TAILIEUCHUNG - The Oxford Companion to Philosophy Part 67

The Oxford Companion to Philosophy Part 67. The book is alphabetized by the whole headings of entries, as distinct from the first word of a heading. Hence, for example, abandonment comes before a priori and a posteriori. It is wise to look elsewhere if something seems to be missing. At the end of the book there is also a useful appendix on Logical Symbols as well as the appendices A Chronological Table of Philosophy and Maps of Philosophy. | 640 natural natural. Belonging to or concerned with the world of nature and so accessible to investigation by the natural sciences. Natural may be contrasted with various terms such as artificial unnatural supernatural non-natural . The first three of these occur in ordinary language though unnatural in particular leads to problems about its real meaning. But non-natural is a philosopher s term and with non-naturalistic is the usual contrast term to natural or naturalistic in philosophy. Roughly it refers to what cannot be studied by the methods of the natural sciences or defined in terms appropriate to them and is applied to subject-matters that are essentially abstract or outside space and time. A famous use of it was made by G. E. Moore who applied it to the term good which he regarded as indefinable. . naturalistic fallacy naturalism. G. E. Moore Principia Ethica Cambridge 1903 sects. 5-14 Natural and Non-natural . natural aristocracy see aristocracy natural. natural deduction. A method of formalizing logic introduced independently by S. Jas kowski in 1934 and Gerhard Gentzen in 1935. All previous mathematical logicians including Frege Russell and Whitehead Hilbert and Heyting intuitionism mathematical had formalized logic axiomatically their method being modelled on the misleading analogy of formal theories. In these formalizations certain logically valid formulae were assumed as axioms from which a minimum of rules of derivation preserving logical validity yielded the rest. This older method required ad hoc definitions of derivability from a set ofpre-misses since not all rules of derivation preserved truth under a given interpretation of the schematic letters it often demanded much ingenuity to obtain the formal theorems. Worse it concentrated philosophical and logical attention on the notion of logical truth in place of that of logical consequence. By contrast a natural deduction system has no axioms but only rules of inference thus placing the .

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