Peter of Ailly: Concepts and Insolubles

remarks (par. 99).- 2. Gregory of Rimini's view: They are never composites (pars. 100-111).- 3. Peter's own view (pars. 112-137).- a. Introductory remarks (par. 112).- b. The composition or non-composition of mental sentences properly so called (pars. 113-128).- i. Conclusion 1: Mental hypothetical are composites (pars. 113-118).- ii. Conclusion 2: Mental categoricals are not composites (pars. 119-124).- iii. Conclusion 3: Mental expressions ought not be called 'complex' because they are really composites (pars. 125-128).- c. Why a mental expression should be called complex (pars. 129-136).- i. Conclusion 4: Not because it is equivalent in signifying to the several utterances or inscriptions that make up a spoken or written expression (pars. 129-130).- ii. Conclusion 5: Not-because it signifies a composition or division among beings (pars. 131-134).- iii. Conclusion 6: Rather because it is equivalent in signifying to several acts of knowing (pars. 135-136).- d. Closing remarks (par. 137).- III. Chapter Two: Truth and falsehood in general (pars. 138-238).- A. Introductory remarks (pars. 138-139).- B. Bad reasons for calling sentences true or false (pars. 140-147).- 1. Conclusion 1: Because they signify what is true or false externally (pars. 140-143).- 2. Conclusion 2: Because of the supposition of their subjects and predicates (pars. 144-147).- C. Why sentences signifying by convention should be called true or false, possible or impossible (pars. 148-157).- 1. Conclusion 3: Their truth or falsehood is based on the truth or falsehood of a corresponding mental sentence properly so called (pars. 148-152).- a. Corollary 1: A conventionally signifying sentence can be true and false at the same time (par. 150).- b. Corollary 2: Such a sentence is distinct from its own truth or falsehood (par. 151).- c. Objection to Corollary 1, with reply (par. 152).- 2. Conclusion 4: The possibility or impossibility of such sentences is based on the possibility or impossibility of a corresponding mental sentence properly so called (pars. 153-157).- a. Corollary 1: The spoken sentence 'No spoken sentence is true' is possible (par. 155).- b. Corollary 2: But it cannot be true (par. 156).- c. Problem and reply (par. 157).- D. Why mental sentences properly so called are true or false, possible or impossible (pars. 158-178).- 1. Introduction to Conclusions 5 and 6 (par. 158).- 2. Conclusion 5: Rule for truth and falsehood of mental sentences properly so called (pars. 159-164).- a. Corollary 1: The cause of the truth of an affirmative is not the same as the cause of the falsehood of the corresponding negative (par. 161).- b. Corollary 2: No mental sentence properly so called can be true and false at the same time (par. 162).- c. Corollary 3: Mental sentences properly so called are identical with their truth or falsehood (par. 163).- d. Corollary 4: The cause of the truth or falsehood of such sentences is the same as the cause of their modal quality (par. 164).- 3. Conclusion 6: Rule for possibility and impossibility of mental sentences properly so called (pars. 165-166).- 4. Further clarification of Conclusions 5 and 6 (pars. 167-170).- 5. Corollaries from Conclusions 4 and 6 (pars. 171-178).- a. Corollary 1 (par. 171).- b. Corollary 2 (pars. 172-174).- i. Objection to Corollary 2, with reply (pars. 173-174).- c. Corollary 3 (par. 175).- d. Corollary 4 (pars. 176-178).- i. Objection to Corollary 4, with reply (par.178).- E. Three doubts about the total significate of a sentence (pars. 179-238).- 1. First doubt: What is the total or adequate significate of 'Every man is an animal'? (par.179).- 2. Second doubt: It seems that there is something true or false besides true or false sentences (pars. 180-182).- a. First argument: E.g., God and God's knowledge (par. 180).- b. Second argument: Before the creation, it was true that the world was going to exist (par. 181).- c. Third argument: If no sentence existed, it would be true that no sentence existed (par. 182).- 3. Third doubt: Something impossible must be the significate of an impossible sentence (par. 183).- 4. Program for the rest of Chapter two (par. 184).