In the article, philosophical and methodological analysis of the program of Hilbert’s formalism as a really working direction for consideration of the bases of modern mathematics is presented. For the professional mathematicians methodological advantages of the program of formalism advanced by David Hilbert, consist primarily in the fact that the highest possible level of theoretical rigor of modern mathematical theories was practically represented there. To resolve the fundamental difficulties of the problem of bases of mathematics, according (...) to Hilbert, the theory of mathematical proof is needed, but contrary to popular belief rigorous formalization of the proof is not a synonym of reliability and rigor of mathematical reasoning from the point of view of the philosophy of the foundations of mathematics. In fact, the consistency of the theories is "more important" than their logical consistency because not every statement, which does not contradict to the reasonable ones, can be attributed to a true statement. However, for working mathematicians, Hilbert is logical and consistent and the axiomatic method and formalism are an essential part of their rules of thinking. (shrink)

One important achievement Rudolf Carnap claimed for his book, The Logical Syntax of Language, was that it effected a synthesis of two seemingly antithetical philosophies of mathematics, logicism and formalism. Reconciling these widely divergent conceptions had been a goal of Carnap’s for several years. But in the years in which Carnap’s synthesis evolved, important intellectual developments influenced the direction of his efforts and, ultimately, the final outcome. These developments were, first of all, the epoch-making theorems proved by Kurt Gödel, (...) which required the abandonment of several theses central to the aims of logicism and formalism. Of far greater significance, in the present context, are the changes in Carnap’s own philosophical outlook, brought about not only by Gödel’s theorems but concurrent discussions within the Vienna Circle as well as his own researches. Consequently, the exact sense in which Carnap attempted the synthesis of logicism and formalism in the Logical Syntax requires careful examination. In what follows below, the evolution of Carnap’s synthesis will be traced, from the first reconciliation he proposed , through the synthesis that appeared with the publication of The Logical Syntax of Language. The aim is to determine which modifications of Carnap’s synthesis were required by Gödel’s theorems, and which were motivated by changes in his own thinking. Although the characteristic theses of both logicism and formalism required profound modifications because of Gödel’s theorems, the philosophical impulses that originally fueled their programs retained much of their former virulence. But the changes in Carnap’s thought that ocurred in the years he was developing his synthesis especially affected his appreciation of the philosophical motivations underwriting the logicist approach, so that much of the philosophical insight that inspired it is lost, and Carnap’s combination of logicism and formalism is a putative synthesis at best. (shrink)

Due to its considerable length, this article is being published in two parts. This first part briefly discusses the intriguing relationship between John Dewey and Albert Barnes, as well as the circumstances behind the creation of the Barnes Foundation and its innovative art-education programs. This is followed by examination of the prominent roles of aesthetic formalism and organic unity in Barnes's writings about the arts and their less technical, more contextual positioning in Dewey's aesthetics. To end Part 1 of (...) the article, a similar dynamic is revealed in Barnes's and Dewey's ultimately disparate understandings of the relationship between form and content in the arts.In its heyday during the first part of the... (shrink)

Due to its considerable length, this article has been published in two parts. Part 1, which appeared in the previous issue of the journal, discussed the intriguing relationship between John Dewey and Albert Barnes, as well as the circumstances behind the creation of the Barnes Foundation and its art education programs. Following this, it established both areas of convergence and divergence in Barnes’s and Dewey’s understandings of aesthetic formalism, organic unity, and form and content in the arts. Part 2 (...) now builds on these findings to explore important differences in their respective treatments of the significant sociocultural context of art. After returning briefly to the question of aesthetic formalism in... (shrink)

This article is concerned with the development of philosophy of science in the 1970s. The explanatory framework is the picture of two fundamental split-offs: the controversial establishment of history and sociology of science and of formal philosophy of science as independent disciplines, against the background of more traditional “conceptual” varieties of philosophy of science. I illustrate these developments, which finally led to somewhat “purified” versions of the respective accounts, by examining a case study, namely, that of the structuralist school, which (...) emerged in the 1970s as an attempt to reconcile historical and formal approaches in philosophy of science. I try to explain the failure of this initial program of “Kuhn Sneedified” and its transition to a more purified formalist version, on the basis of the fact that the former attempt was caught somewhere amid the purism of conceptual, historical, and formal accounts of philosophy of science. (shrink)

