A Treatise on Logic: Or, The Laws of Pure Thought; Comprising Both the Aristotelic and Hamiltonian Analyses of Logical Forms, and Some Chapters of Applied Logic

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Sever and Francis, 1864 - 450 páginas
 

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Página 423 - Intuitions can be now known to us only by an act of remembrance ; and as the strength of a chain is the strength of its weakest link...
Página 392 - It consists in ascribing the character of general truths to all propositions which are true in every instance that we happen to know of.
Página 24 - And a little attention will discover that it is not necessary (even in the strictest reasonings) that significant names which stand for ideas should, every time they are used, excite in the understanding the ideas they are made to stand for : in reading and discoursing, names being for the most part used as letters are in Algebra...
Página 297 - Englishmen or not-Englishmen,' to the exclusion of the third possibility of a mixed force, so it is false to say, ' Every body must move in the place where it is, or in the place where it is not,' to the exclusion of the third possibility of moving partly in the one and partly in the other.
Página 444 - were to determine to play for their whole property, what would be the effect of this agreement? The one would only double his fortune, and the other reduce his to naught. What proportion is there between the loss and the gain? The same that there is between all and nothing. The gain of the one is but a moderate sum, — the loss of the other is numerically infinite, and morally so great that the labour of his whole life may not perhaps suffice to restore his property.
Página 392 - ... apprehension. If, then, the processes which bring these cases within the same category with the rest require that we should assume the universality of the very law which they do not at first sight appear to exemplify, is not this a petitio principii? Can we prove a proposition by an argument which takes it for granted? And if not so proved, on what evidence does it rest?
Página 392 - To an inhabitant of Central Africa, fifty years ago, no fact probably appeared to rest on more uniform experience than this, that all human beings are black. To Europeans, not many years ago, the proposition, All swans are white, appeared an equally unequivocal instance of uniformity in the course of nature. Further experience has proved to both that they were mistaken; but they had to wait fifty centuries for this experience.
Página 290 - ... 2. None but Whites are civilized : the ancient Germans were Whites : therefore they were civilized. 3. None but Whites are civilized : the Hindoos are not Whites : therefore they are not civilized. 4. None but civilized people are Whites : the Gauls were Whites : therefore they were civilized. 5. No one is rich who has not enough : no miser has enough : therefore no miser is rich. 6. If penal laws against Papists were , enforced, they would be aggrieved : but penal laws against them are not enforced...
Página 23 - Words are the fortresses of thought. They enable us to realize our dominion over what we have already overrun in thought, — to make every intellectual conquest the basis of operations for others still beyond. Or another illustration : You have all heard of the process of tunnelling, of tunnelling through a sand-bank. In this operation it is impossible to succeed unless every foot — nay, almost every inch — in our progress be secured by an arch of masonry, before we attempt the excavation of...
Página 150 - Mathematics. so denominated, and thought proper, we have seen, is the cognition of one object of thought by another, in or under which it is mentally included ; in other words, thought is the knowledge of a thing through a concept or general notion, or of one notion through another.

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