Over the years, mathematics and statistics have become increasingly important in the social sciences1 . A look at history quickly confirms this claim. At the beginning of the 20th century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in their formulation and establishment. Moreover, many practitioners considered mathematical methods to be inappropriate and simply unsuited to foster our understanding of the social domain. Notably, the famous Methodenstreit also (...) concerned the role of mathematics in the social sciences. Here, mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical, and especially statistical, methods were standardly used, and their value in the social sciences became relatively uncontested. The use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and form hypotheses, and almost all of them use (to a greater or lesser extent) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new subdisciplines, and the establishment of specialized journals and societies. Indeed, subdisciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments can be observed in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a certain style of doing economics became more and more under attack in the last decade or so. Recent developments in behavioral economics and experimental economics can also be understood as a reaction against the dominance (and limitations) of an overly mathematical approach to economics. There are similar debates in other social sciences. It is, however, important to stress that problems of one method (such as axiomatization or the use of set theory) can hardly be taken as a sign of bankruptcy of mathematical methods in the social sciences tout court. This chapter surveys mathematical and statistical methods used in the social sciences and discusses some of the philosophical questions they raise. It is divided into two parts. Sections 1 and 2 are devoted to mathematical methods, and Sections 3 to 7 to statistical methods. As several other chapters in this handbook provide detailed accounts of various mathematical methods, our remarks about the latter will be rather short and general. Statistical methods, on the other hand, will be discussed in-depth. (shrink)

Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08. -/- Constance Reid was an insider of the Berkeley-Stanford logic circle. Her San Francisco home was in Ashbury Heights near the homes of logicians such as Dana Scott and John Corcoran. Her sister Julia Robinson was one of the top mathematical logicians of her generation, as was Julia’s husband Raphael Robinson for whom Robinson Arithmetic was named. Julia was a Tarski PhD and, in recognition (...) of a distinguished career, was elected President of the American Mathematics Society. https://en.wikipedia.org/wiki/Julia_Robinson http://www.awm-math.org/noetherbrochure/Robinson82.html. (shrink)

Computational tools might tempt us to renounce complete cer- tainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correct- ness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be (...) too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding. (shrink)

Nền kinh tế nước ta đang chuyển biến mạnh mẽ từ nền kinh tế bao cấp sang kinh tế thị trường, nhất là từ khi nước ta gia nhập WTO. Đảng và chính phủ đã đề ra rất nhiều các chính sách để cải tiến các thể chế quản lý nền kinh tế và tài chính. Thị trường chứng khoán Việt Nam đã ra đời và đang đóng một vai trò quan trọng trong việc huy động vốn phục vụ cho (...) việc phát triển nền kinh tế quốc dân. Việc phân tích tác động của các chính sách đến nền kinh tế vĩ mô và nền tài chính, những đối sách của chính phủ ta và chính phủ các nước đối với cuộc khủng khoảng tài chính toàn cầu là các vấn đề rất thời sự đang thu hút sự chú ý của nhiều nhà kinh tế và toán học. (shrink)

This is the book of abstracts of the 19th Brazilian Logic Conferences. The Brazilian Logic Conferences (EBL) is one of the most traditional logic conferences in South America. Organized by the Brazilian Logic Society (SBL), its main goal is to promote the dissemination of research in logic in a broad sense. It has been occurring since 1979, congregating logicians of different fields — mostly philosophy, mathematics and computer science — and with different backgrounds — from undergraduate students to senior (...) researchers. The meeting is an important moment for the Brazilian and South American logical community to join together and discuss recent developments of the field. The areas of logic covered in the conference spread over foundations and philosophy of science, analytic philosophy, philosophy and history of logic, mathematics, computer science, informatics, linguistics and artificial intelligence. Previous editions of the EBL have been a great success, attracting researchers from all over Latin America and elsewhere. -/- The 19th edition of EBL takes place from May 6-10, 2019, in the beautiful city of João Pessoa, at the northeast coast of Brazil. It is conjointly organized by Federal University of Paraíba (UFPB), whose main campus is located in João Pessoa, Federal University of Campina Grande (UFCG), whose main campus is located in the nearby city of Campina Grande (the second-largest city in Paraíba state) and SBL. It is sponsored by UFPB, UFCG, the Brazilian Council for Scientific and Technological Development (CNPq) and the State Ministry of Education, Science and Technology of Paraíba. It takes place at Hotel Luxxor Nord Tambaú, privileged located right in front Tambaú beach, one of João Pessoa’s most famous beaches. (shrink)

