Aristotle's Modal Logic: Essence and Entailment in the OrganonRichard Patterson develops three striking theses in the book. First, there is a fundamental connection between Aristotle's logic of possibility and necessity and his metaphysics, a connection extending far beyond the widely recognized tie to scientific demonstration and relating to the more basic distinction between the essential and accidental properties of a subject. Second, although Aristotle's views on modal logic depend in very significant ways on his metaphysics, this does not entail any sacrifice in logical rigor. Third, once one has grasped the nature of the relationship, one can better understand certain genuine difficulties in the system of logic and also appreciate its strengths in terms of the purposes for which it was created. |
Contents
Introduction | 1 |
12 Main themes of this work | 11 |
The basic modal proposition | 15 |
22 Some initial problems about conversion | 23 |
problems for modal predicates | 30 |
24 Further problems for de dicto and for a modal dictummodal predicate alternation | 33 |
25 Strong cop vs de dicto | 35 |
26 The four predicables as syllogistic terms | 38 |
53 Qualitative conversion on the cop reading | 135 |
54 Term conversion | 136 |
55 Ampliation | 141 |
Twoway possibility syllogisms | 145 |
62 Problematic Barbara and scientific demonstration | 149 |
63 Two invalidity proofs | 154 |
64 One problematic one assertoric premise | 155 |
65 First proof of Barbara A ppp | 159 |
27 Two readings of the necessity proposition | 41 |
28 Two notes on Aristotles concrete terms | 44 |
29 An important moral | 46 |
210 Intensional relations and the unity of the two cop readings | 47 |
211 Conversion of necessity propositions | 48 |
212 De dicto conversion as parasitic on strong cop | 52 |
Syllogisms with two necessity premises | 54 |
31 The general parallel to assertoric syllogisms | 56 |
32 Firstfigure syllogisms | 57 |
33 Strong cop and scientific demonstration | 58 |
34 The surprising strength of some firstfigure mixed cop moods and their relation to scientific demonstration | 60 |
35 Secondfigure syllogisms | 63 |
36 The third figure and the even more surprising strength of some weak cop premises | 66 |
37 The ekthesis proofs for Baroco and Bocardo | 70 |
Mixed syllogisms one assertoric and one necessity premise | 75 |
42 Mixed assertoriccop necessity syllogisms | 81 |
43 The two Barbaras and a close look at some univocal readings | 87 |
Twoway possibility some basic preliminaries | 124 |
51 The structure of twoway possibility propositions | 125 |
52 The affirmative form of twoway Possibility propositions | 132 |
66 Second proof for Barbara A ppp | 164 |
67 Omnitemporal premises? | 166 |
68 Nortmann on A15 and possibleworlds semantics | 176 |
69 A few remaining assertoricproblematic curiosities from the first figure | 182 |
first figure | 185 |
discovery before our very eyes of an ingenious proof | 188 |
612 The spread of a prooftheoretic infection | 192 |
613 An important principle overlooked | 194 |
614 Thirdfigure syllogisms | 198 |
615 A day in the sun for ekthesis | 203 |
Aristotles perfect syllogisms | 206 |
71 Plain syllogisms and the dictum de omni | 207 |
72 Perfection of perfect modal moods | 214 |
73 Applies to allnone again | 220 |
Principles of construction | 225 |
Categorical propositions and syllogisms | 235 |
Notes | 241 |
| 283 | |
| 287 | |
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Aristotle's Modal Logic: Essence and Entailment in the Organon Richard Patterson No preview available - 1995 |
Common terms and phrases
accidentally Agora ampliation Animal argument Aristotelian Aristotle Aristotle says Aristotle's modal logic assertoric conclusion assertoric premise asserts Barbara NAN Baroco Becker belong Bocardo Camestres categorical proposition Celarent Cesare chapter contingent counterexample Darapti Darii definition dictum differentia discussion endechesthai entail essence essential example fact fails to apply Ferio figure first-figure moods follows formal genus Horse Human huparchein interpretation invalid kata major minor premise modal copula modal operator modal propositions modal syllogisms modal syllogistic necessarily applies necessary necessity premise necessity propositions negative obvious omnitemporality one-way possibility passage Patzig perfect syllogisms Peter Geach plain possibility conclusion possibly fails Posterior Analytics pp/p predicate logic premise pairs principle Prior Analytics problematic qualitative conversion relation Robin Smith Ross scientific demonstration second-figure semantics simply sort species statement strong cop Theophrastus third-figure true two-way possibility propositions two-way possibly applies valid weak cop white things Wieland worst false