15a Some More Three-Item Syllogisms - Logic Philosophy Spirituality

THE LOGIC OF CAUSATION

Phase Two: Microanalysis

Chapter 15 – Some More Three-Item Syllogisms

In the previous chapter, we examined positive absolute three-item syllogism. In the present chapter, we shall look for other syllogistic forms, involving relative or negative causative propositions. But keep in mind that this endeavor does not exhaust the matter: we shall eventually still be obliged to develop four-item syllogism.

1.Special Cases of Three-item Syllogism.

We shall now consider special cases of three-item syllogism, involvingweak determinations relative to the major and/or minor item. That is, three-item syllogism with major premise of form Q(P)R or R(P)Q and/or minor premise of form P(R)Q or Q(R)P, with eventual conclusions of absolute form PR or relative form P(Q)R.

Note well that such syllogisms still involveonly three items, even though one or more propositions in them are ofrelative weakdetermination. Such cases may conceivably arise in practice, though very rarely. For each of the three figures, we may conceive of seven such subfigures, in addition to the already dealt with standard Aristotelian arrangement. The eight subfigures are labeled ‘a’ and ‘j’ to ‘p’, for convenience, in the table below.

Table 15.1.Subfigures of syllogism with three items only.

	With PR conclusion				With P(Q)R conclusion
Subfigures	a	j	k	l	m	n	o	p
Figure 1	QR	QR	Q(P)R	Q(P)R	QR	QR	Q(P)R	Q(P)R
	PQ	P(R)Q	PQ	P(R)Q	PQ	P(R)Q	PQ	P(R)Q
	PR	PR	PR	PR	P(Q)R	P(Q)R	P(Q)R	P(Q)R
Figure 2	RQ	RQ	R(P)Q	R(P)Q	RQ	RQ	R(P)Q	R(P)Q
	PQ	P(R)Q	PQ	P(R)Q	PQ	P(R)Q	PQ	P(R)Q
	PR	PR	PR	PR	P(Q)R	P(Q)R	P(Q)R	P(Q)R
Figure 3	QR	QR	Q(P)R	Q(P)R	QR	QR	Q(P)R	Q(P)R
	QP	Q(R)P	QP	Q(R)P	QP	Q(R)P	QP	Q(R)P
	PR	PR	PR	PR	P(Q)R	P(Q)R	P(Q)R	P(Q)R

Notice that in each figure there are two sets of four subfigures, with conclusions of form PR or P(Q)R. Only subfigure ‘a’ has been treated by macroanalysis, the other seven here were simply ignored in Phase One (being very special cases, not likely to often arise). They become relevant here only because they serve to clarify what we mean by three-item (as against four-item) syllogism.

Moods with major premise of form Q(P)R or R(P)Q involve a weak determination relative to the minor item P; and those with minor premise of form P(R)Q or Q(R)P involve a weak determination relative to the major item R. Their summary moduses are given in the following table. Note that the forms P(Q)R and Q(P)R yield the same moduses.

Table 15.2.Summary moduses for weak premises relative to the minor item P or to the major item R.

				p_P	p_P	p_R	p_R	q_P	q_P	q_R	q_R
Row labl	P	Q	R	QR	RQ	PQ	QP	QR	RQ	PQ	QP
a	1	1	1	1	1	1	1	∙	∙	∙	∙
b	1	1	0	0	∙	∙	∙	∙	1	1	1
c	1	0	1	∙	0	0	∙	1	∙	∙	1
d	1	0	0	1	1	1	∙	∙	∙	∙	0
e	0	1	1	∙	∙	∙	0	1	1	1	∙
f	0	1	0	1	∙	∙	1	∙	0	0	∙
g	0	0	1	∙	1	1	1	0	∙	∙	∙
h	0	0	0	∙	∙	∙	∙	1	1	1	1

The above table may be proved by appropriate reshuffling of columns and rows: in each case, we obtain the same summary modus of partial or contingent causation. For instance, forp_QRP, move column P to the right of columns Q and R, then reorder the rows to ‘aebfcgdh’ (so that the sequences of QRP are 111, 110, 101, 100, etc.) – the result is summary modus 10.1.1.. as required to prove.

