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Full-Text Articles in Logic and Foundations of Mathematics

A Logistic Approximation To The Cumulative Normal Distribution, Shannon R. Bowling, Mohammad T. Khasawneh, Sittichai Kaewkuekool, Byung R. Cho Jan 2009

A Logistic Approximation To The Cumulative Normal Distribution, Shannon R. Bowling, Mohammad T. Khasawneh, Sittichai Kaewkuekool, Byung R. Cho

Engineering Management & Systems Engineering Faculty Publications

This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors’ knowledge, the …

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What Is A “Real” Argument?, G. C. Goddu Jan 2009

What Is A “Real” Argument?, G. C. Goddu

Philosophy Faculty Publications

Numerous informal logicians and argumentation theorists restrict their theorizing to what they call “real” arguments. But is there a clear distinction to be made between “real” and “non-real” arguments? Here I explore four possible accounts of the alleged distinction and argue that none can serve the theoretical uses to which the distinction is most often put.

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Male Adolescents Of Divorce: The Relationship With Their Noncustodial Father, Christine L. Kerr Dec 2008

Male Adolescents Of Divorce: The Relationship With Their Noncustodial Father, Christine L. Kerr

All-Inclusive List of Electronic Theses and Dissertations

Since the divorce rate in the United States began to rise dramatically in the 1970s, researchers have studied the impact of divorce on those involved. The research indicates that children whose parents divorce are more likely than children whose parents remain married to suffer from a lower level of well-being and are at greater risk for a myriad of ills including poorer school performance and increased behavior problems. While few researchers have focused on the impact of divorce on male adolescents specifically, studies of adolescent males in general indicate they are at risk for a variety of problems including poor …

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The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza Jan 2008

The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza

MPP Published Research

Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …

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Domain Specific Identity Commitment And Alcohol Use And Problems, Alison Glanville Aug 2007

Domain Specific Identity Commitment And Alcohol Use And Problems, Alison Glanville

All-Inclusive List of Electronic Theses and Dissertations

Identity formation is an important developmental task of the college years. Previous research has demonstrated that identity commitment, as defined by James Marcia, is related to decreased substance use and problems. That is, individuals who are identity achieved or foreclosed use substances less frequently and experience fewer substance-related problems than do individuals who are classified in the statuses of identity diffused or moratorium. However, Marcia discussed identity as developing in two domains, the occupational and the ideological (religious beliefs and political ideology). To date, no studies have examined in which domain commitment is associated with a decrease in substance use …

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Strokes Of Existence: The Connection Of All Things, Mari Gorman Jan 2007

Strokes Of Existence: The Connection Of All Things, Mari Gorman

Graduate Student Publications and Research

Acted or real—and all life is real whether one is acting or not—the common denominator and consistent, ubiquitous reality of life and all behavior is that it manifests in the form of relationships on all scales. But what is a relationship? Until now, the answer to this question has not been sufficiently known. As a result of many years of empirical research that began with the aim of discovering what is going on in a gifted actor when s/he is playing a character that can be observed and experienced as a living, intuitive being, and based on the knowledge that …

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A Philosophical Examination Of Proofs In Mathematics, Eric Almeida Jan 2007

A Philosophical Examination Of Proofs In Mathematics, Eric Almeida

Undergraduate Review

No abstract provided.

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A Theory Of Argument (Book Review), G. C. Goddu Jan 2007

A Theory Of Argument (Book Review), G. C. Goddu

Philosophy Faculty Publications

A Theory of Argument is an advanced textbook “written for upper-level undergraduate students who have completed at least one prior course in argumentation theory, critical thinking, informal logic, formal logic, or some other related discipline” (ix). This puts Vorobej’s book in a unique position since, to my knowledge, there are no other second course undergraduate textbooks with a nonsymbolic focus. (Second course symbolic logic textbooks written for undergraduates, rather than primarily for graduate students, were relatively rare until recently; the past decade has seen a proliferation in such texts.)

