Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.
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Chagrov A. & Zakharyaschev M. Modal Logic 1997 (Oxford 1997)
Fitting M. & Mendelsohn R.L. First-order Modal Logic 1998 (Synthese Historical Library, 277; Dordrecht 1998)
Knuuttila S. Kretzmann N., Kenny A., Pinborg J. & Stump E. ‘Modal Logic’ The Cambridge History of Later Medieval Philosophy From the Rediscovery of Aristotle to the Desintegration of Scholasticism 1100-1600 1982 (Cambridge-London-New York-New Rochelle-Melbourne-Sydney 1982, 342-357)
Knuuttila S. Modalities in Medieval Philosophy 1993 (London-New York 1993)
de Libera A. see Lambertus Autissiodorensis; Roger Bacon
Prior A.N. Time and Modality 1957 (Oxford 1957)
de Rijk L.M. ‘Some Thirteenth Century Tracts on the Game of Obligation, III’ Vivarium 1976 14 26 49 (1976),
Lambert of Auxerre, ‘Properties of Terms’, 104; idem, Logica (Summa Lamberti) VIII, 205. ‘Significatio termini est intellectus rei ad quem intellectum representandum [representandum om. Alessio] rei vox imponitur ad voluntatem instituentis.’
Lambert of Auxerre, ‘Properties of Terms’, 106; Lambert of Auxerre, Logica (Summa Lamberti), VIII, 206: ‘Quarto modo dicitur suppositio acceptio termini pro [pro: S.L. Uckelman, per: Alessio] se sive pro re sua, vel pro aliquo supposito contempto sub re sua vel pro aliquibus suppositis contemptis sub re sua.’
Lambert of Auxerre, ‘Properties of Terms’, 109; Lambert of Auxerre, Logica (Summa Lamberti), VIII, 208: ‘Naturalis suppositio est quam habet terminus a se et a natura se.’
Lambert of Auxerre, ‘Properties of Terms’, 110; idem, Logica (Summa Lamberti), VIII, 209: ‘Simplex suppositio est illa secundum quam tenetur terminus pro se vel pro re sua, non habito respectu ad supposita sub se contempta.’
Lambert of Auxerre, ‘Properties of Terms’, 111; idem, Logica (Summa Lamberti), VIII, 209: ‘Discreta est illa quam habet terminus discretus in se, [. . .] ut quando sumitur terminus communis cum pronomine determinato.’
Lambert of Auxerre, ‘Properties of Terms’, 111; idem, Logica (Summa Lamberti), VIII, 210: ‘Communis est illa que termino communi convenit.’
Lambert of Auxerre, ‘Properties of Terms’, 112; idem, Logica (Summa Lamberti), VIII, 211: ‘Exilis immobilis est illa quam habet terminus communis quando de necessitate tenetur pro pluribus suppositis sub se contemptis, non tamen pro omnibus, nec sub ipso potest fieri descensus.’
Lambert of Auxerre, ‘Properties of Terms’, 116; idem, Logica (Summa Lamberti), VIII, 213: ‘Ad explanationem istius regule secundum quod terminus communis ibi ponitur ad differentiam termini discreti, qui non potest restringi nec ampliari.’
Lambert of Auxerre, ‘Properties of Terms’, 114; idem, Logica (Summa Lamberti), VIII, 212: ‘Quarto modo dicitur appellatio acceptio termini pro supposito vel pro suppositis actu existentibus.’
Lambert of Auxerre, ‘Properties of Terms’, 115; idem, Logica (Summa Lamberti), VIII, 213: ‘Sciendum autem quod proprie loquendo non dicuntur appellata nisi sint actualiter existentia; appellatur enim proprie quod est, et non quod non est, et ideo bene dicitur quod appellatio est pro existentibus suppositis vel pro supposito.’
Lambert of Auxerre, ‘Properties of Terms’, 116; idem, Logica (Summa Lamberti), VIII, 213: ‘Terminus communis substantialis vel accidentalis non restrictus aliunde supponens vel apponens verbo presentis temporis non habenti vim ampliandi a se nec ab alio, restringitur ad supponendum pro presentibus, si appellata habeat; si vero non, recurrit ad non existentes [existentiam]’.
Lambert of Auxerre, ‘Properties of Terms’, 134; idem, Logica (Summa Lamberti), VIII, 226: ‘Restrictio est minoratio ambitus termini communis, secundum quam pro paucioribus suppositis teneter terminus communis quam exigat sua actualis suppositio.’
