Remarks on Mathematical Or Demonstrative Reasoning

J. Green, 1837 - 135 páginas

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Página iii - Read not to contradict and confute, nor to believe and take for granted: But to weigh and consider.
Página 47 - In this case then, when the mind cannot so bring its ideas together, as by their immediate comparison, and as it were juxta-position or application one to another, to perceive their agreement or disagreement, it is fain, by the intervention of other ideas (one or more, as it happens) to discover the agreement or disagreement which it searches ; and this is that which we call reasoning.
Página 18 - In this place we are concerned with nominal definitions only, (except, indeed, of logical terms,) because all that is requisite for the purposes of reasoning (which is the proper province of Logic) is, that a term shall not be used in different senses : a real definition of any thing belongs to the science or system which is employed about that thing.
Página 54 - From this general contrast it will easily be seen, how an excessive study of the mathematical sciences not only does not prepare, but absolutely incapacitates the mind, for those intellectual energies which philosophy and life require.
Página 51 - ... practice, or that even if it had not, it might not still be a dignified and interesting pursuit. One of the chief impediments to the attainment of a just view of the nature and object of logic, is the not fully understanding, or not sufficiently keeping in mind, the SAMENESS of the reasoning process in all cases.
Página 12 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 46 - The next degree of knowledge is, where the mind perceives the agreement or disagreement of any ideas, but not immediately.
Página 32 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.
Página 47 - Now, in every step reason makes in demonstrative knowledge, there is an intuitive knowledge of that agreement or disagreement it seeks with the next intermediate idea, which it uses as a proof : for if it were not so, that yet would need a proof; since without the perception of such agreement or disagreement there is no knowledge produced. If it be perceived by itself, it is intuitive knowledge : if it cannot be perceived by itself, there is need of some intervening idea, as a common measure, to...
Página 47 - Those intervening ideas which serve to show the agreement of any two others, are called proofs; and where the agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration, it being shown to the understanding, and the mind made to see that it is so.

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