Brouwer's philosophy of mathematics is usually regarded as an intra-subjective, even solipsistic approach, an approach that also underlies his mathematical intuitionism, as he strived to create a mathematics that develops out of something inner and a-linguistic. Thus, points of connection between Brouwer's mathematical views and his views about and the social world seem improbable and are rarely mentioned in the literature. The current paper aims to challenge and change that. The paper employs a socially oriented prism to examine (...) Brouwer's views on the construction, use, and practice of mathematics. It focuses on Brouwer's views on language, his social interactions, and the importance of group context as they appear in the significs dialogues. It does so by exploring the establishment and dissolution of the significs movement, focusing on Gerrit Mannoury's influence and relationship with Brouwer and analyzing several fragments from the significs dialogues while emphasizing the role Brouwer ascribed to groups in forming and sharing new ideas. The paper concludes by raising two questions that challenge common historical and philosophical readings of intuitionism. (shrink)

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and (...) the lowest cost, and one of the important methods that have been used in the management of companies we offer in this research two methods, Dynamic programming method. This method has been used in many practical matters and helped decision-makers in companies to achieve a maximum profit and less cost by formulating the reality of the state of the company and the data provided by decision-makers with a dynamic mathematical model that is solved using methods of solving dynamic models and we will provide in this research an example of this through the issue of choosing the optimal investment for the budget of a company so that it achieves a maximum profit, and the method of programming with integers: the method that provided these companies with solutions with integer values suitable for the nature of its work, through the use of the binary integer in the formulation of the appropriate mathematical model on the one hand, and on the other hand, the use of the binary integer variable helped to convert some nonlinear models that lead to some practical problems into linear models, and it should be noted here that in the previous two methods there is something indeterminable because we must make a decision in choosing or not choosing something, but the optimal solution that we will get remains A specific value because we are building the mathematical model for any realistic issue through the data provided by those responsible for the work and these data are calculated quantities and therefore they are uncertain values because their validity depends on the circumstances surrounding the work environment, they may be exposed to increase or decrease, and therefore the optimal solution on which the company will base its decision is suitable for specific values and any change in them can cause the company an uncalculated loss, so in this research we will use the concepts of neutrosophic science, the branch of science founded by the American scientist Florentin Smarandache in 1995 based on his belief that there is no absolute truth, a science that is interested in the study of ideas and concepts that are neither true nor false, but just in between, and we will take the data (calculated quantities) neutrosophic values that are specified or unspecified values are any set close to the calculated quantities, then the resulting mathematical model is a neutrosophic model and the optimal solution has neutrosophic values and thanks to the indefinite uncertainty that these values have, companies from the development of appropriate plans for all circumstances and thus achieve the greatest profit and the lowest cost, and we will clarify the above through two issues, the issue of optimal designation of a warehouse site, which we will formulate the mathematical model of using the neutrosophic integer programming method - and the issue of capital budget, which we will present in two different forms, we use in the first form the neutrosophic integer programming method and in the second the neutrosophic dynamic programming method. (shrink)

There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our (...) strategy is to frame current narratives of mathematics from a virtue-theoretic perspective. We identify the practice of mathematizing, put forward by Freudenthal’s ‘Realistic mathematics education’, as virtuous and use it to evaluate different narratives. We show that this can help to render the narratives more adequately, and to provide implications for societal organization. (shrink)

Kant and the Concept of Community, edited by Charlton Payne and Lucas Thorpe, gathers together some of the best known figures in contemporary Kant scholarship. This fine collection traces Kant’s concept of community from its Precritical roots to its role in The Critique of Pure Reason, before going on to investigate the subsequent transformations it would undergo in Kant’s later works on ethics, religion, history, politics, and aesthetics. With very few exceptions, all of the essays in this collection are interesting (...) and informative, with signature pieces by Béatrice Longuenesse, Paul Guyer, Allen Wood, Onora O’Neill, and Susan Shell. This is a highly recommended collection suitable for advanced undergraduates, graduate students, and professionals. (shrink)

US citizens perceive their society to be one of the most diverse and religiously tolerant in the world today. Yet seemingly intractable religious intolerance and moral conflict abound throughout contemporary US public life - from abortion law battles, same-sex marriage, post-9/11 Islamophobia, public school curriculum controversies, to moral and religious dimensions of the Black Lives Matter and Occupy Wall Street movements, and Tea Party populism. Healthy Conflict in Contemporary American Society develops an approach to democratic discourse and (...) coalition-building across deep moral and religious divisions. Drawing on conflict transformation in peace studies, recent American pragmatist thought, and models of agonistic democracy, Jason Springs argues that, in circumstances riven with conflict between strong religious identities and deep moral and political commitments, productive engagement may depend on thinking creatively about how to constructively utilize conflict and intolerance. The result is an approach oriented by the recognition of conflict as a constituent and life-giving feature of social and political relationships. (shrink)

