7b 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).

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

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

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).

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

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