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Articles 1  19 of 19
FullText Articles in Philosophy
Are Logic And Math Relevant To Social Debates?, Michael A. Lewis
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
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
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
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
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.
Academia Will Not Save You: Stories Of Being Continually “Underrepresented”, Lynette Deaun Guzmán
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 ...
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
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 longterm 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 comparisonofquantities, 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 “NonIgnorabimus”, Andrea Reichenberger
From Solvability To Formal Decidability: Revisiting Hilbert’S “NonIgnorabimus”, 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 ...
Mathematicians Versus Philosophers In Recent Work On Mathematical Beauty, Viktor Blåsjö
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 ...
Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou
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
Adversus Mathematicos, Christopher Norris
Journal of Humanistic Mathematics
A poem about relationship between mathematics and the human experience of time.
WabiSabi Mathematics, JeanFrancois Maheux
WabiSabi Mathematics, JeanFrancois 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 wabisabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabisabi mathematics” by showing (1) how wabisabi mathematics is conceivable; (2) how wabisabi mathematics is observable; and (3) why we should bother about wabisabi mathematics
A Beautiful Proof By Induction, LarsDaniel Öhman
A Beautiful Proof By Induction, LarsDaniel 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 5choosable. I give a selfcontained 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
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
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 ...
Wandering About: Analogy, Ambiguity And Humanistic Mathematics, William M. Priestley
Wandering About: Analogy, Ambiguity And Humanistic Mathematics, William M. Priestley
Journal of Humanistic Mathematics
This article concerns the relationship between mathematics and language, emphasizing the role of analogy both as an expression of a mathematical property and as a source of productive ambiguity in mathematics. An historical discussion is given of the interplay between the notions of logos, litotes, and limit that has implications for our understanding and teaching of Dedekind cuts and, more generally, for a humanistic notion of the role of mathematics within liberal education.
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Journal of Humanistic Mathematics
The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the ...
The Mathematical Cultures Network Project, Brendan P. Larvor
The Mathematical Cultures Network Project, Brendan P. Larvor
Journal of Humanistic Mathematics
The UK Arts and Humanities Research Council has agreed to fund a series of three meetings with associated publications on mathematical cultures. This note describes the project.
Prove It!, Kenny W. Moran
Prove It!, Kenny W. Moran
Journal of Humanistic Mathematics
A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.