An Investigation of the Laws of Thought: On which are Founded the Mathematical Theories of Logic and ProbabilitiesWalton and Maberly, 1854 - 424 pages |
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a₁ algebraic application assume babilities c₁ C₂ cause chapter cloth coefficients conception conclusion condition connexion constituents deduce definition deliberative assembly denoted determine DIONYSIUS LARDNER disjunctive proposition Edition elements elimination equa equal events whose probabilities exist expression F. W. NEWMAN factor Fcap function given Hence hypothesis indefinite independent interpretation involved laws of thought logical equation M₁ method minor limit natural evils nature necessary object observed occur p₁ P₂ particular phænomenon premises present preventive of pain primary propositions principle Prob problem processes productive of pleasure Prop question reasoning reduced relation represent respect result second member secondary propositions simple events sition solution supposed syllogism system of equations t₁ t₂ theory of probabilities things tion treatise true truth universe universe of discourse V₁ whence καὶ
Popular passages
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.
Page 212 - I understand the affections of substance, or that which is in another thing, by which thing also it is conceived. 6. By God, I understand the Being absolutely infinite, that is the substance consisting of infinite attributes, each of which expresses an eternal and infinite essence.
Page 24 - That Language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted. It is proposed in this chapter to inquire what it is that renders Language thus subservient to the most important of our intellectual faculties. In the various steps of this inquiry we shall be led to consider the constitution of Language, considered as a system adapted to an end or purpose; to investigate its elements; to seek to determine their mutual relation and...
Page 27 - ... 1st. Literal symbols, as x, y, drc., representing things as subjects of our conceptions. 2nd. Signs of operation, as + , — , X , standing for those operations of the mind by which the conceptions of things are combined or resolved so as to form new conceptions involving the same elements.
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 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...