## A Letter to Augustus De Morgan, Esq. ...: On His Claim to an Independent Re-discovery of a New Principle in the Theory of Syllogism |

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A Letter to Augustus de Morgan, Esq; on His Claim to an Independent Re ... Sir, William Hamilton No preview available - 2013 |

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Addition admit affirms afford allegations ANALYTIC OF LOGICAL answer Aristotle assertion aware believe Cambridge paper Cambridge Philosophical Society CAMDEN STREET canon of syllogism Categorical Syllogisms charge common doctrine comprehend concealment confusion contained contrary correspondence course DEAR SIR declare definite quantity discovery doctrine of Conversion doctrine of syllogism document EDINBURGH effective number Euclid exclusive excogitated expressed quantity extension quantity fact figures friend Dr gism give history of logic honourable hypothesis indefinite inference letter Logicians manifest mathematical middle term minor premise never obedient servant premises previously principle prize essay professed PROFESSOR DE MORGAN propositions Prospectus prove publication publicly published quantified predicate question receipt received recollection reference regard Requirements retract scheme of quantification second system second view secondary originality Sir William Hamilton subject and predicate subject or predicate supposed supposition Supreme Canon third scheme thought tion truth universal whilst whole words writing written

### Popular passages

Page 15 - In the second place, the self-evident truth, — That we can only rationally deal with what we already understand, determines the simple logical postulate,' — To state explicitly what is thought implicitly. From the consistent application of this postulate, on which Logic ever insists, but which Logicians have never fairly obeyed, it follows : — that, logically, we ought to take into account the quantity, always understood in thought, but usually, and for manifest reasons, elided in its expression,...

Page 46 - In fact, definite and indefiniie are the only quantities of which we ought to hear in Logic; for it is only as indefinite that particular, it is only as definite that individual and general, quantities have any (and the same) logical avail. 2°- The revocation of the two Terms of a Proposition to their true relation ; a proposition being always an equation of its subject and its predicate.

Page 8 - By mutual confidence, and mutual aid, Great deeds are done, and great discoveries made . The wise new prudence from the wise acquire And one brave hero fans another's fire.

Page 16 - The revocation of the two Terms of a Proposition to their true relation; a proposition being always an equation of its subject and its predicate. 3°, The consequent reduction of the Conversion of Propositions from three species to one — that of Simple Conversion. 4°, The reduction of all the General Laws of Categorical Syllogisms to a Single Canon.

Page 47 - 6°. The abrogation of all the Special Laws of Syllogism. " 7°. A demonstration of the exclusive possibility of Three Syllogistic Figures; and (on new grounds) the scientific and final abolition of the Fourth. " 8°. A manifestation that Figure is an unessential variation in syllogistic form ; and the consequent absurdity of Reducing the syllogisms of the other figures to the first. " 9°. An enouncement of one Organic Principle for each Figure. " 10°. A determination of the true number of the...

Page 47 - ... as legitimate ; and many relations, which heretofore lay hid, now come forward into the light On the one hand, therefore, Logic certainly becomes more complex. But on the other, this increased complexity proves only to be a higher development. The developed Syllogism is, in effect, recalled, from multitude and confusion, to order and system. Its laws, erewhile many, are now few, — we might say one alone, — but thoroughgoing. The exceptions, formerly so perplexing, have fallen away ; and the...

Page 47 - That, in the second and third figures, the extremes holding both the same relation to the middle term, there is not, as in the first, an opposition and subordination between a term major and a term minor mutually containing and contained, in the counter wholes of Extension and Comprehension. " 15°. Consequently, in the second and third figures, there is no determinate major and minor premise, and there are two indifferent conclusions; whereas, in the first, the premises are determinate, and there...

Page 48 - E tenebris tantis tam clarum extollere lumen qui primus potuisti inlustrans commoda vitae, te sequor, o Graiae gentis decus, inque tuis nunc ficta pedum pono pressis vestigia signis, non ita certandi cupidus quam propter amorem...

Page 42 - What worse relation of subject and predicate subsists between either of two terms and a common third term, with which both are related, and one at least positively so— that relation subsists between these two terms themselves.

Page 43 - I, it affirms, whilst 0 denies, Of some (or few or many). Thus A affirms, as E denies, And definitely either : Thus I affirms, as O denies, And definitely neither. A half, left semi-definite, Is worthy of its score ; U, then, affirms, as Y denies, This, neither less nor more.