Remarks on mathematical or demonstrative reasoning:its connexion with logic [&c.].J. Green, 1837 - 135 sider |
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Side 11
... triangle , circle , and so on , so far as they are de- finable . And the student would have little occasion to pore over these definitions if all the terms were previously familiar to him , and all had that fixed and clear meaning in ...
... triangle , circle , and so on , so far as they are de- finable . And the student would have little occasion to pore over these definitions if all the terms were previously familiar to him , and all had that fixed and clear meaning in ...
Side 13
... he says , " certain connexions are supposed to exist , from which it is asserted that certain con- sequences will follow . Thus , in an isosceles triangle , the angles at the base are equal , THE MEANING OF TERMS . 13.
... he says , " certain connexions are supposed to exist , from which it is asserted that certain con- sequences will follow . Thus , in an isosceles triangle , the angles at the base are equal , THE MEANING OF TERMS . 13.
Side 14
Edward Tagart. triangle , the angles at the base are equal , or , if a triangle be isosceles , the angles at the base will be equal . Here the hypothesis or supposition is , that the triangle has two equal sides ; the consequence ...
Edward Tagart. triangle , the angles at the base are equal , or , if a triangle be isosceles , the angles at the base will be equal . Here the hypothesis or supposition is , that the triangle has two equal sides ; the consequence ...
Side 15
... triangles , circles , and squares in the mathematical sense . But if it be so , even admitting all this , still let us ... triangle as if it could possibly mean a circle , nor about parallel lines as if they were not equidistant at all ...
... triangles , circles , and squares in the mathematical sense . But if it be so , even admitting all this , still let us ... triangle as if it could possibly mean a circle , nor about parallel lines as if they were not equidistant at all ...
Side 16
... triangle to another mind by a definition or descrip- tion . It is the object of the definition to single out that quality or property in the mind's conception of the thing which distinguishes it most completely from every other object ...
... triangle to another mind by a definition or descrip- tion . It is the object of the definition to single out that quality or property in the mind's conception of the thing which distinguishes it most completely from every other object ...
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Vanlige uttrykk og setninger
abstraction admitted agreement or disagreement algebra analysis applied argument Aristotle assent attention called character circle clear cogency common reasoning conceptions conclusion connexion definitions demonstrative reasoning Dissertation distinct Dugald Stewart Edinburgh reviewer Encyclopædia Britannica equal Essay ethics Euclid evidence exact faculties feeling figure and quantity geometrical reasoning geometry Hartley human hypothesis ideas of figure importance inquiry intuitive knowledge knowledge language Laplace lative laws of thought Locke logic magnitudes mathe mathematical reasoning mathematical science mathematical studies matical reasoning matter meaning measure or test ment mental metaphysical middle term mind modes moral moral constitution Natural Philosophy nature nexion notions number and figure object observations peculiar perceive philosophy physical science Playfair premises principles proof proposition reader remarks rience says sense sensible impressions simple ideas Sir James soning straight line student syllogism tain term Logic things signified tical tion treatise triangle true truth Whately Whately's Whewell words writers
Populære avsnitt
Side iii - Read not to contradict and confute, nor to believe and take for granted: But to weigh and consider.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 46 - The next degree of knowledge is, where the mind perceives the agreement or disagreement of any ideas, but not immediately.
Side 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.
Side 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...
Side 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.