In Science without numbers Hartry Field attempted to formulate a nominalist version of Newtonian physics?one free of ontic commitment to numbers, functions or sets?sufficiently strong to have the standard platonist version as a conservative extension. However, when uses for abstract entities kept popping up like hydra heads, Field enriched his logic to avoid them. This paper reviews some of Field's attempts to deflate his ontology by inflating his logic.

This paper is a nontechnical exposition of the author's view that mathematics is a science of patterns and that mathematical objects are positions in patterns. the new elements in this paper are epistemological, i.e., first steps towards a postulational theory of the genesis of our knowledge of patterns.

Both phenomenologists and analytical philosophers of mathematics should profit from this excellent exposition and defense of Husserl's account of mathematical knowledge. Tieszen places Philosophie der Arithmetik in the context of Husserl's later phenomenological thinking and demonstrates thereby that Husserl's contributions to the philosophy of mathematics are much more important than most of us, influenced by Frege's denigrating critique of Husserl's early psychologism, had thought. He also makes a convincing case for the phenomenological approach to constructive mathematics.

In lieu of an abstract, here is a brief excerpt of the content:February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 179 THE EARLY “IRON CURTAIN” Michael D. Stevenson Schulich School of Business, York U. / Russell Research Centre, McMaster U. Toronto, on m3j 1p3 / Hamilton, on l8s 4l6, Canada [email protected] Patrick Wright. Iron Curtain: from Stage to Cold War. Oxford: Oxford U. P., 2007. Pp. xvii, 488. isbn 978-0-19-923150-8. £18.99 (hb); £12.99 (pb). In his famous Westminster (...) College address on 5 March 1946 in Fulton, Missouri, Winston Churchill Wred one of the opening salvos of the Cold War by proclaiming that from “Stettin in the Baltic to Trieste in the Adriatic an iron curtain” had been lowered across Europe. Patrick Wright’s intriguing and provocative book does not examine the phrase “iron curtain” in its popular Cold War context. Instead, he maintains that many characteristics of this metaphor, “including the pronounced sense of theatricality it would bring to international politics, were inherited from the period before the Second World War” (p. 18). Wright divides Iron Curtain into two primary chronological sections, the Wrst covering the period from 1914 to 1920. An iron curtain originally referred to the steel safety screen that descended in English theatres, beginning in the lateeighteenth century, to separate the audience from the often catastrophic Wres that broke out on the stage. The phrase entered the lexicon of international relations in January 1915 when British author and paciWst Violet Page (writing under the pseudonym Vernon Lee) published an article lamenting that “War’s cruelties and recriminations, War’s monstrous iron curtain” (p. 80) had alienated European nations such as England and Germany sharing a common cultural heritage. But the barrier quickly moved east in the aftermath of the 1917 Russian Revolution and “took the form not just of exaggerated political rhetoric, but of an economic blockade enforced by naval power” (p. 171), as the Allies sought to contain the infection of Bolshevism. Wright devotes most attention in this section to documenting the 1920 visit to Russia by the British delegation jointly sponsored by the Trades Union Congress and the Labour Party, which sought to penetrate the dense fog of Allied anti-Bolshevik propaganda and validate the delegation members’ own preconceived views about the nascent socialist utopia in Russia. British delegates witnessed images both of progress carefully stagemanaged by their hosts and of terrible economic dislocation and poverty caused by the Allied blockade and the civil war, which allowed the majority of them to return home to lavish praise on the Soviet experiment that would, in their minds, inevitably fulWl its potential once the Bolshevik government became stable. February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd 180 Reviews 1 “The Future of Europe”, European AVairsz 1, no. 1 (April 1949): 3. The second section of Wright’s book examines Western reports of life behind the iron curtain between 1920 and 1939. Here, the author focuses heavily on the theatrical nature of Soviet attempts to create modern-day Potemkin villages that werez—zwith a limited number of exceptionsz—zaccepted as reality by an endless parade of left-wing visitors. A second British Trades Union Congress delegation in 1924, for example, received a dramatically embellished picture of Soviet economic progress that included a train journey past a long-abandoned factory belching smoke created by burning wet straw frantically provided by Russian peasants; the resulting report of the delegation “repeatedly collapsed into the most abject conformity with the Soviet view of reality” (p. 245). The most tragic examples of Western visitors’ blindness to the truth occurred during the 1930s famine deliberately induced by Stalin, and Wright exposes a wide cast of characters who adopted a blinkered view of conditions in the ussr. Among intellectuals, Wright documents the 1931 visit of George Bernard Shaw, who cavalierly dismissed reports of widespread food shortages while dining sumptuously in Moscow’s Hotel Metropole. Among journalists, Wright develops the case of Walter Duranty, the New York Timesz correspondent who knuckled under to demands of Soviet censors to produce sanitized accounts denying or ignoring the famine in order to protect his privileged place in that... (shrink)

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence (...) of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology. (shrink)

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between (...) studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice. (shrink)

Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre?1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of (...) unsaturated entities. (shrink)

