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 "

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=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_ "

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