Handbook of the History of Logic: - Fordham University Faculty

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4 Medieval Modal Theories and Modal Logic Simo Knuuttila Treatments of the Paradoxes of Self-reference Mikko Yrjönsuuri Developments in the Fifteenth and Sixteenth Centuries E. Jennifer Ashworth Relational Logic of Juan Caramuel Petr Dvoˇrák Port Royal: The Stirrings of Modernity Russell Wahl Index 505 579 609 645 667 701
PREFACE As modern readers will be aware, one of logic’s most fruitful periods filled the comparatively small space from the mid-19 th century to the third quarter of the century that followed. While classical mathematical logic remains securely situated in the mainstream of the subject, alternative approaches arising from research programmes in computer science and philosophy have also flourished. It speaks to the intellectual gravitas of mathematical logic that it should have dominated utterly for a century and a quarter, but other developments have had longer runs, none more so than logic in the five centuries between the 11 th and 16 th . This is staying power of formidable heft, one of the main reasons for which is the rich scope of logical enquiry during this period. The same is true of modern symbolic logic. In the period of its exclusivity, it exhibited an agreeable complexity, with a reach that extends from classical treatments of proof theory, set theory, model theory and recursion theory, to variations that encompass intuitionist, modal, many-valued, relevant and dialogue logic, among others. No doubt this complexity is part of the explanation of the dominance of symbolic logic. If so, a similar explanation attaches to the staying power of mediaeval logic, whose range is easily as robust as its modern cousin. While the mediaeval tradition never abandoned the central fact of the syllogism as its organizing focus, it subjects this focus to the creative tensions of adaptation, extension and creative reinterpretation. All in all, the logicians of the middle ages rang the project of logic through virtually all the changes that characterize modern logic, at times rivaling the new developments in conceptual sophistication and theoretical robustness. The coverage of mediaeval logic is striking, extending from treatments of logical consequence to the intricate rules of logical disputations, from amalgamations of preceding traditions, whether Aristotelian or Arabic, to the development of new insights into quantification, from investigations of meaning to the exploration of modal contexts, from enquiry into the paradoxes to the stirrings of the logic of relations, and much more. It is agreed that logic lost the vigour and high reputation achieved in the middle ages, as the Renaissance emerged as Europe’s dominant intellectual and cultural force, but it is wrong to say that logic was sent into an impotent retirement in this period. It is more accurate to speak of hibernation, a period of quiescence during which logic was renewing itself for the challenge of a looming modernity. Astride the gap between Renaissance and the new world of learning is the work of the Port Royal logicians, included here for its role as a beacon. The Port Royal logicians disliked technical formalisms, and are in that respect the forbears of modern informal logic. But these same logicians did some of the best of the early work in probability theory, thus anticipating the rise of inductive logic.
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Page 6 and 7: viii Preface It remains to be seen
Page 8 and 9: x Terence Parsons University of Cal
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46 John Marenbon position, but to a
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48 John Marenbon of the relationshi
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50 John Marenbon mother of Christ,
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52 John Marenbon and Boethius’s v
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54 John Marenbon (for w) as a word
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56 John Marenbon and his followers
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58 John Marenbon [Aristotle, 1966]
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60 John Marenbon [Green-Pedersen, 1
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62 John Marenbon [Martin, 1991] C.