In its recent statement 'Sex Selection and Preimplantation Genetic Diagnosis', the Ethics Committee of the American Society of Reproductive Medicine concluded that preimplantation genetic diagnosis for sex selection for non-medical reasons should be discouraged because it poses a risk of unwarranted gender bias, social harm, and results in the diversion of medical resources from genuine medical need. We critically examine the arguments presented against sex selection using preimplantation genetic diagnosis. We argue that sex selection should be available, at (...) least within privately funded health care. (shrink)

What does it mean to be a modern American today? These slides summarize the discussion from five lectures delivered in winter 2019 at the University of Oregon's Osher Lifelong Learning Institute. The lectures themselves are available on YouTube -/- Just how different is American from other cultural identities? We have thought of ourselves as the specially modern nation, spreading the revolutionary gospel of freedom from traditional restrictions. Some condemn this American exceptionalism, while others celebrate it. Don't take (...) sides too quickly, there are deep issues here. -/- -- The first lecture poses the question whether American identity is a rigid given set of traditional substantive values, or a free floating modern identity with at most a set of formal procedural values. -/- -- The second and third lectures dismantle these options, arguing that any substantive identity must include areas of inner freedom and mobility, and any formal procedural identity needs substantive style and content in order to exist at all. Personal and social identities are two leveled, with given values and projects plus inner self-reflection and space for revision. -/- -- The fourth lecture argues that what makes American identity special is neither its substantive values nor its modern formalism, which are shared with other modern nations, but rather the particular slant of its second level attitudes and practices towards first level substance. -/- -- The fifth lecture asks what America can learn and teach in an increasingly multicultural world. (shrink)

C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed (...) with many fortunate circumstances, not least of which was entering the field when mathematical logic, after only six decades of toil, had just reaped one of its most important harvests with publication of the monumental Principia Mathematica. It was a time of joyful optimism which demanded an historical account and a sober philosophical critique. Lewis was one of the first to apply to mathematical logic the Aristotelian dictum that we do not understand a living institution until we see it growing from its birth. (shrink)

This contribution aims to explore the historical predecessors of the Five Percenter model of self-realization, as popularized by Hip Hop artists such as Supreme Team, Rakim Allah, Brand Nubian, Wu-Tang Clan, or Sunz of Man. As compared to frequent considerations of the phenomenon as a creative mythological background for a socio-political struggle, Five Percenter teachings shall be discussed as contemporary interpretations of historical models of self-realization in various philosophical, religious, and esoteric systems. By putting the coded system of the tenfold (...) Supreme Mathematics as one of its core teachings in context with the Pythagorean Tetractys, an arrangement of ten points in four lines, the commonalities between the sequence and concepts attributed to the respective numbers will be demonstrated. (shrink)

This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in RCA0. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in RCA0. This approach yields a proof of Arrow's theorem in RCA0, (...) and thus in PRA, since Arrow's theorem can be formalised as a Π01 sentence. Finally we show that Fishburn's possibility theorem for countable societies is equivalent to ACA0 over RCA0. (shrink)

Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it has become (...) the enabling science behind the complexity of contemporary knowledge, from gene interpretation to bank risk. Mathematical understanding is all the more necessary for future jobs, as well as remaining, as ever, a prophylactic against the more corrosive philosophical views emanating from the humanities. (shrink)

The present yearbook (which is the fourth in the series) is subtitled Trends & Cycles. It is devoted to cyclical and trend dynamics in society and nature; special attention is paid to economic and demographic aspects, in particular to the mathematical modeling of the Malthusian and post-Malthusian traps' dynamics. An increasingly important role is played by new directions in historical research that study long-term dynamic processes and quantitative changes. This kind of history can hardly develop without the application (...) of mathematical methods. There is a tendency to study history as a system of various processes, within which one can detect waves and cycles of different lengths – from a few years to several centuries, or even millennia. The contributions to this yearbook present a qualitative and quantitative analysis of global historical, political, economic and demographic processes, as well as their mathematical models. This issue of the yearbook consists of three main sections: (I) Long-Term Trends in Nature and Society; (II) Cyclical Processes in Pre-industrial Societies; (III) Contemporary History and Processes. We hope that this issue of the yearbook will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural sciences. (shrink)

