THE LOGIC OF CAUSATION
Phase One: Macroanalysis
Chapter 7 – Reduction of Positive Moods.
Section 2. Reductions in Figure 1.
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 |
Next section (continuation of same chapter)