pg_xivpg_xvCONTENTSBOOK I.THINGS AND THEIR ATTRIBUTES.CHAPTER I.INTRODUCTORY.page‘Things’1‘Attributes’〃‘Adjuncts’〃CHAPTER II.CLASSIFICATION.‘Classification’1½‘Class’〃‘Peculiar’ Attributes〃‘Genus’〃‘Species’〃‘Differentia’〃‘Real’ and ‘Unreal’, or ‘Imaginary’, Classes2‘Individual’〃A Class regarded as a single Thing2½pg_xviCHAPTER III.DIVISION.§ 1.Introductory.‘Division’3‘Codivisional’ Classes〃§ 2.Dichotomy.‘Dichotomy’3½Arbitrary limits of Classes〃Subdivision of Classes4CHAPTER IV.NAMES.‘Name’4½‘Real’ and ‘Unreal’ Names〃Three ways of expressing a Name〃Two senses in which a plural Name may be used5CHAPTER V.DEFINITIONS.‘Definition’6Examples worked as models〃pg_xviiBOOK II.PROPOSITIONS.CHAPTER I.PROPOSITIONS GENERALLY.§ 1.Introductory.Technical meaning of “some”8‘Proposition’〃‘Normal form’ of a Proposition〃‘Subject’, ‘Predicate’, and ‘Terms’9§ 2.Normal form of a Proposition.Its four parts:—(1) ‘Sign of Quantity’〃(2) Name of Subject〃(3) ‘Copula’〃(4) Name of Predicate〃§ 3.Various kinds of Propositions.Three kinds of Propositions:—(1) Begins with “Some”. Called a ‘Particular’ Proposition: also a Proposition ‘in I’10(2) Begins with “No”. Called a ‘Universal Negative’ Proposition: also a Proposition ‘in E’〃(3) Begins with “All”. Called a ‘Universal Affirmative’ Proposition: also a Proposition ‘in A’〃pg_xviiiA Proposition, whose Subject is an Individual, is to be regarded as Universal〃Two kinds of Propositions, ‘Propositions of Existence’, and ‘Propositions of Relation’〃CHAPTER II.PROPOSITIONS OF EXISTENCE.‘Proposition of Existence’11CHAPTER III.PROPOSITIONS OF RELATION.§ 1.Introductory.‘Proposition of Relation’12‘Universe of Discourse,’ or ‘Univ.’〃§ 2.Reduction of a Proposition of Relation to Normal form.Rules13Examples worked〃§ 3.A Proposition of Relation, beginning with “All”, is a Double Proposition.Its equivalence totwoPropositions17pg_xix§ 4.What is implied, in a Proposition of Relation, as to the Reality of its Terms?Propositions beginning with “Some”19Propositions beginning with “No”〃Propositions beginning with “All”〃§ 5.Translation of a Proposition of Relation into one or more Propositions of Existence.Rules20Examples worked〃BOOK III.THE BILITERAL DIAGRAM.CHAPTER I.SYMBOLS AND CELLS.The Diagram assigned to a certain Set of Things, viz. our Univ.22Univ. divided into ‘thex-Class’ and ‘thex′-Class’23The North and South Halves assigned to these two Classes〃Thex-Class subdivided into ‘thexy-Class’ and ‘thexy′-Class’〃The North-West and North-East Cells assigned to these two Classes〃Thex′-Class similarly divided〃The South-West and South-East Cells similarly assigned〃The West and East Halves have thus been assigned to ‘they-Class’ and ‘they′-Class’〃Table I.Attributes of Classes, and Compartments, or Cells, assigned to them25pg_xxCHAPTER II.COUNTERS.Meaning of a Red Counter placed in a Cell26Meaning of a Red Counter placed on a Partition〃American phrase “sitting on the fence”〃Meaning of a Grey Counter placed in a Cell〃CHAPTER III.REPRESENTATION OF PROPOSITIONS.§ 1.Introductory.The word “Things” to be henceforwards omitted27‘Uniliteral’ Proposition〃‘Biliteral’ do.