Institutional review board delays may hinder the successful completion of federally funded research in the U.S. military. When this happens, time-sensitive, mission-relevant questions go unanswered. Research participants face unnecessary burdens and risks if delays squeeze recruitment timelines, resulting in inadequate sample sizes for definitive analyses. More broadly, military members are exposed to untested or undertested interventions, implemented by well-intentioned leaders who bypass the research process altogether. To illustrate, we offer two case examples. We posit that IRB delays often appear (...) in the service of managing institutional risk, rather than protecting research participants. Regulators may see more risk associated with moving quickly than risk related to delay, choosing to err on the side of bureaucracy. The authors of this article, all of whom are military-funded researchers, government stakeholders, and/or human subject protection experts, offer feasible recommendations to improv... (shrink)

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between (...) studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice. (shrink)

This paper consists of commentaries about and the reprint of an autobiographical essay authored by Italian medium Eusapia Palladino and published in 1910. The details of the essay are discussed in terms of the writings of other individuals about the life and performances of the medium. The essay conveys a view of Palladino as a person who has suffered much in life and has a mission to help scientific research into mediumship. Typical of the positive emphasis in autobiographies in general, (...) the medium did not discuss negative aspects of her performances. Due to the fact that the essay appeared during Palladino's visit to New York City in which many authors branded her as a fraud, it may be speculated that the purpose of this autobiography was to elicit sympathy from the American public. While some of the statements that Palladino made about phenomena are consistent with the statements of other authors who have written about her, there are several statements that show alternate or incomplete versions of particular events in her life. The differences suggests that Palladino's essay and other discussions about the medium's life are not reliable when it comes to specific details and to biographical accuracy. (shrink)

By a logical theory I mean a formal system together with its semantics, meta-theory, and rules for translating ordinary language into its notation. Logical theories can be used descriptively (for example, to represent particular arguments or to depict the logical form of certain sentences). Here the logician uses the usual methods of empirical science to assess the correctness of his descriptions. However, the most important applications of logical theories are normative, and here, I argue, the epistemology is that of wide (...) reflective equilibrium. The result is that logic not only assesses our inferential practice but also changes it. I tie my discussion to Thagard's views concerning the relationship between psychology and logic, arguing against him that psychology has and should have only a peripheral role in normative (and most descriptive) applications of logic. (shrink)

We have seen that despite Feferman's results Gödel's second theorem vitiates the use of Hilbert-type epistemological programs and consistency proofs as a response to mathematical skepticism. Thus consistency proofs fail to have the philosophical significance often attributed to them.This does not mean that consistency proofs are of no interest to philosophers. We know that a ‘non-pathological’ consistency proof for a system S will use methods which are not available in S. When S is as strong a system as we are (...) willing to entertain seriously then a consistency proof for it will yield no epistemological gain. But in other cases philosophers might argue that the proof uses methods which are merely different rather than stronger than those available in the system in question. This claim has been made, for example, in the case of the constructive consistency proofs for elementary number theory. Similar philosophical investigations can be made on relative consistency proofs, since these differ from each other in the principles they employ. For example, most relative consistency proofs can be carried out within elementary number theory, but without using the theory of real numbers, no one has been able to prove the consistency of Quine's ML relative to that of his NF.What about the consistency of all mathematics or of some strong system for set theory? How do we answer the skeptic? Since here a convincing proof is not possible, we have established that the skeptic demands too much. We cannot be certain that our axioms are free from contradiction and must treat them as hypotheses which may be abandoned or modified in the face of further mathematical experience. This attitude is taken by many foundational workers who also go on to voice opinions about thelikelihood that various systems are consistent. Since these opinions are variously supported by appeals to the clarity of the mathematical concept formalized, the existence or non-existence of ‘weird’ models for the system and actual empirical experience with the system, this is surely a fruitful area for philosophical research. (shrink)

This paper is concerned with the genesis of mathematical knowledge. While some philosophers might argue that mathematics has no real subject matter and thus is not a body of knowledge, I will not try to dissuade them directly. I shall not attempt such a refutation because it seems clear to me that mathematicians do know such things as the Mean Value Theorem, The Fundamental Theorem of Arithmetic, Godel's Theorems, etc. Moreover, this is much more evident to me than any philosophical (...) view of mathematics I know of — including my own. So I am going to take mathematics as my starting point. (shrink)

This review essay evaluates Karl Maton's Knowledge and Knowers: Towards a Realist Sociology of Education as a recent examination of the sociological causes and effects of education in the tradition of the French social theorist Pierre Bourdieu and the British educational sociologist Basil Bernstein. Maton's book synthesizes the scholarship of Bourdieu and Bernstein and complements their work with “discoveries” from the world of systemic functional linguistics to produce a new “realist sociology of education.” It does so by means of (...) Legitimation Code Theory, defined as a “toolkit” to analyze knowledge construction in cultural fields, especially education. The authors of this review essay take a polyphonic approach in assessing this ambitious synthesis, offering four perspectives on Maton's book. Brian Barrett provides a Bernsteinian perspective; Dan Schubert approaches the book from his grounding in Bourdieu; and Susan Hood contributes a view from systemic functional linguistics. Michael Grenfell weaves these three perspectives together and provides introductory and concluding reflections. They aim, through their combined expertise, to use Maton's book as an occasion to take stock of the state of the field of sociology of education generally and to reflect on the questions: What is its nature and what type of knowledge does it express? To what uses may it be set and what is its place within the larger project of educational theory? (shrink)

We argue that Horgan's program for nominalizing science fails, because its translation of quantitative statements destroys the inferential structures of explanations, predictions and retrodictions of nonquantitative scientific facts.

