7c Reductions in Figure 2

First, note that six moods in subfigure 2d have inconsistent premises. Specifically, if the minor premise (which has form P(S)Q) involves a strong determination, then it conflicts with any weak determination of same polarity in the major premise (which has form R(P)Q).

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 when it concerns partial causation (see clause (ii) 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 when it concerns contingent causation (see clause (ii) of that).

Additionally, we may directly reduce a number of moods in figure 2 to figure 1, by converting the major premise. This is feasible when the major premise involves only strong causation; i.e. subfigures 2a and 2b are thus reducible respectively to subfigures 1a and 1b. This is not feasible when the major premise involves weak causation, since its conversion results in negation of the complement; which means that subfigures 2c and 2d have to be evaluated relatively independently (i.e. within the same figure, even if possibly through some moods reduced to figure 1).

222, 224-225, 227-228, 233-234, 236-238, 241, 244-248, 252, 254-255, 257-258, 263-264, 266-268, 271, 273-278, 281-282, 284-288.

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	211	m	n	p	q
major	mn	yes	yes	no	no
minor	mn	by	by	since	since
concl.	mn	111	111	m	n
§2	212	m	n	p	q
major	mn	yes	no	no	yes
minor	mq	by	since	since	by
concl.	mq	112	q	m	112
§2	213	m	n	p	q
major	mn	no	yes	yes	no
minor	pn	since	by	by	since
concl.	pn	p	113	113	n
§6	214	m	n	p	q
major	mn	no	no	yes	yes
minor	pq	since	since	by	by
concl.	pq	p	q	114	114
§11	215	m	n	p	q
major	mn	yes	no	no	no
minor	m	by	by	since	by
concl.	m	115	115	m	115
§11	216	m	n	p	q
major	mn	no	yes	no	no
minor	n	by	by	by	since
concl.	n	116	116	116	n
§17	217	m	n	p	q
major	mn	no	no	yes	no
minor	p	since	by	by	by
concl.	p	p	117	117	117
§17	218	m	n	p	q
major	mn	no	no	no	yes
minor	q	by	since	by	by
concl.	q	118	q	118	118

Ref.	Mood #	Elements of conclusion implied?
§3	221	m	n	p	q
major	mq	no	yes	no	no
minor	mn	by	by	by	since
concl.	n	MA	256	MA	n
§4	222	m	n	p	q
major	mq	no	no	no	no
minor	mq	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§5	223	m	n	p	q
major	mq	q of major premise and
minor	pn	n of minor premise
concl.	**	are incompatible
§8	224	m	n	p	q
major	mq	no	no	no	no
minor	pq	by	by	by	by
concl.