Our program is ambitious, as is any attempt to match life (in our case real science) with virtue (e.g., exactness). We want our semantics to be not only simia mathematicae but also ancilla scientiae: built more geometrico and at the same time relevant, nay useful, to live science. The goal of exactness may sound arrogant but is actually modest, for the more we rigorize the more we are forced to leave out of consideration, at least for the time being. (...) As to the service intention: we should try to be of some help to science because the latter faces semantic problems but has no tools of its own for solving them. If it had such tools scientists would not engage in spirited polemics over matters of sense and reference, as they often do. Witness the debates on whether the relativistic and quantum theories are concerned with sentient observers, whether population genetics refers to populations taken as wholes, whether psychology is actually concerned with the brain, and whether the sense of a theory is excreted by its mathematical formalism or is determined by the way the theory is tested.A semantics of science should help settle these and similar issues. Moreover it should give sound advice as to how to formulate scientific theories so as to avoid such imprecisions and ambiguities as may give rise to debates of the kind. Constructing such a semantics, both exact and relevant to science, should be more rewarding than either manufacturing neat but irrelevant theories or pursuing erratic polemics on meaning and meaning changes. Research supported by a Killam grant awarded by the Canada Council. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Guide to Personal Knowledge: The Philosophy of Michael Polanyi: Tacit Knowledge, Emergence and the Fiduciary Program by Dániel Paksi and Mihály HéderAlessio TartaroPAKSI, Dániel and Mihály Héder. Guide to Personal Knowledge: The Philosophy of Michael Polanyi: Tacit Knowledge, Emergence and the Fiduciary Program. Wilmington, Del.: Vernon Press, 2022. xxiii + 209 pp. Cloth, $65.00Famous for the concept of "tacit knowledge," Polanyi is a figure who looms (...) over twentieth-century philosophy without ever establishing himself as one of its major protagonists. Yet, Polanyi tackled central problems in twentieth-century Western philosophy and offered [End Page 358] insightful and original analyses thereof. In Personal Knowledge, Polanyi articulates ideas about metaphysics, mathematics, evolution, philosophy and sociology of science, epistemology, philosophy of language, political theory, theology, and more. The richness of the contents, but also their deep unity, make Polanyi's work a unique piece in the philosophical landscape of his time, full of fruitful insights that are still relevant nowadays.Guide to Personal Knowledge, written by two of the leading experts on Polanyi's philosophy, deserves the merit of providing an accessible introduction to this complex work. The book is divided into thirteen chapters, each corresponding to the respective chapter of Personal Knowledge. In each chapter, Paksi and Héder clearly explain Polanyi's main ideas, presenting them in the same order as they appear in Personal Knowledge. The chapters are introduced by a "Goals of the chapter" section that provides a series of key points, where the authors summarize Polanyi's objectives in the corresponding chapter of Personal Knowledge.The Guide is interspersed with many direct quotations from Personal Knowledge that allow the reader to link the Guide to the original text. The use of figures and tables illuminates even the most complex concepts, such as "tacit integration" and the difference between "random and ordered systems." The Guide is enriched by twenty-five boxes that provide information on ideas, authors, and concepts directly or indirectly referenced by Polanyi in Personal Knowledge. These boxes are a valuable supplement. In some cases, they offer insight into contemporary events, theories, and scholars to which Polanyi alludes but that he does not elaborate on, for example, about the role of the Michelson-Morley experiments in Einstein's development of the theory of relativity. In other cases, boxes develop a comparison between Polanyi's ideas and related philosophical figures, such as Thomas Kuhn and Samuel Alexander. Thanks to the boxes, the reader gains a richer and more complete view of Polanyi's thought.In the preface, Paksi and Héder preliminarily introduce some key concepts for understanding Polanyi's work, including "objectivity," "trust" and "fiduciary program," "tacit knowledge," "intellectual passions," "deceptive substitution," "moral inversion," "operational principles," "logic of achievement," and "emergence." Their analysis always proves faithful to Polanyi's thought, and the authors show how these concepts are interrelated and constitute the pillars of Personal Knowledge's argumentative structure. Other equally crucial concepts in Polanyi's work, for example, "commitment," "indwelling," "tradition," "conviviality," "anthropogenesis," "ultrabiology," are not introduced in the preface, but they are explored in depth in the respective chapters.The thirteen chapters of the book recapitulate in detail the main thematic segments of Personal Knowledge. The critique of objectivism and positivist views of science is explained and analyzed in chapters 1 to 4. This critique is articulated on several levels. Polanyi first criticizes [End Page 359] objectivism because it attempts to remove the personal element from scientific knowledge in order to pursue ever higher degrees of formalism, neutrality, and impersonality. Polanyi asserts, however, that the personal element is irreducible, and then proceeds to demonstrate how it operates: in the evaluation of probability statements (chapter 2), in the appreciation of ordered patterns (chapter 3), and in the practice of skills (chapter 4). The ineliminability of the personal element shows that objectivism is false. Paksi and Héder brilliantly retrace the train of thought that leads Polanyi to this conclusion.The second theme that runs across Personal Knowledge concerns the tacit foundation of human intellectual abilities and, consequently, of science and society. In chapter 6, the authors follow Polanyi's disparate arguments about animal intelligence, human... (shrink)

