INDEX.
Abscissio infiniti, [316].
Absolute Name, [63].
Absorption, Laws of, [475].
Abstract Names, [16]–19; can the distinction between generals and singulars be applied to them, [19]–21.
Accidental Proposition, [49].
Acquired Perceptions, [414].
Added Determinants, Immediate Inference by, [148], 9.
Addition, sign of, in symbolic logic, [468] n.
Aequipollence, [133] n.
Affirmative Proposition, [92].
All, as a sign of quantity, [97]–100.
Alternant, [277]; [468]; [479].
Alternative Combination of Terms, [468], 9; of Propositions, [479].
Alternative Judgments and Propositions, [84], [275]; two types, [276], 7; their import, [277]–82; their reduction to the form of conditionals or hypotheticals, [282]–4.
Alternative Syllogisms, [359]–62.
Alternative Terms, [276]; [468].
Ambiguous Middle, [288].
Ambiguous Term, Fallacy of, [288].
Ampliative Proposition, [49].
Analytic Propositions, [50]–2; nature of the analysis involved in them, [53]–6.
And, its logical signification, [469].
Antecedent, [250].
Antilogism, [332]; [334]; [335]; [336] n.
Apodeictic Judgments and Propositions, [86]–91; [98]–100. See also [Modal Propositions].
Argument à fortiori, [384]–6; [467].
Aristotelian doctrine of Modals, [85], 6.
Aristotelian Sorites, [370]–3.
Aristotle, [130]; [329]; [367]; [396].
Assertoric Judgments and Propositions, [86]–91; scheme of assertoric and modal propositions, [282].
Attributive Term, [180].
Bailey, S., [337] n. ; [427] n.
Bain, A., on general and singular names, [12], [14] n. ; on connotation, [26] n. ; on verbal propositions, [50] n. ; on definition, [55]; [126] n. ; on conversion, [131] n., on obversion, [133] n. ; on syllogisms with two singular premisses, [298], 9; on the mixed hypothetical syllogism, [354], 5; [426] n. ; [442]; [457] n.
Barbara, Celarent, &c., [319]–22.
Baynes, T. S., [96]; [129] n. ; on the quantification of the predicate, [196], [199].
Bentham, Jeremy, [445].
Boethius, [134] n., [134] n.2.
Boole, Laws of Thought, [192]; [210] n. ; [299] n. ; [453]; [456]; [470] n. ; [473] n. ; [475] n. ; [476] n. ; [506]; [508]; [510] n. ; [512], 13; [515], 16.
Bosanquet, B., on the parts of logic, [8]; on logical meaning and psychical idea, [28]; on language, [29]; on parts in intension, [36] n. ; on the connotation of proper names, [45] n. ; [46] n. ; on the reference to time in judgments, [77]; his classification of judgments, [80]; on the particular proposition, [101]; on the nature of significant denial, [122]–4; [259] n. ; on the reciprocal character of conditionals and hypotheticals, [270]–3; on the import of disjunctives, [280], [283]; on conversion, [422]; [451] n.
Bowen, F., [133] n. ; [201]; [328].
Bradley, F. H., [53], 4; [211] n. ; [451]; [462] n.
Categorical Propositions, [82]; see also [Propositions].
Categorical Syllogism, see [Syllogism].
Change of Relation, Inference by, [148]; [260], 1.
Clarke, R. F., [102] n. ; [106] n. ; [443]; [445].
Class mode of interpreting propositions, [181]–4. 540
Classification, [447].
Co-division, [443].
Collective use of names, [15], [16]; of the word all, [97], 8.
Combination of Complex Propositions, [498]–501
Commutativeness, Law of, [470] n.
Complementary Names, [62].
Complementary Propositions, [132]; [143], 4; [161].
Complex Conception, Immediate Inference by, [149].
Complex Constructive Dilemma, [364].
Complex Destructive Dilemma, [364].
Complex Propositions, [478]; their opposition, [478]; their simplification, [481]–3; resolution into equivalent compound propositions, [483]–5; omission of terms, [485]; introduction of terms, [485], 6; interpretation of anomalous forms, [486], 7; their obversion, [488], 9; their conversion, [489], 90; their contraposition, [490]–3; their combination, [498]–502; inferences from their combination, [504]–8; elimination from complex propositions, [508]–12.
Complex Terms, [468]–477; order of their combination, [469], 70; their opposition, [470]–2; their simplification, [472]–6; summary of formal equivalences, [476].
Composition, Fallacy of, [16] n.
Compound Judgments and Propositions, [82]–4; their modality, [90], 1; [478]–80; their opposition, [480]; their formal equivalences, [480], 1.
Comprehension, [26], 7; [30]; [31]–3; law of variation with exemplification, [37]; relation to denotation, [38], 9; reading of propositions in comprehension, [187], 8.
Concept, not the logical unit, [9].
Concepts, empirical, metaphysical, and logical, [27], 8.
Concepts and names, [10].
Conceptualist treatment of Logic, [4], 5; [10], 11; [66]–8.