〃Proposition ‘in terms of’ certain Letters〃§ 2.Representation of Propositions of Existence.The Proposition “Somexexist”28Three other similar Propositions〃The Proposition “Noxexist”〃Three other similar Propositions29The Proposition “Somexyexist”〃Three other similar Propositions〃The Proposition “Noxyexist”〃Three other similar Propositions〃The Proposition “Noxexist” isDouble, and is equivalent to the two Propositions “Noxyexist” and “Noxy′exist”30pg_xxi§ 3.Representation of Propositions of Relations.The Proposition “Somexarey”〃Three other similar Propositions〃The Proposition “Someyarex”31Three other similar Propositions〃Trio of equivalent Propositions, viz. “Somexyexist” = “Somexarey” = “Someyarex”〃‘Converse’ Propositions, and ‘Conversion’〃Three other similar Trios32The Proposition “Noxarey”〃Three other similar Propositions〃The Proposition “Noyarex”〃Three other similar Propositions〃Trio of equivalent Propositions, viz. “Noxyexist” = “Noxarey” = “Noyarex”33Three other similar Trios〃The Proposition “Allxarey” isDouble, and is equivalent to the two Propositions “Somexarey” and “Noxarey′”〃Seven other similar Propositions34Table II.Representation of Propositions of Existence34Table III.Representation of Propositions of Relation35CHAPTER IV.INTERPRETATION OF BILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS.Interpretation ofDiagram representing x y exists36And of three other similar arrangements〃pg_xxiiInterpretation ofDiagram representing x y does not exist〃And of three other similar arrangements〃Interpretation ofDiagram representing x exists37And of three other similar arrangements〃Interpretation ofDiagram representing x exists with and without y〃And of three other similar arrangements〃Interpretation ofDiagram representing x does not exist〃And of three other similar arrangements〃Interpretation ofDiagram representing all x are y〃And of seven other similar arrangements38BOOK IV.THE TRILITERAL DIAGRAM.CHAPTER I.SYMBOLS AND CELLS.Change of Biliteral into Triliteral Diagram39Thexy-Class subdivided into ‘thexym-Class’ and ‘thexym′-Class’40pg_xxiiiThe Inner and Outer Cells of the North-West Quarter assigned to these Classes〃Thexy′-Class, thex′y-Class, and thex′y′-Class similarly subdivided〃The Inner and Outer Cells of the North-East, the South-West, and the South-East Quarter similarly assigned〃The Inner Square and the Outer Border have thus been assigned to ‘them-Class’ and ‘them′-Class’〃Rules for finding readily the Compartment, or Cell, assigned to any given Attribute or Attributes〃Table IV.Attributes of Classes, and Compartments, or Cells, assigned to them42CHAPTER II.REPRESENTATION OF PROPOSITIONS IN TERMS OFxANDm, OR OFyANDm.§ 1.Representation of Propositions of Existence in terms ofxandm, or ofyandm.The Proposition “Somexmexist”43Seven other similar Propositions〃The Proposition “Noxmexist”44Seven other similar Propositions〃§ 2.Representation of Propositions of Relation in terms ofxandm, or ofyandm.The Pair of Converse Propositions “Somexarem” = “Somemarex”〃Seven other similar Pairs〃The Pair of Converse Propositions “Noxarem” = “Nomarex”〃Seven other similar Pairs〃The Proposition “Allxarem”45Fifteen other similar Propositions〃Table V.Representations of Propositions in terms ofxandm46Table VI.Representations of Propositions in terms ofyandm47Table VII.Representations of Propositions in terms ofxandm48Table VIII.Representations of Propositions in terms ofyandm49pg_xxivCHAPTER III.REPRESENTATION OF TWO PROPOSITIONS OF RELATION, ONE IN TERMS OFxANDm, AND THE OTHER IN TERMS OFyANDm, ON THE SAME DIAGRAM.The Digits “I” and “O” to be used instead of Red and Grey Counters50Rules〃Examples worked〃CHAPTER IV.INTERPRETATION, IN TERMS OFxANDy, OF TRILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS OR DIGITS.Rules53Examples worked54BOOK V.SYLLOGISMS.CHAPTER I.INTRODUCTORY.‘Syllogism’56‘Premisses’〃‘Conclusion’〃‘Eliminands’〃‘Retinends’〃‘Consequent’〃The Symbol “∴”〃Specimen-Syllogisms57pg_xxvCHAPTER II.PROBLEMS IN SYLLOGISMS.§ 1.Introductory.