Logic and Foundations of Mathematics Commons^™

Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder

Humanistic Mathematics Network Journal

No abstract provided.

Base And Subbase In A Number System, Walter S. Sizer

Humanistic Mathematics Network Journal

No abstract provided.

Tesselland: A Mathematical Oddment, Martin Glover

Humanistic Mathematics Network Journal

No abstract provided.

Bridging To Infinity, Mike Pinter

Humanistic Mathematics Network Journal

The author's own experiences as a mathematics student and teacher have influenced how he thinks about the infinite. Author Madeleine L'Engle has also shaped his thinking with her writing. The author offers some thoughts that connect some of L'Engle's writing with his experience.

Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

A Brief Look At Mathematics And Theology, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Fermat's Enigma By Simon Singh, Matthew Becker

Humanistic Mathematics Network Journal

No abstract provided.

Sylvester: Ushering In The Modern Era Of Research On Odd Perfect Numbers, Steven Gimbel, John Jaroma

Philosophy Faculty Publications

In 1888, James Joseph Sylvester (1814-1897) published a series of papers that he hoped would pave the way for a general proof of the nonexistence of an odd perfect number (OPN). Seemingly unaware that more than fifty years earlier Benjamin Peirce had proved that an odd perfect number must have at least four distinct prime divisors, Sylvester began his fundamental assault on the problem by establishing the same result. Later that same year, he strengthened his conclusion to five. These findings would help to mark the beginning of the modern era of research on odd perfect numbers. Sylvester's bound stood …

Developing Into Series And Returning From Series: A Note On The Foundations Of Eighteenth-Century Analysis, Giovanni Ferraro, Marco Panza

MPP Published Research

In this paper we investigate two problems concerning the theory of power series in 18th-century mathematics: the development of a given function into a power series and the inverse problem, the return from a given power series to the function of which this power series is the development. The way of conceiving and solving these problems closely depended on the notion of function and in particular on the conception of a series as the result of a formal transformation of a function. After describing the procedures considered acceptable by 18th-century mathematicians, we examine in detail the different strategies—both direct and …

History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego

Humanistic Mathematics Network Journal

The main goal of this essay is to discuss, informally, an intuitive approach to the history of mathematics as an academic discipline. The initial point of departure includes the analysis of some traditional definitions of the concept of 'history' taken from standard dictionaries. This concise dissection attempts to suggest the complexity of the discipline.

A Brief Look At Mathematics And Theology, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Notes On Formal Constructivism, D. Joyner, P. Lejarraga

Humanistic Mathematics Network Journal

Our aim is to sketch some ideas related to how we (as in, we two) think we (as in, we humans) think. "That theory is useless. It isn't even wrong." - Wolfgang Pauli. Our hope in this paper is to provide a theory, admittedly somewhat vague, of how we think about mathematics. We also hope our ideas do not cause the reader to be reminded of Pauli's quote above. These notes were motivated by the interesting book by Changeaux and Connes.

Aphorisms, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

Limits Highlights From Over 2000 Years Of Developments In Calculus Limits, Lauri A. Nevalainen

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Mathematisation Of The Science Of Motion And The Birth Of Analytical Mechanics : A Historiographical Note, Marco Panza

MPP Published Research

Usually, one speaks of mathematization of a natural or social science to mean that mathematics comes to be a tool of such a science: the language of mathematics is used to formulate its results, and/or some mathematical techniques is employed to obtain these results.

Fivefolded Asymmetrical Hand: A Poetic Essay, S. Robert Wilson

Humanistic Mathematics Network Journal

No abstract provided.

A Note On The Decimal Numeral System, Shaharir Bin Mohamad Zain

Humanistic Mathematics Network Journal

No abstract provided.

Naïve Thoughts On The Paradox Of Gödel, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

What "Is" Mathematics?: In Memoriam Of Gian-Carlo Rota, Gian-Carlo Rota

Humanistic Mathematics Network Journal

No abstract provided.

Hamilton's Icosian Calculus And His Icosian Game, Katye O. Sowell

Humanistic Mathematics Network Journal

No abstract provided.

Abstracting Aristotle’S Philosophy Of Mathematics, John J. Cleary

Research Resources

In the history of science perhaps the most influential Aristotelian division was that

between mathematics and physics. From our modern perspective this seems like an unfortunate deviation from the Platonic unification of the two disciplines, which guided Kepler and Galileo towards the modern scientific revolution. By contrast, Aristotle’s sharp distinction between the disciplines seems to have led to a barren scholasticism in physics, together with an arid instrumentalism in Ptolemaic astronomy. On the positive side, however, astronomy was liberated from commonsense realism for the conceptual experiments of Aristarchus of Samos, whose heliocentric hypothesis was not adopted by later astronomers because …

La Révolution Scientifique, Les Révolutions, Et L'Histoire Des Sciences. Comment Ernest Coumet Nous A Libérés De L'Héritage D'Alexandre Koyré, Marco Panza

MPP Published Research

Dans son intervention au colloque Koyré (Paris, 1986), Ernest Coumet a suggéré que le terme «révolution scientifique» ne désigne pas chez Koyré un événement historique, mais un idéaltype, au sens de Max Weber. L'auteur discute d'abord cette thèse de Coumet et expose les arguments que ce dermier apporte pour la soutenir. Dans la deuxième partie de l'article, il critique l'usage de la notion de révolution en histoire des sciences, en s'opposant en particulier à la possibilité de distinguer dans les productions des savants une «pensée scientifique» qui serait influencée par la «pensée philosophique» et dont les bouleversements marqueraient l'avènement d'une …

Dialectics And The Dao: On Both, A And Non-A In Neutrosophy And Chinese Philosophy, Feng Liu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces readers to a new approach to dialectical logic: neutrosophy. Specifically it proposes a multi-valued logic in which the statement “both A and Non-A,” historically rejected as logically incoherent, is treated as meaningful. This unity of opposites constitutes both the objective world and the subjective world –a view with deep roots in Buddhism and Daoism, including the I-Ching. This leads in turn to the presentation of a framework for the development of a contradiction oriented learning philosophy inspired by the Later Trigrams of King Wen in the I-Ching. We show that although A and Non-A are logically inconsistent, …

What Is The Thing Called “Humanistic Mathematics?”, Tamar Apel

Humanistic Mathematics Network Journal

No abstract provided.

A Reflection On The Word: Remembering The Word “Word” Is Reflexive, Paul Fjelstad, Ivan Ginchev

Humanistic Mathematics Network Journal

No abstract provided.

A Collection Of Ideas On Systems And Their Extensions, Paul Fjelstad

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: What Is Mathematics, Really? By Reuben Hersh, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

An Informal History Of Classical Rhetoric For Mathematicians (Plato And Aristotle), Phillip Keith, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

To My Students, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

The Moral Significance Of Indetectable Effects, Sven Ove Hansson

RISK: Health, Safety & Environment (1990-2002)

A reassessment of Parfit's fifth "mistake in moral mathematics."