Introduction to Logic and to the Methodology of the Deductive SciencesOxford University Press, 6 de jan. de 1994 - 256 páginas Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw upon the concepts and principles presented in the first section. Numerous exercises and an introduction to the theory of real numbers are also presented. Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject. |
Conteúdo
I | 3 |
On the Sentential Calculus | 17 |
The use of implications in mathematics | 26 |
Laws of sentential calculus | 34 |
III | 49 |
20 | 58 |
22 | 65 |
25 | 71 |
VI | 109 |
38 | 116 |
Consistency and completeness of a deductive theory | 125 |
Laws | 145 |
VIII | 159 |
51 | 168 |
Theorems on subtraction | 174 |
Methodological Considerations on the Constructed | 181 |
333 | 78 |
29 | 87 |
Manyplace relations functions of several variables | 98 |
58 | 189 |
Foundations | 201 |
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Introduction to Logic and to the Methodology of the Deductive Sciences Alfred Tarski,Jan Tarski Visualização parcial - 1994 |
Termos e frases comuns
Abelian group Alfred Tarski analogous antecedent apply arbitrary argument arithmetic assert axiom system axioms of System bijective function called Chapter commutative law concepts consequent consider consisting construction contains contrapositive deductive sciences deductive theory defined definiens definition denote derived designatory function discussed disjunction domain elementary elements equation equinumerous equipollent equivalent example exercise exists a number expressions false footnote formula free variables geometry group with respect identity implication instance integers interpretation irreflexive law of trichotomy laws of sentential LEIBNIZ's law logician mathematical discipline meaning method methodology multiplication natural numbers numbers x objects obtain occur particular phrase positive number preceding primitive terms proof of Theorem properties proved quantifiers reader real numbers relation less replace rule Section 37 segments sentential calculus sentential function set of numbers statements substitution symbol System A(2 Tarski theorems theory of relations true sentence truth tables words
Passagens mais conhecidas
Página i - Choice sequences: a chapter of intuitionistic mathematics 4. JL Bell: Boolean-valued models and independence proofs in set theory (1st edition) 5. Krister Seberberg: Classical propositional operators: an exercise in the foundation of logic 6.
Página xiii - It arises, perhaps, from the circumstance that, for the purpose of an adequate methodological treatment, an empirical science may have to be considered not merely as a scientific theory - that is, as a system of asserted statements arranged according to certain rules - but rather as a complex consisting partly of such statements and partly of human activities. It should be added that in striking opposition to the high development of the empirical sciences themselves, the methodology of these sciences...
Página xii - And on the methodology of the empirical sciences Tarski has commented: "The knowledge of logic is of course valuable in the study of this methodology, as it is in the case of any other discipline. It must be admitted, however, that logical concepts and methods have not, up to the present, found any specific or fertile applications in this domain.