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Visualization in Logic and Mathematics
2005In the last two decades there has been renewed interest in visualization in logic and mathematics. Visualization is usually understood in different ways but for the purposes of this article I will take a rather broad conception of visualization to include both visualization by means of mental images as well as visualizations by means of computer ...
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Non-Deductive Logic in Mathematics
The British Journal for the Philosophy of Science, 1987The author discusses the notion of degree of non-deductive support given to hypotheses by various kinds of mathematical evidence. After looking at the examples of the Riemann hypothesis, Fermat's theorem an all intersection numbers I(f,h) when h runs over all algebroid plane curves not having f as a branch).
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The Logic of Mathematical Discovery Vs. the Logical Structure of Mathematics
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1978Mathematics offers us a puzzling contrast. On the one hand it is supposed to be the paradigm of certain and final knowledge: not fixed to be sure, but a steadily accumulating coherent body of truths obtained by successive deduction from the most evident truths.
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From Logic to Mathematical Logic
2011Although methods of logic and were obviously present in many cultures, which all used some intricate systems of reasoning, it is commonly accepted that explicit analysis of the principles of reasoning were developed independently in China, India, and Greece. The later being the most influential to the systems of logic in the West.
Radomir S. Stanković, Jaakko Astola
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Logic with elements of mathematical logic
2023In the textbook, traditional logic is presented from the point of view of mathematical logic. Mathematization begins with the study of the topic "Concept", continues with the topic "Judgment" and reaches its greatest effectiveness in the study of deductive reasoning.
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Logic and Intuition in Mathematics and Mathematical Education
2007A good mathematics teacher is not only a good mathematician, but also a good teacher. In other words, a good mathematics teacher is not only able to solve mathematical problems, (s)he is also able to explain how mathematical problems are solved. Many mathematicans (and mathematics teachers) are, however, able to solve mathematical problems without ...
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2001
Abstract Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. It is a major element in theoretical computer science and has undergone a huge revival with the every- growing importance of computer science.
René Cori +2 more
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Abstract Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. It is a major element in theoretical computer science and has undergone a huge revival with the every- growing importance of computer science.
René Cori +2 more
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Communicative Rationality, Logic, and Mathematics
2008Based upon some explanations of the notions of communicative rationality in the sense of Habermas, and of communicative logic in the sense of the late C. S. Peirce, the author argues that the final meaning of mathematics is to be an aid for the rational communication of man.
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The Logic of Mathematical Discovery versus The Logical Structure of Mathematics
1998Abstract Mathematics offers us a puzzling contrast. On the one hand it is supposed to be the paradigm of certain and final knowledge: not fixed, to be sure, but a steadily accumulating coherent body of truths obtained by successive deduction from the most evident truths.
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2007
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem ...
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This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem ...
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