7d Reductions in Figure 3

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).

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

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.

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	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	pn	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	q of major premise and
minor	mq	m of minor premise
concl.	**	are incompatible
§5	323	m	n	p	q
major	mq	q of major premise and
minor	pn	n of 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	pn	no	yes	yes	No
minor	mn	since	by	by	since
concl.	pn	p	131	131	N
§5	332	m	n	p	q
major	pn	p of major premise and
minor	mq	m of minor premise
concl.	**	are incompatible
§4	333	m	n	p	q
major	pn	p of major premise and
minor	pn	n of minor premise
concl.	**	are incompatible
§8	334	m	n	p	q
major	pn	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§14	335	m	n	p	q
major	pn	no	yes	no	no
minor	m	by	by	by	since
concl.	n	136	136	136	n
§13	336	m	n	p	q
major	pn	no	no	no	no
minor	n	by	by	by	by
concl.	*nil*	135	135	135	135
§20	337	m	n	p	q
major	pn	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	334	334	334	334
§19	338	m	n	p	q
major	pn	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	p and q of major premise and
minor	mq	m of minor premise
concl.	**	are incompatible
§9	343	m	n	p	q
major	pq	p and q of major premise and
minor	pn	n of 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	pn	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	pn	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	p of major premise and
minor	mq	m of minor premise
concl.	**	are incompatible
§22	373	m	n	p	q
major	p	p of major premise and
minor	pn	n of 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	q of major premise and
minor	mq	m of minor premise
concl.	**	are incompatible
§21	383	m	n	p	q
major	q	q of major premise and
minor	pn	n of 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