The Elements of Logic: In Four Books. Designed Particularly for Young Gentlemen at the University; and to Prepare the Way to the Study of Philosophy and the Mathematics

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E.F. Backus, at the Albany bookstore, No. 45 State-street, 1811 - Logic - 261 pages
 

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Page 165 - 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 165 - 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 connexion 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 165 - 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 149 - 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 6 - Logic, which may be justly styled the history of the humanmind, inasmuch as it traces the progress of our knowledge, from our first and simple perceptions, through all their different combinations, and all those numerous deductions that result from variously comparing them one with another. It is thus that we are let into the natural frame and contexture of our own minds, and learn in what manner we ought to conduct our thoughts, in order to arrive at truth, and avoid error. We...
Page 180 - A dilemma is an argument by which we endeavour to prove the absurdity or falsehood of some assertion. In order to this, we assume a conditional proposition, the antecedent of which is the assertion to be disproved, and the consequent a disjunctive proposition, enumerating all the possible suppositions upon which that assertion can take place. If then it appears, that all these several suppositions are to be rejected, it is plain, that the antecedent or assertion itself must be so too.
Page 158 - Here then we apply the general truth to some obvious instance, and this is what properly constitutes the reasoning of common life. For men in their ordinary transactions and intercourse one •with another, have for the most part to do only with particular objects. Our friends and relations, their characters and...
Page 184 - That in which the middle term is the subject of the major proposition, and the predicate of the minor.
Page 38 - ... the series may be carried on without confusion to any length we please. " This artful combination of names to mark the gradual increase of numbers, is perhaps one of the greatest refinements of the human understanding, and particularly deserves our admiration for the manner of the composition } the several denominations being so contrived as to distinguish exactly the stages of the progression, and point out the distance from the beginning of the series. By this means it happens that our ideas...
Page 96 - But in order to the better underftanding of what follows, it will be necefiary to obferve, that there is a certain Gradation in the Compofition of our Ideas. The Mind of Man is very limited in its Views, and cannot take in a great Number of Objects at once. We are therefore fain to proceed by Steps, and make our firft Advances fubfervient to thofe which follow.

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