‘Concrete’ and ‘Abstract’ Propositions59Method of translating a Proposition from concrete into abstract form〃Two forms of Problems〃§ 2.Given a Pair of Propositions of Relation, which contain between them a Pair of codivisional Classes, and which are proposed as Premisses: to ascertain what Conclusion, if any, is consequent from them.Rules60Examples worked fully〃The same worked briefly, as models64§ 3.Given a Trio of Propositions of Relation, of which every two contain a Pair of codivisional Classes, and which are proposed as a Syllogism: to ascertain whether the proposed Conclusion is consequent from the proposed Premisses, and, if so, whether it is complete.Rules66Examples worked briefly, as models〃pg_xxviBOOK VI.THE METHOD OF SUBSCRIPTS.CHAPTER I.INTRODUCTORY.Meaning ofx1,xy1, &c.70‘Entity’〃Meaning ofx0,xy0, &c.〃‘Nullity’〃The Symbols “†” and “¶”〃‘Like’ and ‘unlike’ Signs〃CHAPTER II.REPRESENTATION OF PROPOSITIONS OF RELATION.The Pair of Converse Propositions “Somexarey” = “Someyarex”71Three other similar Pairs〃The Pair of Converse Propositions “Noxarey” = “Noyarex”〃Three other similar Pairs〃The Proposition “Allxarey”72The Proposition “Allxarey” isDouble, and is equivalent to the two Propositions “Somexexist” and “Noxandy′”〃Seven other similar Propositions〃Rule for translating “Allxarey” from abstract into subscript form, andvice versâ〃pg_xxviiCHAPTER III.SYLLOGISMS.§ 1.Representation of Syllogisms.Rules73§ 2.Formulæ for Syllogisms.Three Formulæ worked out:—Fig. I.xm0†ym′0¶xy075its two Variants (α) and (β)〃Fig. II.xm0†ym1¶x′y176Fig. III.xm0†ym0†m1¶x′y′177Table IX.Formulæ and Rules78Examples worked briefly, as models〃§ 3.Fallacies.‘Fallacy’81Method of finding Forms of Fallacies82Forms best stated inwords〃Three Forms of Fallacies:—(1) Fallacy of Like Eliminands not asserted to exist〃(2) Fallacy of Unlike Eliminands with an Entity-Premiss83(3) Fallacy of two Entity-Premisses〃§ 4.Method of proceeding with a given Pair of Propositions.Rules84pg_xxviiiBOOK VII.SORITESES.CHAPTER I.INTRODUCTORY.‘Sorites’85‘Premisses’〃‘Partial Conclusion’〃‘Complete Conclusion’ (or ‘Conclusion’)〃‘Eliminands’〃‘Retinends’〃‘consequent’〃The Symbol “∴”〃Specimen-Soriteses86CHAPTER II.PROBLEMS IN SORITESES.§ 1.Introductory.Form of Problem87Two Methods of Solution〃§ 2.Solution by Method of Separate Syllogisms.Rules88Example worked〃pg_xxix§ 3.Solution by Method of Underscoring.‘Underscoring’91Subscripts to be omitted〃Example worked fully92Example worked briefly, as model93Seventeen Examination-Papers94BOOK VIII.EXAMPLES, WITH ANSWERS AND SOLUTIONS.CHAPTER I.EXAMPLES.§ 1.Propositions of Relation, to be reduced to normal form97§ 2.Pairs of Abstract Propositions, one in terms ofxandm, and the other in terms ofyandm, to be represented on the same Triliteral Diagram98§ 3.Marked Triliteral Diagrams, to be interpreted in terms ofxandy99§ 4.Pairs of Abstract Propositions, proposed as Premisses: Conclusions to be found100pg_xxx§ 5.Pairs of Concrete Propositions, proposed as Premisses: Conclusions to be found101§ 6.Trios of Abstract Propositions, proposed as Syllogisms: to be examined106§ 7.Trios of Concrete Propositions, proposed as Syllogisms: to be examined107§ 8.Sets of Abstract Propositions, proposed as Premisses for Soriteses: Conclusions to be found110§ 9.Sets of Concrete Propositions, proposed as Premisses for Soriteses: Conclusions to be found112CHAPTER II.ANSWERS.Answers to§ 1125§ 2126§ 3127§ 4〃§ 5128§ 6130§ 7131§ 8132§ 9〃pg_xxxiCHAPTER III.SOLUTIONS.§ 1.Propositions of Relation reduced to normal form.Solutions for § 1134§ 2.Method of Diagrams.Solutions for§ 4 Nos. 1 to 12136§ 5 〃 1 to 12138§ 6 〃 1 to 10141§ 7 〃 1 to 6144§ 3.Method of Subscripts.Solutions for§ 4146§ 5 Nos. 13 to 24147§ 6148§ 7150§ 8155§ 9157NOTES164APPENDIX, ADDRESSED TO TEACHERS165NOTES TO APPENDIX195INDEX.§ 1. Tables197§ 2. Words &c. explained〃