The influence of religious beliefs to several leading mathematicians in early Soviet years, especially among members of the Moscow Mathematical Society, had drawn the attention of militant Soviet marxists, as well as Soviet authorities. The issue has also drawn significant attention from scholars in the post-Soviet period. According to the currently prevailing interpretation, reported purges against Moscow mathematicians due to their religious inclination are the focal point of the relevant history. However, I maintain that historical data arguably offer (...) reasons to cast reasonable doubts on this interpretation. In this paper, by reviewing the relevant literature, I raise some methodological and philosophical concerns, in an attempt to contribute to a better understanding of the issue. I maintain that an efficient line of reasoning is to discuss issues in the context of their making, taking into consideration the specific features of each era’s culture. Thus, by focusing on P.A. Nekrasov’s case, I attempt to point to an alternative interpretation, in which the different treatment of religious inclined mathematicians by Soviet authorities is explained in the context of the ideological confrontation between two contrasting worldviews, as part of the ongoing class war in the several phases of Soviet history. (shrink)

The focus of this chapter is on efforts to create a new mathematics, with my prime interest being the role of mathematics in comprehending a world consisting first and foremost of processes, and examining what developments in mathematics are required for this. I am particularly interested in developments in mathematics able to do justice to the reality of life. Such mathematics could provide the basis for advancing ecology, human ecology and ecological economics and thereby assist in the transformation of (...) class='Hi'>society and civilization so that we augment life rather than undermining the conditions for our existence. It was in the process of grappling with these problems that I was drawn to investigate the tradition of intuitionism in mathematics and the role of intuition in mathematics, science and philosophy, and then to consider Whitehead’s work on mathematics and its philosophy in relation to these. (shrink)

Monsters lurk within mathematical as well as literary haunts. I propose to trace some pathways between these two monstrous habitats. I start from Jeffrey Jerome Cohen’s influential account of monster culture and explore how well mathematical monsters fit each of his seven theses. The mathematical monsters I discuss are drawn primarily from three distinct but overlapping domains. Firstly, late nineteenth-century mathematicians made numerous unsettling discoveries that threatened their understanding of their own discipline and challenged their intuitions. The (...) great French mathematician Henri Poincaré characterised these anomalies as ‘monsters’, a name that stuck. Secondly, the twentieth-century philosopher Imre Lakatos composed a seminal work on the nature of mathematical proof, in which monsters play a conspicuous role. Lakatos coined such terms as ‘monster-barring’ and ‘monster-adjusting’ to describe strategies for dealing with entities whose properties seem to falsify a conjecture. Thirdly, and most recently, mathematicians dubbed the largest of the sporadic groups ‘the Monster’, because of its vast size and uncanny properties, and because its existence was suspected long before it could be confirmed. (shrink)

This paper reconstructs the American reception of logical positivism in the early 1930s. I argue that Moritz Schlick (who had visiting positions at Stanford and Berkeley between 1929 and 1932) and Herbert Feigl (who visited Harvard in the 1930-31 academic year) played a crucial role in promoting the *Wissenschaftliche Weltauffassung*, years before members of the Vienna Circle, the Berlin Group, and the Lvov-Warsaw school would seek refuge in the United States. Building on archive material from the Wiener Kreis Archiv, (...) the Harvard University Archives, and the Herbert Feigl Papers, as well as a large number of publications in American philosophy journals from the early 1930s, I reconstruct the subtle transformation of the American philosophical landscape in the years immediately preceding the European exodus. I argue that (1) American philosophical discussions about meaning and significance and (2) internal dynamics in the Vienna Circle between 1929 and 1931 significantly impacted the way in which US philosophers came to perceive logical positivism. (shrink)

American Indian Thought is a contemporary collection of twenty-two essays written by Indigenous persons with Western philosophical training, all attempting to formulate, and/or contribute to a sub-discipline of, a Native American Philosophy. The contributors come from diverse tribal, educational, philosophical, methodological, etc., backgrounds, and there is some tension among aspects of the collection, but what is more striking is the harmony and the singularity of the collection’s intent. Part of this singularity may derive from the solidarity among its (...) authors. In addition to the fact that all belong to Indigenous tribes, there is also a striking sensitivity to the interconnection between distinct Western disciplines—particularly between philosophy and poetry. I take the latter to be a thread which can be strategically woven into the center of the anthology’s weave. In this book discussion, I aim to draw out the poetic aspects of five of the anthology’s essays, which deal with philosophy, metaphysics, epistemology, ethics and aesthetics, respectively. In this way, I hope to illuminate a poetic quality at the heart of the collection, and thus also of the burgeoning field of Native American or Indigenous philosophy in general. In the process, I will also consider ways in which Indigenous philosophy resonates with the Western philosophical traditions of phenomenology and American pragmatism. With the latter tradition in particular this connection has become more fully appreciated, especially through the work of Bruce Wilshire and Scott Pratt. (shrink)