In his article The Foundations of Mathematics (1925) Ramsey was concerned with the nature of the statements of 'pure mathematics' and the way these statements differ from those in empirical sciences. He thought that the answer given to these questions by Hilbert and the formalist school according to which mathematical statements are meaningless formulas, is unsatisfactory for several reasons, which will not be discussed here. He also expressed serious doubts about the intuitionist program developed by Brouwer and Weyl. It (...) is the logicist school of Frege, Russell and Whitehead, which attempted to reduce mathematics to few logical concepts, that came closest to Ramsey’s views, although he was not completely satisfied with it, either. (shrink)

In recent years, the practices of work organizations have raised increasing concerns regarding individual privacy at work. It is clear that people expect and value privacy in their personal lives. However, the extent to which privacy perceptions influence individuals’ work attitudes is less clear. Research has explored the extent to which employee perceptions of privacy derive from characteristics of the programs themselves. However, there is a paucity of research that examines how the characteristics of the individual employee may influence perceptions (...) of these programs. In this study we seek to shed light on this issue, as we examine how the individual ethical orientation of employees influences perceptions of a variety of human resource programs that have the potential to be perceived as invasive. Results indicate that ethical orientation exerts direct effects on perceived invasiveness of programs and exerts both direct and indirect effects on perceived appropriateness of programs. Implications for research and for managers adopting privacy-related programs are discussed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Art of Interpreting Art PAUL BAROLSKY “The quality of the prose is just as important in nonfiction as in fiction.” —Robert Caro If as Horace famously wrote in the Ars poetica the aim of poetry is to instruct and delight, why shouldn’t the goal of all writing be the same? Why should all readers not enjoy as well as learn from what they read? In the realm of (...) academe, however, although much writing instructs, far too little delights. This is so because the goal of academic writing is primarily that of conveying information and knowledge or of developing new ideas. Delight or pleasure are not of primary academic concern. Too few scholars care sufficiently about how they write. Too many academics write in unreadable prose. Often their writing is ponderous, indeed pompous, because they are insecure in the face of theoretical, philosophical or scientific writing. The outcome can be quite hideous. Sometimes, dare I say often, their writing is dreadfully dry and dull. In the Humanities, the arts, by which I mean those that have been called the spatial arts, that is, architecture, sculpture, and painting, can be studied from a wide variety of perspectives. As some observers have noted, however, frequently in the academic study of art and its history, art as such recedes from view and drops out of the discussion. Art becomes primarily the illustration of something else, something other than itself. It comes to be the illustration of the global, colonial, sexual, political, theological, social, economic, religious, anthropological, philosophical, technological, scientific, or theoretical. It is too often not sufficiently appreciated for its own sake as art. Do I sound as if I am writing about the much-scorned notion of “art for art’s sake?” Yes, but not exactly. Since the arion 28.1 spring/summer 2020 102 the art of interpreting art nineteenth century, when Gautier wrote, l’art pour l’art meant just that, the celebration of art for its own sake. Eventually, however, that notion came to be disparaged as too limited, since it supposedly failed to address the various kinds of associations between art and the other phenomena listed above. The notion of art for its own sake unfortunately came to be seen as a manifestation of aestheticism or formalism— both often regrettably terms of opprobrium. Not long ago a graduate teaching fellow in a prestigious art history program had her students read my essay on the role of writing about art which was published in the spring/ summer 2018 issue of this journal. The first part of that essay concerned atrocious writing, which, our teaching fellow said, made her students laugh—yes, laugh! They presumably laughed because the prose of scholars was so very bad—ridiculous in the root sense of the word, laughable. One example of pompous diction that I have cited often because it is so laughably absurd, is the definition one art historical scholar has given of sex as “inter-corporeal relationality.” No wonder the students laughed! With considerable amusement, the graduate teaching fellow to whom I have just referred told me that she rather doubted her students bothered to read the second part of the essay she assigned, even though it included some exemplary writing about art. Why should they have bothered to read examples of excellent writing? After all, their teachers, who too often do not themselves write well, do not encourage students to think sufficiently about their prose. Let me add to the cluster of grotesque writing illustrated in the Arion article to which I have referred one more example of how bad academic writing about art can be in order to remind the reader of the kind of absurd nonsense or blather that one encounters throughout the Humanities. It comes from a highly esteemed author who “describes influence as a notion which provides a support—of too magical a kind to be very amenable to analysis—for the facts of transmission and com- Paul Barolsky 103 munication; which refers to an apparently causal process (but with neither rigorous delineation nor theoretical definition) the phenomena of resemblance or repetition; which links, at a distance and through time—as if through the mediation of... (shrink)

