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Mathematical Objects and the Evolution of Rigor
"... ABSTRACT: In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is cosubstantia1 with th ..."
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ABSTRACT: In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is cosubstantia1
Mathematical Objects and the Evolution of Rigor
"... ABSTRACT: In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is cosubstantia1 with th ..."
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ABSTRACT: In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is cosubstantia1
AND THE CATEGORIZATION OF MATHEMATICAL OBJECTS
"... Abstract. In [2] Lakoff and Nuñez develop a basis for the cognitive science of embodied mathematics. For them, the abstract concepts and reasonings of mathematics are grounded in the conceptual processes that we develop in our interaction with the physical world. Through the use of conceptual metaph ..."
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metaphor these cognitive devices are projected to the realm of mathematical reasoning. In this paper we employ the methods spelled out in [2] to make a thorough study of the equivalence relation, a particular mathematical object. In particular we identify the primary cognitive metaphors at play
Alan Turing and the Mathematical Objection
 Minds and Machines 13(1
, 2003
"... Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet accord ..."
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Cited by 5 (3 self)
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machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical objection ” to his view that machines can think. Logicomathematical reasons, stemming from his own work, helped
Field on the Contingency of Mathematical Objects
"... Any sceptic about abstract mathematical entities has somehow to come to terms with two facts: that many of the laws of physical science are formulated in ways which involve overt reference to mathematical entities, and that mathematical theory is pervasively applied in the practice of science. Hartr ..."
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of Mathematical Objects", and that response is the topic of this note. Unfortunately, much of Field's latest discussion is given to sniping at earlier formulations of the difficulty which were explicitly discarded in our (1992), and some confusion may thereby have been caused about the exact focus
The Coordination of Arm Movements: An Experimentally Confirmed Mathematical Model
 Journal of neuroscience
, 1985
"... This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematic ..."
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Cited by 686 (18 self)
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mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate
Circumscription and Generic Mathematical Objects
 NOTES OF THE 4TH INTERNATIONAL WORKSHOP ON NONMONOTONIC REASONING
, 1992
"... We investigate the possibility of using circumscription for characterizing the concept of a generic object in the context of a formalized mathematical theory. We show that conventional circumscriptive policies do not give the intuitively expected results for elementary geometry, and that there is a ..."
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Cited by 6 (2 self)
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We investigate the possibility of using circumscription for characterizing the concept of a generic object in the context of a formalized mathematical theory. We show that conventional circumscriptive policies do not give the intuitively expected results for elementary geometry, and that there is a
XML and the Communication of Mathematical Objects
"... Software programs of various sorts must exchange mathematical formulas and objects as data. This thesis examines the emerging standards for this type of exchange, including MathML and OpenMath. Both of these standards are based on the Extensible Markup Language (XML) and address dierent aspects of t ..."
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Software programs of various sorts must exchange mathematical formulas and objects as data. This thesis examines the emerging standards for this type of exchange, including MathML and OpenMath. Both of these standards are based on the Extensible Markup Language (XML) and address dierent aspects
Mathematical Objects The Reality of
"...  math education, exposition & use. We can also infer some values of mathematics. There are implications for: We will see that math discourse is: highly nuanced for object status, highly structured, and that math objects have attached values.  How do math objects enter math discourse?  How are ..."
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 math education, exposition & use. We can also infer some values of mathematics. There are implications for: We will see that math discourse is: highly nuanced for object status, highly structured, and that math objects have attached values.  How do math objects enter math discourse?  How
Results 1  10
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715,525