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	pn	since	by	by	since
concl.	pn	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	pn	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