Symbolic Logic and Its ApplicationsLongmans, Green, 1906 - 141 páginas |
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Términos y frases comunes
A(AB AB'C alternative an+1 antecedent AºBº apply argument Barbara Bramantip called Canon CHAPTER compound statement constituents contains conventions Darapti datum definition denial denote the implication denote the statement different numbers enthymeme equivalent evident example expressed factor false find the limits formal certainty formal impossibility formula gism Hence horse HUGH MACCOLL Let A denote Let denote let the symbol limits of x logicians London Mathematical Society major premise mathematics meaningless ment minor premise missing premise nearer superior limit nearest inferior limit negative non-implicational numbers or ratios omitted positive infinity possible proposition proved redundant required to find respectively denote strongest conclusion suppose syllogism syllogistic Symbolic Universe synonym TABLE OF LIMITS term tion traditional logic true undistributed universe of discourse valid values or meanings variable words words distributed x₁ y₁
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Página 57 - These propositions are called the major premise, the minor premise, and the conclusion. 3. The middle term must be distributed once at least, and must not be ambiguous. ; 4. No term must be distributed in the conclusion which was not distributed in one of the premises. 5. From negative premises nothing can be inferred. 6. •• If one premise be negative, the conclusion must be negative; and vice versa, to prove a negative conclusion one of the premises must be negative. From the above rules may...
Página 20 - No one shall be a member both of the general and library committees unless he be also on the financial committee. 3. No member of the library committee shall be on the financial committee.
Página 83 - It has been pointed out by Ohm that reasoning to the following effect occurs in some works on mathematics : — " A magnitude required for the solution of a problem must satisfy a particular equation, and as the magnitude x satisfies this equation, it is therefore the magnitude required.
Página 57 - As they put it, the middle term must be distributed at least once in the premises, otherwise the minor term may be compared with one part and the major with another part of it. From Some men are poets, Some men are Indians, nothing follows.
Página 14 - I merely mean that the symbol, word, or collection of words, denoted by A, sometimes represents a truth and sometimes an untruth ". As an instance he gives '• Mrs. Brown is not at home ". Here it is plain that what is variable primarily is the meaning of the form of words. What is expressed by the form of words at any given instant is not itself variable ; but at another instant something else, itself equally invariable, is...
Página 59 - ... distributed in the conclusion unless it is also distributed in one of the premises; (5) no conclusion can be drawn from two negative premises; (6) if one premise is negative, the conclusion must be negative...
Página 40 - Y is true (law of detachment) (e) if X implies Y and Y implies Z then X implies Z (law of syllogism); (f) if X implies Y and Y implies X then X = Y.
Página 43 - Here is an extremely simple example of a scheme of correct reasoning: if every A is B, and every B is C, then every A is C.
Página ix - I define a statement as any sound, sign, or symbol (or any arrangement of sounds, signs, or symbols) employed to give information ; and I define a proposition as a statement which, in regard to form, may be divided into two parts respectively called subject and predicate.