The paper gives a historically informed reconstruction of Frege's view of statements of number. The reconstruction supports Frege's claim that a statement can be 'about a concept' although it does not contain a singular term referring to the concept. Hence, Frege's philosophy of number is not subject to the problems Frege sees for singular reference to concepts.

A deficit in the number of organs available for transplantation persists even with an increase in donation rates. One possible choice of donor for organs that appears under-referred and/or unaccepted is patients with primary brain tumours. In spite of advances in the treatment of high-grade primary central nervous system (CNS) tumours, the prognosis remains dire. A working group on organs from donors with primary CNS tumours showed that the risk of transmission is small and outweighs the benefits of waiting (...) for a normal donor, in survival and organ life-years, with caveats. This paper explores the possibility that, if information on organ donation were made available to patients and their families with knowledge of their inevitable fate, perhaps some will choose to donate. It would be explained that to achieve this, elective ventilation would be performed in their final moments. This would obviate the consent question because of an advance statement. It is accepted that these are sensitive matters and there will be logistic issues. This will need discussion with the public and other professionals, but it could increase the number of donors and can be extrapolated to encompass other primary CNS tumours. (shrink)

What are the meanings of number expressions, and what can they tell us about questions of central importance to the philosophy of mathematics, specifically 'Do numbers exist?' This Element attempts to shed light on this question by outlining a recent debate between substantivalists and adjectivalists regarding the semantic function of number words in numerical statements. After highlighting their motivations and challenges, I develop a comprehensive polymorphic semantics for number expressions. I argue that accounting for the numerous meanings (...) and how they are related leads to a strengthened argument for realism, one which renders familiar forms of nominalism highly implausible. (shrink)

Originally published in 1995, The Antievolution Works of Arthur I. Brown is the third volume in the series, Creationism in Twentieth Century America. The volume brings together original sources from the prominent surgeon and creationist Arthur I. Brown. Brown discredited evolution as it was contrary to the 'clear statements of scripture' which he believed infallible, stating evolution instead to be both a hoax and 'a weapon of Satan'. The works included focus on Brown's polemic through his early twentieth century writings. (...) The essays focus on his scientific investigations and provide a negative commentary upon Darwin's theory of evolution instead focusing on biblical explanations for evolution. As a scientist Brown's unique view of evolution from a creationist and scientific viewpoint provides a fascinating lens through which to view the historical debates surrounding evolution and provides a unique insight into how Darwinian theory affected both the scientific and religious communities. This book will be of interest to natural historians, and theologians as well as academics of philosophy and history. (shrink)

The field of numerical cognition provides a fairly clear picture of the processes through which we learn basic arithmetical facts. This scientific picture, however, is rarely taken as providing a response to a much‐debated philosophical question, namely, the question of how we obtain number knowledge, since numbers are usually thought to be abstract entities located outside of space and time. In this paper, I take the scientific evidence on how we learn arithmetic as providing a response to the philosophical (...) question of how we obtain number knowledge. I reject the view that numbers are abstract entities located outside of space and time and, alternatively, derive from the scientific evidence a novel account of the nature of numbers. In this account, numbers are reifications of the counting procedure and arithmetic statements are seen as describing the functioning of counting and calculation techniques. (shrink)

What is central to the progression of a sequence is the idea of succession, which is fundamentally a temporal notion. In Kant's ontology numbers are not objects but rules (schemata) for representing the magnitude of a quantum. The magnitude of a discrete quantum 11...11 is determined by a counting procedure, an operation which can be understood as a mapping from the ordinals to the cardinals. All empirical models for numbers isomorphic to 11...11 must conform to the transcendental determination of time-order. (...) Kant's transcendental model for number entails a procedural semantics in which the semantic value of the number-concept is defined in terms of temporal procedures. A number is constructible if and only if it can be schematized in a procedural form. This representability condition explains how an arbitrarily large number is representable and why Kant thinks that arithmetical statements are synthetic and not analytic. (shrink)

According to genuine modal realism, some things (including numbers and properties) lack distinct counterparts in different worlds. So how can they possess any of their properties contingently? Egan (2004) argues that to explain such accidental property possession, the genuine modal realist must depart from Lewis and identify properties with functions, rather than with sets of possibilia. We disagree. The genuine modal realist already has the resources to handle Egan's proposed counterexamples. As we show, she does not need to amend her (...) analysis of possibility statements, or her theory of what properties are. (shrink)

