Introduction to Logic and to the Methodology of the Deductive SciencesOxford University Press, 6 Oca 1994 - 256 sayfa 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. |
İçindekiler
On the Use of Variables 1 Constants and variables | 3 |
Expressions containing variables sentential and designatory functions | 4 |
Construction of sentences in which variables occuruniversal and existential sentences | 7 |
Universal and existential quantifiers free and bound variables | 8 |
The importance of variables in mathematics | 12 |
Exercises | 13 |
On the Sentential Calculus 6 Logical constants the old logic and the new logic | 17 |
Sentential calculus the negation of a sentence the conjunc tion and the disjunction of sentences | 18 |
Fundamental laws of the theory of identity | 50 |
Identity of objects and identity of their designations the use of quotation marks | 53 |
Numerical quantifiers | 58 |
On the Theory of Relations | 81 |
Oneone relations or bijective functions and onetoone | 96 |
On the Deductive Method | 109 |
Formalization of definitions and proofs formalized deductive | 122 |
Laws | 145 |
Implications or conditional sentences implications in the material meaning | 21 |
The use of implications in mathematics | 26 |
Equivalence of sentences | 29 |
The formulation of definitions and its rules | 30 |
Laws of sentential calculus | 32 |
The symbolism of sentential calculus compound sentential functions and truth tables | 34 |
An application of laws of sentential calculus in inference | 39 |
Rules of inference complete proofs | 42 |
Exercises | 44 |
On the Theory of Identity 16 Logical concepts outside sentential calculus the concept of identity | 49 |
Other relations among numbers | 151 |
Laws | 159 |
Closed systems of sentences | 167 |
Theorems on subtraction | 174 |
Methodological Considerations on the Constructed | 181 |
Further simplification of the axiom system possible | 189 |
The problem of completeness of the constructed theory | 195 |
Foundations | 201 |
Diğer baskılar - Tümünü görüntüle
Introduction to Logic and to the Methodology of the Deductive Sciences Alfred Tarski,Jan Tarski Sınırlı önizleme - 1994 |
Sık kullanılan terimler ve kelime öbekleri
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 considerations consisting construction contains contrapositive decision problem 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 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 problem 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 true sentence truth tables words Ахом
Popüler pasajlar
Sayfa 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.
Sayfa 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...
Sayfa 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.