pg_xivpg_xvCONTENTSBOOK I.THINGS AND THEIR ATTRIBUTES.CHAPTER I.INTRODUCTORY.page‘Things’1‘Attributes’〃‘Adjuncts’〃CHAPTER II.CLASSIFICATION.‘Classification’1½‘Class’〃‘Peculiar’ Attributes〃‘Genus’〃‘Species’〃‘Differentia’〃‘Real’ and ‘Unreal’, or ‘Imaginary’, Classes2‘Individual’〃A Class regarded as a single Thing2½pg_xviCHAPTER III.DIVISION.§ 1.Introductory.‘Division’3‘Codivisional’ Classes〃§ 2.Dichotomy.‘Dichotomy’3½Arbitrary limits of Classes〃Subdivision of Classes4CHAPTER IV.NAMES.‘Name’4½‘Real’ and ‘Unreal’ Names〃Three ways of expressing a Name〃Two senses in which a plural Name may be used5CHAPTER V.DEFINITIONS.‘Definition’6Examples worked as models〃pg_xviiBOOK II.PROPOSITIONS.CHAPTER I.PROPOSITIONS GENERALLY.§ 1.Introductory.Technical meaning of “some”8‘Proposition’〃‘Normal form’ of a Proposition〃‘Subject’, ‘Predicate’, and ‘Terms’9§ 2.Normal form of a Proposition.Its four parts:—(1) ‘Sign of Quantity’〃(2) Name of Subject〃(3) ‘Copula’〃(4) Name of Predicate〃§ 3.Various kinds of Propositions.Three kinds of Propositions:—(1) Begins with “Some”. Called a ‘Particular’ Proposition: also a Proposition ‘in I’10(2) Begins with “No”. Called a ‘Universal Negative’ Proposition: also a Proposition ‘in E’〃(3) Begins with “All”. Called a ‘Universal Affirmative’ Proposition: also a Proposition ‘in A’〃pg_xviiiA Proposition, whose Subject is an Individual, is to be regarded as Universal〃Two kinds of Propositions, ‘Propositions of Existence’, and ‘Propositions of Relation’〃CHAPTER II.PROPOSITIONS OF EXISTENCE.‘Proposition of Existence’11CHAPTER III.PROPOSITIONS OF RELATION.§ 1.Introductory.‘Proposition of Relation’12‘Universe of Discourse,’ or ‘Univ.’〃§ 2.Reduction of a Proposition of Relation to Normal form.Rules13Examples worked〃§ 3.A Proposition of Relation, beginning with “All”, is a Double Proposition.Its equivalence totwoPropositions17pg_xix§ 4.What is implied, in a Proposition of Relation, as to the Reality of its Terms?Propositions beginning with “Some”19Propositions beginning with “No”〃Propositions beginning with “All”〃§ 5.Translation of a Proposition of Relation into one or more Propositions of Existence.Rules20Examples worked〃BOOK III.THE BILITERAL DIAGRAM.CHAPTER I.SYMBOLS AND CELLS.The Diagram assigned to a certain Set of Things, viz. our Univ.22Univ. divided into ‘thex-Class’ and ‘thex′-Class’23The North and South Halves assigned to these two Classes〃Thex-Class subdivided into ‘thexy-Class’ and ‘thexy′-Class’〃The North-West and North-East Cells assigned to these two Classes〃Thex′-Class similarly divided〃The South-West and South-East Cells similarly assigned〃The West and East Halves have thus been assigned to ‘they-Class’ and ‘they′-Class’〃Table I.Attributes of Classes, and Compartments, or Cells, assigned to them25pg_xxCHAPTER II.COUNTERS.Meaning of a Red Counter placed in a Cell26Meaning of a Red Counter placed on a Partition〃American phrase “sitting on the fence”〃Meaning of a Grey Counter placed in a Cell〃CHAPTER III.REPRESENTATION OF PROPOSITIONS.§ 1.Introductory.The word “Things” to be henceforwards omitted27‘Uniliteral’ Proposition〃‘Biliteral’ do.