Lambert of Auxerre, ‘Properties of Terms’, 137; idem, Logica (Summa Lamberti), VIII, 228: ‘Ampliatio est extensio ambitus termini communis secundum quod teneri potest terminus communis pro pluribus suppositis quam exigit sua actualis suppositio.’
Lambert of Auxerre, ‘Properties of Terms’, 138; idem, Logica (Summa Lamberti), VIII, 228: ‘Quedam enim sunt nomina que habent virtutem ampliandi ut possibile, necessarium; et similiter quedam verba ut potest [. . .]; similiter et quedam adverbia ut potentialiter necessario [. . .]’
Lambert of Auxerre, ‘Properties of Terms’, 138; idem, Logica (Summa Lamberti), VIII, 229: ‘Verba quorum actus comparatus ad subiectum de subiecto dicitur, in subiecto tamen non est, ut sunt ista: potest, opinatur, laudatur.’
Lambert of Auxerre, ‘Properties of Terms’, 138; idem, Logica (Summa Lamberti), VIII, 229: ‘Illa dicuntur ampliare ad tempora que faciunt terminum extendi ad omnes differentias temporis.’
Lambert of Auxerre, ‘Properties of Terms’, 129; idem, Logica (Summa Lamberti), VIII, 223: ‘Terminus communis accidentalis non restrictus aliunde supponens verbo preteriti temporis, supponere potest pro presentibus et preteritis; apponens vero solum [Kretzmann and Stump, terminum Alessio] supponit pro preteritis; si vero fuerit terminus substantialis supponens vel apponens verbo preteriti temporis, semper pro preteritis supponit.’
Lambert of Auxerre, ‘Properties of Terms’, 129; idem, Logica (Summa Lamberti), VIII, 223: ‘Terminus communis accidentalis non restrictus aliunde supponens verbo futuri temporis, supponere potest pro presentibus et futuris; apponens vero solum tenetur pro futuris; si vero fuerit terminus substantialis supponens vel apponens verbo futuri temporis, semper tenetur pro futuris.’
Cf. Knuuttila (1993), passim.
Lambert of Auxerre, ‘Properties of Terms’, 138; idem, Logica (Summa Lamberti), VIII, 229: ‘Unde cum dicitur: ‘home est animal necessario’ aliud est ac si diceretur: ‘id est, in omni tempore convenit homini esse animal’, scilicet in presenti preterito et futuro.’
Such as Chagrov and Zakharyaschev (1997), §3.5.
See Fitting and Mendelsohn (1998), 89. One exception to this view is Arthur Prior (1957), who believes that a coherent philosophical treatment of quantified modal logic can be given.
Fitting and Mendelsohn (1998), 94.
Lambert of Auxerre, ‘Properties of Terms’, 123; idem, Logica (Summa Lamberti), VIII, 219: “Nam nullo homine existente hec est falsa: ‘omnis homo est’, ergo sua contradictoria erit vera, hec sciliect: ‘aliquis homo non est’.”
Lambert of Auxerre, ‘Properties of Terms’, 138; idem, Logica (Summa Lamberti), VIII, 229: ‘Terminum [tenet] pro suppositis actu et non existentibus.’
Lambert of Auxerre, ‘Properties of Terms’, 117; idem, Logica (Summa Lamberti), VIII, 214: ‘Ad cognoscendum autem que verba ampliant et que non, sciendum quod ad substantiam actus potest comparari duplicitier: uno modo quantum ad illud in quo est et de quo enunciatur[. . .] alio modo tamquam ad id de quo enunciatur non tamen in ipso est.’
Lambert of Auxerre, ‘Properties of Terms’, 133; idem, Logica (Summa Lamberti), VIII, 225: ‘Dicendum quod: ‘album erit Socrates’ habet duas acceptiones: potest enim accipi sub hoc sensu: id quod erit album erit Sortes; vel sub isto: quod est album erit Sortes.’
See, e.g., Knuuttila (1982), 347-348, 354-357.
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Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.
All Time | Past Year | Past 30 Days | |
---|---|---|---|
Abstract Views | 443 | 38 | 5 |
Full Text Views | 126 | 3 | 0 |
PDF Views & Downloads | 39 | 3 | 0 |