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Articles 331 - 352 of 352
Full-Text Articles in Education
Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno
Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno
ACMS Conference Proceedings 1979
Some people view a conjoining of Christianity and Mathematics as improper. They miss the point of the relationship. The content of mathematics is not affected by Christianity. The relationship does not concern what, or how (the Christian doesn’t solve equations or differentiate differently), but it concerns why. It concerns such things as the interpretation and appreciation of the beauty, the symmetries, the coincidences, the remarkable properties, man’s creative role, etc. This paper explores the relationship between Christianity and mathematics as part of a panel discussion on the topic.
On Kuyk’S Complementarity In Mathematics, Gene B. Chase
On Kuyk’S Complementarity In Mathematics, Gene B. Chase
ACMS Conference Proceedings 1979
This paper examines Willem Kuyk’s book, Complementarity in Mathematics, and the interplay between the subjects of mathematics.
Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart
Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart
ACMS Conference Proceedings 1979
This essay will consider a few ways that realism in the modern philosophy of mathematics might be understood and defined.
Intuitionism, Terence H. Perciante
Intuitionism, Terence H. Perciante
ACMS Conference Proceedings 1979
Intuitionism derives philosophically from Kant's Conceptualism -- the object of the mathematical knowledge only have reality within the mind, they do not have reality apart from our thinking. This paper examines the nature of intuitionism and its strengths.
Non-Standard Calculus, Ron Friewald
Non-Standard Calculus, Ron Friewald
ACMS Conference Proceedings 1979
This paper is intended to provide a very cursory introduction to how “nonstandard calculus” works, giving a sketch of how elementary calculus can be presented using hyperreal numbers.
Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma
Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma
ACMS Conference Proceedings 1979
This article surveys the different views of mathematical methodology that occurred from ancient Greek times through the early modern period up until its codification around 1900. After summarizing the axiomatic approach advocated by Aristotle and implemented in mathematics by Euclid, the talk explores the character of analysis in ancient Greek times, its development into a symbolic algebra by Viete and Descartes, and its expansion into a calculus of fluxions and differentials by Newton and Leibniz. The article concludes by touching on the recovery and transformation of the deductive ideal for mathematics by Pasch, Peano, and Hilbert during the late nineteenth …
Two Philosophical Problems About Mathematics, Stephen Barker
Two Philosophical Problems About Mathematics, Stephen Barker
ACMS Conference Proceedings 1979
Mathematics is a flourishing field of human endeavor, a field that is accorded great respect and high standing. For 2500 years or more, many of the best minds available have worked in this field; and the results produced have indirectly been of enormous value to other fields, such as physics, engineering, architecture, economics, and so on. But with is mathematics about? Physics studies moving bodies; engineering studies bridges; architecture studies buildings; economics studies commercial behavior: here there are phenomena we can point to that constitute the subject matter. But what does mathematics study? If you answer “Numbers”, or “Abstract types …
Introduction (1979), Robert Brabenec
Introduction (1979), Robert Brabenec
ACMS Conference Proceedings 1979
No abstract provided.
Table Of Contents (1979), Association Of Christians In The Mathematical Sciences
Table Of Contents (1979), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1979
A Second Conference on the Foundations of Mathematics
A Christian Point Of View, A. Wayne Roberts
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?
Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase
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.
Current Work On Mathematical Truth, Michael Detlefsen
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.
Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes
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.
Recent Problems In The Foundationsof Mathematics, Terence H. Perciante
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 …
Infinity & Reality, John W. Warner
Infinity & Reality, John W. Warner
ACMS Conference Proceedings 1977
This paper examines the topics of infinity and reality as relevant to the conference, proposing a possible relationship between the two in order to stimulate further discussions.
A Brief Introduction To Gödel’S Theorems, Michael Detlefsen
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.
Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley
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 …
Existence In Mathematics, Willis Alberda
Existence In Mathematics, Willis Alberda
ACMS Conference Proceedings 1977
Contemplation of the existence of mathematical entities for very apparent reasons generates a mental cycling of arguments dealing with the nature of mathematical truth, meaning in mathematics, and the obviously related question of which of these two problems should be solved first. The problem of the existence of mathematical entities dates from the first thoughts and ideas of a mathematical nature. The problem of existence in mathematics is fundamental to the domain of speculation and research on the foundations of mathematics. When we try to put ourselves in the place of those philosophers who first explored this problem we must …
The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis
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, …
Epistomology To Ontology, Charles R. Hampton
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.
Introduction (1977), Robert Brabenec
Introduction (1977), Robert Brabenec
ACMS Conference Proceedings 1977
No abstract provided.
Table Of Contents (1977), Association Of Christians In The Mathematical Sciences
Table Of Contents (1977), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1977
No abstract provided.