## Principles of the Algebra of Logic: With Examples |

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### Common terms and phrases

adjective ALEXANDER MACFARLANE Algebra of Quality analytical arithmetical value Axiom of Immediate ball Boole Boole's characters chemical equation co-efficient compound equation conclusion consider contain contradic Contraposition cubes deduced denote dependent disjunctive equation equal equation is true equivalent event example expand expression factor formal given data given equation greater Hence Immediate Inference inalternative independent individual inessential investigation involve irrepugnant judgment latter Laws of Thought left-hand member logical equation Mathematics means method minor limits Morgan Multiply Natural Philosophy necessarily negative Observation.—The obtained operation positive and single preceding Article Principle of Identity proposition Quaternions refers respect right-hand member Rule of Signs Similarly single and positive single positively singular values statement Substance Suppose Syllogisms symbol of Quantity Theory of Probability things tion truth Ueberweg universe is divided x is single x=y+z xy=o xy=v xy=x xy=y yz=n

### Popular passages

Page 144 - That wherever the properties A and B are combined, either the property C, or the property D, is present also ; but they are not jointly present.

Page 8 - In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes...

Page 7 - ... following classification be considered. CLASS I. 5. Appellative or descriptive signs, expressing either the name of a thing, or some quality or circumstance belonging to it. To this class we may obviously refer the substantive proper or common, and the adjective. These may indeed be regarded as differing only in this respect, that the former expresses the substantive existence of the individual thing or things to which it refers ; the latter implies that existence. If we attach to the adjective...

Page 148 - B or £, or both of them, there either the property C or the property D will be found, but not both of them. And conversely, wherever the property C or D is found singly, there the property A will be found in conjunction with either B or E, or both of them. Let it then be required to ascertain, first, what in any particular...

Page iv - Shall we then err in regarding that as the true science of Logic which, laying down certain elementary laws, confirmed by the very testimony of the mind, permits us thence to deduce, by uniform processes, the entire chain of its secondary consequences, and furnishes, for its practical applications, methods of perfect generality...

Page 147 - That wherever the property A is found in conjunction with either B or E, or both of them, there either the property C or the property D will be found, but not both of them. And conversely, wherever the property C or D is found singly, there the property A will be found in conjunction with either B or E, or both.

Page ix - ... to investigate the foundations of the analytical method of reasoning about Quality, with special reference to the principles laid down by Boole as the basis of his calculus, and to the observations which have been published by various philosophers concerning these principles. I bring forward a new theory of the operation of the mind in reasoning about Quality, which enables me to correct Boole's principles, and place them on a clear rational basis.

Page 9 - ... the space they occupy, is,' that the sign of identity = connecting the members of the corresponding equations, implies that the things which they represent are identical, not simply that they are found in the same portion of space. Let it in like manner be affirmed, that the reason why the symbol 1 in secondary propositions represents, not the universe of events, but the eternity in whose successive moments and periods they are evolved, is, that the same sign of identity connecting the logical...

Page 7 - Let it further be agreed, that by the combination xy shall be represented that class of things to which the names or descriptions represented by x and y are simultaneously applicable. Thus, if x alone stands for "white things," and y for "sheep," let xy stand for "white sheep;" and in like manner, if z stand for "horned things," and x and y retain their previous interpretations, let zxy represent "horned white sheep," ie that collection of things to which the name "sheep," and the descriptions "white"...