it creates a privately subsidized fund not available to the general investing public. It destroys unsuccessful incubator funds. The few successful funds will report higher incubation returns than the market return in advertisements intended to attract money from individual investors. This practice is currently allowed by the SEC. The evidence is that incubation returns are not a good predictor of subsequent fund performance and likely serve to mislead unsuspecting investors.

A mutual fund family incubates a fund when it creates a privately subsidized fund not available to the general investing public. It destroys unsuccessful incubator funds. The few successful funds will report higher incubation returns than the market return in advertisements intended to attract money from individual investors. This practice is currently allowed by the SEC. The evidence is that incubation returns are not a good predictor of subsequent fund performance and likely serve to mislead unsuspecting investors.

The distinction between discovery and justification is ambiguous. This obscures the debate over a logic of discovery. For the debate presupposes the distinction. Real discoveries are well established. What is well established is justified. The proper distinctions are three: initial thinking, plausibility, and acceptability. Logic is not essential to initial thinking. We do not need good supporting reasons to initially think of an hypothesis. Initial thoughts need be neither plausible nor acceptable. Logic is essential, as Hanson noted, to both plausibility (...) and acceptability. An hypothesis needs good supporting reasons to be either plausible or acceptable. Such reasons need not be relative to the particular scientific theory undergoing test at the time. There is no fundamental difference between reasons relevant to plausibility and acceptability. The difference is one of degree. Acceptability requires more than plausibility. (shrink)

Here, for the first time, the world's two leading authorities—Tom Regan, who argues for animal rights, and Carl Cohen, who argues against them—make their respective case before the public at large. The very terms of the debate will never be the same. This seminal moment in the history of the controversy over animal rights will influence the direction of this debate throughout the rest of the century.

Biologists rely heavily on the language of information, coding, and transmission that is commonplace in the field of information theory developed by Claude Shannon, but there is open debate about whether such language is anything more than facile metaphor. Philosophers of biology have argued that when biologists talk about information in genes and in evolution, they are not talking about the sort of information that Shannon’s theory addresses. First, philosophers have suggested that Shannon’s theory is only useful for developing a (...) shallow notion of correlation, the so-called causal sense of information. Second, they typically argue that in genetics and evolutionary biology, information language is used in a semantic sense, whereas semantics are deliberately omitted from Shannon’s theory. Neither critique is well-founded. Here we propose an alternative to the causal and semantic senses of information: a transmission sense of information, in which an object X conveys information if the function of X is to reduce, by virtue of its sequence properties, uncertainty on the part of an agent who observes X. The transmission sense not only captures much of what biologists intend when they talk about information in genes, but also brings Shannon’s theory back to the fore. By taking the viewpoint of a communications engineer and focusing on the decision problem of how information is to be packaged for transport, this approach resolves several problems that have plagued the information concept in biology, and highlights a number of important features of the way that information is encoded, stored, and transmitted as genetic sequence. (shrink)

BackgroundThe state of the world is one with scarce medical resources where longevity is not equally distributed. Given such facts, setting priorities in health entails making difficult yet unavoidable decisions about which lives to save. The business of saving lives works on the assumption that longevity is valuable and that an early death is worse than a late death. There is a vast literature on health priorities and badness of death, separately. Surprisingly, there has been little cross-fertilisation between the academic (...) fields of priority setting and badness of death. Our aim is to connect philosophical discussions on the badness of death to contemporary debates in health priorities.DiscussionTwo questions regarding death are especially relevant to health priorities. The first question is why death is bad. Death is clearly bad for others, such as family, friends and society. Many philosophers also argue that death can be bad for those who die. This distinction is important for health priorities, because it concerns our fundamental reasons for saving lives. The second question is, ‘When is the worst time to die?’ A premature death is commonly considered worse than a late death. Thus, the number of good life years lost seems to matter to the badness of death. Concerning young individuals, some think the death of infants is worse than the death of adolescents, while others have contrary intuitions. Our claim is that to prioritise between age groups, we must consider the question of when it is worst to die.ConclusionsDeprivationism provides a more plausible approach to health priorities than Epicureanism. If Deprivationism is accepted, we will have a firmer basis for claiming that individuals, in addition to having a health loss caused by morbidity, will have a loss of good life years due to mortality. Additionally, Deprivationism highlights the importance of age and values for health priorities. Regarding age, both variants of Deprivationism imply that stillbirths are included in the Global Burden of Disease. Finally, we suggest that the Time-Relative Interest Account may serve as an alternative to the discounting and age weighting previously applied in the Global Burden of Disease. (shrink)

In his historical perspective on the changes in scientific thought over the last 100 years, Carl N. Degler explores the study of social evolution and the ongoing search for human nature. In Search of Human Nature provides a detailed perspective on the reasons behind the shifting emphasis in social thought from biology, to culture, and again to biology. Degler examines why these changes took place, the evidence and people fostering these changes and why students of human nature decided to (...) accept this momentous change in thought. He suggests varying ideologies as the underlying force behind this shift in the study of social science. From Darwin's theory that human social behaviour has drastically evolved from animals, to the belief that human experience serves as the basic differentiating factor in humans, Degler provides a thorough and captivating examination of the roots of human behaviour. (shrink)

Based on author's dissertation--Yale University.

The fundamental tenet of modern empiricism is the view that all non-analytic knowledge is based on experience. Let us call this thesis the principle of empiricism. [1] Contemporary logical empiricism has added [2] to it the maxim that a sentence makes a cognitively meaningful assertion, and thus can be said to be either true or false, only if it is either (1) analytic or self-contradictory or (2) capable, at least in principle, of experiential test. According to this so-called empiricist criterion (...) of cognitive meaning, or of cognitive significance, many of the formulations of traditional metaphysics and large parts of epistemology are devoid of cognitive significance--however rich some of them may be in non-cognitive import by virtue of their emotive appeal or the moral inspiration they offer. Similarly certain doctrines which have been, at one time or another, formulated within empirical science or its border disciplines are so contrived as to be incapable of test by any conceivable evidence; they are therefore qualified as pseudo- [p. 42:] hypotheses, which assert nothing, and which therefore have no explanatory or predictive force whatever. This verdict applies, for example, to the neo-vitalist speculations about entelechies or vital forces, and to the "telefinalist hypothesis" propounded by Lecomte du Noüy. (shrink)