Hölder’s review of Robert Graßmann’s Theory of Number provides the first statement of Hölder’s most significant tenets concerning the distinction between the genetic and axiomatic presentation of mathematics, the mature expression of which is found in Hölder’s book The Mathematical Method of 1924. By translating Hölder’s review into English, I hope to make this unique document known to a wider public. In my introductory note I provide some context to Hölder’s paper and a few other remarks concerning the (...) translation work. (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)

The Purpose of this paper is to ask how far Locke can be said to have anticipated modern theories of number, particularly the intuitionist theory of Brouwer and Heyting. It has in mind Mr Edward E. Dawson's statement that Locke's account of number was not merely ‘a good effort in his own day’ but that ‘what Locke had to say really was quite fundamental, and a good deal of modern mathematics assumes his position, either explicitly or implicitly’. (...) Mr Dawson thinks that some of the central notions of the intuitionist theory are already present in the Essay Concerning Human Understanding , II, xvi, ‘Of Number’. We should like to examine the view. (shrink)

Hölder’s review of Robert Graßmann’s Theory of Number provides the first statement of Hölder’s most significant tenets concerning the distinction between the genetic and axiomatic presentation of mathematics, the mature expression of which is found in Hölder’s book The Mathematical Method of 1924. By translating Hölder’s review into English, I hope to make this unique document known to a wider public. In my introductory note I provide some context to Hölder’s paper and a few other remarks concerning the (...) translation work. (shrink)

I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The (...) view can be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (shrink)

Part of Frege's concern about whether number words are properties of objects was that if they could be construed as such it would lend support to the view that truths of arithmetic were empirical truths. Such concern is ill-founded. Even if number words do apply to objects as predicates, this does not entail that numerical truths would be empirical, any more than the fact that ‘bachelor’ and ‘unmarried’ are predicates of objects entails that their relationship is an empirical (...) one. The account of number words as predicates given here, consequently, should not be taken as supportive of any one particular theory concerning arithmetic truth rather than another.The view of number words that emerges above from the criticism of Frege's arguments is that sentences containing number words can and do say something about objects in a collective and syncategorematic way. That is, they say something about classes of objects, when it is clear what is to count as an object. Whether this view commits us to accepting certain ontological entities, classes of individuals, above and beyond individuals themselves, I am not prepared to say, and at any rate this question falls beyond the intended scope of this essay. To those who would eschew abstract entities, however, it may be noted that the ontological problems that arise are not peculiar to this view; they seem no more or less severe than those that arise in connection with other collective predicate statements, as, for example, “Blue whales are becoming extinct.”The view presented here also does not pretend to be a fatal criticism of the logicist program. Taking our cue from the above noted fact that syncategorematic predicates share in a common ‘partial’ abstract sense, it seems reasonable to say that it is just the set of such partial senses of number words, and the relationships that hold between such senses, that the logicist and the pure number theorist investigate. (shrink)

A nominalist account of statements of number (e.g., ‘There are exactly two moons of Mars’) is rebutted.

Theorems of arithmetic are used, perhaps essentially, to reach conclusions about the natural world. This applicability can be explained in a natural way by analogy with the applicability of statements of law to the world. ;In order to carry out an ontological argument for my thesis, I assume the existence of universals as a working hypothesis. I motivate a theory of laws according to which statements of law are singular statements about scientific properties. Such statements entail generalizations about instances of (...) those properties. My task, then, is to show that theorems of arithmetic, in application, are similar to statements of law in this respect. On the basis of my working hypothesis, I argue that there are inclining reasons to think that cardinal numbers are scientific properties whose instances occur in the natural world. The works of Mill, Frege and Benacerraf play central roles in these arguments. ;In general, I urge that there are no conclusive epistemological or ontological factors which preclude arithmetical truths from being laws of nature. Consequently, I think we can extend any semantic theory which is adequate for statements of law to theorems of arithmetic. This would apply even to a theory of predication which does not involve commitment to universals. So, to the degree that my argument succeeds with the working hypothesis, it also supports the unconditioned thesis that arithmetical truths are laws of nature. (shrink)