It has often been remarked that Bohr's writings on the interpretation of quantum mechanics make scant reference to the mathematical formalism of quantum theory; and it has not infrequently been suggested that this is another symptom of the general vagueness, obscurity and perhaps even incoherence of Bohr's ideas. Recent years have seen a reappreciation of Bohr, however. In this article we broadly follow this "rehabilitation program". We offer what we think is a simple and coherent reading of Bohr's (...) statements about the interpretation of quantum mechanics, basing ourselves on primary sources and making use of and filling lacunas in|recent secondary literature. We argue that Bohr's views on quantum mechanics are more firmly connected to the structure of the quantum formalism than usually acknowledged, even though Bohr's explicit use of this formalism remains on a rather global and qualitative level. In our reading, Bohr's pronouncements on the meaning of quantum mechanics should first of all be seen as responses to concrete physical problems, rather than as expressions of a preconceived philosophical doctrine. In our final section we attempt a more detailed comparison with the formalism and conclude that Bohr's interpretation is not far removed from present-day non-collapse interpretations of quantum mechanics. (shrink)

John Searle’s Chinese room argument is a celebrated thought experiment designed to refute the hypothesis, popular among artificial intelligence scientists and philosophers of mind, that “the appropriately programmed computer really is a mind”. Since its publication in 1980, the CRA has evoked an enormous amount of debate about its implications for machine intelligence, the functionalist philosophy of mind, theories of consciousness, etc. Although the general consensus among commentators is that the CRA is flawed, and not withstanding the popularity of the (...) systems reply in some quarters, there is remarkably little agreement on exactly how and why it is flawed. A newcomer to the controversy could be forgiven for thinking that the bewildering collection of diverse replies to Searle betrays a tendency to unprincipled, ad hoc argumentation and, thereby, a weakness in the opposition’s case. In this paper, treating the CRA as a prototypical example of a ‘destructive’ thought experiment, I attempt to set it in a logical framework, which allows us to systematise and classify the various objections. Since thought experiments are always posed in narrative form, formal logic by itself cannot fully capture the controversy. On the contrary, much also hinges on how one translates between the informal everyday language in which the CRA was initially framed and formal logic and, in particular, on the specific conception of possibility that one reads into the logical formalism. (shrink)

This paper reconstructs the history of the introduction and use of iterative algorithms in conservation biology in the 1980s and early 1990s in order to prioritize areas for protection as nature reserves. The importance of these algorithms was that they led to greater economy in spatial extent (“efficiency”) in the selection of areas to represent biological features adequately (that is, to a specified level) compared to older methods of scoring and ranking areas using criteria such as biotic “richness” (the number (...) of features of interest). The development of these algorithms was critical to producing a research program for conservation biology that was distinct from ecology and eventually led to what came to be called systematic conservation planning. Very similar algorithmic approaches were introduced independently in the 1980–1990 period in Australia, South Africa, and (arguably) the United Kingdom. The key rules in these algorithms were the use of rarity and what came to be called complementarity (the number of new or under-represented features in an area relative to those that had already been selected). Because these algorithms were heuristic, they were not guaranteed to produce optimal (most “efficient”) solutions. However, complementarity came to be seen as a principle rather than a rule in an algorithm and its use was also advocated for the former reason. Optimal solutions could be produced by reformulating the reserve selection problem in a mathematical programming formalism and using exact algorithms developed in that context. A dispute over the relevance of full optimality arose and was never resolved. Moreover, exact algorithms could not easily incorporate criteria determining the spatial configuration of networks of selected areas, in contrast to heuristic algorithms. Meanwhile metaheuristic algorithms emerged in the 1990s and came to be seen as a credible more effective alternative to the heuristic algorithms. Ultimately what was important about these developments was that the reserve selection problem came to be viewed a complex optimal decision problem under uncertainty, resource, and other constraints. It was a type of problem that had no antecedent in traditional ecology. (shrink)

As is well known, the late Husserl warned against the dangers of reifying and objectifying the mathematical models that operate at the heart of our physical theories. Although Husserl’s worries were mainly directed at Galilean physics, the first aim of our paper is to show that many of his critical arguments are no less relevant today. By addressing the formalism and current interpretations of quantum theory, we illustrate how topics surrounding the mathematization of nature come to the fore naturally. (...) Our second aim is to consider the program of reconstructing quantum theory, a program that currently enjoys popularity in the field of quantum foundations. We will conclude by arguing that, seen from this vantage point, certain insights delivered by phenomenology and quantum theory regarding perspectivity are remarkably concordant. Our overall hope with this paper is to show that there is much room for mutual learning between phenomenology and modern physics. (shrink)