Concrete Names, [16]–19.
Conditional Propositions, distinguished from hypothetical propositions, [249]–52; their import, [252]–6; their relation to categoricals, [253]–6; their opposition, [256]–8; immediate inferences from them, [259]–61; their alleged reciprocal character, [270]–3.
Conditional Syllogisms, [348]–51.
Conjunctive combination of terms, [468]; of propositions, [478], 9.
Conjunctive Judgments and Propositions, [83].
Conjunctive Terms, [468].
Connotation, [24]–7; distinguished from etymology, [28]; how far variable, [28], 9; [31]–3; law of variation with denotation, [37].
Connotative mode of interpreting propositions, [184]–6.
Connotative Names, [40]–7.
Consequent, [250].
Constructive Dilemma, [363], 4.
Constructive Hypothetical Syllogism, [352].
Contingent Judgments, [85].
Continuous Questioning, Fallacy of, [372] n.
Contra-complementary Propositions, [132]; [143], 4; [161].
Contradiction, Law of, [147]; [454]–8; [474].
Contradiction in terms, [53] n.
Contradictory Opposition, [109]; [111]–14; [119]; [121]; how affected by the existential import of propositions, [227]–32.
Contradictory Propositions, see [Contradictory Opposition].
Contradictory Terms, [61], 2; [470], 1.
Contraposition of Propositions, [134]–7; attempts to reduce contraposition to syllogistic form, [151]–3; illustrated by Euler’s diagrams, [161]; how affected by the existential import of propositions, [223]–7; of conditionals, [259], 60; of hypotheticals, [268]–70; is contraposition a process of inference, [422], 3; of complex propositions, [490]–3.
Contraposition per accidens, [136].
Contrapositive, see [Contraposition].
Contrary Opposition, [119]; [114], 5; [118]; how affected by the existential import of propositions, [227]–32.
Contrary Propositions, see [Contrary Opposition].
Contrary Terms, [62], 3.
Contraversion, [133] n. ; [134] n.
Conventional Intension, [23]; [26], 7.
Converse, [127].
Converse Relation, Immediate Inference by, [149]–51.
Conversion by Contraposition, see [Contraposition].
Conversion by Limitation, [129].
Conversion by Negation, [134] n.
Conversion of Propositions, [126]–130; legitimacy of the process, [130]–2; attempts to reduce conversion to syllogistic form, [152]; illustrated by Euler’s diagrams, [160], 1; how 541 affected by the existential import of propositions, [223]–7; of conditionals, [259], 60; of hypotheticals, [268], 9; is conversion a process of inference, [422], 3; not to be based exclusively on the three laws of thought, [465], 6; of complex propositions, [489], 90.
Conversion per accidens, [128], 9.
Conversio pura et impura, [129] n.
Conversio Syllogismi, [322].
Convertend, [127].
Convertible Copula, [388].
Copula, [93].
Correlative Name, [63].
Criterion of Consistency, Jevons’s, [217] n. ; [219]; [232], 3.
Deductio ad impossibile, or ad absurdum, [319].
Definition by type, [34].
De Morgan, A., use of the terms contrary and contradictory, [62] n. ; [101] n. ; [104]; [104] n. ; on conversion, [126] n. ; [133] n. ; on contraposition, [136]; [153] n. ; on the proposition ω, [206], 7; [210] n. ; [217] n. ; on the existential import of propositions, [219], [232]; on the syllogistic rules, [290], [292]; [314]; on the mnemonic verses, [319]; on the numerically definite syllogism, [377]; on the argument à fortiori, [385], 6; on the logic of relatives, [387], 8; on immediate inferences and the laws of thought, [466]; [495].
Denial, Nature of, [119]–24.
Denotation, [29]–31; [31]–3; law of variation with connotation, [37]; relation to comprehension, [38], 9.
Destructive Dilemma, [363], 4.
Destructive Hypothetical Syllogism, [352].
Determination, [468].
Development of Terms, [474].
Diagrams, their use in Logic, [156], 7; Euler’s, [157]–62; Lambert’s, [163]–6; Venn’s, [166]–8; development of Euler’s diagrams, [170]–4; of Lambert’s diagrams, [174]–6; application of diagrams to syllogistic reasonings, [341]–6.
Dichotomy, see [Division by Dichotomy].
Dicta for the second, third, and fourth figures, [337], 8.
Dictum de diverso, [337] n.
Dictum de excepto, [338] n.
Dictum de exemplo, [337] n., [338] n.
Dictum de omni et nullo and the ordinary rules of the syllogism, [301], 2.
Dictum de reciproco, [338].
Dilemma, [363]–6.
Direct reduction, [318]; of Baroco and Bocardo, [323], 4.
Disjunctive Judgments and Propositions, [83], 4; [275]–84.
Disjunctive Syllogisms, [359]–62.
Disjunctive Terms, see [Alternative Terms].
Distinction, [443].
Distribution, Laws of, [472], 3.
Distribution of terms in a proposition, [95], 6; illustrated by Euler’s diagrams, [159], [60].