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LOGIC AT THE TURN OF THE TWELFTH CE
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Logic at the Turn of the Twelfth Ce
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84 Ian Wilks question. 2 And second
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90 Ian Wilks standings of universal
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92 Ian Wilks one characteristic whi
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94 Ian Wilks understandings they ge
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96 Ian Wilks and further discussion
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98 Ian Wilks mental acts; general t
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100 Ian Wilks 1998a, p. 175]; he ca
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102 Ian Wilks fail to achieve propo
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104 Ian Wilks be something for the
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106 Ian Wilks Whatever philosophica
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108 Ian Wilks Abelard’s preferenc
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110 Ian Wilks to represent the cont
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112 Ian Wilks bial construal of the
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114 Ian Wilks nal plus the three ne
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116 Ian Wilks these persons, and no
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118 Ian Wilks tents in the first fi
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120 Ian Wilks minor which then diff
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122 Ian Wilks supply these criteria
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124 Ian Wilks by this tendency. He
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126 Ian Wilks firm as genuine entai
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128 Ian Wilks between the anteceden
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130 Ian Wilks (extensionally) “eq
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132 Ian Wilks as appropriate for to
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134 Ian Wilks conditions under whic
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136 Ian Wilks am not an animal, I a
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138 Ian Wilks [Abelard, 1970, p. 49
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140 Ian Wilks catalogue of such pat
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142 Ian Wilks itself. The relations
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144 Ian Wilks The problem with this
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146 Ian Wilks Another Abelardian th
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148 Ian Wilks This indeed is the ap
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150 Ian Wilks commonplace in the tw
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152 Ian Wilks BIBLIOGRAPHY “[Abel
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154 Ian Wilks [Green-Pedersen, 1984
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156 Ian Wilks [Rosier-Catach, 1999]
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158 Terence Parsons Medieval author
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160 Terence Parsons “Some categor
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162 Terence Parsons Every A is B co
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164 Terence Parsons true. This may
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166 Terence Parsons Figure 1 (ch 4)
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168 Terence Parsons 1.7 Quantifying
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170 Terence Parsons Every A is B Ev
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172 Terence Parsons In modern logic
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174 Terence Parsons The purpose of
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176 Terence Parsons 2.3 Extending t
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178 Terence Parsons Infinitizing ne
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180 Terence Parsons that is not a m
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182 Terence Parsons rule says that
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184 Terence Parsons The parasitic t
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186 Terence Parsons For example,
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188 Terence Parsons a term in a pro
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190 Terence Parsons signify the sam
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192 Terence Parsons this is what Oc
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194 Terence Parsons example, person
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196 Terence Parsons He continues wi
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198 Terence Parsons Since Sherwood
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200 Terence Parsons William says th
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202 Terence Parsons The term ‘thi
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204 Terence Parsons proposition (fo
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206 Terence Parsons makes no differ
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208 Terence Parsons A bishop was gr
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210 Terence Parsons a natural intui
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212 Terence Parsons In both of thes
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214 Terence Parsons The subject is
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216 Terence Parsons I believe that
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218 Terence Parsons neither should
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220 Terence Parsons 6.3 I promise y
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222 Terence Parsons 7 MODES OF SUPP
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224 Terence Parsons that result due
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226 Terence Parsons Personal suppos
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228 Terence Parsons supposition whe
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230 Terence Parsons the predicates
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232 Terence Parsons 7.4 Locality Sh
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234 Terence Parsons [D] a distribut
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238 Terence Parsons 7.6 Rules of In
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240 Terence Parsons The premise is
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242 Terence Parsons is similar to a
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244 Terence Parsons Every donkey is
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246 Terence Parsons one may descend
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248 Terence Parsons mode of supposi
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250 Terence Parsons above, allowed
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252 Terence Parsons if the term is
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254 Terence Parsons 8.5 Modes cause
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256 Terence Parsons understand ‘t
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258 Terence Parsons The reverse pri
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260 Terence Parsons mode of supposi
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262 Terence Parsons to formulate a
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264 Terence Parsons some P can alwa
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266 Terence Parsons Still other aut
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268 Terence Parsons Determinate: Ex
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270 Terence Parsons DEFAULT: A main
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272 Terence Parsons Change every ma
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274 Terence Parsons other modes can
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276 Terence Parsons Therefore, ‘d
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278 Terence Parsons [Dineen, 1990]
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280 Terence Parsons [Spade, 1988] P
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282 Henrik Lagerlund and references
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284 Henrik Lagerlund never very con
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286 Henrik Lagerlund present in Al-
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288 Henrik Lagerlund term is hence
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290 Henrik Lagerlund He notes furth
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292 Henrik Lagerlund (3.1.21) ‘Ev
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294 Henrik Lagerlund These five dif
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296 Henrik Lagerlund There are thre
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298 Henrik Lagerlund There is also
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300 Henrik Lagerlund about differen
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302 Henrik Lagerlund Such propositi
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304 Henrik Lagerlund He says that a
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306 Henrik Lagerlund matter. If the
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308 Henrik Lagerlund from the early
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310 Henrik Lagerlund Kilwardby. Nec
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312 Henrik Lagerlund Instead Boethi
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314 Henrik Lagerlund way that one l
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316 Henrik Lagerlund This definitio
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318 Henrik Lagerlund natural (or ne
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320 Henrik Lagerlund would make the
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322 Henrik Lagerlund On Predicables
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324 Henrik Lagerlund of their predi
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326 Henrik Lagerlund nowadays sort
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328 Henrik Lagerlund III. Every B i
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330 Henrik Lagerlund XIV. Every B i
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332 Henrik Lagerlund the conclusion
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334 Henrik Lagerlund (1) Differenti
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336 Henrik Lagerlund On Supposition
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338 Henrik Lagerlund On Fallacies T
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340 Henrik Lagerlund (5) ‘Both’
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342 Henrik Lagerlund substance ‘S
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344 Henrik Lagerlund [Averroes, 196
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346 Henrik Lagerlund [Patterson, 19
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348 Ria van der Lecq signification.
