Philosophy Commons^™

Tarski And Bachmann In Regina: A Magical Connection, James T. Smith

Journal of Humanistic Mathematics

This is a personal account of an intersection of the schools of research in foundations of geometry founded by Alfred Tarski and Friedrich Bachmann. Their academic lineages and the origins of the schools are also described, as well as the mathematics that resulted from this intersection.

Entre Rêve Et Résignation – Références Intertextuelles Dans Les Chemins Qui Montent (1957) De Mouloud Feraoun, Inès Kremer

Journal of Amazigh Studies

Résumé :

Malgré la présence évidente et continue des références intertextuelles dans les romans de Mouloud Feraoun, celles-ci n’ont été que rarement étudiées. C’est notamment dans son troisième roman, Les chemins qui montent, que les renvois à la littérature orale de la Kabylie comme à l’œuvre romanesque et philosophique d’Albert Camus se prêtent particulièrement à une analyse approfondie. Ils révèlent la résignation profonde du protagoniste qui se refuse à la révolte métaphysique au sens camusien, révolte rendue impossible par la condition coloniale.

Mots clés : Feraoun, intertextualité, Camus, et littérature orale kabyle

Abstract:

Despite the importance of intertextual references …

Locked In Functions: A Short Poem For Robert Langlands, Virgilio A. Rivas

Journal of Humanistic Mathematics

This short poem is inspired by Robert Langlands, recipient of the 2018 Abel Prize. The poem tries to sum up in poetic language, as brief but substantial as it can be, the philosophical and rhetorical connotation of his contributions to mathematics, from automorphic forms to number theory, and the famous Langlands programme, among others. Also partly inspired by Edward Frenkel's tribute to Langlands, the book Love and Mathematics, the poem seeks to capture the philosophical beauty of mathematics that privileges the importance of 'functions' over 'passions', consistent with Langlands' purely mathematical side.

From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm

Journal of Humanistic Mathematics

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical …

Beyond Ethics: Considerations For Centering Equity-Minded Data Science, Nathan Alexander, Carrie Diaz Eaton, Anelise H. Shrout, Belin Tsinnajinnie, Krystal Tsosie

Journal of Humanistic Mathematics

In this paper, we utilize duoethnography - a research method in which practitioners discursively interrogate the relationships between culture, context, and the mechanisms which shape individual autobiographical experiences - to explore what may be beyond ethics in the context of data science. Although ethical frameworks have the ability to reflect cultural priorities, a singular view of ethics, as we explore, often fails to speak to the multiple and diverse priorities held both within and across institutional spaces. To that end, this paper explores multiple perspectives, epistemologies, and worldviews that can collectively push researchers towards considerations of a data science education …

A Case For Ethics In The Mathematics Major Curriculum, Feryal Alayont

Journal of Humanistic Mathematics

When our students enter the workforce, be it in academia or in business, industry, government, they will be forced to make decisions about various ethical dilemmas. Once in a while, the scandalous stories like that of Enron, the three German auto-makers’ diesel fuel pact, and the Equifax data breach make the headlines. However, employees at every workplace are faced with small to large-scale ethical situations almost daily. In our majors’ future careers, a manager can be using an inappropriate graphic to display data to make the numbers look better, or the data collection processes used in a large public policy …

Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler

Journal of Humanistic Mathematics

Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …

Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel

Journal of Humanistic Mathematics

Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.

Book Review: Reckonings: Numerals, Cognition, And History By Stephen Chrisomalis, Milton Rosa, Daniel Clark Orey

Journal of Humanistic Mathematics

This review of Reckonings shares our thoughts on the diverse insights presented by Stephen Chrisomalis’s version of the history of numerical notation. Chrisomalis suggests that members of distinct cultural groups write numbers as an active choice in accordance with their own sociocultural contexts, which reflect the influences of historical, cognitive, social, economic, political, environmental, and cultural factors. This book integrates comparative, cognitive, and evolutionary understandings on numerical cognition with historical and linguistic evidence on the use and transformation of numeral systems through the historical advancement of numeracy. Chrisomalis offers an interesting historical perspective on numbers that builds upon three main …

Special Issue Call For Papers: Ethics In Mathematics, Catherine Buell, Victor Piercey

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Ethics in Mathematics. Please send your abstract submissions via email to the guest editors by September 1, 2021. Initial submission of complete manuscripts is due December 1, 2021. The issue is currently scheduled to appear in July 2022.

Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling

Journal of Humanistic Mathematics

Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in …

Are Logic And Math Relevant To Social Debates?, Michael A. Lewis

Journal of Humanistic Mathematics

Social debates, as well as discussions about certain highly charged issues, such as racism, gender identity, and sexuality, usually turn on the uses or mentions of key words. That is, the conclusions we can draw from such discussions depend on how certain terms are used or mentioned in them. Yet participants in social debates may often fail to precisely define their terms or fail to make important distinctions in terms uttered by others. Both logic and mathematics pay attention to the importance of precise definitions when it comes to engaging in discussions, arguments, or proofs. Logic also makes an important …

Tired: A Reflection On Asceticism And The Value Of Quantitative Assessment, Frances Dean

Journal of Humanistic Mathematics

I have spent a lot of time thinking this past year and a half about the relationship between asceticism and success. As a mathematics student and a collegiate athlete, I have far too often gotten caught up in the pursuit of objective standards. This chase has left me burnt out and broken. Existential philosophy has been my greatest asset in discerning the true purpose of asceticism. I reflect on this journey and the nature of assessment in this short reflection.

Engaging The Paradoxical: Zeno's Paradoxes In Three Works Of Interactive Fiction, Michael Z. Spivey

Journal of Humanistic Mathematics

For over two millennia thinkers have wrestled with Zeno's paradoxes on space, time, motion, and the nature of infinity. In this article we compare and contrast representations of Zeno's paradoxes in three works of interactive fiction, Beyond Zork, The Chinese Room, and A Beauty Cold and Austere. Each of these works incorporates one of Zeno's paradoxes as part of a puzzle that the player must solve in order to advance and ultimately complete the story. As such, the reader must engage more deeply with the paradoxes than he or she would in a static work of fiction. …

Book Review: What Is A Mathematical Concept? Edited By Elizabeth De Freitas, Nathalie Sinclair, And Alf Coles, Brendan P. Larvor

Journal of Humanistic Mathematics

This is a review of What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles (Cambridge University Press, 2017). In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms ‘mathematical’ and ‘concept’. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim the canonical question ‘what is a mathematical concept?’ from the philosophy of mathematics. This review comments …

Maths Living In Social Arenas, From Practice To Foundations, Nigel Vinckier

Journal of Humanistic Mathematics

Maths comes to life in human interaction. This has consequences for the mathematics itself. This paper discusses how this ``coming to life'' of mathematics in different social arenas influences the foundations of maths. We will argue that this influence is profound, to the extent that it is hard to upkeep the idea that there is or should be one foundation on which all mathematics can be built.

Contemplations Of Meaning, Danny Goler

The STEAM Journal

Contemplation on how we construct meaning.

Academia Will Not Save You: Stories Of Being Continually “Underrepresented”, Lynette Deaun Guzmán

Journal of Humanistic Mathematics

My entire life I have had to navigate educational structures labeled (by other people) as “underrepresented” in my fields—mathematics and mathematics education. As many people who are similarly labeled in this way know, this meant I had to navigate oppressive structures that positioned me as lesser (e.g., white supremacy, patriarchy). Making sense of these repeated interactions, I wrote my dissertation as a series of three articles, each prefaced with an essay that situated a broader social, cultural, and political context and also connected to my lived experiences navigating academia. These essays were some of my most personal academic writing, and …

Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

Journal of Humanistic Mathematics

Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …

From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger

Journal of Humanistic Mathematics

The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of solvability is commonly identified with the decision problem. Given this identification, there is not the slightest doubt that Hilbert’s conviction was falsified by Gödel’s proof and by the negative results for the decision problem. On the other hand, Gödel’s theorems do offer a solution, albeit a negative one, in the form of an impossibility proof. In this sense, Hilbert’s optimism may still be justified. Here I argue that …

A Life Absolutely Bare? A Reflection On Resistance By Irregular Refugees Against Fingerprinting As State Biopolitical Control In The European Union, Ziang Zhou

Claremont-UC Undergraduate Research Conference on the European Union

In a legally transitory category, irregular refugees- experience a double precariousness. They risk their lives to travel across treacherous seas to Europe for a better life. However, upon the long-awaited embarkation on the European land, they are exposed once again to the precariousness of the asylum application. They are “powerless”, “with no rights” and “to be sacrificed” as Giorgio Agamben and Hannah Arendt suggested in their respective understanding of a “bare life”, la nuda vita. In light of the administrative difficulties in managing asylum application, the European Union introduced the “Dublin Agreement”, which stipulates mandatory biometric data collection for …

Mathematicians Versus Philosophers In Recent Work On Mathematical Beauty, Viktor Blåsjö

Journal of Humanistic Mathematics

Recent attempts at defining mathematical beauty fall roughly into two schools of thought. One takes its starting point in the subjective experience of the mathematician and characterises mathematical beauty in cognitive terms. The other seeks to reduce beauty to objective notions such as truth, symmetry, or simplicity. This second approach is popular among analytic philosophers, who are committed to seeing mathematics and science as prototypically rational enterprises. I criticise this stance on the grounds that this commitment makes its supporters approach beauty in mathematics not with a genuine desire to sympathetically understand it, but with the preconceived goal of explaining …

Elements Of Art, Mike Doyle

The STEAM Journal

Through these paintings and my writing I share how elements of art and science overlap in the strokes of paint that create the perceptions of something familiar in our minds.

Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou

Journal of Humanistic Mathematics

In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a 'mathematical atomism' was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not.

Adversus Mathematicos, Christopher Norris

Journal of Humanistic Mathematics

A poem about relationship between mathematics and the human experience of time.

Wabi-Sabi Mathematics, Jean-Francois Maheux

Journal of Humanistic Mathematics

Mathematics and aesthetics have a long history in common. In this relation however, the aesthetic dimension of mathematics largely refers to concepts such as purity, absoluteness, symmetry, and so on. In stark contrast to such a nexus of ideas, the Japanese aesthetic of wabi-sabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabi-sabi mathematics” by showing (1) how wabi-sabi mathematics is conceivable; (2) how wabi-sabi mathematics is observable; and (3) why we should bother about wabi-sabi mathematics

A Beautiful Proof By Induction, Lars-Daniel Öhman

Journal of Humanistic Mathematics

The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

Mathematical Proofs: The Beautiful And The Explanatory, Marcus Giaquinto

Journal of Humanistic Mathematics

Mathematicians sometimes judge a mathematical proof to be beautiful and in doing so seem to be making a judgement of the same kind as aesthetic judgements of works of visual art, music or literature. Mathematical proofs are also appraised for explanatoriness: some proofs merely establish their conclusions as true, while others also show why their conclusions are true. This paper will focus on the prima facie plausible assumption that, for mathematical proofs, beauty and explanatoriness tend to go together.

To make headway we need to have some grip on what it is for a proof to be beautiful, and for …

Explanatory Proofs And Beautiful Proofs, Marc Lange

Journal of Humanistic Mathematics

This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples …

Pigs Feet, Jesse W. Standlea

The STEAM Journal

My sculpture “Pigs Feet” has literal foundations upon casts of live pig’s feet. I locally sourced the pig’s feet before casting them. My sculpture makes use of a once cutting edge casting technology, alginate. Alginate molds were once the standard in dentistry. Alginate is an appealing casting material as it is refined from brown seaweeds, is both food and skin safe, it is suitable for educators, for artists and engineers alike.