The number of speaking actors in Old Comedy has been much discussed, but no consensus has been reached. The old assumption that the number was three, as in tragedy, was shaken when it was realized that some scenes of Aristophanes have four characters on-stage at once, all taking part in the dialogue: for example, in Lys. 77–253 we have Lysistrate, Kalonike, Myrrhine, and Lampito, and in Frogs 1414–81 we have Dionysos, Aiskhylos, Euripides, and Plouton. Rees therefore argued that (...) there was no fixed number, but that view was not generally accepted. A more widely held view is that there were three principal actors with additional performers for small parts. However, there is no evidence contemporary with Aristophanes which distinguishes three actors from the others in this way, and it is probable that writers of later periods who mention three actors are referring to their own times and did not have authentic information about the fifth century. The passage which DFA, p. 149, seems to regard as the most trustworthy is in a brief account of comedy attributed to Tzetzes: πιγενμενος δ Κρατνος κατστησε μν πρτον τ ν τ κωμδ πρσωπα μεχρ τριν, στσας τν ταξαν4 DFA paraphrases this as ‘Cratinus reduced the disorderliness and, in some sense, fixed the number of regular actors at three’. But πρσωπα means ‘masks’ or ‘characters’; it does not mean ‘actors’ . What the writer meant by saying that Kratinos settled the masks or characters in comedy at ‘up to three’ is not clear, but his statement is useless as evidence for the number of actors. (shrink)

A realist view of numbers often rests on the following thesis: statements like ‘The number of moons of Jupiter is four’ are identity statements in which the copula is flanked by singular terms whose semantic function consists in referring to a number (henceforth: Identity). On the basis of Identity the realists argue that the assertive use of such statements commits us to numbers. Recently, some anti-realists have disputed this argument. According to them, Identity is false, and, thus, we (...) may deny that the relevant statements commit us to numbers. The present paper argues that the correct linguistic analysis of the relevant number statements supports the anti-realist view that Identity is false. However, as will further be shown, pace the anti-realist, this analysis does not establish that such statements do not commit us to numbers after all. (shrink)

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

This book is a comprehensive and unique text and reference in medical ethics. By far the most inclusive set of primary documents and articles in the field ever published, it contains over 100 selections. Virtually all pieces appear in their entirety, and a significant number would be difficult to obtain elsewhere. The volume draws upon the literature of history, medicine, philosophical and religious ethics, economics, and sociology. A wide range of topics and issues are covered, such as law and (...) medicine, truth-telling by the physician, research, population policy, genetics, abortion, dying, and individual rights in medical care. The selections span the centuries, beginning with material from the works of Hippocrates, continuing through Thomas Percival, John Stuart Mill, and Claude Bernard, down to modern commentators like Henry K. Beecher, Walsh McDermott, David L. Bazelon, Paul Freund, H. L. A. Hart, John Rawls, Paul Ramsey, Richard McCormick, Rashi Fein, and Bernard Barber. The text has eight major divisions, beginning with sections on the ethical dimensions of the physician-patient relationship in history; the moral bases of medical ethics; and regulation, compulsion, and protection of the consumer in clinical medicine and public health. Each of these sections includes key essays that appear for the first time. All of the book's major divisions contain primary documents: codes such as the Hippocratic Oath, Medieval Law for the Regulation of Medicine, and the first as well as the most recent code of the American Medical Association; court decisions, including those on Karen Quinlan and on abortion in the United States and West Germany; government documents such as the statement of the National Commission on the Protection of Human Subjects, the Tuskegee Syphilis Report, the British Parliamentary debate on euthanasia, and the Council of Europe on rights of the sick and dying; and various published guidelines such as the Harvard Medical School brain death criteria, the American Hospital Association on patient's rights, and Pope Pius XII on the prolongation of life. Cases that illustrate moral dilemmas are provided for discussion purposes. Each section is preceded by a succinct editor's introduction. The documents and essays are of practical value for practitioners and students in medicine, law, ethics, and counselling, and for individual patients and groups concerned with medical care. Through encompassing divergent viewpoints, the essays and primary documents were selected to encourage humane practices and deepen understanding of the multiple traditions that shaped and do shape the development of medicine. (shrink)