Distributive use of names, [15], 16; of the word all, [97], 8.
Division, see [Logical Division], [Metaphysical Division], [Division by Dichotomy], &c.
Division by Dichotomy, [445]; all valid division reducible to dichotomy, [445], 6; is division by dichotomy a formal process, [447]–9.
Division, Fallacy of, [16] n.
Dixon, E. T., [237] n.
Double Negation, Principle of, [459].
Duality, Law of, [460].
Duality of Formal Equivalences, [472].
Dual Terms, [475].
Eduction, [127] n.
Elimination, involved in syllogistic reasoning, [300]; the problem of elimination in logic, [508], 9; rules for elimination, [509]–12.
Empirical Concepts, [27], 8.
Empirically Universal Propositions, [99].
Enthymeme, [367], 8.
Enumeration, [441].
Enumerative Universal Propositions, [98].
Epicheirema, [369].
Episyllogism, [369].
Equality, Symbol of, [189]–91.
Equations in Logic, [189]–91; their types, [191]–4;.expression of propositions as equations, [194].
Equipollent Propositions, [117].
Equivalent Propositions, [117]; tables of equivalent propositions, [141]; [146]; [208]; [481].
Equivalent Terms, Table of, [476].
Equivocal Term, [65].
Essential Proposition, [50].
Etymology and Connotation, [28].
Euler’s diagrams, five-fold scheme, [157]–62; seven-fold scheme, [170]–4; their application to the 542 quantification of the predicate, [200]–4; to syllogistic reasonings, [288], [341]–4.
Eversion, [127] n.
Excluded Middle, Law of, [61] n. ; [147]; [458]–63; [474].
Exclusion, Law of, [475].
Exclusive Figure, [316].
Exclusive Proposition, [205].
Exemplification, [31]–5; law of variation with comprehension, [37].
Exemplicative Name, [41].
Existence and the Universe of Discourse, [210]–13.
Existential Import of Propositions, nature of the questions involved, [214]; how far formal logic concerned with them, [215]–17; various suppositions, [218]–20; bearing on immediate inferences, [223]–7; on the doctrine of opposition, [227]–32; existential import of the propositions included in the traditional schedule, [234]–44; of modal propositions, [244], 5; of conditional propositions, [255], 6; problem in connexion with hypotheticals, [256], 7; bearing of the existential import of propositions upon the validity of syllogistic reasonings, [390]–4.
Existential Propositions, [218]; their relation to the traditional forms of proposition, [221]–3.
Explicative Proposition, [50].
Exponible Proposition, [104] n.
Extension of Names and Concepts, [22]; distinguished from denotation, [29], 30; how related to intension, [31]–40; propositions in extension and intension, [177]–88.
Extensive Definition, [31]–5.
Extensively Verbal Proposition, [51] n.
Few, as a sign of quantity, [103], 4.
Figures of the Syllogism, [300]; their special rules, [309]–13; their peculiarities and uses, [315]–17; equivalence of the special rules of the first three figures, [335]; schemes of valid moods in figures 1, 2, and 3, [336]–8; dicta for figures 2, 3, and 4, [337], 8; figures of the conditional syllogism, [349], 50; of the hypothetical syllogism, [349], 50; of the hypothetico-categorical syllogism, [352], 3.
Folk-lore, Universe of, [213] n.
Form of a Proposition, [3]; [92]; [150], 1.
Form and Matter, [2], 3.
Formal Contradictories, [62] n.
Formal Logic, [1]–3.
Formal Obversion, [133] n.
Formal Propositions, [52], 3.
Fourth Figure, [328], 9; its moods regarded as indirect moods of the first figure, [329]–31; moods of the fourth figure, [334], 5; dictum, [338].
Fowler, T., [133] n. ; [205]; [325], 6; [349]; [365].
Fundamental Syllogism, [314] n.
Fundamentum divisionis, [441].
Fundamentum relationis, [64].
Galenian Figure, [328].
General Names, [11]–13.
General Propositions, [103].
Goclenian Sorites, [370]–3.
Grammatical Analysis of a Proposition, [92] n.
Greek Mythology, Universe of, [213] n.
Green, T. H., [42] n. ; [54] n.
Ground or reason of a belief, distinguished from cause of a belief, [414].
Hamilton, Sir W., on singular propositions, [102], 3; [104]; [105]; his scheme of diagrams, [156] n. ; his use of Euler’s diagrams, [159]; on judgments in extension and intension, [184] n. ; his doctrine of the quantification of the predicate, [195] ff.; his fundamental postulate of logic, [195], 6; on the interpretation of some, [200], 1; [321] n. ; [326] n. ; on the doctrine of reduction, [327] n. ; on the mixed hypothetical syllogism, [354]–6; [368] n. ; [371] n. ; on figure of sorites, [373] n. ; on ultra-total distribution of the middle term, [377]; on the unfigured syllogism, [378] n. ; [396] n. ; on the law of contradiction, [455]; [462]; bases formal inferences on the three laws of thought, [464], 5.
