## The Mathematical Analysis of Logic: Being an Essay Towards a Calculus of Deductive Reasoning |

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admit aﬁirmative aﬂirmative altl analysis application arbitrary elective symbol assert auxiliary equations Calculus categorical Propositions class whose members classiﬁcation coeﬂicient common conditional Proposition conditional syllogism Constructive Dilemma deduced DEDUCTIVE REASONING deﬁned deﬁnition Destructive Dilemma determined disjunctive Proposition Elective Equations elective expressions elective functions equivalent example existence expanded express the Proposition false ﬁgure ﬁnal ﬁnd ﬁrst premiss ﬁrst term ﬁxed GEORGE BOOLE given Proposition hypothetical hypothetical Syllogism implies indeﬁnite independent of h individuals interpretation involved Logic logicians Mathematics medium of comparison method middle term minor premiss moduli multiplied mutually exclusive negation not-Xs not-Z original equation particular predicate primitive equations reasoning reducible reference remark represent resolvable result of elimination satisﬁed scientiﬁc second equation second member Solution of Elective theorem tion true truth unity universal vanish whence X is true Xs are not-Ys Xs are Ys Ys are Xs