viz.
"No xy exist" = "No x are y" = "No y are x" 33
Three other similar Trios "
The Proposition "All x are y" is _Double_, and is equivalent
to the two Propositions "Some x are y" and "No x are _y'_" "
Seven other similar Propositions 34
=Tables II, III.= Representation of Propositions of
Existence and Relation 34, 35
CHAPTER IV.
_INTERPRETATION OF BILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS._
·-------·
|(.)| |
Interpretation of |---|---| 36
| | |
·-------·
And of three other similar arrangements "
pg-xxii
·-------·
|( )| |
Interpretation of |---|---| "
| | |
·-------·
And of three other similar arrangements "
·-------·
| (.) |
Interpretation of |---|---| 37
| | |
·-------·
And of three other similar arrangements "
·-------·
|(.)|(.)|
Interpretation of |---|---| "
| | |
·-------·
And of three other similar arrangements "
·-------·
|( )|( )|
Interpretation of |---|---| "
| | |
·-------·
And of three other similar arrangements "
·-------·
|(.)|( )|
Interpretation of |---|---| "
| | |
·-------·
And of seven other similar arrangements 38
=BOOK IV.=
=THE TRILITERAL DIAGRAM.=
CHAPTER I.
_SYMBOLS AND CELLS._
Change of Biliteral into Triliteral Diagram 39
The xy-Class subdivided into 'the xym-Class' and
'the xym'-Class' 40
pg-xxiii
The Inner and Outer Cells of the North-West Quarter
assigned to these Classes "
The xy'-Class, the x'y-Class, and the
x'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 'the m-Class' and 'the _m'_-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 them 42
CHAPTER II.
_REPRESENTATION OF PROPOSITIONS IN TERMS
OF x AND m, OR OF y AND m._
§ 1.
_Representation of Propositions of Existence in terms
of x and m, or of y and m._
The Proposition "Some xm exist" 43
Seven other similar Propositions "
The Proposition "No xm exist" 44
Seven other similar Propositions "
§ 2.
_Representation of Propositions of Relation in terms
of x and m, or of y and m._
The Pair of Converse Propositions
"Some x are m" = "Some m are x" "
Seven other similar Pairs "
The Pair of Converse Propositions
"No x are m" = "No m are x" "
Seven other similar Pairs "
The Proposition "All x are m" 45
Fifteen other similar Propositions "
=Tables V, VI, VII, VIII.= Representations of
Propositions in terms of x and m, or of
y and m 46 to 49
pg-xxiv
CHAPTER III.
_REPRESENTATION OF TWO PROPOSITIONS
OF RELATION, ONE IN TERMS OF x AND m,
AND THE OTHER IN TERMS OF y AND m,
ON THE SAME DIAGRAM._
The Digits "I" and "O" to be used instead of Red and
Grey Counters 50
Rules "
Examples worked "
CHAPTER IV.
_INTERPRETATION, IN TERMS OF x AND y,
OF TRILITERAL DIAGRAM, WHEN MARKED
WITH COUNTERS OR DIGITS._
Rules 53
Examples worked 54
=BOOK V.=
=SYLLOGISMS.=
CHAPTER I.
_INTRODUCTORY._
'=Syllogism=' 56
'=Premisses=' "
'=Conclusion=' "
'=Eliminands=' 57
'=Retinends=' "
'=Consequent=' "
The Symbol ".'." "
Specimen-Syllogisms "
pg-xxv
CHAPTER II.
_PROBLEMS IN SYLLOGISMS._
§ 1.
_Introductory._
'=Concrete=' and '=Abstract=' Propositions 59
Method 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._
Rules 60
Examples worked fully "
The same worked briefly, as models 64
§ 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._
Rules 66
Examples worked briefly, as models "
pg-xxvi
=BOOK VI.=
=THE METHOD OF SUBSCRIPTS.=
CHAPTER I.
_INTRODUCTORY._
Meaning of x_{1}, xy_{1}, &c. 70
'=Entity=' "
Meaning of x_{0}, xy_{0}, &c. "
'=Nullity=' "
The Symbols "+" and "¶" "
'=Like=' and '=unlike=' Signs "
CHAPTER II.
_REPRESENTATION OF PROPOSITIONS OF RELATION._
The Pair of Converse Propositions
"Some x are y" = "Some y are x" 71
Three other similar Pairs "
The Pair of Converse Propositions
"No x are y" = "No y are x" "
Three other similar Pairs "
The Proposition "All x are y" 72
The Proposition "All x are y" is _Double_,
and is equivalent to the two Propositions "Some x
exist" and "No x and y'" "
Seven other similar Propositions "
Rule for translating "All x are y" from abstract
into subscript form, and _vice versâ_ "
pg-xxvii
CHAPTER III.
_SYLLOGISMS._
§ 1.
_Representation of Syllogisms._
Rules 73
§ 2.
_Formulæ for Syllogisms._
Three Formulæ worked out:--
Fig. I. xm_{0} + ym'_{0} ¶ xy_{0} 75
its two Variants (a) and (b) "
Fig. II. xm_{0} + ym_{1} ¶ x'y_{1} 76
Fig. III. xm_{0} + ym_{0} + m_{1} ¶ x'y'_{1} 77
=Table IX.= Formulæ and Rules 78
Examples worked briefly, as models "
§ 3.
_Fallacies._
'=Fallacy=' 81
Method of finding Forms of Fallacies 82
Forms best stated in _words_ "
Three Forms of Fallacies:--
(1) Fallacy of Like Eliminands not asserted to exist "
(2) Fallacy of Unlike Eliminands with an Entity-Premiss 83
(3) Fallacy of two Entity-Premisses "
§ 4.
_Method of proceeding with a given Pair of Propositions._
Rules 84
pg-xxviii
=BOOK VII.=
=SORITESES.=
CHAPTER I.
_INTRODUCTORY._
'=Sorites=' 85
'=Premisses=' "
'=Partial Conclusion=' "
'=Complete Conclusion=' (or '=Conclusion=') "
'=Eliminands=' "
'=Retinends=' "
'=consequent=' "
The Symbol ".'." "
Specimen-Soriteses 86
CHAPTER II.
_PROBLEMS IN SORITESES._
§ 1.
_Introductory._
Form of Problem 87
Two Methods of Solution "
§ 2.
_Solution by Method of Separate Syllogisms._
Rules 88
Example worked "
pg-xxix
§ 3.
_Solution by Method of Underscoring._
'=Underscoring=' 91
Subscripts to be omitted "
Example worked fully 92
Example worked briefly, as model 93
Seventeen Examination-Papers 94
=BOOK VIII.=
=EXAMPLES, WITH ANSWERS AND SOLUTIONS.=
CHAPTER I.
_EXAMPLES._
§ 1.
_Propositions of Relation, to be reduced to normal form_ 97
§ 2.
_Pairs of Abstract Propositions, one in terms of x and m,
and the other in terms of y and m, to be represented on
the same Triliteral Diagram_ 98
§ 3.
_Marked Triliteral Diagrams, to be interpreted in terms
of x and y_ 99
§ 4.
_Pairs of Abstract Propositions, proposed as Premisses:
Conclusions to be found_ 100
pg-xxx
§ 5.
_Pairs of Concrete Propositions, proposed as Premisses:
Conclusions to be found_ 101
§ 6.
_Trios of Abstract Propositions, proposed
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