Hamiltonian scheme of propositions, [79]; [195] ff.
Hobhouse, L. T., [69] n.
Hypothetical Dilemma, [363] n.
Hypothetical Judgments and Propositions, [83], 4; distinguished from conditional propositions, [249]–52; their import, [261]–4; their opposition, [264]–8; immediate inferences from them, [268]–70; their relation to categoricals, [270]; their alleged reciprocal character, [270]–3.
Hypothetical Syllogisms, [348]–57.
Hypothetico-Categorical Syllogism, [348], 9; [352]–7.
Identity, Law of, [147]; [451]–4.
Illicit major and illicit minor, [289]; involve indirectly undistributed 543 middle, [298]; apparent exceptions to the rule against illicit major, [298].
Immediate Inferences, [126]–53; how affected by the existential import of propositions, [223]–7; from conditional propositions, [259]–61; from hypothetical propositions, [268]–70; can they be based exclusively on the three laws of thought, [464]–6; from complex propositions, [488]–494.
Imperfect Figures, [330].
Implication and Meaning, [71], 2; [177]; [178] n. ; [421]–3.
Import of Propositions, nature of the enquiry, [70]–4.
Inclusion, Law of, [475].
Indefinite Name, [59]–61.
Indefinite Proposition, [105].
Independent Propositions, [118].
Indesignate Proposition, [105].
Indirect Moods, [329]–31.
Indirect Reduction, [318], 9; [331]–7.
Individual Name, [11].
Individual Proposition, [102].
Inequality, Symbols of, [193].
Inference, nature of, [413], 4; paradox of, [414], 5; conclusion in what sense different from premisses, [415]–20; limiting cases, [422], 3; is conversion a process of inference, [422], 3; is contraposition a process of inference, [422], 3; is syllogism a process of inference, [423]–30.
Infinitation, [133] n.
Infinite Name, [59]–61.
Infinite Proposition, [106], 7.
Integration, [201] n.
Intension of Names and Concepts, [22]; conventional, subjective, and objective, [23]–7; how related to extension, [31]–40; propositions in intension and extension, [177]–88.
Intensive Definition, [32]–5.
Intensively Verbal Proposition, [51] n.
Inverse, [139].
Inverse Problem, [525]–535.
Inversion of Propositions, [137]–9; validity of the process, [139], [40]; illustrated by Euler’s diagrams, [161]; how affected by the existential import of propositions, [223]–7; of hypotheticals, [269].
Invertend, [139].
Jevons, W. S., [12] n. ; [19] n. ; [20] n. ; his use of the term connotation, [26]; [37] n. ; regards proper names as connotative, [41]–3; on relative names, [63], 4; on contradictory opposition, [111]–14; on conversion, [130]; [133] n. ; on contraposition, [136] n. ; [139]; [152] n. ; his use of Euler’s diagrams, [159]; on types of logical equations, [191], 2; on the interpretation of some, [202]; [205] n. ; [210] n. ; on questions about existence in logic, [217] n. ; his criterion of consistency, [217] n., [219], [232], 3; [220] n. ; on the import of disjunctives, [279]; on the order of premisses in a syllogism, [287]; on negative premisses, [295]; on the ordinary syllogistic conclusion, [300]; [349]; [365]; [366]; [416]; on division by dichotomy, [445], 6; [449]; his principle of the substitution of similars, [453], 4; on the law of duality, [460]; [470] n. ; [472] n. ; [473]; [475]; [495]; on Boole’s System of Logic, [506] n. ; [507] n. ; on the inverse problem, [525], 6, [529], [30].
Johnson, W. E., [31] n. ; on the import of propositions, [70] n. ; on the formulation of propositions, [72]; on multiple quantification, [106] n. ; [132] n. ; [144] n. ; on the proposition ω, [206] n. ; on the distinction between conditional and hypothetical propositions, [249] n. ; [265] n. ; [293] n. ; on the special rules of the syllogistic figures, [311] n. ; on dicta for the third and fourth figures, [338]; [388]; [469] n. ; on the analysis of ordinary categorical propositions, [479], 80; on the synthesis of propositions, [481] n. ; his notation for the solution of inverse problems, [533], 4.
Jones, Miss E. E. C., [126] n. ; [134] n. ; [148] n. ; [151]; [190] n. ; on the existential import of propositions, [244] n. ; on conditional propositions, [256] n. ; [260]; on hypothetical propositions, [264] n. ; on the use of the term alternative, [275]; on the nature of inference, [416] n. ; [418] n. ; on division and classification, [447].
Judgment, the logical unit, [8], 9.
Judgments, as related to propositions, [66]–8; their essential characteristics, [70]; their objective reference, [74]–6; their universality, [76], 7; their reference to time, [76], 7; their necessity, [77], 8; their classification, [79]–81; their division according to relation, [82]; into simple and compound, [82]–4; their modality, [84]–91; their quantity and quality, [91], 2. See also [Propositions].
Judgments of actuality, [88].