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Walton On Argument Structure, G. C. Goddu Jan 2007

Walton On Argument Structure, G. C. Goddu

Philosophy Faculty Publications

In previous work I argued against (i) the likelihood of finding a theoretically sound foundation for the linked/convergent distinction and (ii) the utility of the distinction even if a sound theoretical basis could be found. Here I subject Douglas Walton’s comprehensive discussion of the linked/convergent distinction found in Argument Structure: A Pragmatic Theory to careful scrutiny and argue that at best Walton’s theory remains incomplete and that attempts to fill out the details will run afoul of at least one of the problems adduced above—i.e., result in either a theoretically unsound distinction or a theoretically sound, but unnecessary distinction.

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François Viète, Between Analysis And Cryptanalysis, Marco Panza Jun 2006

François Viète, Between Analysis And Cryptanalysis, Marco Panza

MPP Published Research

François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète's major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète's 'new algebra' relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète's algebraic analysis is not an analysis in the same …

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Adolescent Fears And Anxieties: A Comparative Analysis Of Parents' And Teachers' Perceptions Of Adolescent Differences, Carolyn B. Miller May 2006

Adolescent Fears And Anxieties: A Comparative Analysis Of Parents' And Teachers' Perceptions Of Adolescent Differences, Carolyn B. Miller

All-Inclusive List of Electronic Theses and Dissertations

The purposes of the study were 1) to compare parents and teachers and students perceptions of students' fears and anxieties, and 2) to determine if there were differences in students' fears and anxieties based on grade level or gender. This study was quantitative in nature. Four hundred eighty-six middle school students in a five through eight configuration, and their parents and teachers were included in the sample. Two surveys were given: The Middle Level Survey was created by the researcher, and the Comprehensive Assessment of School Climate is a National Study of School Evaluation (NS SE) product created by Kelley, …

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Cognitive, Personality, And Demographic Attributes Of Student Change, Jeanne Marie Hemy Dec 2005

Cognitive, Personality, And Demographic Attributes Of Student Change, Jeanne Marie Hemy

All-Inclusive List of Electronic Theses and Dissertations

This study was an examination as to whether cognitive, personality, and demographic attributes of students have changed over time. Archival data for 10 cohorts of freshman students from a private Midwest engineering institution were used. Data consisted of Myers-Briggs Type Indicator (MBTI) results, Learning Environment Preferences (LEP) results, and demographics. ANOV As were performed for all interval data and Chi-Square analyses for all nominal data. Statistical significance was found for MBTI Thinking-Perceiving and Sensing-Intuition scales, LEP Cognitive Complexity Index scores, and demographic variables including age, parental education level, and SAT scores. Results are discussed in terms of practical significance, trends …

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On Frege’S Alleged Indispensability Argument, Pieranna Garavaso Jun 2005

On Frege’S Alleged Indispensability Argument, Pieranna Garavaso

Philosophy Publications

The expression ‘indispensability argument’ denotes a family of arguments for mathematical realism supported among others by Quine and Putnam. More and more often, Gottlob Frege is credited with being the first to state this argument in section 91 of the Grundgesetze der Arithmetik. Frege's alleged indispensability argument is the subject of this essay. On the basis of three significant differences between Mark Colyvan's indispensability arguments and Frege's applicability argument, I deny that Frege presents an indispensability argument in that very often quoted section of the Grundegesetze.

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Some Sober Conceptions Of Mathematical Truth, Marco Panza Mar 2005

Some Sober Conceptions Of Mathematical Truth, Marco Panza

MPP Published Research

It is not sufficient to supply an instance of Tarski’s schema, ⌈“p” is true if and only if p⌉ for a certain statement in order to get a definition of truth for this statement and thus fix a truth-condition for it. A definition of the truth of a statement x of a language L is a bi-conditional whose two members are two statements of a meta-language L’. Tarski’s schema simply suggests that a definition of truth for a certain segment x of a language L consists in a statement of the form: ⌈v(x) is true if and only if τ(x)⌉, …

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The Reach Of Abduction: Insight And Trial (Book Review), G. C. Goddu Jan 2005

