Symbolic Logic and Its ApplicationsLongmans, Green, 1906 - 141 sider |
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A(AB AB'C alternative an+1 antecedent apply argument asserts Barbara Bramantip called Canon caught compound statement constituents containing conventions Darapti datum definition denial denote the implication distributed enthymeme equivalent evident example expressed factor false find the limits formal certainty formal impossibility formula gism given implication Hence horse HUGH MACCOLL individual infer inferior limit Let A denote Let denote Let the symbol limits of x logicians London Mathematical Society major premise mathematics meaningless ment negative non-implicational non-Z notation numbers or ratios omitted positive infinity possible premise required proposition proved respectively denote round square simplest form stag strongest conclusion suppose syllogism syllogistic Symbolic Universe synonym TABLE OF LIMITS taken at random tion traditional logic true undistributed Universe of Discourse valid values or meanings variable weakest premise words X₁ y₁ zero
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Side 62 - 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...
Side 25 - No one shall be a member both of the general and library committees unless he be also on the financial committee.
Side 90 - 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.
Side 62 - 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.
Side 19 - 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...
Side 64 - ... 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...
Side 45 - 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.
Side 48 - 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.
Side 2 - 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.
Side 49 - January 1880. must be shot,' and that this order were carried out to the letter. Could he afterwards exculpate himself by saying that it was all an unfortunate mistake, due to the deplorable ignorance of his subordinates ; that if these had, like him, received the inestimable advantages of a logical education, they would have known at once that what he really meant was 'If he is a spy, he must be shot'?