One puzzling feature of talk about properties, propositions and natural numbers is that statements that are explicitly about them can be introduced apparently without change of truth conditions from statements that don't mention them at all. Thus it seems that the existence of numbers, properties and propositions can be established`from nothing'. This metaphysical puzzle is tied to a series of syntactic and semantic puzzles about the relationship between ordinary, metaphysically innocent statements and their metaphysically loaded counterparts, statements that explicitly mention (...) numbers, properties and propositions, but nonetheless appear to be equivalent to the former. I argue that the standard solutions to the metaphysical puzzles make a mistaken assumption about the semantics of the loaded counterparts. Instead I propose a solution to the syntactic and semantic puzzles, and argue that this solution also gives us a new solution to the metaphysical puzzle. I argue that instead of containing more semantically singular terms that aim to refer to extra entities, the loaded counterparts are focus constructions. Their syntactic structure is in the service of presenting information with a focus, but not to refer to new entities. This will allow us to spell out Frege's metaphor of content carving. (shrink)

We study Lebesgue and Atsuji spaces within subsystems of second order arithmetic. The former spaces are those such that every open covering has a Lebesgue number, while the latter are those such that every continuous function defined on them is uniformly continuous. The main results we obtain are the following: the statement “every compact space is Lebesgue” is equivalent to $\hbox{\sf WKL}_0$ ; the statements “every perfect Lebesgue space is compact” and “every perfect Atsuji space is compact” are (...) equivalent to $\hbox{\sf ACA}_0$ ; the statement “every Lebesgue space is Atsuji” is provable in $\hbox{\sf RCA}_0$ ; the statement “every Atsuji space is Lebesgue” is provable in $\hbox{\sf ACA}_0$ . We also prove that the statement “the distance from a closed set is a continuous function” is equivalent to $\Pi^1_1\hbox{-\sf CA}_0$. (shrink)

To any metric space it is possible to associate the cardinal invariant corresponding to the least number of rectifiable curves in the space whose union is not meagre. It is shown that this invariant can vary with the metric space considered, even when restricted to the class of convex subspaces of separable Banach spaces. As a corollary it is obtained that it is consistent with set theory that any set of reals of size ℵ 1 is meagre yet there (...) are ℵ 1 rectifiable curves in R 3 whose union is not meagre. The consistency of this statement when the phrase "rectifiable curves" is replaced by "straight lines" remains open. (shrink)

This is a dialogue in which five characters are involved. Various issues in the philosophy of mathematics are discussed. Among those issues are these: numbers as abstract objects, our knowledge of numbers as abstract objects, a proof as showing a mathematical statement to be true as opposed to the statement being true in virtue of having a proof.

In this article, we give a summary of Leonhard Euler’s work on the pentagonal number theorem. First we discuss related work of earlier authors and Euler himself. We then review Euler’s correspondence, papers and notebook entries about the pentagonal number theorem and its applications to divisor sums and integer partitions. In particular, we work out the details of an unpublished proof of the pentagonal number theorem from Euler’s notebooks. As we follow Euler’s discovery and proofs of the (...) pentagonal number theorem, we pay attention to Euler’s ideas about when we can consider a mathematical statement to be true. Finally, we discuss related results in the theory of analytic functions. (shrink)

On September 6, 2004, using the Isabelle proof assistant, I verified the following statement: (%x. pi x * ln (real x) / (real x)) ----> 1 The system thereby confirmed that the prime number theorem is a consequence of the axioms of higher-order logic together with an axiom asserting the existence of an infinite set. All told, our number theory session, including the proof of the prime number theorem and supporting libraries, constitutes 673 pages of proof (...) scripts, or roughly 30,000 lines. This count includes about 65 pages of elementary number theory that we had at the outset, developed by Larry Paulson and others; also about 50 pages devoted to a proof of the law of quadratic reciprocity and properties of Euler’s ϕ function, neither of which are used in the proof of the prime number theorem. The page count does not include the basic HOL library, or properties of the real numbers that we obtained from the HOL-Complex library. (shrink)

Statements about the behavior of biochemical entities (e.g., about the interaction between two proteins) abound in the literature on molecular biology and are increasingly becoming the targets of information extraction and text mining techniques. We show that an accurate analysis of the semantics of such statements reveals a number of ambiguities that have to be taken into account in the practice of biomedical ontology engineering: Such statements can not only be understood as event reporting statements, but also as ascriptions (...) of dispositions or tendencies that may or may not refer to collectives of interacting molecules or even to collectives of interaction events. (shrink)

It is not obvious how one might reconcile Frege's claim that different numbers may not 'belong to the same thing' with his apparent identification of one pair with two boots, even if one grants his view of 'statements of number'. I suggest a way. It requires some revision of the semantic theory that is generally attributed to Frege.

