The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's DictumMacmillan, 1869 - 86 ページ |
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ABCD ABCD ABCd ABCDE ABCDEF act of reasoning adjective affirmative proposition analogy appears apply Aristotle Aristotle's dictum assert axiom axiom of Euclid Boole Boole's canon conclusion connexion consists conveniunt copula corresponding sides proportional deductive reasoning dictum de omni differs equal-sided equivalent Euclid example expression fallacy figure follows form of inference forms of reasoning formulæ George Bentham hence identity inch indefinite indirect induction inequalities infallible instance Iron J. S. Mill law of duality Laws of Thought logical doctrine logicians mathematical reasoning means ment metals are elements method mind monarch negative proposition obtain ordinary oxygen pins possible combinations pound weight premises principle of substitution proposition or equation quæ quantification quantity relation represented resemblance right-angled second member self-evident self-luminous Sir William Hamilton slips Socrates stitution straight-edge substitution of similars syllogism symbols System of Logic term element tion triangle true truth undecomposable substance
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62 ページ - But those animals profit by experience, and avoid what they have found to cause them pain, in the same manner, though not always with the same skill, as a human creature. Not only the burnt child, but the burnt dog, dreads the fire. I believe that, in point of fact, when drawing inferences from our personal experience, and not from maxims handed down to us by books or tradition, we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general...
69 ページ - The same attributes may be assigned to distinct but similar things, provided they can be shown to accompany the points of resemblance in the things, and not the points of difference. But since the pre-supposition of a power of discerning to what part of the things the attributes belong, is indispensable, the argument itself depends for its weight upon something external to itself, and sinks into a mere exposition.
64 ページ - Analogical reasoning, in this sense, may be reduced to the following formula:—Two things resemble each other in one or more respects ; a certain proposition is true of the one; therefore it is true of the other.
62 ページ - From instances which we have observed, we feel warranted in concluding that what we found true in those instances holds in all similar ones, past, present, and future, however numerous they may be.
62 ページ - I believe that, in point of fact, when drawing inferences from our personal experience, and not from maxims handed down to us by books or tradition, we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general proposition. We are constantly reasoning from ourselves to other people, or from one person to another, without giving ourselves the trouble to erect our observations into general maxims of human or external nature.
63 ページ - It is not only the village matron, who, when called to a consultation upon the case of a neighbor's child, pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her Lucy. We all, where we have no definite maxims to steer by, guide ourselves in the same way...
65 ページ - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
5 ページ - Copernicus, excited admiration from its first appearance. That the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an allcontaining system of logic, would not have been believed until it was proved. When Hobbes, in the time of the Commonwealth, published his ' Computation or Logique,' he had a remote glimpse of some of the points which are placed in the light of day by Mr....
74 ページ - ... if two terms agree with one and the same third, they agree with each other: secondly, if one term agrees and another disagrees with one and the same third, these two disagree with each other.
3 ページ - Atque revera quemadmodum majorem rerum humanarum notitiam et maturius judicium ab homine sene expectamus quam a juvene, propter experientiam et rerum, quas vidit, et audivit, et cogitavit, varietatem et copiam; eodem modo et a nostra aetate (si vires suas nosset, et experiri et intendere vellet) majora multo quam a priscis temporibus expectari par est; utpote aetate mundi grandiore, et infinitis experimentis et observationibus aucta et cumulata.