We are concerned in this paper to establish the rationality of American legal realism by adopting a theory of reconstruction. American realism is plagued with dichotomies in relating theory and practice; and the need to broach these dichotomies involves transcendence of experience and transference of consciousness. In doing this, we have both to excavate and to justify its philosophy, logic and science. American legal realism has its root in the philosophy of pragmatism and a logic that sets (...) out the essential elements associated with the making and determination of the law through instrumentality of the court. The validity of this category of legal theory tends to lie on the extent of immediate use to which law can be put or the benefits it can afford the American society. Believing in the possibility of a realistic theory of law that is purely American precludes belief in universal understanding of human legal experience distinct from the understanding gained through the cultural lenses of the American people. Although American realists differ remarkably even within a single paradigm, nevertheless three areas of logical unity among them are that: They bear a cross relevance, a complementing and interlocking of results, and a similar faith in attacking legal problems. A completely empirical understanding of American legal realism seems nebulous, because causality presupposes the interaction of American liberal and legalistic political attitudes. Legalism is the life wire of American culture and this makes distribution of rights and legal predictability possible: incidentally language is an important instrument for making this happens. Countries seeking to adopt the American model of legal order or something similar to it should be capable of an equivalent orientation in terms of formulating their philosophy, logic and science of adjudication. (shrink)

We extend Langdon Winner's idea that artifacts have politics into the realm of mathematics. To do so, we first provide a list of examples showing the existence of mathematical artifacts that have politics. In the second step, we provide an argument that shows that all mathematical artifacts have politics. We conclude by showing the implications for embedding ethics into mathematical curricula. We show how acknowledging that mathematical artifacts have politics can help mathematicians design better exercises for (...) their mathematics students. (shrink)

While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of commentators in recent decades with a view to piecing together a coherent approach to ethics in mathematics. Calls for a Hippocratic Oath for mathematicians are examined and it is concluded that while lessons can be learned from the medical profession, the relation of mathematicians to those affected by their work is (...) significantly different. There is something to be learned also from the codes of conduct of cognate but professionalised quantitative disciplines such as engineering and accountancy, as well as from legal principles bearing on professional work. We conclude with recommendations that professional societies in mathematics should sponsor an (international) code of ethics, institutional mission statements for mathematicians and syllabuses of ethics courses for incorporation into mathematics degrees. (shrink)

This study primarily assessed students' achievement in mathematics using a mobile educational application to help them learn and adapt to changes in education. The study involved selected Grade 9 students at a public high school in Nueva Vizcaya, Philippines. This study used a quasi-experimental method, particularly a post-test control group design. Descriptive statistics such as frequencies, percent, mean, and standard deviation were used to describe the achievement of the students in mathematics. A t-test for independent samples was also computed to (...) determine if there is a significant difference between the students’ achievement in mathematics after using the mobile educational application by the control and experimental groups. Results revealed that students' achievement in mathematics was very proficient after using the application. Moreover, the usage of educational mobile applications has a better impact on students' achievement in mathematics than the traditional approach to teaching. Teachers are encouraged to place priority on solving problems. Overall, the use of the mobile educational application can enhance learning in mathematics, thus the continued use of the said application is advised. (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we (...) go through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

Mathematical objects are divided into (1) those which are autonomous, i.e., not dependent for their existence upon mathematicians’ conscious acts, and (2) intentional objects, which are so dependent. Platonist philosophy of mathematics argues that all objects belong to group (1), Brouwer’s intuitionism argues that all belong to group (2). Here we attempt to develop a dualist ontology of mathematics (implicit in the work of, e.g., Hilbert), exploiting the theories of Meinong, Husserl and Ingarden on the relations between autonomous and (...) intentional objects. In particular we develop a phenomenology of mathematical works, which has the stratified intentional structure discovered by Ingarden in his study of the literary work. (shrink)

The underlying objective of this project is to examine the ways in which the exclusionary status of Muslim-Americans remains unchallenged within John Rawls’ version of political liberalism. Toward this end, I argue that the stipulation of genuine belief in what is reasonably accessible to others in our society is an unreasonable expectation from minorities, given our awareness of how we are perceived by others. Second, using the work of Lisa Schwartzman, I show that Rawls’ reliance on abstraction of closed (...) society legitimizes the exclusion of citizens with marginal social locations. And finally, applying Charles Mills’ critique of ideal theory, I argue that Rawls’ idealization of a posture of civic friendship detracts from a discussion of equally significant societal values while sustaining existing social hierarchies. (shrink)

An account of presentations at an historic (4/30/1977) meeting of the recently formed Society for Philosophy and Technology in conjunction with the Western Division of the American Philosophical Association in Chicago. Speakers on theoretical topics included David Lovekin, Michael Zimmerman, Bernard Gendron and Nancy Holmstrom, and several individuals involved in "outreach activities.".

