## An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities |

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An Investigation of the Laws of Thought: On which are Founded the ... George Boole Limited preview - 1958 |

### Common terms and phrases

algebraic application Aristotle assume babilities cause chapter coefficients combination compound event conception conclusion connexion consists constituents deduce definition deliberative assembly denoted determine disjunctive proposition elements elimination equa equal event x events whose probabilities exist expression factor Hence hypothesis implied indefinite independent inference interpretation involved law of duality laws of thought logical equation logical value method middle terms minor limit natural evils nature necessary object observed occur particular premises present preventive of pain primary propositions principle Prob problem processes productive of pleasure Prop question reasoning reduced reference relation represent respect result satisfy science of Logic second member secondary propositions sexy+ simple events sition solution supposed syllogism system of equations theory of probabilities things tion treatise true truth universe of discourse vanish whence white balls Xi Xi

### Popular passages

Page 212 - Being absolutely infinite, that is the substance consisting of infinite attributes, each of which expresses an eternal and infinite essence.

Page 1 - The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic...

Page 6 - There is not only a close analogy between the operations of the mind in general reasoning and its operations in the particular science of Algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted.

Page 8 - Now this being premised, the requirements of a general method in Logic seem to be the following:— 1st. As the conclusion must express a relation among the whole or among a part of the elements involved in the premises, it is requisite that we should possess the means of eliminating those elements which we desire not to appear in the conclusion, and of determining the whole amount of relation implied by the premises among the elements which we wish to retain. Those elements which do not present...

Page 42 - In eveiy 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.

Page 68 - Second, that the formal processes of solution or demonstration be conducted throughout in obedience to all the laws determined as above, without regard to the question of the interpretability of the particular results obtained...

Page 37 - Let us conceive, then, of an Algebra in which the symbols x, y, z, &c. admit indifferently of the values 0 and 1, and of these values alone. The laws, the axioms, and the processes, of such an Algebra will be identical in their whole extent with the laws, the axioms, and the processes of an Algebra of Logic.

Page 364 - there was a necessary cause in the formation of the solar system for the inclinations being what they are" (so nearly identical)? "The answer to this," says Mr. Keynes, "was pointed out by D'Alembert"... "De Morgan could have reached a similar result whatever the configuration might have been" (pp. 293-294). A whole host of questions are raised by the author's criticism of his predecessors. I...

Page 422 - The laws of thought, in all its processes of conception and of reasoning, in all those operations of which language is the expression or the instrument, are of the same kind as are the laws of the acknowledged processes of Mathematics.

Page 212 - Those things which have nothing mutually in common with one another cannot through one another be mutually understood, that is to say, the conception of the one does not involve the conception of the other.