It’s sometimes suggested that we can (in a sense) settle the truth-value of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in Clarke-Doane (2020b) and a series of recent APA presentations, Clarke-Doane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the model-theoretic representability of languages like ours) we (...) can’t know ourselves to have any such freedom. (shrink)

It was shown by Frege that four of the five axioms of Peano can be regarded as analytical truths; and it was shown by Russell that the remaining axiom cannot be regarded as being analytically true or even as being analytically false, that this axiom thus is to be regarded as a synthetic statement. In using the concept of apriority in the sense of Reichenbach, it can be shown that this synthetic axiom is to be regarded as an apriorical (...) truth within the usual background theory of measuring theories, which are used not as generalizations of empirical results but as— not moreover provable— preconditions of receiving measuring results and of ordering these results. Furthermore, the systems of numbers, starting with the natural numbers, are developed in a way such that the pre-rational numbers— but not the rational ones— turn out to be those ones which are used in performing measurements according to such theories, while the pre-real numbers— but not the real ones— then turn out to be those ones which are used in using such measuring theories together with their background theories for purely theoretical reasons. (shrink)

Within the context of global debates about safety and ethics of supporting women to give birth at home, it is important to analyse documents governing midwifery and obstetric practice and influence decision‐making around place of birth. In Australia, the United States and the United Kingdom, relatively small numbers of women choose to give birth at home despite their midwifery colleges' support. In the United States and Australia, the obstetric colleges do not support homebirth and these countries have lower numbers of (...) women who birth at home, compared with the United Kingdom. There are numerous regulatory and industry challenges for midwives attending homebirths. This paper reports on a Foucauldian analysis of Australian obstetric and midwifery colleges' position statements about homebirth, who have conflicting views, with the view to understanding their arguments and underlying assumptions. The documents highlighted tensions between competing discourses of risk and autonomy and differences in academic argument. Opportunities for strengthening their statements are highlighted. The methodology is applicable for future analysis of similar documents governing practice in other countries. (shrink)

The authorship criteria of the International Committee of Medical Journal Editors (ICMJE) are widely accepted in biomedical journals, but many studies in large and prestigious journals show that a considerable proportion of authors do not fulfill these criteria. We investigated authorship contributions in a small medical journal outside the scientific mainstream, to see if poor adherence to authorship criteria is common in biomedical journals. We analyzed statements on research contribution, as checked by the corresponding author, for individual authors of 114 (...) research articles, representing 475 authors, submitted to the Croatian Medical Journal (CMJ) from 1999 to 2000. Only 40% of authors fulfilled the ICMJE authorship criteria. The authors listed first on the by-line were more likely to fulfill the authorship criteria than all other authors on the by-line. The percentage of authors fulfilling the ICMJE criteria of authorship decreased with the increase in the number of authors listed on the by-line. These results indicate that poor adherence to ICMJE authorship criteria is poor across biomedical journals, regardless of the size of the scientific community. Authorship and contributorship in biomedical journals, as well as editorial ethical responsibilities towards authorship criteria need critical redefinition and education of both editors and authors. (shrink)

The traditional recognition method of whitewash behavior of accounting statements needs to analyze a large number of special data samples. The learning rate of the algorithm is low, resulting in low recognition accuracy. To solve the aforementioned problems, this article proposes a method to identify the whitewash behavior of university accounting statements based on the FCM clustering algorithm. This article analyzes the motivation of university accounting statement whitewashing behavior, studies the common means of statement whitewashing, and establishes (...) a fuzzy set for the identification of university accounting statement whitewashing behavior. By calculating the fuzzy partition coefficient, the membership matrix of whitewash behavior recognition is established, and the whitewash behavior is classified through the iteration of the FCM algorithm. The comparative experimental results show that the recognition method has good recognition performance, low recognition error rate, and recognition accuracy of 82%. (shrink)

Statements about the behavior of biological entities, e.g. about the interaction between two proteins, abound in the literature on molecular biology and are increasingly becoming the targets of information extraction and text mining techniques. We show that an accurate analysis of the semantics of such statements reveals a number of ambiguities that is necessary to take into account in the practice of biomedical ontology engineering. Several concurring formalizations are proposed. Emphasis is laid on the discussion of biological dispositions.

