Remarks on mathematical or demonstrative reasoning:its connexion with logic [&c.].J. Green, 1837 - 135 páginas |
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Página ix
... assent to mathematical processes Fewness of premises and of terms in mathematical Page . 1 5 10 20 22 27 33 36 . reasoning • 38 Distinctness and simplicity of ideas of number and figure 40 Final and essential characteristic of ...
... assent to mathematical processes Fewness of premises and of terms in mathematical Page . 1 5 10 20 22 27 33 36 . reasoning • 38 Distinctness and simplicity of ideas of number and figure 40 Final and essential characteristic of ...
Página 10
... assent to this . One definition may be better than another of a line , or a straight line , of a circle , or of parallel lines ; but its superiority can only consist in fixing more clearly that sense of the word about to be 10 ...
... assent to this . One definition may be better than another of a line , or a straight line , of a circle , or of parallel lines ; but its superiority can only consist in fixing more clearly that sense of the word about to be 10 ...
Página 35
... Assent . " " Rational assent to any proposition may be defined a readiness to affirm it to be true , proceeding from a close association of the ideas sug- gested by the proposition , with the idea or internal HARTLEY ON PROPOSITIONS . 35.
... Assent . " " Rational assent to any proposition may be defined a readiness to affirm it to be true , proceeding from a close association of the ideas sug- gested by the proposition , with the idea or internal HARTLEY ON PROPOSITIONS . 35.
Página 36
... assent , which we recognise in connexion with the processes of arithmetic , algebra , and geometry . How much there is in habit may be easily and irresistibly shown . Thus we say that 2 and 3 make 5 , and the three angles of a triangle ...
... assent , which we recognise in connexion with the processes of arithmetic , algebra , and geometry . How much there is in habit may be easily and irresistibly shown . Thus we say that 2 and 3 make 5 , and the three angles of a triangle ...
Página 37
... assent be so ready ? Who will assert it ? And why ? —because we are not in the habit of attending to high numbers and advanced propositions . Doubt , ignorance , and difficulty attach themselves to our terms . He who has just risen from ...
... assent be so ready ? Who will assert it ? And why ? —because we are not in the habit of attending to high numbers and advanced propositions . Doubt , ignorance , and difficulty attach themselves to our terms . He who has just risen from ...
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Términos y frases comunes
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
Pasajes populares
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.