Logic and Foundations of Mathematics Commons^™

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.

A-Logic, Richard Bradshaw Angell

Philosophy Faculty Research Publications

A-LOGIC is a full-length book (600+ pg). It functions as a system of logic designed to: 1) solve the standard paradoxes and major problems of standard mathematical logic; 2) minimize that logic's anomalies with respect to ordinary language, yet; 3) prove that all theorems in mathematical logic are tautologies.

It covers lst order logic the logic of the words "and", "or", "not", "all" and "some". But it also has a non truth functional "if...then" and differs in its definition of validity, its semantics and its theorems. In the book A-logic is contrasted step by step with standard mathematical logic as …

Vagueness, Ignorance, And Margins For Error, Kenton Machina, Harry Deutsch

Faculty Publications - Philosophy

We argue that the epistemic theory of vagueness cannot adequately justify its key tenet–that vague predicates have precisely bounded extensions, of which we are necessarily ignorant. Nor can the theory adequately account for our ignorance of the truth values of borderline cases. Furthermore, we argue that Williamson's promising attempt to explicate our understanding of vague language on the model of a certain sort of "inexact knowledge" is at best incomplete, since certain forms of vagueness do not fit Williamson's model, and in fact fit an alternative model. Finally, we point out that a certain kind of irremediable inexactitude postulated by …

What's The Reason?, Kenton Machina, Mark Siderits

Faculty Publications - Philosophy

"What's the Reason?" is an informal applied logic textbook in 5 chapters. It includes discussions of the nature of good everyday and academic reasoning, common mistakes in everyday reasoning, and overall informal argument assessment.

The 'Most Important And Fundamental' Distinction In Logic, G. C. Goddu

Philosophy Faculty Publications

In this paper I argue that the debate over the purported distinction between deductive and inductive arguments can be bypassed because making the distinction is unnecessary for successfully evaluating arguments. I provide a foundation for doing logic that makes no appeal to the distinction and still performs all the relevant tasks required of an analysis of arguments. I also reply to objections to the view that we can dispense with the distinction. Finally, I conclude that the distinction between inductive and deductive arguments is not one of the most important and fundamental ideas in logic, but rather is unnecessary.

Critical Thinking By Alec Fisher (Book Review), G. C. Goddu

Philosophy Faculty Publications

The aim of Critical Thinking is to explicitly and directly teach critical thinking skills and to facilitate the use of these skills to subjects and contexts beyond critical thinking (v, 1). Though the book is primarily intended as an introductory textbook for the teaching of critical thinking, Fisher maintains that the "material is presented in such a way that it can be worked through on a self-study basis"(vi).

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

Humanistic Mathematics Network Journal

No abstract provided.

Trends. Logic Limitations And Missile Defense, Ibpp Editor

International Bulletin of Political Psychology

This article discusses the limitations of logic in truth-finding using public discourse on national missile defense as an example.

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."

The Difference Between Pure And Applied Mathematics, Adrian Riskin

Humanistic Mathematics Network Journal

No abstract provided.

Leibniz: His Philosophy And His Calculi, Eric Ditwiler

Humanistic Mathematics Network Journal

No abstract provided.

Critique Of A.C. Graham's Reconstruction Of The Neo-Mohist Canons, Jane Geaney

Religious Studies Faculty Publications

A. C. Graham's Later Mohist Logic, Ethics, and Sciences (1978) is the only Western-language translation of the obscure and textually corrupt chapters of the Mozi that purportedly constitute the foundations of ancient Chinese logic. Graham's presentation and interpretation of this difficult material has been largely accepted by scholars. This article questions the soundness of Graham's reconstruction of these chapters (the so-called "Neo-Mohist Canons"). Upon close examination, problems are revealed in both the structure and the content of the framework Graham uses to interpret the Canons. Without a more reliable framework for interpreting the text, it seems best to remain skeptical …

Platonism And All That…, Robert P. Burn

Humanistic Mathematics Network Journal

No abstract provided.

Effect Of Item Clarity And Probability Of Item Endorsement On Response Latencies On Personality Test Items, James R. Kinney

All-Inclusive List of Electronic Theses and Dissertations

In this study, regression analysis was used to examine the affects of item clarity and probability of endorsement on response latencies of 60 undergraduates responding on personality test items from the Sixteen Personality Factor Questionnaire (16 Personality Factor test) (Cattell, Eber, & Tatsuoka, 1970, 5th Edition). Response latencies to personality test items, though frequently studied, have yet to be operationally utilized in the interpretation of personality tests. Forty-four items from the 16 Personality Factor test were selected. Each item from the original test was rated for clarity and matched with an emotionally neutral statement with an equivalent number of words. …