The Principles of Logic: For High Schools and Colleges |
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Common terms and phrases
absurd affirmative conclusion attributes Cæsar categorical categorical proposition cause Classification clusion coextensive comprehends conceive consequent contained contrary Definition denotes Denying the antecedent Disjunctive Syllogisms distribute the predicate division earth Enthymeme Euathlus excluded expression extensive quantity extreme fallacy false fErIO finite Formal Fallacies free agent genus Hamilton's harmony of thought Hence hypothetical Hypothetical Syllogisms illicit process implies the falsity implies the truth Induction and Analogy infer intersects intuitions invalid involves judgment Law of Contradictories laws of thought logical major premise major term Mathematical induction method middle term mind minor term moon moral motion non-P non-S object observed order to distribute petitio principii phenomena polygon polytomy Prem principle prove Real induction reasoning reductio ad absurdum relation responsible agent right angles space is infinite species subordinate theological conceptions thing tion tive triangles true undistributed middle valid moods warrant whole
Popular passages
Page 145 - it will argue nothing against the trustworthiness of consciousness that all, or any of its deliverances, are inexplicable, are incomprehensible; that is, that we are unable to conceive through a higher notion how that is possible, which the deliverance avouches actually to be. To make the comprehensibility of a datum of consciousness the criterion of its truth would be, indeed, the climax of absurdity.
Page 121 - A miracle is an effect or event contrary to the established constitution or course of things ; or a sensible suspension or controlment of, or deviation from, the known laws of nature, wrought either by the immediate act, or by the concurrence, or by the permission of God, for the proof or evidence of some particular doctrine, or in attestation of the authority of some particular person.
Page 149 - All men are mortal: that the general principle, instead of being given as evidence of the particular case cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised with it, is dispelled by evidence aliunde; and then what remains for the syllogism to prove?
Page 115 - Whatever be the most proper mode of expressing it, the proposition that the course of nature is uniform, is the fundamental principle, or general axiom, of Induction. It would yet be a great error to offer this large generalization as any explanation of the inductive process. On the contrary, I hold it to be itself an instance of induction, and induction by no means of the most obvious kind.
Page 114 - Major that is suppressed, as being in all cases substantially the same: viz. that what belongs to the individual or individuals we have examined, belongs (certainly, or probably, as the case may be) to the whole class under which they come.
Page 148 - It must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say, All men are mortal, Socrates is a man, therefore Socrates is mortal; it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, Socrates is mortal...
Page 144 - Taking it as a whole: space, it is evident, must either be limited, that is, have an end, and circumference; or unlimited, that is, have no end, no circumference. These are contradictory suppositions; both, therefore, cannot, but one must, be true. Now let us try positively to comprehend, positively to conceive,* the possibility of either of these two mutually exclusive alternatives. Can we represent, or realize in thought, extension as absolutely limited? in other words, can we mentally hedge round...
Page 46 - Also it is manifest, that nothing has parts till it be divided; and when a thing is divided, the parts are only so many as the division makes them. Again, that a part of a part is a part of the whole...
Page 119 - Polygons are classified according to the number of sides. A triangle is a polygon of three sides. A quadrilateral is a polygon of four sides. A pentagon is a polygon of five sides. A hexagon is a polygon of six sides.
Page 148 - ; that the general principle, instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised with it is dispelled by evidence...