Judgments of necessity, [88].
Judgments of possibility, [88].
Kant, his classification of judgments, [81]; his doctrine of modality, [86]; 544 [91], 2; [104] n. ; [106]; on the figures of the syllogism, [327] n. ; on the mixed hypothetical syllogism, [354], 5.
Ladd Franklin, Mrs, on negative terms, [60] n. ; [142] n. ; [147] n. ; on the import of propositions, [179] n. ; on the existential import of propositions, [218] n. ; [231] n., [241] n., [242] n. ; [323] n. ; on the antilogism, [332]; [510] n.
Lambert, J. H., his diagrammatic scheme, [163]–6, [174]–6; on the uses of the different syllogistic figures, [316], 7; [326] n. ; on dicta for the different figures, [337] n., [338]; application of his diagrammatic scheme to syllogistic reasonings, [344], 5.
Language as the instrument of thought, [3]–5.
Laws of Thought, [147]; [450], 1; law of identity, [451]–4; law of contradiction, [454]–8; law of excluded middle, [458]–63; are the laws of thought also laws of things, [463], 4; their mutual relations, [464]; how far they establish immediate inferences, [464]–6; mediate inferences, [466], 7.
Lewis Carroll, Game of Logic, [219] n.
Liar, Sophism of the, [457], 8.
Limitative Proposition, [106].
Limited Identities, [192].
Lindsay, T. M., [201] n.
Logic, definition of, [1]; formal and material, [1]–3; its connexion with language, [3]–5; its relation to psychology, [5], 6; its utility, [6], 7; its abstract character, [68]–70.
Logical Division, [441], 2; its rules, [443]–5; all valid division reducible to dichotomy, [445], 6; place of the doctrine of division in logic, [446]–9; division and classification, [447].
Logical Concepts, [27], 8.
Logical Doctrine, its three parts, [8], 9.
Lotze, H., on negative terms, [59] n., [61] n. ; on general and universal judgments, [99] n. ; [126] n. ; [129] n. ; on negative premisses, [296] n. ; criticism of Jevons, [300]; [424] n. ; [425] n.
McColl, H., [263] n.
Mackenzie, J. S., [322] n.
Major Premiss, [287]; Mill’s view of its function, [429].
Major Term, [285], 6.
Mansel, H. L., [51] n. ; on opposition, [109] n. ; [115]; on conversion per accidens, [129] n. ; [130] n. ; on contraposition, [134] n. ; on material consequence, [150]; [152] n. ; on the import of disjunctives, [279] n. ; [319] n. ; on indirect moods, [330] n. ; [337] n. ; [357] n. ; on the dilemma, [365]; [367]; [368] n. ; on the argument à fortiori, [385] n., [386]; [424] n. ; [443]; on the place of division in logic, [446]–8; on the law of identity, [454]; bases syllogistic inferences on the laws of thought, [466], 7.
Material Consequence, [150]; [386].
Material Contradictories, [62] n.
Material Contrariety, [115] n.
Material Obversion, [133] n.
Matter of a Proposition, [3]; [92]; [150], 1.
Meaning and Implication, [71], 2; [177]; [178] n. ; [421]–3.
Mediate Inference, [151]; and the laws of thought, [466], 7.
Membra dividentia, [441].
Metaphysical Concepts, [27], 8.
Metaphysical Division, [412], 3.
Metaphysical Universality, [105] n.
Metathesis praemissarum, [321].
Methods of Abbreviation, Boole’s, [475] n. ; [476] n.
Middle Term, [285], 6; its ultra-total distribution, [376]–8.
Mill, J. S., on names, [9] n. ; [20] n. ; on connotation, [24], 5; on connotative names, [40]; regards proper names as non-connotative, [41], 2; his distinction between real and verbal propositions, [54] n. ; on negative names, [61] n. ; his classification of propositions, [80], 1; on the import of propositions, [182]; [186] n. ; on the quantification of the predicate, [198]; on the existential import of propostions, [219]; [243] n. ; on figure of sorites, [373], 4; [378] n. ; [387]; [414]; on immediate inferences, [419]; his doctrine that in every syllogism there is a petitio principii, [424]–30; on division and classification, [446]; on the law of identity, [452]; [466]; on the law of contradiction, [455], 6; on the law of excluded middle, [461]–3.
Minor Premiss, [287].
Minor Term, [285], 6.
Minto, W., [134] n.
Mixed Hypothetical Syllogism, [348], 9; [352]–7.
Mnemonics for the valid moods of the syllogism and their redaction to the first figure, [319]–22; for the direct reduction of Baroco and Bocardo, [323], 4; for the indirect moods of the first figure, [329], 30. 545
Modal Consequence, Immediate Inference by, [151].
Modal Propositions, [90] n. ; their opposition, [116], 7; [231], 2; their existential import, [244], 5; [258]; [266], 7; distinctive symbols for them, [258]; scheme of assertoric and modal propositions, [282]. See also [Conditional Propositions] and [Hypothetical Propositions].
Modality of Judgments, [84]–91.
