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additional extent affirmative aggregate angles applied assertion or denial attribute animal called Cambridge Transactions class animal clusion coinadequate combinations complement compound conclusion connexion contained contradiction convertible copula deficient denied dependent different quantities distinction equal essential Everything exemplar system extent and intent external false Formal Logic full intent genus gism giving X))Z identical inalternative incompossible independent inessential inference irrepugnant joined laws of thought logicians mathematicians mathematics matter of thought means metaphysical metical middle term mind minor premise mode necessary negative not-X not-Y notation notion number of instances object of thought onymatic particular syllogisms partient post 8vo predicate primary phase proof qualities reader repugnant alternatives Sir William Hamilton species spurious strengthened particular subcontrary subidentical supercontrary superidentical syllabus symbols tension things transitive transposible true unit-syllogism universal proposition utmost vague extent whole words Xs are Ys Xs nor Ys xy m Xy Ys are Zs YZ XZ
Page 34 - may be predicated of any one who studies a branch or a case, without afterwards making it part of a larger whole. Accordingly, it is always worth while to generalise, were it only to give power over the particular. This principle, of daily familiarity to the mathematician, is almost unknown to the logician.
Page 27 - series of elegant extracts—out of the forms of thinking. Whether the form that it exhibits as legitimate be stronger or weaker, be more or less frequently applied; — that, as a material and contingent consideration, is beyond its purview.
Page 41 - 132. The name of greatest extension, and of least intension, of which we speak, is the universe. 133. The contrary of an aggregate is the compound of the contraries of the aggregants: either one of the two X, Y, or both not-X and
Page 41 - either (X, Y) or (xy). The contrary of a compound is the aggregate of the contraries of the components; either both X and Y, or one of the two,
Page 24 - either or both. The second (8) is true in all cases in which either X or Y has two or more instances in existence : its contrary is ' X and Y are singular and identical; there is but one X, there is but one
Page 34 - is suggested. Nobody who has ever returned to quadratic equations after the study of equations of all degrees, or who has done the like, will deny my assertion that
Page 27 - 73. The following passage, written by Sir William Hamilton himself, should be quoted in every logical treatise: for it ought to be said, and cannot be said better. " Whatever is operative in thought, must be taken into account, and consequently be overtly expressible in logic; for logic must be, as to be it professes, an unexclusive reflex of thought, and not merely an arbitrary selection— a series of elegant
Page 32 - The uneducated acquire easy and accurate use of the very simplest cases of transformation of propositions and of syllogism. The educated, by a higher kind of practice, arrive at equally easy and accurate use of some more complicated cases : but not of all those which are treated in ordinary logic. Euclid may have been ignorant of the identity of " Every X is Y " and
Page 31 - Y is fastened to Z ' give ' X is fastened to Z'. * All the copulae used in this syllabus are transitive. The intransitive copula cannot be treated without more extensive consideration of the combination of relations than I have now opportunity to give: a second part of this syllabus, or an augmented edition, may contain something on this subject.