# THE LOGIC OF CAUSATION

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THE LOGIC OF CAUSATION

Phase One: Macroanalysis

Chapter 7 – Reduction of Positive Moods.

First, note that ten moods in subfigure 1d have inconsistent premises. Specifically, if the minor premise (which has form P(S)Q) 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 (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). 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, whether it concerns partial causation (see clause (iii) of that) or contingent causation (see clause (ii) of that).

Summary of figure 1.

· 30 valid moods:

111-118, 121, 124-125, 128, 131, 134, 136-137, 141, 144, 147-148, 151-152, 155, 161, 163, 166, 171, 174, 181, 184.

· 24 moods without conclusion (nil):

126-127, 135, 138, 145-146, 153-154, 156-158, 162, 164-165, 167-168, 175-178, 185-188.

· 10 impossible moods (**):

122-123, 132-133, 142-143, 172-173, 182-183.

Total of moods = 30 valid and 34 invalid = 64.

 Table 7.3.Sources of validity or invalidity in figure 1.

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? §1 111 m n p q major mn yes yes no no minor mn by by since since concl. mn 155 166 m n §2 112 m n p q major mn yes no no yes minor mq by since since by concl. mq 155 q m 118 §2 113 m n p q major mn no yes yes no minor np since by by since concl. np p 166 117 n §6 114 m n p q major mn no no yes yes minor pq since since by by concl. pq p q 117 118 §11 115 m n p q major mn yes no no no minor m by by since by concl. m 155 112 m 111 §11 116 m n p q major mn no yes no no minor n by by by since concl. n 113 166 111 n §17 117 m n p q major mn no no yes no minor p since by by by concl. p p 114 MA 113 §17 118 m n p q major mn no no no yes minor q by since by by concl. q 114 q 112 MA

 Ref. Mood # Elements of conclusion implied? §3 121 m n p q major mq yes no no yes minor mn by since since by concl. mq 155 q m 181 §4 122 m n p q major mq q of major premise and minor mq m of minor premise concl. ** are incompatible §5 123 m n p q major mq q of major premise and minor np n of minor premise concl. ** are incompatible §8 124 m n p q major mq no no no yes minor pq by since by by concl. q MA q MA 128,184 §13 125 m n p q major mq yes no no no minor m by by since by concl. m 155 121 m MA §14 126 m n p q major mq no no no no minor n by by by by concl. nil MA 121 121 MA §19 127 m n p q major mq no no no no minor p by by by by concl. nil 124 124 124 MA §20 128 m n p q major mq no no no yes minor q by since by by concl. q 124 q 124 MA

 Ref. Mood # Elements of conclusion implied? §3 131 m n p q major np no yes yes no minor mn since by by since concl. np p 166 171 n §5 132 m n p q major np p of major premise and minor mq m of minor premise concl. ** are incompatible §4 133 m n p q major np p of major premise and minor np n of minor premise concl. ** are incompatible §8 134 m n p q major np no no yes no minor pq since by by by concl. p p MA 137,174 MA §14 135 m n p q major np no no no no minor m by by by by concl. nil 131 MA MA 131 §13 136 m n p q major np no yes no no minor n by by by since concl. n 131 166 MA n §20 137 m n p q major np no no yes no minor p since by by by concl. p p 134 MA 134 §19 138 m n p q major np no no no no minor q by by by by concl. nil 134 134 MA 134

 Ref. Mood # Elements of conclusion implied? §7 141 m n p q major pq no no yes yes minor mn since since by by concl. pq p q 171 181 §9 142 m n p q major pq p, q of major premise and minor mq m of minor premise concl. ** are incompatible §9 143 m n p q major pq p, q of major premise and minor np n of minor premise concl. ** are incompatible §10 144 m n p q major pq no no yes yes minor pq since since by by concl. pq p q 147,174 148,184 §23 145 m n p q major pq no no no no minor m by by by by concl. nil 141 141 MA MA §23 146 m n p q major pq no no no no minor n by by by by concl. nil 141 141 MA MA §25 147 m n p q major pq no no yes no minor p since by by by concl. p p 144 MA MA §25 148 m n p q major pq no no no yes minor q by since by by concl. q 144 q MA MA

 Ref. Mood # Elements of conclusion implied? §12 151 m n p q major m yes no no no minor mn by by since by concl. m 155 121 m 111 §15 152 m n p q major m yes no no no minor mq by by since by concl. m 155 112 m MA §16 153 m n p q major m no no no no minor np by by by by concl. nil 113 MA MA 113 §24 154 m n p q major m no no no no minor pq by by by by concl. nil 114 114 124 MA §27 155 m n p q major m yes no no no minor m by by since by concl. m MA 112 m 111 §28 156 m n p q major m no no no no minor n by by by by concl. nil 113 121 111 111 §29 157 m n p q major m no no no no minor p by by by by concl. nil 113 114 124 113 §30 158 m n p q major m no no no no minor q by by by by concl. nil 114 112 112 152

 Ref. Mood # Elements of conclusion implied? §12 161 m n p q major n no yes no no minor mn by by by since concl. n 131 166 111 n §16 162 m n p q major n no no no no minor mq by by by by concl. nil MA 112 112 MA §15 163 m n p q major n no yes no no minor np by by by since concl. n 113 166 MA n §24 164 m n p q major n no no no no minor pq by by by by concl. nil 114 114 MA 134 §28 165 m n p q major n no no no no minor m by by by by concl. nil 131 112 111 111 §27 166 m n p q major n no yes no no minor n by by by since concl. n 113 MA 111 n §30 167 m n p q major n no no no no minor p by by by by concl. nil 113 114 163 113 §29 168 m n p q major n no no no no minor q by by by by concl. nil 114 112 112 134

 Ref. Mood # Elements of conclusion implied? §18 171 m n p q major p no no yes no minor mn since by by by concl. p p 141 MA 131 §21 172 m n p q major p p of major premise and minor mq m of minor premise concl. ** are incompatible §22 173 m n p q major p p of major premise and minor np n of minor premise concl. ** are incompatible §26 174 m n p q major p no no yes no minor pq since by by by concl. p p 134 MA 134 §31 175 m n p q major p no no no no minor m by by by by concl. nil 131 135 135 131 §32 176 m n p q major p no no no no minor n by by by by concl. nil 131 141 136 131 §33 177 m n p q major p no no no no minor p by by by by concl. nil 134 134 MA 134 §34 178 m n p q major p no no no no minor q by by by by concl. nil 134 134 138 134

 Ref. Mood # Elements of conclusion implied? §18 181 m n p q major q no no no yes minor mn by since by by concl. q 141 q 121 MA §22 182 m n p q major q q of major premise and minor mq m of minor premise concl. ** are incompatible §21 183 m n p q major q q of major premise and minor np n of minor premise concl. ** are incompatible §26 184 m n p q major q no no no yes minor pq by since by by concl. q 124 q 124 MA §32 185 m n p q major q no no no no minor m by by by by concl. nil 141 121 121 125 §31 186 m n p q major q no no no no minor n by by by by concl. nil 126 121 121 126 §34 187 m n p q major q no no no no minor p by by by by concl. nil 124 124 124 127 §33 188 m n p q major q no no no no minor q by by by by concl. nil 124 124 124 MA

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2016-06-13T10:29:31+00:00