- 5. Gregory of Rimini's theory of 'complexly significables' (pars. 185-189).- 6. Refutation of Gregory's view (pars. 190-209).- a. Conclusion 1: There are no complexly significables in Gregory's sense (pars. 191-195).- b. Conclusion 2: Everything is, in a sense, complexly significable (pars. 196-197).- c. Conclusion 3: Nothing is the adequate or total significate of a mental sentence properly so called (pars. 198-199).- d. Conclusion 4: A mental sentence properly so called signifies exactly what its parts signify, or the parts of the corresponding spoken sentence. Yet the sentence as a whole signifies in some way that is not signified by any part (pars. 200-201).- e. Conclusion 5: Contradictory sentences signify exactly the same things, but in different ways (pars. 202-203).- f. Conclusion 6: No dictum of a mental sentence properly so called supposits for anything if taken significatively (pars. 204-209).- 7. Reply to doubts (pars. 210-238).- a. To the first doubt, in par. 179: Nothing is the total significate (pars. 210-221).- i. How to treat infinitives (pars. 213-221).- ?. Conclusion 1 (pars. 213-215).- ?. Conclusion 2 (pars. 216-218).- ?. Conclusion 3 (par. 219).- ?. Conclusion 4: Infinitives should be used only where 'that'-clauses can be used (pars. 220-221).- b. To the second doubt, in pars. 180-182 (pars. 222-234).- i. Created and uncreated truths (pars. 222-228).- ?. Conclusion 1: There is a truth outside the soul in addition to created sentences (pars. 222-223).- ?. Conclusion 2: There is no truth outside the soul besides created and uncreated sentences (pars. 224- 225).- ?. Conclusion 3: God is a true sentence (pars. 226-228).- ii. Reply to first argument, in par. 180: God is an uncreated sentence (par. 229).- iii. Reply to second argument, in par. 181: That truth was then God (pars. 230-231).- iv. Reply to third argument, in par. 182: The antecedent is impossible (pars. 232-234).- ?. Objection and reply: What about eternal falsehoods? (pars. 233-234).- c. To the third doubt, in par. 183 (pars. 235-238).- i. One reply: The inference is invalid (par. 235).- ii. An alternative reply: To concede the inference and to deny that it requires the existence of impossibles (pars. 236-237).- iii. Comparison of the two replies: The first is preferable (par. 238).- IV. Chapter Three: Sentences having reflection on themselves (pars. 239-336).- A. Introductory remarks (par. 239).- B. Descriptions (pars. 240-252).- 1. Description 1: Signification (par. 240).- 2. Description 2: Sentence having reflection on itself (par. 241).- 3. Description 3: Insoluble sentence (par. 242).- 4. Corollaries from descriptions (pars. 243-252).- a. Corollary 1: Self-reference requires a term signifying a sentence (par. 243).- b. Refutation of earlier views (pars. 244-252).- i. Corollary 2: Not every sentence signifies itself to be true (pars. 244-246).- ii. Corollary 3: Against Marsilius of Inghen (pars. 247-248).- iii. Corollary 4: Not every sentence has two significations, one material and one formal, against Marsilius (pars. 249-250).- iv. Corollary 5: Against Marsilius (par. 251).- v. Corollary 6: Many sentences thought to be insolubles are not, against Marsilius and others (par. 252).- C. Distinctions: Various kinds of self-reference (pars. 253-261).- 1. Distinction 1: Some self-referential sentences signify themselves to be false, others do not (pars. 253-254).- 2. Distinction 2: Some of the former do so independently of every situation, others do not (pars. 255-256).- 3. Distinction 3: Some of the former do so directly, others indirectly (par. 257).- 4. Distinction 4: Some of the latter do so immediately, others by means of others sentences (par. 258).- 5. Distinction 5: Some of the latter do so by means of sentences they themselves signify, others rather by means of sentence by which they are signified to exist (par. 259).- 6. Distinction 6: Some of the former do so by means of sentences of which they are parts, others do not (par. 260).- 7. Summary (par. 261).- D. Corollaries from distinctions (pars. 262-271).- 1. Corollary 1 (par. 262).- 2. Corollary 2 (pars. 263-270).- a. Objection and reply (pars. 264-270).- 3. Corollary 3 (par. 271).- E. Which kinds of sentences can have reflection on themselves? (pars. 272-336).