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350 Ria van der Lecq intellectus (c
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352 Ria van der Lecq the mind, extr
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354 Ria van der Lecq everyone, they
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356 Ria van der Lecq other words, t
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358 Ria van der Lecq term represent
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360 Ria van der Lecq nature of a sp
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362 Ria van der Lecq about men in t
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364 Ria van der Lecq The second opi
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366 Ria van der Lecq Both refer to
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368 Ria van der Lecq first mode tha
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370 Ria van der Lecq that is not th
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372 Ria van der Lecq the second hal
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374 Ria van der Lecq ‘second inte
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376 Ria van der Lecq the intellect
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378 Ria van der Lecq or ‘horsenes
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380 Ria van der Lecq that are real
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382 Ria van der Lecq it. 176 And wh
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384 Ria van der Lecq significance.
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386 Ria van der Lecq [Bacon, 1988]
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388 Ria van der Lecq [Rosier, 1983]
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390 Gyula Klima relations between l
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392 Gyula Klima regarded as attempt
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394 Gyula Klima . . . it is essenti
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396 Gyula Klima are supposed to be
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398 Gyula Klima m at t, namely, the
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400 Gyula Klima stead, representing
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402 Gyula Klima it is a substantial
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404 Gyula Klima of various ontologi
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406 Gyula Klima committed to positi
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408 Gyula Klima terance and knowing
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410 Gyula Klima does not have to me
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412 Gyula Klima namely, those to wh
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414 Gyula Klima Concepts and mental
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416 Gyula Klima signify all their s
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418 Gyula Klima provided they are n
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420 Gyula Klima So, when we say tha
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422 Gyula Klima context, the condit
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424 Gyula Klima semantic closure (i
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426 Gyula Klima a given situation i
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428 Gyula Klima This simple modific
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430 Gyula Klima in which the object
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LOGICINTHE14 th CENTURY AFTER OCKHA
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Logic in the 14 th Century after Oc
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1.2 A survey of the traditions Logi
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elsewhere, in particular in Italy.
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Some A is B (1) Every A is B (3) Lo
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it is still by and large murky terr
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MEDIEVAL MODAL THEORIES AND MODAL L
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1.7 Essentialist Assumptions Mediev
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(31) (p → Oq) & − L(p → q). M
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TREATMENTS OF THE PARADOXES OF SELF
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Treatments of the Paradoxes of Self
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Proof. Treatments of the Paradoxes
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DEVELOPMENTS IN THE FIFTEENTH AND S
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Developments in the Fifteenth and S
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646 Petr Dvoˇrák 2 CARAMUEL’S L
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648 Petr Dvoˇrák ter characterist
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650 Petr Dvoˇrák ad extra as some
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652 Petr Dvoˇrák equivalences (wh
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654 Petr Dvoˇrák the two provided
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656 Petr Dvoˇrák that of arectisa
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658 Petr Dvoˇrák view of relation
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660 Petr Dvoˇrák In dealing with
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662 Petr Dvoˇrák As has been said
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664 Petr Dvoˇrák Things, which ar
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PORT ROYAL: THE STIRRINGS OF MODERN
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Port Royal: The Stirrings of Modern
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702 appellata, 416 appellation, 188
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704 Cassiodorus, 1, 2, 5, 22, 25 In
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706 determinate modality, 114 deter
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708 clear and distinct, 671 identir
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710 material essence realism, 86 Ma
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712 antiqua responsio, 440 nova res
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714 484, 552-556, 559 pseudo-Scotus
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716 narrow distributive, 267-276 pe
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718 Wyclif, J., 441, 442, 450, 452,
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