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We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the...
“Spinoza and the Philosophy of Science:Mathematics,Motion,and Being”
Spinoza Motion Mechanics Philosophy of Science Mathematics
2016/5/31
This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the...
Summary Mathematics in Greek Philosophy网站包括泰利士、阿那克西曼德、毕达格拉斯、毕达格拉斯派等。
Justifying Definitions in Mathematics—Going Beyond Lakatos
definitions in mathematics justification of definitions Lakatos mathematical reasoning
2009/4/27
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case stud...
SPIRITUAL ASPIRATIONS CONNECTED WITH MATHEMATICS: THE EXPERIENCE OF AMERICAN UNIVERSITY STUDENTS
AMERICAN UNIVERSITY STUDENTS MATHEMATICS
2008/10/28
In the1960s I got a Ph.D. in mathematics and worked for about 10 years in the Mathematics Department of a large University. Thereafter I left mathematics to work in cognition, philosophy of science, r...
The purpose of the investigation was to ascertain what mathematical problem solving is in the primary and secondary mathematics classroom. Participants (N=20) were primarily university professors with...
MAKING MATHEMATICS INCLUSIVE: INTERPRETING THE MEANING OF CLASSROOM ACTIVITY
MEANING CLASSROOM ACTIVITY
2008/10/28
Kei te pirangi au kia uwhi koe I o karu, ka tuwhera I to hinengaro.
“E tu ana koe i te kokona o tetahi ruma tapawha, a, e ahu ana koe ki waenganui I te ruma. Kia ata haere te hikoi, whai haere I te p...
This paper is part of a study that explores learning difficulties in mathematics from the children’s point of view. An interview with a group of ten to eleven year old students is analysed with respec...
UNDERSTANDING MATHEMATICS
UNDERSTANDING MATHEMATICS
2008/10/28
The word “understanding” is widely used in discussion about learning and doing mathematics. It can mean many things. This paper will concentrate on a meaning which it will be claimed is central to t...
MATHEMATICS AND THE MORAL SCIENCES:The Value of Value-Free Mathematics
Value Value-Free Mathematics
2008/10/28
Most modern practitioners of the art of mathematics, as well as those who only admire it from afar (some with not a little trepidation), share an image of mathematics as a realm of abstract thought, w...
EPISTEMOLOGY PLUS VALUES EQUALS CLASSROOM IMAGE OF MATHEMATICS
the impact of values mathematics
2008/10/28
What is the impact of values on the mathematics classroom? In this paper I advance the thesis that an epistemology or philosophy of mathematics combined with a set of values provides the basis for the...
Finitary and Infinitary Mathematics, the Possibility of Possibilities and the Definition of Probabilities.
many-minds quantum theory finitary and infinitary mathematics
2008/4/22
Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and ...
On Optimism and Opportunism in Applied Mathematics (Mark Wilson Meets John von Neumann on Mathematical Ontology)
Applied mathematics axiomatic method
2008/4/22
Applied mathematics often operates by way of shakily rationalized expedients that can neither be understood in a deductive-nomological nor in an anti-realist setting. Rather do these complexities, so ...
Spacetime, Structural Realism, and the Substantival/Relational Debate: An Ontological Investigation from the Perspective of Structural Realism in the Philosophy of Mathematics
spacetime structural realism substantivalism relationism
2008/4/21
This essay explores structural realist interpretation of spacetime with special emphasis on the close interrelationship between, on the one hand, ontological debates in spacetime structural realism an...
The Mathematics of Non-Individuality
quasi-sets indiscernibible objects indistinguishability quantum objects
2008/4/21
Some of the forerunners of quantum theory regarded the basic entities of such theories as 'non-individuals'. One of the problems is to treat collections of such 'things', for they do not obey the axio...