Modus ponendo ponens, [352] n. ; [362].
Modus ponendo tollens, [361], 2.
Modus ponens, [352].
Modus tollendo ponens, [360]; [362].
Modus tollendo tollens, [352] n. ; [362].
Modus tollens, [352]; its reduction to the modus ponens, [354].
Monck, W. H. S., [30] n. ; [56] n. ; [207] n. ; [380] n. ; [448].
Moods of the Syllogism, [309]; what moods are legitimate in each figure, [309]–13; subaltern moods, [313], 14; strengthened moods, [314], 15; equivalence of the moods of the first three figures, [333], 4; moods of figure 4, [334], 5; scheme of valid moods of figure 1, [336]; of figure 2, [336], 7; of figure 3, [337], 8; moods of the conditional syllogism, [349], 50; of the hypothetical syllogism, [349], 50; of the hypothetico-categorical syllogism, [352], 3; of the disjunctive syllogism, [359]–62.
Moral Universality, [105] n.
Most, as a sign of quantity, [103], 4; effect of its recognition as a sign of quantity on the rules of the syllogism, [376], 7.
Multiple Quantification, [105], 6; [265] n.
Multiplication, sign of, in symbolic logic, [468] n.
Musschenbroek, P. van, Institutiones Logicae, [322].
Names and Concepts, [10], 11.
Necessary Judgments, [85]–91.
Necessity of Judgments, [77], 8.
Negative Premisses, [289]; [292], 3; [295]–7.
Negative Propositions, [92].
Negative Terms, [57]–61; their elimination from propositions, [144]–6.
Nominalist treatment of Logic, [4], 5; [10], 11; [66]–8.
Numerically definite Propositions, [104].
Numerically definite Syllogism, [377], 8.
Numeerical Moods of the Syllogism, [400]–3.
Objective distinctions of Modality, [87]–90.
Objective Extension, [30].
Objective Intension, [24]; [26], 7.
Objective reference in Judgments, [74]–6.
Obverse, [133].
Obversion of Propositions, [133], 4; how affected by the existential import of propositions, [223]–7; of hypothetical propositions, [269]; of complex propositions, [488], 9.
Obvertend, [133].
Octagon of Opposition, [144].
Opposition of Complex Terms, [470]–2.
Opposition of Propositions, [109]–19; illustrated by Euler’s diagrams, [160]; how affected by the existential import of propositions, [227]–31; of modal propositions, [231], 2; of conditional propositions, [256]–8; of hypothetical propositions, [264]–8; of complex propositions, [478]; of compound propositions, [480].
Or, its logical signification, [469].
Ostensive Reduction, [318].
Partial Identities, [192].
Particular Propositions, [100]–2; their existential import, [238], 9; [245], 6.
Partition, [442].
Peirce, C. S., [336] n.
Perfect Figure, [329], 30.
Permutation, [133] n.
Petitio Principii and the Syllogism, [424]–30.
Petrus Hispanus, [290], 1; [329] n.
Physical Definition, [442].
Physical Division, [442], 3.
Plurative Propositions, [103].
Polylemma, [363] n.
Polysyllogism, [368], 9.
Pope John XXI, [291]; [329] n.
Porphyry, Tree of, [35] n. ; [445].
Port Royal Logic, [105] n. ; [113] n. ; [297] n. ; [313] n. ; [337] n. ; [368] n. ; [432], 3.
Positive Name, [57].
Postulate of Logic, Hamilton’s, [195], 6.
Predicate of a Proposition, [92]; how to be distinguished from the subject, [96], 7.
Predicative Interpretation of Propositions, [179]-81.
Principium divisionis, [441].
Privative Conception, Immediate Inference by, [133] n.
Problematic Judgments, [86]–91. See also [Modal Propositions].
Progressive Argument, [369].
Proper Names, [13], 14; [15] n. ; have no 546 corresponding abstracts, [17] n. ; are non-connotative, [41]–7; have subjective intension and comprehension, [42]; may become connotative when used to designate a certain type of person, [45].
Propositio secundi adjacentis, [93]; tertii adjacentis, [93].
Propositional forms, [53]; their interpretation, [70]–2.
Propositions, as related to Judgments, [66]–8; their interpretation, [68], [70]–2; problem of their import, [70]–4; their formulation, [72], 3; their classification, [79]–81; their division according to relation, [82]; their division into simple and compound, [82]–4; their division according to modality, [84]–91; their division according to quantity, [91], 2; their division according to quality, [92]; the traditional scheme, [92]–95; their opposition, [109]–19; their mutual relations, [117]–19, [142]–4; connecting two terms, [132]; connecting two terms and their contradictories, [141], [146]; their diagrammatic representation, [156]–76; in extension and in intension, [177]–88; predicative mode of interpretation, [179]–81; class mode of interpretation, [181]–4; connotative mode of interpretation, [184]–6; subject interpreted in connotation and predicate in denotation, [186], 7; in comprehension, [187], 8; propositions expressed as equalities and inequalities, [193], 4; sixfold schedule including Y and η, [207]–9; existential import of propositions, [234]–45; direct import and implications of a proposition, [420]–3. See also [Complex Propositions], [Conditional Propositions], [Judgments], &c.
