The Quarterly Journal of Pure and Applied Mathematics, Volume 41J.W. Parker, 1910 |
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Autres éditions - Tout afficher
The Quarterly Journal of Pure and Applied Mathematics, Volume 6 James Joseph Sylvester,James Whitbread Lee Glaisher Affichage du livre entier - 1864 |
Expressions et termes fréquents
a₁ Algebra asymptotic autotomic axis B₁ binode bitangential developable Boole Boole's bounded function closest contact co-sets coefficients conic node constant content zero continuous function continuous with respect convergent corresponding cosh countable set cubic cubic surface curve cyclic group denote derived difference equation equal expression factors finite follows formulæ given Hence homographic Ibid integral intersection Laws of Thought Leibniz line of curvature linear lines of closest logarithms logic Math mathematics method nodal cone null-function number of points obtain operators P₁ paper propositions prove quantity quartic relations result roots satisfy spinodal straight line symbols tangent cone tangent planes theorem theory total number triangle ABC unique limit values variable velocity W. H. YOUNG µ³ ат
Fréquemment cités
Page 318 - THEY who are acquainted with the present state of the theory of Symbolical Algebra, are aware, that the validity of the processes of analysis does not depend upon the interpretation of the symbols which are employed, but solely upon the laws of their combination.
Page 332 - 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 and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the...
Page 318 - Whenever the nature of the subject permits our reasoning processes to be, without danger, carried on mechanically, the language should be constructed on as mechanical principles as possible ; while in the contrary case, it should be so constructed that there shall be the greatest possible obstacles to a merely mechanical use of it.
Page 325 - I design to illustrate, are the following : (1) That the business of Logic is with the relations of classes, and with the modes in which the mind contemplates those relations. (2) That antecedently to our recognition of the existence of propositions, there are laws to which the conception of a class is subject, — laws which are dependent upon the constitution of the intellect, and which determine the character and form of the reasoning process.
Page 329 - 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 325 - That those laws are, furthermore, such, that all equations which are formed in subjection to them, even though expressed under functional signs, admit of perfect solution, so that every problem in logic can be solved by reference to a general theorem. (5) That the forms under which propositions are actually exhibited, in accordance with the principles of this calculus, are analogous with those of a philosophical language.
Page 325 - That the business of Logic is with the relations of classes, and with the modes in which the mind contemplates those relations. (2) That antecedently to our recognition of the existence of propositions, there are laws to which the conception of a class is subject, — laws which are dependent upon the constitution of the intellect, and which determine the character and form of the reasoning process. (3) That those laws are capable of mathematical expression, and that they thus constitute the basis...
Page 330 - ... opinions differing widely from each other, and often wholly opposed to his own, were carefully considered ; and whatever was likely to help him in the great work which he had undertaken, was eagerly sought. Mental science became his study ; mathematics were his recreation. So...
Page 330 - From this time forward he applied himself diligently to a course of study and reflection on psychological subjects, with a view to the production of a much more elaborate and exhaustive work than either of those above named. He felt that the inquiry on which he had entered was worthy of his best powers ; and that in seeking to perfect his theory of deductive reasoning, he was rendering an important service to science. He meditated deeply on the nature and constitution of the human intellect. The...
Page 319 - Aristotelian arrangement, [8] but it soon became apparent that restrictions were thus introduced, which were purely arbitrary and had no foundation in the nature of things.