The main question addressed in this essay is whether quarks have been observed in any sense and, if so, what might be meant by this use of the term, observation. In the first (or introductory) section of the paper, I explain that well-known researchers are divided on the answers to these important questions. In the second section, I investigate microphysical observation in general. Here I argue that Wilson's analogy between observation by means of high-energy accelerators and observation by means of (...) microscopes is misleading, for at least three reasons. Moreover, so long as high-energy observation is accomplished by means of spark or bubble chambers, then sentences about these observations do not meet Maxwell's criterion, that observation statements are quickly decidable. I argue, however, that this criterion is not a good norm for what is observable in high-energy physics, both because it would result in our describing a great many allegedly observed particle events as unobserved or theoretical, and because it fails to distinguish the reasons why some observation statements might not be quickly decidable. Most important, Maxwell's criterion fails because, contrary to Hanson's analysis, it presupposes that seeing does not involve both seeing as and seeing that.With this background concerning what is meant by general microphysical observation, in the third section of the essay, I discuss what might be meant by a more particular type of observation, that of the quark via scattering events. I employ Feinberg's distinction concerning observation of manifest, versus existent, particles and claim that the alleged indirect observation of quarks as existent particles is really based on a retroductive inference. I explain which premise in the retroductive argument appears most open to the charge of being theoretical (in a damaging sense) and less substantiated by observation. (shrink)

When Russell argued for his ontological convictions, for instance that there are negative facts or that there are universals, he expressed himself in English. But Wittgenstein must have noticed that from the point of view of Russell's ideal language these ontological statements appear to be pseudo-propositions. He believed therefore that what these statements pretend to say, could not really be said but only shown. Carnap discovered a way out of this mutism: what in the material mode of speech of the (...) object language looks like a pseudo-proposition can be translated into a perfectly meaningful proposition in the formal mode of speech (in the metalinguistic mode of speech of the logical syntax of language). But is this ascent into the metalanguage necessary? Taking advantage of Lésniewski's logical system there exists another way outwe can expand the number of categories of our ideal language. But Leniewski's formulas raise another profound problem, the problem of semantical muteness (cf. W. G. Lycan Semantic Competence and Funny Functors Monist 64 (1979), 209–222). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 375 7he Westminster Dictionary of Christian Ethics. Edited by JAMES F. CHILDRESS and J mrn MACQUARRIE. Philadelphia: The Westminster Press, 1986. Pp. xvii + 678. $29.95. This is a second, revised edition of The Dictionary of Christian Ethics, prepared by John Macquarrie and published in 1967. This new edition follows Macquarrie's conception of a dictionary, but expands it. It includes several subject areas, basic ethical concepts, biblical (...) ethics, theological ethics, philosophical ethics, non-Cbistian ethics; psychological, 8ociological, political, and other relevant concepts; and articles on substantial issues such as war and abortion. The criterion for selection, as stated by the editor, was the importance of the topic for Christian ethical reflection. The aim was to indicate both what is agr.eed upon and what is controversial. About 40% of the entries from the first edition have been included. These are generally updated so as to include recent developments. The selection of subjects, the way in which they are treated and the list of contributors, reflect the ecumenical character of contemporary Christian ethics. The dictionary includes a host of valuable contributions. Readers who consults the work will no doubt evaluate the entries in terms of their particular purposes. This reviewer found most useful the entries which expla~ned particular basic concepts, for example Autonomy; those dealing with schools of thought, for example, Platonic Ethics, Marxist Ethics, or the contribution of particular traditions, for example, Jewish Ethics, Puritan Ethics, Official Roman Catholic Social Teaching, Eastern Orthodox Christian Ethics, and the many entries dealing with Biomedical Ethics and peace issues. 'rhere are a number of articles on topics which are most important, but for which it is often difficult to find a succinct and comprehensive treatment; such are the contributions on "Embodiment," and " Feminist Ethics." There are a number of useful entries on urg.ent contemporary questions such as Energy and Environmental Ethics. Practical questions such as the care of the aged and the ethics of counseling are also addressed. Each article has a short bibliography appended. Numerous cross-references to other relevant entries are most helpful in providing complementary information. There is a thorough index of names. The dictionary is not conceived as a compendium of the accepted or " official " ethical teachings of churches or religious traditions. Mention could be made, however, of the entry on " Official Roman Catholic Social Teaching." '¥here such teachings exist, they am usually indicated. There are some cases where the churches and/or traditions clearly differ. The approach which is most helpful to ethical debate is to acknowledge such differences clearly, with an appropriate statement of the relevant teaching. The editor himself (James F. Childress), in his own contributions, fol- 376 BOOK REVIEWS lows this p1'0cedure. Some Roman Catholic readers may find the articles on Abortion and Contraception, while excellent in other ways, less satisfactory in this respect. The general focus seems intended to be " middle of the road "; more conservative or radical groups may find their views insufficiently represented. No doubt some of the positions presented would be disputed by Christian ethicists. But the treatment of difficult points is balanced and fair. There are, unfortunately, some inaccuracies. The following examples deserve mention. In the article on Nullity, the Roman Catholic annulment is wrongly equated with papal dissolution of the marriage bond. In the article on Virtue, it is said that St. Thomas held that along with the infused supernatural virtues there are "infused natural virtues." St. Thomas spoke ratht>r of infused theological virtues and infused moral virtues (I. II, Q.63, 3.) In the article on deterrence, it is stated that the strategy of "mutual assured destruction ", dating from the 1960s, still provides the framework of American deterrence strategy. This point would be challenged by some representat.ives of the military, who claim that M.A.D. has not been policy for some years. The same article interprets the U.S. Bishops' Pastoral Letter, The Challenge of Peace. as basing its (conditional) acceptance of nuclear deterrence on the distinction between threatening to do an immoral aet without intending to do it, and threat coupled with the intent. That is, deterrence is aceepted as a "bluff." This is not a correct reading... (shrink)