〃Proposition ‘in terms of’ certain Letters〃§ 2.Representation of Propositions of Existence.The Proposition “Somexexist”28Three other similar Propositions〃The Proposition “Noxexist”〃Three other similar Propositions29The Proposition “Somexyexist”〃Three other similar Propositions〃The Proposition “Noxyexist”〃Three other similar Propositions〃The Proposition “Noxexist” isDouble, and is equivalent to the two Propositions “Noxyexist” and “Noxy′exist”30pg_xxi§ 3.Representation of Propositions of Relations.The Proposition “Somexarey”〃Three other similar Propositions〃The Proposition “Someyarex”31Three other similar Propositions〃Trio of equivalent Propositions, viz. “Somexyexist” = “Somexarey” = “Someyarex”〃‘Converse’ Propositions, and ‘Conversion’〃Three other similar Trios32The Proposition “Noxarey”〃Three other similar Propositions〃The Proposition “Noyarex”〃Three other similar Propositions〃Trio of equivalent Propositions, viz. “Noxyexist” = “Noxarey” = “Noyarex”33Three other similar Trios〃The Proposition “Allxarey” isDouble, and is equivalent to the two Propositions “Somexarey” and “Noxarey′”〃Seven other similar Propositions34Table II.Representation of Propositions of Existence34Table III.Representation of Propositions of Relation35CHAPTER IV.INTERPRETATION OF BILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS.Interpretation ofDiagram representing x y exists36And of three other similar arrangements〃pg_xxiiInterpretation ofDiagram representing x y does not exist〃And of three other similar arrangements〃Interpretation ofDiagram representing x exists37And of three other similar arrangements〃Interpretation ofDiagram representing x exists with and without y〃And of three other similar arrangements〃Interpretation ofDiagram representing x does not exist〃And of three other similar arrangements〃Interpretation ofDiagram representing all x are y〃And of seven other similar arrangements38BOOK IV.THE TRILITERAL DIAGRAM.CHAPTER I.SYMBOLS AND CELLS.Change of Biliteral into Triliteral Diagram39Thexy-Class subdivided into ‘thexym-Class’ and ‘thexym′-Class’40pg_xxiiiThe Inner and Outer Cells of the North-West Quarter assigned to these Classes〃Thexy′-Class, thex′y-Class, and thex′y′-Class similarly subdivided〃The Inner and Outer Cells of the North-East, the South-West, and the South-East Quarter similarly assigned〃The Inner Square and the Outer Border have thus been assigned to ‘them-Class’ and ‘them′-Class’〃Rules for finding readily the Compartment, or Cell, assigned to any given Attribute or Attributes〃Table IV.Attributes of Classes, and Compartments, or Cells, assigned to them42CHAPTER II.REPRESENTATION OF PROPOSITIONS IN TERMS OFxANDm, OR OFyANDm.§ 1.Representation of Propositions of Existence in terms ofxandm, or ofyandm.The Proposition “Somexmexist”43Seven other similar Propositions〃The Proposition “Noxmexist”44Seven other similar Propositions〃§ 2.Representation of Propositions of Relation in terms ofxandm, or ofyandm.The Pair of Converse Propositions “Somexarem” = “Somemarex”〃Seven other similar Pairs〃The Pair of Converse Propositions “Noxarem” = “Nomarex”〃Seven other similar Pairs〃The Proposition “Allxarem”45Fifteen other similar Propositions〃Table V.Representations of Propositions in terms ofxandm46Table VI.Representations of Propositions in terms ofyandm47Table VII.Representations of Propositions in terms ofxandm48Table VIII.Representations of Propositions in terms ofyandm49pg_xxivCHAPTER III.REPRESENTATION OF TWO PROPOSITIONS OF RELATION, ONE IN TERMS OFxANDm, AND THE OTHER IN TERMS OFyANDm, ON THE SAME DIAGRAM.The Digits “I” and “O” to be used instead of Red and Grey Counters50Rules〃Examples worked〃CHAPTER IV.INTERPRETATION, IN TERMS OFxANDy, OF TRILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS OR DIGITS.Rules53Examples worked54BOOK V.SYLLOGISMS.CHAPTER I.INTRODUCTORY.‘Syllogism’56‘Premisses’〃‘Conclusion’〃‘Eliminands’〃‘Retinends’〃‘Consequent’〃The Symbol “∴”〃Specimen-Syllogisms57pg_xxvCHAPTER II.PROBLEMS IN SYLLOGISMS.§ 1.Introductory.