Temporal freedom in mathematical thought: A philosophical–empirical enquiry

2015 ◽  
Vol 37 ◽  
pp. 18-35 ◽  
Author(s):  
Mona Nosrati
Keyword(s):  
1953 ◽  
Vol 60 (8) ◽  
pp. 559
Author(s):  
F. Bagemihl ◽  
E. R. Stabler
Keyword(s):  

2020 ◽  
Vol 18 (3) ◽  
pp. 273-288
Author(s):  
James Hill

This article investigates the role of instinct in Hume's understanding of human reason. It is shown that while in the Treatise Hume makes the strong reductive assertion that reason is ‘nothing but’ an instinct, in the First Enquiry the corresponding statement has been modified in several ways, rendering the relation between instinct and reason more complex. Most importantly, Hume now explicitly recognises that alongside instinctive experimental reasoning, there is a uniquely human intellectual power of intuitive and demonstrative reason that is not itself an instinct. At first sight it may look as if this intellectual reason, that is capable of grasping ‘relations of ideas’, is not even grounded in instinct but is a thoroughly non-natural element in human nature. On closer analysis, however, it is shown that intellectual reason, in its apprehension of ‘abstract’ and general relations, is dependent on language – the use of ‘terms’ – and that language itself is grounded in instinctive associations of ideas. Thus, Hume's overall view is that even the intellect is an outgrowth of instinct and his conception of human nature is, therefore, shown to be fully naturalistic. Yet this naturalism can still make room for the ‘exceptionalism’ of human mathematical thought, which has no counterpart in the animal kingdom where language is lacking.


2020 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Chinedu Victor Obasi

Mathematics is a human creation, which has been developing for more than four thousand years. It emerged as a response to different social and economic needs of civilizations. Historical development of mathematics stresses that mathematics as a science has always been connected to economic and social context and development of society. There is little or no research that promotes using historical content in mathematics lessons in the Nigeria context. In this paper, we model the use of history of mathematical thought (HMT) in mathematics instruction and solved the formulated model equation using integrating factor. The rate at which HMT is used by teachers in mathematics instruction is assumed to be proportional to the number of teachers that do not use HMT. The analysis suggests that with time, only a fraction of teachers can use HMT in teaching mathematics due to the fact that they will not remember to use it, and additional recruitment of teachers will result in only marginal improvement in the usage of HMT.


Author(s):  
Stephen Woodcock

One of the greatest challenges in mathematics education is in fostering an understanding of what mathematicians would recognise as “mathematical thought.” We seek to encourage students to develop the transferable skills of abstraction, problem generalization and scalability as opposed to simply answering the specific question posed. This difference is perhaps best illustrated by the famous – but likely apocryphal – tale of Gauss’s school days and his approach to summing all positive integers up to and including 100, rather than just summing each sequentially. Especially with the rise of technology-enabled marking and results-focussed tutoring services, the onus is on the educator to develop new types of question which encourage and reward the development of mathematical processes and deprioritise results alone. Some initial work in this area is presented here.


2013 ◽  
Vol 380-384 ◽  
pp. 1734-1737
Author(s):  
Xiang Ping Xiao

As its international status, mastering C programming language is very important, for example the java language, popular and widely used at present, which has all kinds of connections with C programming language. In the C language, the bubbling sort, which has the knowledge of the cycle and array, has been seen as classic examples to explain, and also is used in a variety of computer exams. One important reason is the bubbling sort itself more classic; another is that it is not easy for students to grasp and understand the bubbling sort. This paper will explore a new teaching method--introduction of mathematical thought--to help students to understand and master the bubbling sort.


This chapter is an attempt to show how mathematical thought has changed in the last two centuries. In fact, with the discovery of the so-called non-Euclidean Geometries, mathematical thinking changed profoundly. With the negation of the postulate for “antonomasia,” that is the uniqueness of the parallel for Euclid, and the construction of a geometric theory equally valid on the logical and coherence plane, called non-Euclidean geometry, the meaning of the word “postulate” or “axiom” changes radically. The axioms of a theory do not necessarily have to be dictated by real evidence. On this basis the constructions of arithmetic and geometry are built. The axiomatic-deductive method becomes the mathematical method. It will also highlight the constant link between mathematics and the reality that surrounds us, which tends to make itself explicit through an artificial, abstract language and with clear and certain grammatical rules. Finally, you will notice the connection with the existing technology, that is the new electronic and digital technology.


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