The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
From inside the book
Results 1-5 of 15
Page 10
... obvious fallacy if we argue in the opposite direc- tion , and infer of elements what we know only of 1 " Lectures on Logic , " vol . i . p . 303 . metals . This is neither authorized by Aristotle's dictum , IO THE SUBSTITUTION OF SIMILARS ,
... obvious fallacy if we argue in the opposite direc- tion , and infer of elements what we know only of 1 " Lectures on Logic , " vol . i . p . 303 . metals . This is neither authorized by Aristotle's dictum , IO THE SUBSTITUTION OF SIMILARS ,
Page 20
... tion at the same time . That most familiar process in mathematical reasoning , of substituting one member of an equation for the other , appears to be the type of all reasoning , and we may fitly name this all - important process the ...
... tion at the same time . That most familiar process in mathematical reasoning , of substituting one member of an equation for the other , appears to be the type of all reasoning , and we may fitly name this all - important process the ...
Page 23
... tion of the process in my own mind , and I must submit to the reader's judgment whether there are exceptions or not to the rule , that we always reason by means of identities or equalities . 19. Turning now to apply these considerations ...
... tion of the process in my own mind , and I must submit to the reader's judgment whether there are exceptions or not to the rule , that we always reason by means of identities or equalities . 19. Turning now to apply these considerations ...
Page 29
... tion of the above form occurs is the mood of the syllogism known by the name Barbara . As an example , we may take the following : - ( 1 ) Iron is a metal , ( 2 ) A metal is an element , therefore ( 3 ) Iron is an element . The ...
... tion of the above form occurs is the mood of the syllogism known by the name Barbara . As an example , we may take the following : - ( 1 ) Iron is a metal , ( 2 ) A metal is an element , therefore ( 3 ) Iron is an element . The ...
Page 36
... is self - evident that P of OP of O , and substituting in the second member the descrip- tion of O we have P of OP of OQ . 1 Thomson's " Outline , " § 88 . 34. In an exactly similar manner we may solve a 36 THE SUBSTITUTION OF SIMILARS ,
... is self - evident that P of OP of O , and substituting in the second member the descrip- tion of O we have P of OP of OQ . 1 Thomson's " Outline , " § 88 . 34. In an exactly similar manner we may solve a 36 THE SUBSTITUTION OF SIMILARS ,
Other editions - View all
Common terms and phrases
abacus ABCD adapted Algebra appended applied Aristotle Arithmetic arranged ATHENÆUM axiom BEGINNERS Bible Boole Calculus Cambridge canon chapter Christ's College CLASS-BOOK cloth combinations Conic Sections consists contains Crown 8vo dictum Education ELEMENTARY TREATISE endeavoured English equal equation Examination Papers exercises Extra fcap formulæ Fourth Edition Geometry George Bentham give Globe 8vo Grammar Greek Head Master Heir of Redclyffe identity illustrations inference Introduction Iron John's College language late Fellow Latin Laws of Thought Lecturer ledge LESSONS logical logicians manual Maps mathematical metals are elements method Metric System Notes numerous Examples ordinary Owens College predicate premises present principles problems Professor proposition pupil R. C. JEBB reader relation Royal Schools Second Edition selected slips student substitution of similars syllogism teachers Testament text-book theory Third Edition tion translation Trigonometry University University of Cambridge Uppingham School volume words
Popular passages
Page 13 - Astronomer Royal :— ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS. Designed for the Use of Students in the Universities. With Diagrams. Second Edition. Crown 8vo. $s. 6d. ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS.
Page 14 - ON SOUND AND ATMOSPHERIC VIBRATIONS. With the Mathematical Elements of Music. Designed for the Use of Students in the University. Second Edition, Revised and Enlarged. Crown 8vo.
Page 9 - THE SEVEN KINGS OF. ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Page 70 - Friends," with briefer Notes. i8mo. 3*. 6d. GREEK TESTAMENT. Edited, with Introduction and Appendices, by CANON WESTCOTT and Dr. FJA HORT. Two Vols. Crown 8vo. [/« the press. HARDWICK — Works by Archdeacon HARDWICK. A HISTORY OF THE CHRISTIAN CHURCH. Middle Age. From Gregory the Great to the Excommunication of Luther. Edited by WILLIAM STUBBS, MA, Regius Professor of Modern History in the University of Oxford. With Four Maps constructed for this work by A. KEITH JOHNSTON.
Page 4 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools. By F. HODGSON, BD, late Provost of Eton. New Edition, revised by FC HODGSON, MA i8mo. 3*.
Page 77 - STUDENT'S GUIDE to the more Correct Understanding of the English translation of the Old Testament, by reference to the Original Hebrew. By WILLIAM WILSON, DD, Canon of Winchester, late Fellow of Queen's College, Oxford. Second Edition, carefully Revised.
Page 38 - PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples. Fourth Edition, revised and enlarged. Crown 8vo. cloth.
Page 24 - Hemming. — AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use of Colleges and Schools. By GW HEMMING, MA, Fellow of St. John's College, Cambridge. Second Edition, with Corrections and Additions. 8vo. cloth. 2s. " There is no book in common use from which so cleat and exact a knmtiledge of the principles of the Calculus can be so readily obtained.
Page 59 - PYLODET— NEW GUIDE TO GERMAN CONVERSATION: containing an Alphabetical List of nearly 800 Familiar Words followed by Exercises, Vocabulary of Words in frequent use ; Familiar Phrases and Dialogues ; a Sketch of German Literature, Idiomatic Expressions, &c. By L. PYLODET.
Page 27 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.