Introduction to Logic by Patrick J. Hurley

By Patrick J. Hurley

Coherent, well-organized textual content familiarizes readers with whole thought of logical inference and its purposes to math and the empirical sciences. half I bargains with formal rules of inference and definition. half II explores straightforward intuitive set concept, with separate chapters on units, family members, and services. final part introduces a number of examples of axiomatically formulated theories.

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This syntactical category includes, for instance, intransitive verbs (in their ordinary meaning) and all those expressions, both simple and complex, which yield statements when they replace intransitive verbs in statements. , expressions which form statements when taken together with two terms each. For instance, the word "likes", when taken together with the terms "John" and "Peter", forms the statement "John likes Peter". This category includes transitive verbs and those expressions, both simple and complex, which yield statements when they replace transitive verbs in statements.

There is a great variety of complex statements of two arguments. Such statements as "John is reading and Mary is cooking", "the watch fell on the floor and the glass broke" are examples of complex statements of two arguments which are conjunctive. , statements in the form "p and q", where p and q stand for any statements. It can easily be realized that a conjunctive statement in the form "p and q" is true if and only if its both main arguments, p and q, are true statements. , for instance, "I catch a taxi or else 1 miss my train", "the pupils are stupid or the teacher lectures unc1early".

In other words, a term (concept) A overlaps with a term (concept) B if each of these two terms (concepts) has its designatum which is not common to both of them, and if there is also a designatum which is common to both. Examples: Soldier, Frenchman; bench, wooden object; bird, predatory animal. The relation is graphically illustrated in Fig. 4. It can easily be seen that the relation of intersection is symmetrical. The relation of disjointedness, or non-empty mutual exclusion, is defined thus: (5) A term (concept) A is disjoint, or non vacuously mutually exclusive, with a term (concept) B means the same as: the extension of the term (concept) A is not included in that of the term (concept) B, and the extension of the term (concept) B is not included in that of the term (concept) A, and the extensions of A and Bare mutually exclusive.

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