The aim of this paper is to discuss the “Austro-American” logical empiricism proposed by physicist and philosopher Philipp Frank, particularly his interpretation of Carnap’s Aufbau, which he considered the charter of logical empiricism as a scientific world conception. According to Frank, the Aufbau was to be read as an integration of the ideas of Mach and Poincaré, leading eventually to a pragmatism quite similar to that of the American pragmatist William James. Relying on this peculiar interpretation, Frank intended (...) to bring about a rapprochement between the logical empiricism of the Vienna Circle in exile and American pragmatism. In the course of this project, in the last years of his career, Frank outlined a comprehensive, socially engaged philosophy of science that could serve as a “link between science and philosophy”. (shrink)

In his essay “Literary Vocation as Occupational Idealism: The Example of Emerson’s ‘American Scholar,’” Rob Wilson compares Ralph Waldo Emerson’s scholar with the present literary intellectual in American society. According to Wilson, rather than becoming the intellectual beacon of hope Emerson envisioned, the American (literary) scholar has become trapped in a kind of intellectual bondage by the very act of writing. That is, Wilson believes that the American scholar, because of the effect of Emersonian idealism, (...) has been subjected to repeating Emersonian moral symbols and aesthetic tropes, which has resulted in the alienation of the critic from American society (Wilson 84). However, as will be seen, Wilson’s .. (shrink)

This two-part paper reconstructs the analytic turn in American philosophy through a comparative longitudinal study of three major philosophy departments: Princeton, Yale, and Columbia. I trace their hiring policies, tenure decisions, curriculum designs, and the external pressures that forced them to continuously adapt their strategies; and I use those analyses to distill some of the factors that contributed to the rapid growth of analytic philosophy between 1940 and 1970. In this first part, I show that philosophers at Princeton, Yale, (...) and Columbia actively tried to promote a ‘humanistic’ conception of philosophy until the early 1950s. I argue that logical positivism and related ‘scientific’ approaches were seen as a fundamental threat to the discipline and that this opposition influenced decision making at all three institutions. While many students and recent graduates saw philosophy as a scientific discipline, senior members of the community deplored the decline of the humanities and appointed mostly humanistic philosophers. I show that this generational conflict was reinforced by demographic, political, and economic developments and argue that these discriminatory practices helped forge a coalition between logical empiricists, scientific pragmatists, and ordinary language philosophers, who all began to identify as ‘analytic’ philosophers after the war. (shrink)

What is the ontological status of mathematical structures? Michael Resnic, Stewart Shapiro and Gianluigi Oliveri, are contemporaries of American philosophers on mathematics, they give Platonic answers on this question.

This paper continues a reconstruction of the analytic turn in American philosophy between 1940 and 1970. The first part of this paper argued that philosophers at Princeton, Yale, and Columbia sought to stimulate ‘humanistic’ approaches to philosophy in their hiring policies and tenure decisions, thereby marginalizing the ‘scientific’ philosophies that were in vogue among their students. This second part unearths some of the mechanisms that contributed to the analytic turn once the movement’s fiercest opponents retired. I argue that a (...) new generation of deans and chairmen initially tried to craft ‘balanced’ departments but that various external variables— competition between elite universities, a shortage of graduates with training in modern logic, and the explosive growth of American higher education—eventually led to major policy shifts. Within a decade, I show, the distorted job market helped tip the balance into the other direction, strongly advantaging departments that had invested in analytic philosophy. By the late 1960s, the movement became so successful that the traditional division between humanistic and scientific approaches began to be replaced by a distinction between analytic and ‘continental’ philosophy, referring to the schools of philosophy that were popular across the Atlantic. American philosophy, by then, just was analytic philosophy. (shrink)

Was there a concept of data before the so-called ‘data revolution’? This paper contributes to the history of the concept of data by investigating uses of the term ‘data’ in texts of the Royal Society's Philosophical Transactions for the period 1665–1886. It surveys how the notion enters the journal as a technical term in mathematics, and charts how over time it expands into various other scientific fields, including Earth sciences, physics and chemistry. The paper argues that in these texts (...) the notion of data is not used merely as a rhetorical category, and also cannot strictly be identified with the category of evidence. Instead, the notion comes with an associated epistemic structure, one that is in line with its development from an early mathematical use. (shrink)

