Explore how mathematics builds on logic, symbols, and precise definitions you can trust.
This concise guide shows why ordinary language can mislead when dealing with numbers, functions, and proof, and how mastering symbolic methods leads to clear, exact thinking.
Through topics like limits and continuity, Cantorian and Dedekindian notions of continuity, and the role of tautology in logic and mathematics, the book frames how rigorous foundations support mathematical reasoning. It contrasts familiar ideas with their formal counterparts and explains why a symbolic approach matters for mastering the subject. The discussion situates these ideas within a broader view of philosophy, aiming to clarify what can be known a priori and what depends on empirical facts.
Ideal for readers of mathematical philosophy and anyone seeking a clear account of how logic underpins the structure of mathematics.
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I ntroduction, and does not aim at giving an exhaustive discussion of the problems with which it deals. It seemed desirable to set forth certain results, hitherto only available to those who have mastered logical symbolism, in a form offering the minimum of difficulty to the beginner. The utmost endeavour has been made to avoid dogmatism on such questions as are still open to serious doubt, and this endeavour has to some extent dominated the choice of topics considered. The beginnings of mathematical logic are less definitely known than its later portions, but are of at least equal philosophical interest. Much of what is set forth in the following chapters is not properly to be called philosophy, though the matters concerned were included in philosophy so long as no satisfactory science of them existed. The nature of infinity and continuity, for example, belonged in former days to philosophy, but belongs now to mathematics. Mathematical philosophy, in the strict sense, cannot, perhaps, be held to include such definite scientific results as have been obtained in this region; the philosophy of mathematics will naturally be expected to deal with questions on the frontier of knowledge, as to which comparative certainty is not yet attained. But speculation on such questions is hardly likely to be fruitful unless the more scientific parts of the principles of mathematics are known. A book dealing with those parts may, therefore, claim to be an introduction to mathematical philosophy, though it can hardly claim, except where it steps outside its province, to be actually dealing with a part of philosophy.
(Typographical errors above are due to OCR software and don't occur in the book.)
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Librería: Books From California, Simi Valley, CA, Estados Unidos de America
paperback. Condición: Good. A few pages showing some markings and notes throughout. Nº de ref. del artículo: mon0003498408
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Librería: Revaluation Books, Exeter, Reino Unido
Paperback. Condición: Brand New. 218 pages. 9.00x6.00x0.50 inches. This item is printed on demand. Nº de ref. del artículo: zk144008047X
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