The Elements of Logic: In Four Books ...

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L. Nichols, & Company, 1802 - Logic - 239 pages
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Page 144 - Just so it is in the mind; would you have a man reason well, you must use him to it betimes, exercise his mind in observing the connection of ideas and following them in train. Nothing does this better than mathematics, which therefore I think should be taught all those who have the time and opportunity, not so much to make them mathematicians as to make them reasonable creatures...
Page 227 - ... we enquire after, may furnish out a train of obvious and known truths, serving distinctly to investigate the said relations. Euclid, in the first book of the elements, has demonstrated, that the three inward angles of a triangle taken together, are equal to two right angles. The reasoning, by which he establishes that proposition, resolves itself into this general principle : things equal to one and the same thing, are equal to one another. Will any one, however, pretend to say, that a bare consideration...
Page 144 - I HAVE mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train ; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning, which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion.
Page 144 - I said above, that the faculties of our souls are improved and made useful to us, just after the same manner as our bodies are. Would you have a man...
Page 163 - Men suffer all their life long under the foolish superstition that they can be cheated. But it is as impossible for a man to be cheated by any one but himself as for a thing to be, and not to be, at the same time.
Page 144 - I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning, which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For, in all sorts of reasoning, every single argument should be managed as a mathematical demonstration : the connexion and dependence of ideas should be followed, till the mind is brought to the source on which it bottoms, and observes the coherence all...
Page 145 - ... in train. Nothing does this better than mathematics; which, therefore, I think should be taught all those who have the time and opportunity ; not so much to make them mathematicians, as to make them reasonable creatures ; for though we all call ourselves so, because we are born to it* if we please : yet we may truly say, nature gives us but the seeds of it ; we are born to be, if we please, rational creatures, but it" is use and exercise only that makes us so, and we are, indeed, so no farther...
Page 98 - Parts, is an intuitive judgment ; nothing more being required to convince us of its truth, than an attention to the ideas of whole and part. And this too is the...
Page 129 - But how can these men think the use of reason necessary to discover principles that are supposed innate, when reason (if we may believe them) is nothing else but the faculty of deducing unknown truths from principles or propositions that are already known? That certainly can never be thought innate which we have need of reason to discover; unless, as I have said, we will have all the certain truths that reason ever teaches us, to be innate. We may as well think the use of reason necessary to...
Page 176 - For we may so propose the truths relating to any part of knowledge, as they presented themselves to the mind in the manner of investigation, carrying on the series of proofs in a reverse order...

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