THE LOGIC OF CAUSATION

Phase One: Macroanalysis

Chapter 7 – Reduction of Positive Moods.

First, note that six moods in subfigure 2d have inconsistent premises. Specifically, if the minor premise (which has form P(S)Q) involves a strong determination, then it conflicts with any weak determination of same polarity in the major premise (which has form R(P)Q).

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

Additionally, we may directly reduce a number of moods in figure 2 to figure 1, by converting the major premise. This is feasible when the major premise involves only strong causation; i.e. subfigures 2a and 2b are thus reducible respectively to subfigures 1a and 1b. This is not feasible when the major premise involves weak causation, since its conversion results in negation of the complement; which means that subfigures 2c and 2d 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 2.

· 18 valid moods:

211-218, 221, 226, 231, 235, 251, 253, 256, 261-262, 265.

· 40 moods without conclusion (nil):

222, 224-225, 227-228, 233-234, 236-238, 241, 244-248, 252, 254-255, 257-258, 263-264, 266-268, 271, 273-278, 281-282, 284-288.

· 6 impossible moods (**):

223, 232, 242-243, 272, 283.

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

 Table 7.4.Sources of validity or invalidity in figure 2.

This table may be read as follows:

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

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

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

Elements of conclusions for which matricial analysis is required are shaded.

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? §1 211 m n p q major mn yes yes no no minor mn by by since since concl. mn 111 111 m n §2 212 m n p q major mn yes no no yes minor mq by since since by concl. mq 112 q m 112 §2 213 m n p q major mn no yes yes no minor np since by by since concl. np p 113 113 n §6 214 m n p q major mn no no yes yes minor pq since since by by concl. pq p q 114 114 §11 215 m n p q major mn yes no no no minor m by by since by concl. m 115 115 m 115 §11 216 m n p q major mn no yes no no minor n by by by since concl. n 116 116 116 n §17 217 m n p q major mn no no yes no minor p since by by by concl. p p 117 117 117 §17 218 m n p q major mn no no no yes minor q by since by by concl. q 118 q 118 118

 Ref. Mood # Elements of conclusion implied? §3 221 m n p q major mq no yes no no minor mn by by by since concl. n MA 256 MA n §4 222 m n p q major mq no no no no minor mq by by by by concl. nil MA MA MA MA §5 223 m n p q major mq q of major premise and minor np n of minor premise concl. ** are incompatible §8 224 m n p q major mq no no no no minor pq by by by by concl. nil MA MA MA MA §13 225 m n p q major mq no no no no minor m by by by by concl. nil 221 222 221 221 §14 226 m n p q major mq no yes no no minor n by by by since concl. n 221 256 221 n §19 227 m n p q major mq no no no no minor p by by by by concl. nil 224 224 224 224 §20 228 m n p q major mq no no no no minor q by by by by concl. nil 222 222 222 222

 Ref. Mood # Elements of conclusion implied? §3 231 m n p q major np yes no no no minor mn by by since by concl. m 265 MA m MA §5 232 m n p q major np p of major premise and minor mq m of minor premise concl. ** are incompatible §4 233 m n p q major np no no no no minor np by by by by concl. nil MA MA MA MA §8 234 m n p q major np no no no no minor pq by by by by concl. nil MA MA MA MA §14 235 m n p q major np yes no no no minor m by by since by concl. m 265 231 m 231 §13 236 m n p q major np no no no no minor n by by by by concl. nil 233 231 231 231 §20 237 m n p q major np no no no no minor p by by by by concl. nil 233 233 233 233 §19 238 m n p q major np no no no no minor q by by by by concl. nil 234 234 234 234

 Ref. Mood # Elements of conclusion implied? §7 241 m n p q major pq no no no no minor mn by by by by concl. nil MA MA MA MA §9 242 m n p q major pq p of major premise and minor mq m of minor premise concl. ** are incompatible §9 243 m n p q major pq q of major premise and minor np n of minor premise concl. ** are incompatible §10 244 m n p q major pq no no no no minor pq by by by by concl. nil MA MA MA MA §23 245 m n p q major pq no no no no minor m by by by by concl. nil 241 241 241 241 §23 246 m n p q major pq no no no no minor n by by by by concl. nil 241 241 241 241 §25 247 m n p q major pq no no no no minor p by by by by concl. nil 244 244 244 244 §25 248 m n p q major pq no no no no minor q by by by by concl. nil 244 244 244 244

 Ref. Mood # Elements of conclusion implied? §12 251 m n p q major m no yes no no minor mn by by by since concl. n 161 161 161 n §15 252 m n p q major m no no no no minor mq by by by by concl. nil 162 162 162 162 §16 253 m n p q major m no yes no no minor np by by by since concl. n 163 163 163 n §24 254 m n p q major m no no no no minor pq by by by by concl. nil 164 164 164 164 §27 255 m n p q major m no no no no minor m by by by by concl. nil 165 165 165 165 §28 256 m n p q major m no yes no no minor n by by by since concl. n 166 166 166 n §29 257 m n p q major m no no no no minor p by by by by concl. nil 167 167 167 167 §30 258 m n p q major m no no no no minor q by by by by concl. nil 168 168 168 168

 Ref. Mood # Elements of conclusion implied? §12 261 m n p q major n yes no no no minor mn by by since by concl. m 151 151 m 151 §16 262 m n p q major n yes no no no minor mq by by since by concl. m 152 152 m 152 §15 263 m n p q major n no no no no minor np by by by by concl. nil 153 153 153 153 §24 264 m n p q major n no no no no minor pq by by by by concl. nil 154 154 154 154 §28 265 m n p q major n yes no no no minor m by by since by concl. m 155 155 m 155 §27 266 m n p q major n no no no no minor n by by by by concl. nil 156 156 156 156 §30 267 m n p q major n no no no no minor p by by by by concl. nil 157 157 157 157 §29 268 m n p q major n no no no no minor q by by by by concl. nil 158 158 158 158

 Ref. Mood # Elements of conclusion implied? §18 271 m n p q major p no no no no minor mn by by by by concl. nil 241 231 231 231 §21 272 m n p q major p p of major premise and minor mq m of minor premise concl. ** are incompatible §22 273 m n p q major p no no no no minor np by by by by concl. nil 233 233 233 233 §26 274 m n p q major p no no no no minor pq by by by by concl. nil 234 234 234 234 §31 275 m n p q major p no no no no minor m by by by by concl. nil 241 231 231 231 §32 276 m n p q major p no no no no minor n by by by by concl. nil 233 231 231 231 §33 277 m n p q major p no no no no minor p by by by by concl. nil 233 233 233 233 §34 278 m n p q major p no no no no minor q by by by by concl. nil 234 234 234 234

 Ref. Mood # Elements of conclusion implied? §18 281 m n p q major q no no no no minor mn by by by by concl. nil 221 241 221 221 §22 282 m n p q major q no no no no minor mq by by by by concl. nil 222 222 222 222 §21 283 m n p q major q q of major premise and minor np n of minor premise concl. ** are incompatible §26 284 m n p q major q no no no no minor pq by by by by concl. nil 224 224 224 224 §32 285 m n p q major q no no no no minor m by by by by concl. nil 221 222 221 221 §31 286 m n p q major q no no no no minor n by by by by concl. nil 221 241 221 221 §34 287 m n p q major q no no no no minor p by by by by concl. nil 224 224 224 224 §33 288 m n p q major q no no no no minor q by by by by concl. nil 222 222 222 222

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