Mathematical objects, if they exist at all, exist independently of our proofs, constructions and stipulations. For example, whether inaccessible cardinals exist or not, the very act of our proving or postulating that they do doesn’t make it so. This independence thesis is a central claim of mathematical realism. It is also one that many anti-realists acknowledge too. For they agree that we cannot create mathematical truths or objects, though, to be sure, they deny that mathematical objects exist at all. I (...) have defended a mathematical realism of sorts. I interpret the objects of mathematics as positions in patterns, and maintain that they exist independently of us, and our stipulations, proofs, and the like. (shrink)

Mathematical explanation is a topic of great contemporary interest in the philosophy of mathematics. The question of whether mathematics can play an explanatory role in empirical science is thought by many to be the key to making progress on the realism versus anti-realism debate in the philosophy of mathematics. Questions about explanation within mathematics are also interesting and are important for the development of a general account of explanation. In a series of groundbreaking papers from 1978 to 1983, Mark Steiner (...) set the agenda for much of the modern debate about mathematical explanation. In the present paper we look at Steiner’s role in advancing mathematical explanation as a central topic in the philosophy of mathematics and his legacy for the modern debates about mathematical explanation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Response to My ReadersMichael S. Hogue (bio)I. IntroductionI often begin writing for personal reasons: to slow my thinking, clarify and organize my thoughts, trace ideas, and sort concepts. Generally, a concern for something I consider wrong about the world motivates me to write. Provoked by such a concern, I write to understand why and how what is wrong came to be that way and why and how I (...) think it can or should be different. I write in reply to H. Richard Niebuhr's moral hermeneutic question, "What's going on?" And yet, while writing typically begins (for me) as a personal search for understanding, this search eventually leads me to (re) discover my formative communities of inquiry and interpretation. None of my questions or ideas, none of my orienting values, none of my interpretive impulses are mine alone. They do not, and cannot, exist independently of others' questions, ideas, values, and interpretations. To use Peirce's metaphor, they are slender fibers braided into a larger cable rather than independent links in a chain. The issues and questions that motivate my research; the topics I care about enough to develop into articles and books; the conceptual, critical, and normative vocabularies I bring to my research and writing; the intellectual traditions that shape the patterns of my thinking—none of these are strictly personal or individual. They have taken root and grown in me as I've learned with and from others. Writing reminds me that, as a person, I am a creature of relational processes because it shows me that my mind is not (exclusively) my own—what and how I think have been formed, animated, and limited by my experience with others in a larger world of experience that is broader and deeper than any individual mind.I open this brief essay with this comment to acknowledge my gratitude and indebtedness not only to the authors of the articles in this special issue (Walter Gulick, Robert Smid, John Teehan, and AJ Turner) but also to the larger community of scholars that comprise the readership of the American Journal of Theology and Philosophy (AJTP) and the Institute for American Religious and Philosophical Thought (IARPT). I attended my first IARPT (HIARPT, at the time) conference about seventeen years ago, soon after completing my Ph.D. I didn't know anyone personally then, but I knew several folks as authors of articles and books I had read in recent years. I discovered IARPT through the bibliography of Victor Anderson's book, Pragmatic Theology: Negotiating [End Page 80] the Intersections of an American Philosophy of Religion and Public Theology. I resonated with Anderson's articulation of a socially engaged public theology that drew from American pragmatist, historicist, and naturalist philosophies of religion. His mind had been where mine was going, into the dissenting tradition of American immanence, or the left wing of American radical theology, as I refer to it.While reading Anderson's book, I learned that many of the authors in his bibliography met every summer as a (relatively?) organized group of like-minded scholars. I joined them the next chance I had. And as things go with this group, I was immediately recruited to serve as the book review editor for the AJTP! Since that first meeting, I've attended as many IARPT meetings as my schedule allows, organized one of the summer conferences, served as AJTP book review editor for several years, and then served for several more years as the AJTP editor (following Michael Raposa's illustrious term!). Most recently, I was honored when Andrew Irvine and Austin Roberts made American Immanence a focus of the 2021 IARPT conference, "Political Thought and the Powers of Democracy: American Thought in the Anthropocene." Gulick's, Smid's, Teehan's, and Turner's articles began as papers for that conference.All this is to say what I have heard many others say through the years: the IARPT/AJTP community of interpretation has become a primary intellectual (and even spiritual) home for me. I am (and we are) fortunate to belong to a group of academic philosophers and theologians who collectively embody a rare (let us hope not... (shrink)