Prosyllogism, [369].
Psychology, its relation to Logic, [5], 6.
Quality of Propositions, [92]; [106]; of conditional propositions, [257], 8; of hypothetical propositions, [264], 5.
Quantification of the Predicate, [195]–209; its application to the syllogism, [378]–84.
Quantity of Propositions, [91], 2; how affected by their quality, [95] n. ; of conditional propositions, [257], 8; of hypothetical propositions, [265].
Quaternio terminorum, [288].
Ramean Tree, [445].
Ray, P. K., [356] n.
Real Propositions, [49].
Reciprocal Equivalences, Schröder’s Law of, [472]; bearing of this law on the inverse problem, [534].
Reductio ad impossibile or per impossibile, [319].
Reduction of Dual Terms, [474], 5.
Reduction of Syllogisms, nature of the process, [318]; direct and indirect reduction, [318], 9; direct reduction of Baroco and Bocardo, [323], 4; extension of the doctrine of reduction, [324], 5; is reduction an essential part of the doctrine of the syllogism, [325]–8; indirect reduction, [331]–7; reduction of conditional and hypothetical syllogisms, [351], 2; of mixed hypothetical syllogisms, [354].
Regressive Argument, [369].
Relation, Division of propositions according to, [82].
Relative Names, [63]–5.
Relatives, Logic of, [149]–51; [387], 8.
Relativity, Law of, [456].
Remotive Propositions, [84].
Robertson, G. C., [357].
Rogers, R. A. P., [294].
Ross, G. R. T., [280].
Schröder, Der Operationskreis des Logikkalkuls, [471] n. ; [472] n. ; [473]; [475]; [511]; [534].
Secondary Opposition, [115].
Secondary Quantification, [105]; [116].
Self-contradiction, [457].
Sextus Empiricus, [424]; [426].
Shyreswood, W., [329] n.
Sigwart, on empirical, metaphysical, and logical concepts, [27], 8; on the names of ultimate elements, [34]; on apparently tautologous propositions, [52] n. ; on negative names, [57]–60; on the reference to time in judgments, [77]; on compound judgments, [82] n., [83] n. ; on modality, [86], 7; on universal judgments, [99] n. ; on negative judgments, [120] n. ; on the grounds of denial, [121]; [128] n. ; on contraposition, [136]; [234] n. ; on hypotheticals, [264], 5; on figures 2 and 3 of the syllogism, [366] n. ; [349]; on the value of the syllogism, [427] n., [428] n. ; on the laws of thought, [451]; on the law of identity, [461], 2; on the law of contradiction, [455]; on the law of excluded middle and the law of twofold negation, [459], 60.
Simple Constructive Dilemma, [364].
Simple Contraposition, [136].
Simple Conversion, [128]. 547
Simple Destructive Dilemma, [364].
Simple Identities, [191].
Simple Judgments and Propositions, [82]; their modality, [86]–90.
Simple Term, [468].
Simplicity, Law of, [473].
Singular Names, [11]–13; may be connotative, [41], 2.
Singular Propositions, [102], 3; their opposition, [115], 16; as premisses in a syllogism, [298], 9.
Solly, Syllabus of Logic, [316] n. ; [395] n. ; [434], 5.
Some, as a sign of quantity, [100], 1; in the doctrine of the quantification of the predicate, [199]–204.
Sophisma polyzeteseos, [372] n.
Sorites, [370]–6.
Spalding, W., [133] n. ; [201] n. ; [321] n. ; [349]; [387]; [445].
Spencer, H., [378] n.
Square of Opposition, [110].
Strengthened Syllogism, [314], 15.
Studies in Logic by Members of the Johns Hopkins University, [323] n. ; [510] n. ; [517]–20.
Subaltern Moods, [313], 14.
Subaltern Opposition, [110]; [117], 18; how affected by the existential import of propositions, [227]–31.
Subalternant and Subalternate, Propositions, [110].
Sub-complementary Propositions, [132]; [143], 4; [161].
Subcontrary Opposition, [110]; [118]; how affected by the existential import of propositions, [227]–31.
Sub-division, [443].
Subject of a Proposition, [92]; how to be distinguished from the predicate, [96], 7.
Subjective distinctions of Modality, [86], 7; [90] n.
Subjective Extension, [30].
Subjective Intension, [23], 4; [26], 7; [29].
Substantial Terms, [12] n. ; [15] n.