In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of that sentence. To do so, we exploited the perfect structural match of grammar and categories of meaning spaces. Here, we give a mathematical foundation, referred to as DisCoCirc, for how sentences interact in texts in order to produce the meaning of that text. First we revisit DisCoCat. While in DisCoCat all meanings are fixed as (...) states, in DisCoCirc word meanings correspond to a type, or system, and the states of this system can evolve. Sentences are gates within a circuit which update the variable meanings of those words. Like in DisCoCat, word meanings can live in a variety of spaces e.g. propositional, vectorial, or cognitive. The compositional structure are string diagrams representing information flows, and an entire text yields a single string diagram in which word meanings lift to the meaning of the entire text. While the developments in this paper are independent of a physical embodiment, both the compositional formalism and suggested meaning model are highly quantum-inspired, and implementation on a quantum computer would come with a range of benefits. We also praise Jim Lambek for his role in mathematical linguistics in general, and the development of the DisCo program more specifically. (shrink)

The development of effective means to enhance research integrity by universities requires baseline measures of individual, programmatic, and institutional factors known to contribute to ethical decision making and behavior. In the present study, master’s thesis and Ph.D. students in the fields of biological, health and social sciences at a research extensive university completed a field appropriate measure of research ethical decision making and rated the seriousness of the research issue and importance for implementing the selection response. In addition they were (...) asked to rate their perceptions of the institutional and departmental research climate and to complete a measure of utilitarian and formalistic predisposition. Female students were found to be more ethical in their decision making compared to male students. The research ethical decision measure was found to be related to participants’ ethical predisposition and overall perception of organizational and departmental research climate; however, formalism was the only individual predictor to reach statistical significance and none of the individual subscales of the research climate measure were significantly correlated to ethicality. Participants’ ratings of the seriousness of the issue were correlated with their ratings of the importance of carrying out their selected response but neither was significantly predictive of the ethicality of their responses. The implications of these findings for the development of more effective training programs and environments for graduate students in research ethics and integrity are discussed. (shrink)

Reconstructions of quantum theory are a novel research program in theoretical physics which aims to uncover the unique physical features of quantum theory via axiomatization. I focus on Hardy’s “Quantum Theory from Five Reasonable Axioms” (2001), arguing that reconstructions represent a modern usage of axiomatization with significant points of continuity to von Neumann’s axiomatizations in quantum mechanics. In particular, I show that Hardy and von Neumann share similar methodological ordering, have a common operational framing, and insist on the empirical (...) basis of axioms. In the reconstruction programme, interesting points of discontinuity with historical axiomatizations include the stipulation of a generalized space of theories represented by a framework and the stipulation of analytic machinery at two levels of generality (first by establishing a generalized mathematical framework and then by positing specific formulations of axioms). In light of the reconstruction programme, I show that we should understand axiomatization attempts as being context–dependent, context which is contingent upon the goals of inquiry and the maturity of both mathematical formalism and theoretical underpinnings within the area of inquiry. Drawing on Mitsch (2022)’s account of axiomatization, I conclude that reconstructions should best be understood as provisional, practical, representations of quantum theory that are well suited for theory development and exploration. However, I propose my context–dependent re–framing of axiomatization as a means of enriching Mitsch’s account. (shrink)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts (...) Frege’s claim that his own view is completely different from Hankel’s formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

There are two reasons for asking such an apparently unanswerable question. First, Max Born's recollections of what Minkowski had told him about his research on the physical meaning of the Lorentz transformations and the fact that Minkowski had created the full-blown four-dimensional mathematical formalism of spacetime physics before the end of 1907, both indicate that Minkowski might have arrived at the notion of spacetime independently of Poincare and at a deeper understanding of the basic ideas of special relativity independently (...) of Einstein. So, had he lived longer, Minkowski might have employed successfully his program of regarding four-dimensional physics as spacetime geometry to gravitation as well. Moreover, Hilbert had derived the equations of general relativity simultaneously with Einstein. Second, even if Einstein had arrived at what is today called Einstein's general relativity before Minkowski, Minkowski would have certainly reformulated it in terms of his program of geometrizing physics and might have represented gravitation fully as the manifestation of the non-Euclidean geometry of spacetime exactly like he reformulated Einstein's special relativity in terms of spacetime. [NOTE: The text of two explanations was taken from my previous paper "Is Gravitation Interaction or just Curved-Spacetime Geometry?" because those explanations had to be repeated in the present paper anyway.]. (shrink)

Since the late nineties there has been an increased interested in probabilistic logic learning, an area within AI that combines machine learning with logic-based knowledge representation and uncertainty reasoning. Several different formalisms for combining first-order logic with probability reasoning have been proposed, and it has been studied how models in these formalisms can be automatically learned from data. -/- This talk starts with a brief introduction to probabilistic logic learning, after which we will focus on a relatively new formalism (...) known as CP-logic. CP-logic stands for “causal probabilistic logic”. It is a knowledge representation formalism that allows us to write down rules that indicate that a certain combination of conditions may cause certain effects with a particular probability (e.g., tossing a coin may cause a result of heads or tails, each with 50% probability). Besides the fact that this formalism is interesting for knowledge representation in itself, it also offers interesting opportunities from the machine learning point of view. Indeed, given the semantics of these CP-logic programs, learning them from data amounts to extracting probabilistic causal influences from data. We will discuss recent research on learning CP-logic programs, including: algorithms for learning them; how they relate to graphical models; and applications of learning CP-logic programs. (shrink)

