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Full-Text Articles in Mathematics

Epistomology To Ontology, Charles R. Hampton Apr 1977

Epistomology To Ontology, Charles R. Hampton

ACMS Conference Proceedings 1977

This paper offers commentary on the various philosophical approaches to the foundations of mathematics and then indicates how these ideas have implications in consideration of the existence question.

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Recent Problems In The Foundationsof Mathematics, Terence H. Perciante Apr 1977

Recent Problems In The Foundationsof Mathematics, Terence H. Perciante

ACMS Conference Proceedings 1977

This paper examines the foundational crises that have haunted twentieth-century mathematics, beginning with a brief review of the effects generated by Gauss, Lobachevsky, and Bolyai who each developed non-Euclidean parallel axiom. Though of mathematical interest in their own right, the significance of the new geometries was greatly magnified when it was discerned that they could be used to adequately model physical space, even to the extent that Einstein’s theory of relativity later employed as its model a non-Euclidean geometry developed by Riemann. The question that obviously presented itself was how could any given geometry be called true when it and …

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The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis Apr 1977

The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis

ACMS Conference Proceedings 1977

In teaching the foundations of mathematics within the framework of a Christian college, and particularly that of a Christian liberal arts college, there are two groups of students which must be served. The first consisted of the non-mathematics majors—those non-scientifically oriented “general anything” students who, as a catalog might put it, are to receive “an introduction to and an appreciation of the history, foundations, culture and applications of mathematics.” The second group consists of the mathematics majors, and the few science majors who have not been frightened away by the calculus. The gulf between these two groups is sufficiently large, …

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A Brief Introduction To Gödel’S Theorems, Michael Detlefsen Apr 1977

A Brief Introduction To Gödel’S Theorems, Michael Detlefsen

ACMS Conference Proceedings 1977

Gödel’s two famous incompleteness theorems are results that have come up a number of times in the discussions at the 1977 ACMS conference. This paper provides a brief and relatively non-technical statement on these results and of their significance for the foundations of mathematics.

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Current Work On Mathematical Truth, Michael Detlefsen Apr 1977

Current Work On Mathematical Truth, Michael Detlefsen

ACMS Conference Proceedings 1977

The overall aim of this paper is to serve as an introduction to the work currently being done on the topic of mathematical truth. It provides an overview of the major developments concerning mathematical truth and also evaluates those developments as potential contributions to mathematician’s understanding of the subject.

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Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley Apr 1977

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley

ACMS Conference Proceedings 1977

Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of …

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Formalizing The Liar Paradox, Frank Meyer Apr 1977

Formalizing The Liar Paradox, Frank Meyer

ACMS Conference Proceedings 1977

No abstract provided.

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God: All Sufficient Or Infinite, Thomas E. Iverson Apr 1977

God: All Sufficient Or Infinite, Thomas E. Iverson

ACMS Conference Proceedings 1977

No abstract provided.

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Getting Their Interest - Initiating Students Into The Study Of Foundational Issues In Mathematics, Harold Heie Apr 1977

Getting Their Interest - Initiating Students Into The Study Of Foundational Issues In Mathematics, Harold Heie

ACMS Conference Proceedings 1977

No abstract provided.

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Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes Apr 1977

Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes

ACMS Conference Proceedings 1977

This paper describes the three types of theory about universals, beginning in each case with a classical historical formulation and moving to its restatement in recent analytic philosophy. It will then suggest ways in which Christian perspectives bear on theories of universals and so on mathematics.

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A Christian Point Of View, A. Wayne Roberts Apr 1977

A Christian Point Of View, A. Wayne Roberts

ACMS Conference Proceedings 1977

Does the fact that you are a Christian affect the way that you teach mathematics? This paper seeks to answer the question, what contributions can a mathematics teacher in a Christian school make to the distinctive purpose of such a school?

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Of Men, Models, And Mathematics, Charles Hatfield Apr 1977

Of Men, Models, And Mathematics, Charles Hatfield

ACMS Conference Proceedings 1977

No abstract provided.

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Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase Apr 1977

Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase

ACMS Conference Proceedings 1977

The purpose of this paper is to show that both sides of the predestination/free-will discussion are admissible in a way that is more profound than simply the wave-particle duality of light. In wave-particle duality there are two competing physical models of reality which are contradictory. This paper will show that not a contradiction but a difference in viewpoint is the fundamental issue in the discussion of predestination and free will. A discussion of Skolem’s paradox is helpful in this demonstration.

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Introduction (1977), Robert Brabenec Apr 1977

Introduction (1977), Robert Brabenec

ACMS Conference Proceedings 1977

No abstract provided.

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Table Of Contents (1977), Association Of Christians In The Mathematical Sciences Apr 1977

Table Of Contents (1977), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1977

No abstract provided.

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Epistemology To Ontology, Charles R. Hampton Jan 1977

Epistemology To Ontology, Charles R. Hampton

ACMS Journal 2004

This paper argues for mathematicians thinking about the philosophy of math, especially Christians. It briefly sketches the limitations of formalism, intuitionism, and logicism and uses Christian concept of creation to argue that one can take the best of each of these philosophies and avoid the pitfalls. It also argues for the real existence of mathematical objects apart from the human mind.

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Recent Problems In The Foundations Of Mathematics, Terence H. Perciante Jan 1977

Recent Problems In The Foundations Of Mathematics, Terence H. Perciante

ACMS Journal 2004

This paper examines the foundational crises that have haunted twentieth-century mathematics, beginning with a brief review of the effects generated by Gauss, Lobachevsky, and Bolyai who each developed non-Euclidean parallel axiom. Though of mathematical interest in their own right, the significance of the new geometries was greatly magnified when it was discerned that they could be used to adequately model physical space, even to the extent that Einstein’s theory of relativity later employed as its model a non-Euclidean geometry developed by Riemann. The question that obviously presented itself was how could any given geometry be called true when it and …

Go to article

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley Jan 1977

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley

ACMS Journal 2004

Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of …

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Finite Topologies And Boolean Matrices, Jon Michael Kelley Jul 1974

Finite Topologies And Boolean Matrices, Jon Michael Kelley

Morehead State Theses and Dissertations

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mathematics at Morehead State University by Jon Michael Kelley in July of 1974.

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A Comparative Study Of Business Arithmetic Students: The Use Of Calculators Vs. Manual Computation, Marietta Crawford May 1970

A Comparative Study Of Business Arithmetic Students: The Use Of Calculators Vs. Manual Computation, Marietta Crawford

Morehead State Theses and Dissertations

A thesis presented to the Business Education Graduate Committee at Morehead State University in partial fulfillment of the requirements for the Degree of Master of Business Education by Marietta Crawford on May 25, 1970.

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