Today’s societies place challenging demands on individuals, who are confronted with complexity in many aspects of their lives. Individuals need to acquire a wide range of competencies in order to overcome the complex challenges of today’s world. Using real-world problems is important not only to hone students’ mathematical thinking and competency but also to prepare them in making well-grounded decisions that involve logical and mathematical reasoning. Thus, this study explored the competence of the students in applying mathematics in (...) real world problems and determined the predictors using the selected profile variables. Regression analysis was used to identify if there are predictors that determine the results of the assessment. The main tool of the study was the Programme for International Student Assessment (PISA) test in mathematics. Findings revealed that the predictors include confidence level, repeated kinder, mother work status and highest level of education to complete. This study could be a guide for determining the strengths and weaknesses of students in applying mathematics in the real world as framework in helping them handle the rigors of connecting math with their lives. (shrink)

In its war on terror, the United States tortured and abused individuals in its custody over a decade. This article examines a specific sort of epistemic response by Americans to the use of torture by their government, the sort of response that enables Americans to operate with epistemic ignorance to maintain a favorable construction of their identity as Americans. I lay out the concept of American ignorance as the active production of false and/or incomplete beliefs about what it means (...) to be an American and explore the mechanism through which this ignorance operates in society. The article argues for accountability to create better epistemic environments necessary for any meaningful shift in how Americans perceive themselves qua Americans. (shrink)

How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry.

A well-ordered society faces a crisis whenever a sufficient number of noncompliers enter into the political system. This has the potential to destabilize liberal democratic political order. This article provides a formal analysis of two competing solutions to the problem of political stability offered in the public reason liberalism literature—namely, using public reason or using convergence discourse to restore liberal democratic political order in the well-ordered society. The formal analyses offered in this article show that using public reason (...) fails completely, and using convergent discourse, although doing better, has its own critical limitations that have not been previously recognized properly. (shrink)

The mental risk poses a high threat to the individuals, especially overseas demographic, including expatriates in comparison to the general Arab demographic. Since Arab countries are renowned for their multicultural environment with half of the population of students and faculties being international, this paper focuses on a comprehensive analysis of mental health problems such as depression, stress, anxiety, isolation, and other unfortunate conditions. The dataset is developed from a web-based survey. The detailed exploratory data analysis is conducted on the dataset (...) collected from Arab countries to study an individual’s mental health and indicative help-seeking pointers based on their responses to specific pre-defined questions in a multicultural society. The proposed model validates the claims mathematically and uses different machine learning classifiers to identify individuals who are either currently or previously diagnosed with depression or demonstrate unintentional “save our souls” (SOS) behaviors for an early prediction to prevent risks of danger in life going forward. The accuracy is measured by comparing with the classifiers using several visualization tools. This analysis provides the claims and authentic sources for further research in the multicultural public medical sector and decision-making rules by the government. (shrink)

In the first part of this investigation we highlight two, seemingly irreconcilable, beliefs that suggest an impending crisis in the teaching, research, and practice of—primarily state-supported—mathematics: (a) the belief, with increasing, essentially faith-based, conviction and authority amongst academics that first-order Set Theory can be treated as the lingua franca of mathematics, since its theorems—even if unfalsifiable—can be treated as ‘knowledge’ because they are finite proof sequences which are entailed finitarily by self-evidently Justified True Beliefs; and (b) the slowly emerging, but (...) powerfully rooted in economic imperatives, belief that only those Justified True Beliefs can be treated as ‘knowledge’ which are, further, categorically communicable as Factually Grounded Beliefs—hence as comprehensible pre-formal ‘mathematical truths’—by any intelligence that lays claims to a mathematical lingua franca. We argue that this seeming irreconcilability merely reflects a widening chasm between an increasing under-estimation of the value to society of ‘semantic arithmetical truth’, and an increasing over-estimation of the value to society of ‘syntactic set-theoretical provability’; a chasm which must be narrowed and bridged explicitly. We thus proffer a Complementarity Thesis which seeks to recognize that mathematical ‘provability’ and mathematical ‘truth’ need to be interdependent and complementary, ‘evidence-based’, assignments-by-convention to the formulas of a formal mathematical language; where (a) the goal of mathematical ‘proofs’ may be viewed as seeking to ensure that any mathematical language intended to formally represent our pre-formal conceptual metaphors and their inter-relatedness is unambiguous, and free from contradiction; whilst (b) the goal of mathematical ‘truths’ must be viewed as seeking to ensure that any such representation does, indeed, uniquely identify and adequately represent such metaphors and their inter-relatedness. Our thesis is that, by universally ignoring the need to introduce goal (b) in our curriculum, the teaching of, and research in, mathematics at the post-graduate level cannnot justify its value to society beyond the mere intellectual stimulation of individual minds. In the second part we appeal to some recent—and hitherto unsuspected—unarguably constructive Tarskian interpretations, of the first-order Peano Arithmetic PA, which establish PA as both finitarily consistent, and categorical. Since we also show that the second order subsystem ACA0 of Peano Arithmetic and PA cannot both be assumed provably consistent, we conclude that there can be no mathematical, or meta-mathematical, proof of consistency for Set Theory. Hence the theorems of any Set Theory are not sufficient for distinguishing between (i) what we can believe to be a ‘mathematical truth’; (ii) what we can evidence as a ‘mathematical truth’; and (iii) what we ought not to believe is a ‘mathematical truth’; whilst the theorems of the first-order Peano Arithmetic PA are sufficient for distinguishing between (i), (ii) and (iii). We conclude from this that the holy grail of mathematics ought to be ‘arithmetical truth’, not ‘set-theoretical proof’. (shrink)