Doctoral programs at U.S. universities play a critical role in the development of human resources both in the United States and abroad. This volume reports the results of an extensive study of U.S. research-doctorate programs in five broad fields: physical sciences and mathematics, engineering, social and behavioral sciences, biological sciences, and the humanities. Research-Doctorate Programs in the United States documents changes that have taken place in the size, structure, and quality of doctoral education since the widely used 1982 editions. This (...) update provides selected information on nearly 4,000 doctoral programs in 41 subdisciplines at 274 doctorate-granting institutions. This volume also reports the results of the National Survey of Graduate Faculty, which polled a sample of faculty for their views on the scholarly quality of program faculty and the effectiveness of doctoral programs in preparing research scholars/scientists. This much-anticipated update of such an essential reference will be useful to education administrators, university faculty, and students seeking authoritative information on doctoral programs. (shrink)

With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the states which are dynamically stable. (...) This fact by itself allows one to work out an interpretation of the formalism which makes it possible to give a satisfactory description of the world in terms of the values taken by an appropriately defined mass density function in ordinary configuration space. A topology based on this function and which is radically different from the one characterizing the Hilbert space is introduced, and in terms of it the idea of similarity of macroscopic situations is precisely defined. Finally, the formalism and the interpretation are shown to yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macro-objective description of reality. (shrink)

A formalism is introduced to represent the connective organization of an evolving neuronal network and the effects of environment on this organization by stabilization or degeneration of labile synapses associated with functioning. Learning, or the acquisition of an associative property, is related to a characteristic variability of the connective organization: the interaction of the environment with the genetic program is printed as a particular pattern of such organization through neuronal functioning. An application of the theory to the development (...) of the neuromuscular junction is proposed and the basic selective aspect of learning emphasized. (shrink)

A comprehensive historical overview of formalist ideas in the philosophy of mathematics.

We summarize the recent progress made by probabilistic programming as a unifying formalism for the probabilistic, symbolic, and data-driven aspects of human cognition. We highlight differences with meta-learning in flexibility, statistical assumptions and inferences about cogniton. We suggest that the meta-learning approach could be further strengthened by considering Connectionist and Bayesian approaches, rather than exclusively one or the other.

Reading through Mechanica1 Intelligence, volume III of Alan Turing's Collected Works, one begins to appreciate just how propitious Turing's timing was. If Turing's major accomplishment in ‘On Computable Numbers’ was to expose the epistemological premises built into formalism, his main achievement in the 1940s was to recognize the extent to which this outlook both harmonized with and extended contemporary psychological thought. Turing sought to synthesize these diverse mathematical and psychological elements so as to forge a union between ‘embodied rules’ (...) and ‘learning programs’. Through their joint service in the Mechanist Thesis each would validate the other: and the frameworks from whence each derived. In this paper I will try to show how Turing's psychological thesis forces us to reassess the consequences of establishing AI on the epistemological foundation that underlies behaviourism. (shrink)

In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-L f. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains (...) a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples. (shrink)

Abstract Contrary to Peter J. Boettke's essay, ?What Went Wrong with Economics??, there is no connection between ?formalism? and the alleged inability of mainstream economists to regard theoretical models as anything other than either depictions of real market economies or bases for criticizing market economies and justifying government intervention. Although Boettke's criticisms of the excesses of formalism are justified, Austrian economists such as Boettke need to justify their view that government interventions into economic affairs are inevitably harmful.

There are plenty of intelligent machines in our world today: digital computers and autonomous robots. At the heart of each of these machines there are automatic formal systems (programs running on a digital computer). Now, if the interpretation of a formal system does not belong to the formal system itself, if the interpretation has to be added, it is worth asking: in the case of these intelligent machines that are massively interspersed in our social interactions, where does the interpretation come (...) from? In this paper, we analyse what we call the invisibility of interpretation. Dealing with various types of formal systems (computers, robots, formalist approaches to Economics), the human source of the interpretation of these systems is sometimes concealed by a formalist restriction. To show how the formalist restriction produces the invisibility of interpretation allows us to underline our responsibility, as human agents, for all this interpretative work—and its importance for us as human beings. (shrink)

