THE LOGIC OF CAUSATION

Phase One: Macroanalysis

Chapter 7 –Reduction of Positive Moods.

First, note that ten moods in subfigure 3d have inconsistent premises. Specifically, if the minor premise (which has form Q(S)P) involves a strong determination, then it conflicts with the weak determination(s) of the major premise (which has form Q(P)R).

For if the minor concerns complete causation, clause (i) of which means that (notP + Q) is impossible – it is incompatible with the major, which implies (notP + Q) is possible, whether it concerns partial causation (see clause (iii) of that) or contingent causation (see clause (ii) of that). Similarly, if the minor concerns necessary causation, clause (i) of which means that (P + notQ) is impossible – it is incompatible with the major, which implies (P + notQ) is possible, whether it concerns partial causation (see clause (ii) of that) or contingent causation (see clause (iii) of that).

Additionally, we may directly reduce a number of moods in figure 3 to figure 1, by converting the minor premise. This is feasible when the minor premise involves only strong causation; i.e. subfigures 3a and 3c are thus reducible respectively to subfigures 1a and 1c. This is not feasible when the minor premise involves weak causation, since its conversion results in negation of the complement; which means that subfigures 3b and 3d have to be evaluated relatively independently (i.e. within the same figure, even if possibly through some moods reduced to figure 1).

Summary of figure 3.

·18 valid moods:

311-313, 315-316, 321, 326, 331, 335, 341, 351, 353, 356, 361-362, 365, 371, 381.

·36 moods without conclusion(nil):

314, 317-318, 324-325, 327-328, 334, 336-338, 344-348, 352, 354-355, 357-358, 363-364, 366-368, 374-378, 384-388.

·10 impossible moods(**):

322-323, 332-333, 342-343, 372-373, 382-383.

Total of moods = 18 valid and 46 invalid = 64.

 Table 7.5.Sources of validity or invalidity in figure 3.

This table may be read as follows:

yes= element of conclusion (m,n,porq) are implied by the given premises.

no= element of conclusion (m,n,porq) are not implied (which does not mean denied) by the given premises.

by= by any sort of reduction to (number of mood used) orMA(matricial analysis).

Elements of conclusions for which matricial analysis is required areshaded.

since= for given premises, if an element of conclusion is valid (yes), then its contrary element is invalid (no).

**= incompatible premises.

nil= no valid conclusion.

 Ref. Mood # Elements of conclusion implied? §1 311 m n p q major mn yes yes no no minor mn by by since since concl. mn 111 111 m n §2 312 m n p q major mn no yes no no minor mq by by by since concl. n MA 365 MA n §2 313 m n p q major mn yes no no no minor np by by since by concl. m 356 MA m MA §6 314 m n p q major mn no no no no minor pq by by by by concl. nil MA MA MA MA §11 315 m n p q major mn no yes no no minor m by by by since concl. n 116 116 116 n §11 316 m n p q major mn yes no no no minor n by by since by concl. m 115 115 m 115 §17 317 m n p q major mn no no no no minor p by by by by concl. nil 314 313 313 313 §17 318 m n p q major mn no no no no minor q by by by by concl. nil 312 314 312 312

 Ref. Mood # Elements of conclusion implied? §3 321 m n p q major mq yes no no yes minor mn by since since by concl. mq 121 q m 121 §4 322 m n p q major mq qof major premise and minor mq mof minor premise concl. ** are incompatible §5 323 m n p q major mq qof major premise and minor np nof minor premise concl. ** are incompatible §8 324 m n p q major mq no no no no minor pq by by by by concl. nil MA MA MA MA §13 325 m n p q major mq no no no no minor m by by by by concl. nil 126 126 126 126 §14 326 m n p Q major mq yes no no No minor n by by since by concl. m 125 125 m 125 §19 327 m n p Q major mq no no no No minor p by by by by concl. nil 324 324 324 324 §20 328 m n p Q major mq no no no No minor q by by by by concl. nil 324 324 324 324