- 1. Introductory remarks (par. 272).- 2. Assumptions about formal and objective signification (pars. 273-280).- a. Assumption 1: Two kinds of signification: objective and formal (par. 273).- b. Assumption 2: Definition of each kind (par. 274).- c. Assumption 3: Anything can signify itself objectively (par.275).- d. Assumption 4: Nothing can distinctly signify itself formally (pars. 276-277).- e. Assumption 5: Spoken and written sentences signify only objectively (par. 278).- f. Assumption 6: Spoken and written sentences signify themselves first of all (pars. 279-280).- 3. The impossibility of self-reference among mental sentences properly so called (pars. 281-336).- a. Introductory remarks (par. 281).- b. Conclusion 1: No mental sentence properly so called can signify itself to be false (pars. 282-301).- i. First proof (pars. 283-284).- ii. Second proof (pars. 285-286).- iii. Third proof (pars. 287-289).- ?. Refutation of other views, including Marsilius of Inghen's (pars. 288-289).- iv. Fourth proof (pars. 290-296).- ?. Refutation of Marsilius' view (pars. 292-296).- v. Corollaries (pars. 297-301).- ?. Corollary 1 (par. 297).- ?. Corollary 2 (pars. 298-299).- ?. Corollary 3 (par. 300).- ?. Corollary 4 (par. 301).- c. Conclusion 2: No mental sentence properly so called can signify itself to be true (pars. 302-306).- d. Conclusion 3: There are no self-referential mental sentences properly so called (pars. 307-310).- e. Objection to Conclusion 1 (pars. 311-326).- i. Statement of the objection (pars. 311-312).- ii. Supposition in mental sentences (pars. 313-326).- ?. Conclusion 1: A part of a mental sentence properly so called cannot supposit for the whole sentence (pars. 313-317).- ?. Conclusion 2: Or for the contradictory of that sentence (pars. 318-319).- ?. Conclusion 3 (pars. 320-321).- ?. Conclusion 4: No part of a conventionally signifying sentence can supposit for a corresponding mental sentence properly so called (pars. 322-323).- ?. Corollaries from Conclusions 1 through 4 (pars. 324-326).- Introductory remarks (par. 324).- Corollary 1: Reply to the objection in pars. 311-312 (par. 325).- Corollary 2 (par. 326).- f. Conclusion 4: Self-reference is possible in sentences signifying by convention, in any of the ways mentioned in pars. 253- 261 (pars. 327-336).- i. Corollary 1: Every insoluble is a spoken, written or mental sentence improperly so called (par. 329).- ii. Corollary 2: Parts of spoken, written or mental sentences improperly so called can supposit for their wholes (pars. 330-336).- ?. Objections to Corollary 2, with replies (pars. 332-336).- V. Chapter Four: Truth and falsehood of insolubles (pars. 337-383).- A. Introductory remarks (par. 337).- B. Assumption 1: Every insoluble has some corresponding mental sentence properly so called (pars. 338-339).- C. Assumption 2: The terms of an insoluble and a mental sentence properly so called corresponding to it signify and supposit for the the same (pars. 340-342).- D. Assumption 3: Howsoever an insoluble signifies the case to be, so does some mental sentence or sentences (pars. 343-344).- E. Assumption 4: Insolubles falsify themselves, and so are false (pars. 345-347).- F. Conclusion 1: Every insoluble corresponds to a true mental sentence (pars. 348-349).- G. Conclusion 2: Every insoluble corresponds to a false mental sentence (pars. 350-353).- H. Conclusion 3: Every insoluble corresponds to two unconjoined mental sentences, one true and one false (pars. 354-358).- 1. Corollary 1 (par. 357).- 2. Corollary 2 (par. 358).- I. Conclusion 4: Insolubles are true and false at the same time (pars. 359-383).- 1. Corollary 1: So are their contradictories (par. 361).- 2. Corollary 2 (par. 362).- 3. Corollary 3: Some apparent contradictories are not contradictory in fact (pars. 363-368).- a. The formation of contradictories (pars. 365-368).- 4. Corollary 4: No insoluble or its contradictory is absolutely true or absolutely false (par. 369).- 5. Objection involving some of the above points (pars. 370-376).- 6. Corollary 5: No insoluble is absolutely impossible (par. 377).- 7. Corollary 6: No insoluble or its contradictory should be absolutely conceded or absolutely denied (pars. 378-383).- Notes.