This essay presents the Aestheticism of the 19th century as the foundational movement of modernist-formalist aesthetics of the 20th century. The main principle of this movement is what I denominate “productive opacity”. Aestheticism has not been recognized as a philosophical aesthetic theory. However, its definition of artwork as an exclusive kind of form—a deep, opaque form—is among the most precise ever given in the discipline. This essay offers an interpretation of aestheticism as a formalist theory, referred to here as “deep (...) formalism”, focusing on the thinking of leading aestheticists, Walter Pater, Oscar Wilde, and James Whistler. These three thinkers defined artwork as a form saturated with an inextricable content, viz. opaque form. (shrink)

In 1926 Hermann Weyl’s Philosophy of Mathematics and Natural Science appeared in Oldenbourg’s Handbuch der Philosophie. At the time Hilbert’s formalist program to “eradicate via proof theory all the foundational questions of mathematics” was in full swing. As a pupil of Hilbert, Weyl was looking to the complete and ultimate success of Hilbert’s program, a confidence evident in Weyl’s treatment of the foundations of mathematics in the original version of Philosophy of Mathematics and Natural Science. But in an (...) appendix to that same text appearing twenty years later, Weyl (1949, p. 219) admitted that this confidence was misplaced. (shrink)

Publication date: 30 November 2016 Source: Author: Olha Bashkir The process of forming program provision for teaching pedagogical disciplines, pedagogy in particular, in pedagogical educational institutions has been characterized in the article on the basis of analyzed pedagogical literature, archival records, and scientific researches in periodicals. Pedagogical educational institutions in Ukraine were reorganized from the institutes of public education to “the united pedagogical institutes” at the beginning of the 30s of the 20th century. The content of programs for disciplines (...) of pedagogical direction has been revealed. They had undergone some changes due to the reformation of higher pedagogical education in Ukraine before the creation of classical pedagogical educational institution. (shrink)

Any logical analysis – and therefore philosophy itself – begins with the question: is there an indubitable knowledge? To answer this question Bertrand Russellappeals to tradition – both mathematical and philosophical – in which he recognizes himself. The process used by Russell, in order to build mathematics on a new foundation, was to build concepts logically, starting from atomic elements and known relationships. For example, a logical construction as that of the “class” is that a sentence, which includes a fixed (...) concept, is turned into a logically equivalent statement (example analyzed by Russell is “Scott” and “the author of Waverley”) which unlike the first, entails relations that include concepts. Thus, the primitive concept can be replaced and removed. The new method was named the “theory of types” and became the intellectual program of Russell and his successors. Among the method’s performances is solving logical and mathematical paradoxes. The importance of Russell’s logical investigations exceeded the reductionist program, stimulating the formalist program of philosophy andmethodology and the logical analysis of the language of science with a logical-mathematical apparatus. This program was definitively concluded, it seems, by Kurt Gödel’s results on the decidability problem in the formal axiomatic systems of P type, a problem closely linked to the question of “truth” and the two other meta-theoretical properties of P formal systems, namely “consistency” and “completeness”. Gödel’s Theorems do not affect the now established legitimacy of a meta-theoretical system concerning the formalizing processes, but prove that the hilbertian original program to reduce mathematics to logic is old and the very meaning of the whole process of realizing it must be analyzed again. Considering that in a formal P system, the decision process is demonstrability of true statements, Gödel’s research findings prove the consubstantial relationship of the four meta-theoretical properties Truth-Consistency-Completeness-Demonstrability. (shrink)

This book explores how and when biology emerged as a science in Germany. Beginning with the debate about organism between Georg Ernst Stahl and Gottfried Leibniz at the start of the eighteenth century, John Zammito traces the development of a new research program, culminating in 1800, in the formulation of developmental morphology. He shows how over the course of the century, naturalists undertook to transform some domains of natural history into a distinct branch of natural philosophy, which attempted not (...) only to describe but to explain the natural world and became, ultimately, the science of biology. (shrink)

There has been considerable discussion in the past about the assumptions and basis of different ethical rules. For instance, it is commonplace to say that ethical rules are defaults rules, which means that they tolerate exceptions. Some authors argue that morality can only be grounded in particular cases while others defend the existence of general principles related to ethical rules. Our purpose here is not to justify either position, but to try to model general ethical rules with artificial intelligence formalisms (...) and to compute logical consequences of different ethical theories. More precisely, this is an attempt to show that progress in non-monotonic logics, which simulates default reasoning, could provide a way to formalize different ethical conceptions. From a technical point of view, the model developed in this paper makes use of the Answer Set Programming (ASP) formalism. It is applied comparatively to different ethical systems with respect to their attitude towards lying. The advantages of such formalization are two-fold: firstly, to clarify ideas and assumptions, and, secondly, to use solvers to derive consequences of different ethical conceptions automatically, which can help in a rigorous comparison of ethical theories. (shrink)

The goal of the paper is to offer an explanation why Frege has changed his Begriffsschrift account of identity to the one presented in Über Sinn und Bedeutung.The main claim of the paper is that in order to better understand Frege’s motivation for the introduction of his distinction between sense and reference, which marks his change of views, one should place this change in its original setting, namely the broader framework of Frege’s fundamental preoccupations with the foundations of arithmetic and (...) logic. The Fregean thesis that mathematics is contentful, and its defense against formalism and psychologism, provides us an valuable interpretative key. Thus, Fregean senses are not just the mere outcome of some profound reflections on language, rather they play an important role in the articulation of Frege’s program in the foundations of arithmetic. (shrink)

A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.