‘Concrete’ and ‘Abstract’ Propositions59Method of translating a Proposition from concrete into abstract form〃Two forms of Problems〃§ 2.Given a Pair of Propositions of Relation, which contain between them a Pair of codivisional Classes, and which are proposed as Premisses: to ascertain what Conclusion, if any, is consequent from them.Rules60Examples worked fully〃The same worked briefly, as models64§ 3.Given a Trio of Propositions of Relation, of which every two contain a Pair of codivisional Classes, and which are proposed as a Syllogism: to ascertain whether the proposed Conclusion is consequent from the proposed Premisses, and, if so, whether it is complete.Rules66Examples worked briefly, as models〃pg_xxviBOOK VI.THE METHOD OF SUBSCRIPTS.CHAPTER I.INTRODUCTORY.Meaning ofx1,xy1, &c.70‘Entity’〃Meaning ofx0,xy0, &c.〃‘Nullity’〃The Symbols “†” and “¶”〃‘Like’ and ‘unlike’ Signs〃CHAPTER II.REPRESENTATION OF PROPOSITIONS OF RELATION.The Pair of Converse Propositions “Somexarey” = “Someyarex”71Three other similar Pairs〃The Pair of Converse Propositions “Noxarey” = “Noyarex”〃Three other similar Pairs〃The Proposition “Allxarey”72The Proposition “Allxarey” isDouble, and is equivalent to the two Propositions “Somexexist” and “Noxandy′”〃Seven other similar Propositions〃Rule for translating “Allxarey” from abstract into subscript form, andvice versâ〃pg_xxviiCHAPTER III.SYLLOGISMS.§ 1.Representation of Syllogisms.Rules73§ 2.Formulæ for Syllogisms.Three Formulæ worked out:—Fig. I.xm0†ym′0¶xy075its two Variants (α) and (β)〃Fig. II.xm0†ym1¶x′y176Fig. III.xm0†ym0†m1¶x′y′177Table IX.Formulæ and Rules78Examples worked briefly, as models〃§ 3.Fallacies.‘Fallacy’81Method of finding Forms of Fallacies82Forms best stated inwords〃Three Forms of Fallacies:—(1) Fallacy of Like Eliminands not asserted to exist〃(2) Fallacy of Unlike Eliminands with an Entity-Premiss83(3) Fallacy of two Entity-Premisses〃§ 4.Method of proceeding with a given Pair of Propositions.Rules84pg_xxviiiBOOK VII.SORITESES.CHAPTER I.INTRODUCTORY.‘Sorites’85‘Premisses’〃‘Partial Conclusion’〃‘Complete Conclusion’ (or ‘Conclusion’)〃‘Eliminands’〃‘Retinends’〃‘consequent’〃The Symbol “∴”〃Specimen-Soriteses86CHAPTER II.PROBLEMS IN SORITESES.§ 1.Introductory.Form of Problem87Two Methods of Solution〃§ 2.Solution by Method of Separate Syllogisms.Rules88Example worked〃pg_xxix§ 3.Solution by Method of Underscoring.‘Underscoring’91Subscripts to be omitted〃Example worked fully92Example worked briefly, as model93Seventeen Examination-Papers94BOOK VIII.EXAMPLES, WITH ANSWERS AND SOLUTIONS.CHAPTER I.EXAMPLES.§ 1.Propositions of Relation, to be reduced to normal form97§ 2.Pairs of Abstract Propositions, one in terms ofxandm, and the other in terms ofyandm, to be represented on the same Triliteral Diagram98§ 3.Marked Triliteral Diagrams, to be interpreted in terms ofxandy99§ 4.Pairs of Abstract Propositions, proposed as Premisses: Conclusions to be found100pg_xxx§ 5.Pairs of Concrete Propositions, proposed as Premisses: Conclusions to be found101§ 6.Trios of Abstract Propositions, proposed as Syllogisms: to be examined106§ 7.Trios of Concrete Propositions, proposed as Syllogisms: to be examined107§ 8.Sets of Abstract Propositions, proposed as Premisses for Soriteses: Conclusions to be found110§ 9.Sets of Concrete Propositions, proposed as Premisses for Soriteses: Conclusions to be found112CHAPTER II.ANSWERS.Answers to§ 1125§ 2126§ 3127§ 4〃§ 5128§ 6130§ 7131§ 8132§ 9〃pg_xxxiCHAPTER III.SOLUTIONS.§ 1.Propositions of Relation reduced to normal form.Solutions for § 1134§ 2.Method of Diagrams.Solutions for§ 4 Nos. 1 to 12136§ 5 〃 1 to 12138§ 6 〃 1 to 10141§ 7 〃 1 to 6144§ 3.Method of Subscripts.Solutions for§ 4146§ 5 Nos. 13 to 24147§ 6148§ 7150§ 8155§ 9157NOTES164APPENDIX, ADDRESSED TO TEACHERS165NOTES TO APPENDIX195INDEX.§ 1. Tables197§ 2. Words &c. explained〃