In the United States, prohibitionist policies are used as the primary approach to combat the negative effect of substance use on society. An extensive academic literature spanning the disciplines of economics, political science, and multiculturalism documents the great social costs of the United States’ “War on Drugs” both nationally and internationally. These costs come with at best marginal effect on substance abuse and other crimes linked to the drug trade. In many cases, there is a reason to believe that (...) these policies exacerbate the problems they aim to address. This article explores psychologists’ ethical commitments to social change concerning such drug policy, given the field of psychology’s expanding commitment to social justice. We examine arguments regarding the boundaries between psychologists’ personal and professional ethics with regard to political participation. Using drug prohibition as an exemplar, we suggest that many psychologists’ political actions and professional ethics may be misaligned. Ultimately, we conclude that the endorsement of prohibitionist drug policies is in direct conflict with the guiding ethical principles put forth by the American Psychological Association’s Ethical Principles of Psychologists and Code of Conduct. (shrink)

The high rate of mathematics education students‟ academic performance in universities has become unbearable. In an attempt to proffer solution to this menace, this study assessed Poll Everywhere eLearning platform, test anxiety, and undergraduates‟ academic performance in Mathematics in Cross River State, Nigeria. The study adopted a quasi-experimental research one control group and one treatment group. The population of this study comprised all the fulltime regular undergraduates offering Education Mathematics in the Department of Science Education, University of Calabar, Calabar, Nigeria. (...) Accidental sampling technique was adopted in selecting a sample of 328 undergraduates who are owners of smartphones from the population. Test-Anxiety Inventory and Mathematics Achievement Test (MAT) were used as data collection instruments. The null hypotheses were tested using independent t-tests and simple linear regression. Findings revealed that Poll Everywhere eLearning platform has a significant effect on students‟ test anxiety and academic performance in Mathematics respectively; there is a moderate negative and significant relationship between students‟ test anxiety and their academic performance in Mathematics. Based on the findings of this study, it was concluded that Poll Everywhere eLearning platform could be used for the effective teaching and examination of learners in Mathematics and other science-related disciplines. This can be done through the design and integration of course modules to the Poll Everywhere online platform. (shrink)

The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal the mathematically (...) exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity. (shrink)

The article provides a historical contextualization of the debates on theory and method within interwar American sociology. This period is often portrayed as the “golden” age of empirical inquiry resulting in proliferation of methodological orientations. It is argued that the demands of professionalization and specialization within the discipline produced a research model which succeeded in analyzing specific issues, but failed to find a convincing answer to the general question of the logic of society’s development.

Peirce and Dewey were generally more concerned with the process of scientific activity than purely mathematical work. However, their accounts of knowledge production afford some insights into the epistemology of mathematical postulates, especially definition and axioms. Their rejection of rationalist metaphysics and their emphasis on continuity in inquiry provides the pretext for the pragmatic a priori – hypothetical and operational assumptions whose justification relies on their fruitfulness in the long run. This paper focuses on the application of this (...) idea to the epistemology of definitions and an account of progress in mathematics, although it has broader implications for the study of conceptual change and the function and basis of presuppositions in the sciences. (shrink)

Many instances have presented mathematics as a difficult subject for students, and some of these difficulties have been perceived as an injustice to those who suffer from it. Meanwhile, no child is to be left behind in building a just society if all were to experience the collective good of mathematics. For this reason, it became necessary to explore pre-service teachers’ perceptions of mathematics as social justice in their lived experiences. In doing this, the qualitative interpretive approach was adopted, (...) where qualitative data was collected, transcribed, and analysed using the case study design. A sample of eleven pre-service teachers were involved in the study. The findings indicated that the pre-service teachers had experienced severe issues of mathematics as social justice in their previous schooling that were unfair to them. However, they now felt mathematics could be interesting if delivered in a manner that let their voices be heard in the delivery process. (shrink)