The notion of life is here presented as a major theme which permeates all of Spinoza’s writings, from the earliest work to the mature statement of his philosophy in the Ethics. Some of the implications of this concept are here outlined, and a number of possible objections to my dynamic interpretation of the concept of life are also explicitated and answered. This artide is a translation of the essay, “Sur une idée directrice de la philosophie de Spinoza,” from (...) Sylvain Zac, Etudes spinozistes, ©1985, Librairie Philosophique J. Vrin. (shrink)

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...) problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians. (shrink)

Allegations of bias against senior judges have not been common in English courts, so the House of Lords had little material to draw on when the Pinochet case was decided. It is therefore worthwhile to compare their Lordships» approach with that of the Federal Constitutional Court in Germany. This court has been selected because: (a) it has a comparable number of judges to the House of Lords and its decisions are unappealable, and (b) its cases have a constitutional and (...) (often) political content—as did the Pinochet case. The Federal Constitutional Court case law is comparatively prolific, so this study has been limited to the last 15 years. The case law covers a wide variety of issues, for example provision of legal opinions or representation, membership of associations, holding of public offices, public statements of opinion. If the standards set in this case law were applied to Lord Hoffmann's position in the Pinochet case, there are grounds for saying that he might not have been excluded. (shrink)

If there are vague numbers, it would be easier to use numbers as semantic values in a treatment of vagueness while avoiding precise cut-off points. When we assign a particular statement a range of values (less than 1 and greater than 0) there is no precise sharp cut-off point that locates the greatest lower bound or the least upper bound of the interval, I should like to say. Is this possible? “Vague Numbers” stands for awareness of the problem. I (...) do not present a serious theory of vague numbers. I sketch some reasons for using a many-value semantics. These reasons refer to my earlier treatments of determinacy and definitions of higher-order borderline cases. I also sketch how definitions of independence use the determinacy operator. The distinction between actually assigned values and values whose assignments are acceptable helps avoid unwanted precise cut-off points. (shrink)

This paper reports on the findings of the third in a series of surveys of large U.S.-based and multinational corporations on their ethics statements. Focusing on four types – values statement, corporate credo, code of ethics and Internet privacy policy – we find growth in the use of these statements over the last decade. We discuss the external communication of these statements, including the avenues that are now used for promotion and their intended audiences. The paper concludes with a (...) number of research issues to be addressed. (shrink)