The Reach Of Abduction: Insight And Trial (Book Review), G. C. Goddu

Philosophy Faculty Publications

The Reach of Abduction is the second volume in a planned three-volume set - A Practical Logic of Cognitive Systems - spanning relevance, abduction, and fallacious reasoning. Despite this fact, Gabbay and Woods write in the preface that "we have written the individual volumes with a view to their being read either as stand-alone works or as linked and somewhat overlapping items in the series" (p. xvii). The aim of The Reach of Abduction is to embed abduction "within a practical logic of cognitive systems" and in so doing, provide "an adequate stand-alone characterization of abduction itself' (p. 9). At …

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Cultural-Competency Training For School-Based Mental Health Service Providers, Natasha Lian Smith Dec 2004

Cultural-Competency Training For School-Based Mental Health Service Providers, Natasha Lian Smith

All-Inclusive List of Electronic Theses and Dissertations

Literature on cultural competence has primarily developed in the fields of counseling psychology and counselor education. The field of school psychology has responded to the increased focus of cultural competency by providing recommended skills needed to provide psychological services in schools to diverse individuals and groups. Currently, research in effective cultural competency training has primarily focused on graduate training programs. This study extends the literature on cultural competency training by developing a training model that is appropriate for professionals who are already working in the field. This study first evaluated the impact of a needs assessment on the preparation of …

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Foundationalism And The Search For Certainty In Mathematics, Natalia Baeza May 2004

Foundationalism And The Search For Certainty In Mathematics, Natalia Baeza

Honors Capstone Projects and Theses

No abstract provided.

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Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder Jan 2004

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.

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Base And Subbase In A Number System, Walter S. Sizer Jan 2004

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

Humanistic Mathematics Network Journal

No abstract provided.

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From Art And Architecture To Mathematics: From Intuition To Insight; From Decoration To Demonstration, John Pottage Jan 2004

From Art And Architecture To Mathematics: From Intuition To Insight; From Decoration To Demonstration, John Pottage

Humanistic Mathematics Network Journal

No abstract provided.

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Tesselland: A Mathematical Oddment, Martin Glover Jan 2004

Tesselland: A Mathematical Oddment, Martin Glover

Humanistic Mathematics Network Journal

No abstract provided.

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Bridging To Infinity, Mike Pinter Jan 2004

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.

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Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips Jan 2004

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

Humanistic Mathematics Network Journal

No abstract provided.

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A Brief Look At Mathematics And Theology, Philip J. Davis Jan 2004

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

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: Fermat's Enigma By Simon Singh, Matthew Becker Jan 2004

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

Humanistic Mathematics Network Journal

No abstract provided.

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Sylvester: Ushering In The Modern Era Of Research On Odd Perfect Numbers, Steven Gimbel, John Jaroma Oct 2003

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 …

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Developing Into Series And Returning From Series: A Note On The Foundations Of Eighteenth-Century Analysis, Giovanni Ferraro, Marco Panza Mar 2003

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 …

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Against The "Ordinary Summing" Test For Convergence, G. C. Goddu Jan 2003

Against The "Ordinary Summing" Test For Convergence, G. C. Goddu

Philosophy Faculty Publications

One popular test for distinguishing linked and convergent argument structures is Robert Yanal's Ordinary Summing Test. Douglas Walton, in his comprehensive survey of possible candidates for the linked/convergent distinction, advocates a particular version of Yanal's test. In a recent article, Alexander Tyaglo proposes to generalize and verify Yanal's algorithm for convergent arguments, the basis for Yanal's Ordinary Summing Test. In this paper I will argue that Yanal's ordinary summing equation does not demarcate convergence and so his Ordinary Summing Test fails. Hence, despite Walton's recommendation or Tyaglo's generalization, the Ordinary Summing Test should not be used for distinguishing linked argument …

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History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego Jun 2002

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.

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A Brief Look At Mathematics And Theology, Philip J. Davis Jun 2002

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

Humanistic Mathematics Network Journal

No abstract provided.

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