Syllogism, [285]; its terms and propositions, [285]–7; its rules as ordinarily stated, [287]–9; corollaries from the rules, [289]–91; restatement of the rules, [291]; their dependence upon one another, [291]–3; statement of the independent rules, [293], 4; proof of the rule of quality, [294], 5; apparent exceptions to the rules, [295]–8; syllogisms with two singular premisses, [298], 9; is the ordinary syllogistic conclusion open to the charge of incompleteness, [300]; figures and moods, [309]–17; reduction of syllogisms, [318]–38; diagrammatic representation of syllogisms, [341]–6; syllogisms with quantified predicates, [378]–84; are all formal inferences reducible to ordinary syllogistic form, [384]–8; validity of syllogistic reasonings how far affected by the existential import of propositions, [390]–4; true conclusion obtainable from false premisses, [394]–6; numerical moods, [400]–3; syllogisms and immediate inferences, [423], 4; syllogistic reasoning and the charge of petitio principii, [424]–30. See also [Conditional Syllogism], [Figures of the Syllogism], &c.
Symbolic Logic, [189]–94; [468] n.
Symbols for Propositions, [93], 4.
Synonymous Proposition, [50].
Synthetic Chain of Reasoning, [369].
Synthetic Proposition, [49].
Tarbell, F. B., [349] n.
Tautology, Laws of, [473].
Terms, Logic of, [11].
Tetralemma, [363] n.
Thomson, W., [195]; [201], 2; [203]; [206]; [315] n. ; [326]; [328], 9; [337] n. ; [344] n. ; [359] n. ; [379].
Time of predication and time in predication, [77]; [451] n.
Totum divisum, [441].
Traditional Scheme of Propositions, [79]; [92]–5; [234]–44.
Transitive Copula, [388].
Transversion, [127] n. ; [148] n. ; [260].
Trilemma, [363] n.
Twofold Negation, Principle of, [459].
Ueberweg, P., on opposition, [109] n. ; on conversion, [126] n. ; [133] n. ; [136] n. ; [151] n. ; on Euler’s diagrams, [162] n. ; on the existential import of propositions, [219] n. ; [255] n. ; on negative premisses, [297] n. ; [316]; form in which he gives the mnemonic verses, [322] n. ; on the reduction of Baroco and Bocardo, [323] n. ; [326]; [344] n. ; [349]; [352] n. ; [366] n. ; [369] n. ; [371] n. ; [424] n. ; [457] n.
Ultra-total distribution of the middle term, [376]–8.
Unconditionally Universal Propositions, [99].
Undistributed Middle, Fallacy of, [288]; involves indirectly illicit process of major or minor, [293]; apparent exception to the rule against undistributed middle, [297], 8.
Unfigured Syllogism, [378] n.
Unity, Law of, [473]. 548
Universal Propositions, [97]–100; their existential import, [235]–8.
Universality of Judgments, [76], 7.
Universe of Attributes, [31] n.
Universe of Discourse, [29], 30; [75], 6; [210]–13; [226] n. ; [234], 5.
Univocal Name, [65].
Veitch, J., [54] n. ; [201] n. ; [203]; [207] n.
Venn, J., [15] n. ; [30] n. ; [44] n. ; on verbal disputes, [50] n. ; on contradictory terms, [62] n. ; [96] n. ; on Hamilton’s geometric scheme, [156] n. ; on Euler’s diagrams, [159], [162] n. ; on Lambert’s diagrams, [165] n. ; his own scheme of diagrams, [166]–8; on the predicative mode of interpreting propositions, [179], [180]; [185] n. ; [193] n. ; [200] n. ; [210] n. ; on the existential import of propositions, [220] n. ; on the inference of particulars from universals, [226] n. ; [235]; [237]; [238]; application of his diagrammatic scheme to syllogistic reasonings, [345], 6; on the logic of relatives, [387], 8; [424] n. ; [506]; [507] n. ; [530].
Verbal Dispute, [50] n.
Verbal Division, [443].
Verbal Propositions, [49]–52.
Wallis, Institutio Logicae, [322] n. ; [330].
Weakened Conclusion, [313], 14.
Weakened Syllogism, [313], 14.
Weaker Premiss, [289] n.
Welton, J., [182]; [183]; [243] n. ; [359] n.
Whately, R., [297] n. ; [323], 4; on the doctrine of reduction, [325]; on the dilemma, [365]; holds that all valid reasoning is reducible to syllogistic form, [387]; his definition of petitio principii, [425]; [433], 4.
Wolf, A., [216] n. ; [221]; [225] n. ; [229] n. ; [231] n.
CAMBRIDGE: PRINTED BY JOHN CLAY, M.A. AT THE UNIVERSITY PRESS.
Transcriber’s Note
This text was prepared from materials kindly provided by the Internet Archive. There are a few changes from the appearance of the original text. In the original, footnotes are numbered consecutively on each page. The superscripted numbers for them are usually placed before, rather than after, punctuation marks. Ellipses are often used without any spacing. In the Exercises, the difference in font size between questions and sample answers is not always adhered to. The formatting of arguments and some proofs is not always copied exactly in this version.
I have put page numbers into the text in red. Footnotes are placed after the paragraphs to which they connect. I have inserted hyperlinks for most cross-references in the text and am responsible for any errors this may have introduced.
The very few typographical errors are corrected and marked with dashed red underlining. In one case, on page [530], I have preferred the wording of the 3rd edition.