This lecture, given at Beijing University in 1984, presents a remarkable (previously unpublished) proof of the Gödel Incompleteness Theorem due to Kripke. Today we know purely algebraic techniques that can be used to give direct proofs of the existence of nonstandard models in a style with which ordinary mathematicians feel perfectly comfortable--techniques that do not even require knowledge of the Completeness Theorem or even require that logic itself be axiomatized. Kripke used these techniques to establish incompleteness by means that could, (...) in principle, have been understood by nineteenth-century mathematicians. The proof exhibits a statement of number theory--one which is not at all "self referring"--and constructs two models, in one of which it is true and in the other of which it is false, thereby establishing "undecidability" (independence). (shrink)

The adoption of codes of ethics or values statements is intended to guide everyday decisions, as well as to influence the perceptions of external stakeholders. Questions have emerged in the literature about whether the effort to substantively direct decision-making in an organization is marginalized by the more obvious symbolic role of values statements. Here the perceived impact of values statements on decision-making in organizations is explored, and a number of positive effects observed. Respondents report that values statements create positive (...) externalities providing guidelines for decision-making, increasing accountability, and clarifying expectations. Yet, both cynicism and perceived management hypocrisy emerged in the survey, which together had strong negative effects on the perceived decision-making impact of values statements. Finally, positive external effects are almost never mentioned by respondents who give their firms high marks on the quality of values statement development, training, and implementation. Yet, such external effects get significantly greater representation in the comments of respondents who report less substance in their firms’ values statement development and implementation processes. In all, the results suggest that the substantive and symbolic roles of values statements are not independent and that external symbolism without internal legitimacy may in the long-run be problematic. (shrink)

Frege proposed that sentences like ‘The number of planets is eight’ be analysed as identity statements in which the number words refer to numbers. Recently, Friederike Moltmann argued that, pace Frege, such sentences be analysed as so-called specificational sentences in which the number words have the same non-referring semantic function as the number word ‘eight’ in ‘There are eight planets’. The aim of this paper is two-fold. First, I argue that Moltmann fails to show that such (...) sentences should be analysed as specificational sentences. Second, I show that even if they are to be analysed in this way, Moltmann’s proposed specificational analysis is unsatisfactory. (shrink)

According to the standard view, alethic (or modal) statements are intensional in that the Principle of Substitution (PS) fails for them -- e.g. substituting 'nine' in "Necessarily, nine is composite" with the co-referring 'the number of planets' turns this statement from true to false. It is argued in the paper that we could avoid ascribing intensionality to alethic statements altogether by separating between singular and functional uses of definite descriptions: on the singular use the description given above amounts (...) to 'the actual number of planets', which is salva veritate substitutable to 'nine' in all alethic statements; on the functional use, in turn, that description is really a function from possible worlds to numbers, and thus the Principle of Substitution is not violated in this case either, since such a function cannot be held to be co-referential with 'nine'. (shrink)

In one of his meetings with members of the Vienna Circle, Wittgenstein discusses Hermann Weyl’s brief conversion to intuitionism and criticizes his arguments against applying the law of the excluded middle to generalizations over the natural numbers. Like Weyl, however, Wittgenstein rejects the classical model theoretic conception of generality when it comes to infinite domains. Nonetheless, he disagrees with him about the reasons for doing so. This paper provides an account of Wittgenstein’s criticism of Weyl that is based on his (...) differing understanding of what a general statement over infinite domains consists in. This difference in their conception of generality is argued to be central to the middle Wittgenstein’s overall stance on intuitionism as well. While Weyl (and other intuitionists) reject the law of the excluded middle on grounds of constructivity, Wittgenstein argues that general statements over infinite domains do not express propositions in the first place. The origin of this position as well as its consequences for contemporary debates on generality are further assessed. (shrink)

A number of recent essays and books have asked how pragmatism, since its inception, informs questions that are central to the theory and practice of rhetoric and communication. Paul Stob’s book makes a significant contribution to that conversation, not least through a demonstration of the depth of William James’s work as a public lecturer and the ways in which James’s conception of public lecturing shaped his larger intellectual perspectives and commitments. John Dewey often gets most of the attention of (...) rhetorical scholars, largely because of several cryptic passages that Dewey penned on the importance of communication. Stob’s work offers an important corrective to those that overemphasize Dewey’s role in founding pragmatism and its relevance to rhetorical studies. His book also offers perhaps the most thorough and detailed articulation of how rhetorical considerations were constitutive features in the development of pragmatism. (shrink)