Efforts to professionalize the field of bioethics have led to the development of the Healthcare Ethics Consultant-Certified (HEC-C) Program intended to credential practicing healthcare ethics consultants (HCECs). Our team of professional ethicists participated in the inaugural process to support the professionalization efforts and inform our views on the value of this credential from the perspective of ethics consultants. In this paper, we explore the history that has led to this certification process, and evaluate the ability of the HEC-C (...) class='Hi'>Program to meet the goals it has set forth for HCECs. We describe the benefits and weaknesses of the program and offer constructive feedback on how the process might be strengthened, as well as share our team’s experience in preparing for the exam. (shrink)

The ArgumentIn contrast to “socialist eugenics” as a set of ideas on how to deal with the biological problems of mankind, “proletarian race hygiene” placed its emphasis on the environmental components of human life. This mode of eugenics always assumed a change in living conditions, or social milieu, to be the key to human betterment. Its objective was a gradualist, thoroughgoing improvement of human working and living conditions in order to bring about a life of harmony, solidarity and equality. These (...) ideas can be traced back to phrenomesmerism at the beginning of the nineteenth century, and developed through a stage closely entwined with the Marxist thought of Daniels, Engels, Bebel, etc.. This tradition was picked up in the early twentieth century by the Austrian sociologist Goldscheid as well as by the developmental biologist Kammerer. These men extended these ideas and incorporated them into the framework of “proletarian race hygiene,” involving as key concepts what they called “human economy” and “organic technology.”. (shrink)

We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, which gave rise to this special issue. Lastly, (...) we provide a summary of the contributions to this issue. (shrink)

Various parallels between Kant's critical program and Hilbert's formalistic program for the philosophy of mathematics are considered.

In his remarkable paper Formalism 64, Robinson defends his eponymous position concerning the foundations of mathematics, as follows:Any mention of infinite totalities is literally meaningless.We should act as if infinite totalities really existed. Being the originator of Nonstandard Analysis, it stands to reason that Robinson would have often been faced with the opposing position that ‘some infinite totalities are more meaningful than others’, the textbook example being that of infinitesimals. For instance, Bishop and Connes have made such claims regarding (...) infinitesimals, and Nonstandard Analysis in general, going as far as calling the latter respectively a debasement of meaning and virtual, while accepting as meaningful other infinite totalities and the associated mathematical framework. We shall study the critique of Nonstandard Analysis by Bishop and Connes, and observe that these authors equate ‘meaning’ and ‘computational content’, though their interpretations of said content vary. As we will see, Bishop and Connes claim that the presence of ideal objects in Nonstandard Analysis yields the absence of meaning. We will debunk the Bishop–Connes critique by establishing the contrary, namely that the presence of ideal objects in Nonstandard Analysis yields the ubiquitous presence of computational content. In particular, infinitesimals provide an elegant shorthand for expressing computational content. To this end, we introduce a direct translation between a large class of theorems of Nonstandard Analysis and theorems rich in computational content, similar to the ‘reversals’ from the foundational program Reverse Mathematics. The latter also plays an important role in gauging the scope of this translation. (shrink)

Social network research is widely considered atheoretical. In contrast, in this article I argue that network analysis often mixes two distinct theoretical frameworks, creating a logically inconsistent foundation. Relationalism rejects essentialism and a priori categories and insists upon the intersubjectivity of experience and meaning as well as the importance of the content of interactions and their historical setting. Formalism is based on a structuralist interpretation of the theoretical works of Georg Simmel. Simmel laid out a neo-Kantian program of (...) identifying a priori categories of relational types and patterns that operate independently of cultural content or historical setting. Formalism and relationalism are internally consistent theoretical perspectives, but there are tensions between them. To pave the way for stronger middle-range theoretical development, I disaggregate the two approaches and highlight the contradictions that must be addressed or resolved for the construction of any general and inclusive theory. (shrink)

The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty’s point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides (...) with Horty’s one, this is not true in more complicated or “realistic” settings in which more than two norms collide. My chosen formalism is so-called input/output logic. A bottom-line example is introduced. It raises the issue of whether the conventional wisdom is right in assuming that normative reasons run parallel to epistemic ones. (shrink)