 Ref. Mood # Elements of conclusion implied? §3 331 m n p Q major np no yes yes No minor mn since by by since concl. np p 131 131 N §5 332 m n p q major np pof major premise and minor mq mof minor premise concl. ** are incompatible §4 333 m n p q major np pof major premise and minor np nof minor premise concl. ** are incompatible §8 334 m n p q major np no no no no minor pq by by by by concl. nil MA MA MA MA §14 335 m n p q major np no yes no no minor m by by by since concl. n 136 136 136 n §13 336 m n p q major np no no no no minor n by by by by concl. nil 135 135 135 135 §20 337 m n p q major np no no no no minor p by by by by concl. nil 334 334 334 334 §19 338 m n p q major np no no no no minor q by by by by concl. nil 334 334 334 334

 Ref. Mood # Elements of conclusion implied? §7 341 m n p q major pq no no yes yes minor mn since since by by concl. pq p q 141 141 §9 342 m n p q major pq pandqof major premise and minor mq mof minor premise concl. ** are incompatible §9 343 m n p q major pq pandqof major premise and minor np nof minor premise concl. ** are incompatible §10 344 m n p q major pq no no no no minor pq by by by by concl. nil MA MA MA MA §23 345 m n p q major pq no no no no minor m by by by by concl. nil 146 146 146 146 §23 346 m n p q major pq no no no no minor n by by by by concl. nil 145 145 145 145 §25 347 m n p q major pq no no no no minor p by by by by concl. nil 344 344 344 344 §25 348 m n p q major pq no no no no minor q by by by by concl. nil 344 344 344 344

 Ref. Mood # Elements of conclusion implied? §12 351 m n p q major m yes no no no minor mn by by since by concl. m 151 151 m 151 §15 352 m n p q major m no no no no minor mq by by by by concl. nil 312 MA 312 312 §16 353 m n p q major m yes no no no minor np by by since by concl. m 356 313 m 313 §24 354 m n p q major m no no no no minor pq by by by by concl. nil 314 314 314 314 §27 355 m n p q major m no no no no minor m by by by by concl. nil 156 156 156 156 §28 356 m n p q major m yes no no no minor n by by since by concl. m 155 155 m 155 §29 357 m n p q major m no no no no minor p by by by by concl. nil 314 313 313 313 §30 358 m n p q major m no no no no minor q by by by by concl. nil 312 314 312 312

 Ref. Mood # Elements of conclusion implied? §12 361 m n p q major n no yes no no minor mn by by by since concl. n 161 161 161 n §16 362 m n p q major n no yes no no minor mq by by by since concl. n 312 365 312 n §15 363 m n p q major n no no no no minor np by by by by concl. nil MA 313 313 313 §24 364 m n p q major n no no no no minor pq by by by by concl. nil 314 314 314 314 §28 365 m n p q major n no yes no no minor m by by by since concl. n 166 166 166 n §27 366 m n p q major n no no no no minor n by by by by concl. nil 165 165 165 165 §30 367 m n p q major n no no no no minor p by by by by concl. nil 314 313 313 313 §29 368 m n p q major n no no no no minor q by by by by concl. nil 312 314 312 312

 Ref. Mood # Elements of conclusion implied? §18 371 m n p q major p no no yes no minor mn since by by by concl. p p 171 171 171 §21 372 m n p q major p pof major premise and minor mq mof minor premise concl. ** are incompatible §22 373 m n p q major p pof major premise and minor np nof minor premise concl. ** are incompatible §26 374 m n p q major p no no no no minor pq by by by by concl. nil 334 334 334 334 §31 375 m n p q major p no no no no minor m by by by by concl. nil 176 176 176 176 §32 376 m n p q major p no no no no minor n by by by by concl. nil 175 175 175 175 §33 377 m n p q major p no no no no minor p by by by by concl. nil 334 334 334 334 §34 378 m n p q major p no no no no minor q by by by by concl. nil 334 334 334 334

 Ref. Mood # Elements of conclusion implied? §18 381 m n p q major q no no no yes minor mn by since by by concl. q 181 q 181 181 §22 382 m n p q major q qof major premise and minor mq mof minor premise concl. ** are incompatible §21 383 m n p q major q qof major premise and minor np nof minor premise concl. ** are incompatible §26 384 m n p q major q no no no no minor pq by by by by concl. nil 324 324 324 324 §32 385 m n p q major q no no no no minor m by by by by concl. nil 186 186 186 186 §31 386 m n p q major q no no no no minor n by by by by concl. nil 185 185 185 185 §34 387 m n p q major q no no no no minor p by by by by concl. nil 324 324 324 324 §33 388 m n p q major q no no no no minor q by by by by concl. nil 324 324 324 324

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