From the above summary moduses, we can derive the alternative moduses listed in the following table. The microanalyses of the strong forms (mandn) are carried over from Table 14.3. Notice the differences between the results below and those for relatives in Table 13.1. Heremq_rel= #s 42, 58, 170, 186, whereas there it = #s 42, 46, 170, 174; similarly, herenp_rel= #s 149-150, 157-158, whereas there it = #s 149-150, 181-182. These differences (two out of four moduses in each case) are simply due to the forms of strong determination the weaks are combined with: there it was with PR, whereas here it is with QR.

Table 15.3.Enumeration of three-item alternative moduses weak positive premises relative to the minor item P or to the major item R.

Determ.	Major Q(P)R	Major R(P)Q	Minor P(R)Q	Minor Q(R)P
m	10, 12, 25-28, 42, 44, 57-60, 130, 132, 138, 140, 145-148, 153-156, 162, 164, 170, 172, 177-180, 185-188	10, 14, 25-26, 29-30, 74, 78, 89-90, 93-94, 130, 134, 138, 142, 145-146, 149-150, 153-154, 157-158, 194, 198, 202, 206, 209-210, 213-214, 217-218, 221-222	66-68, 70-72, 74-76, 78-80, 130-132, 134-136, 138-140, 142-144, 194-196, 198-200, 202-204, 206-208	66-68, 82-84, 98-100, 114-116, 130-132, 146-148, 162-164, 178-180, 194-196, 210-212, 226-228, 242-244
n	10, 14, 25-26, 29-30, 74, 78, 89-90, 93-94, 130, 134, 138, 142, 145-146, 149-150, 153-154, 157-158, 194, 198, 202, 206, 209-210, 213-214, 217-218, 221-222	10, 12, 25-28, 42, 44, 57-60, 130, 132, 138, 140, 145-148, 153-156, 162, 164, 170, 172, 177-180, 185-188	66-68, 82-84, 98-100, 114-116, 130-132, 146-148, 162-164, 178-180, 194-196, 210-212, 226-228, 242-244	66-68, 70-72, 74-76, 78-80, 130-132, 134-136, 138-140, 142-144, 194-196, 198-200, 202-204, 206-208
p_rel	149-152, 157-160, 181-184, 189-192	147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224	147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224	135-136, 151-152, 167-168, 183-184, 199-200, 215-216, 231-232, 247-248
q_rel	42, 46, 58, 62, 106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254	74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252	74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252	98, 100, 102, 104, 106, 108, 110, 112, 226, 228, 230, 232, 234, 236, 238, 240
mq_rel	42, 58, 170, 186	74, 90, 202, 218	74, 76, 202, 204	98, 100, 226, 228
np_rel	149-150, 157-158	147-148, 155-156	147-148, 211-212	135-136, 199-200
p_relq_rel	190	220	220	232

w_rel	42, 46, 58, 62, 106, 110, 122, 126, 149-152, 157-160, 170, 174, 181-184, 186, 189-192, 234, 238, 250, 254	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	98, 100, 102, 104, 106, 108, 110, 112, 135-136, 151-152, 167-168, 183-184, 199-200, 215-216, 226, 228, 230-232, 234, 236, 238, 240, 247-248
c_rel	10, 12, 14, 25-30, 42, 44, 46, 57-60, 62, 74, 78, 89-90, 93-94, 106, 110, 122, 126, 130, 132, 134, 138, 140, 142, 145-160, 162, 164, 170, 172, 174, 177-192, 194, 198, 202, 206, 209-210, 213-214, 217-218, 221-222, 234, 238, 250, 254	10, 12, 14, 25-30, 42, 44, 57-60, 74, 76, 78, 89-90, 92-94, 106, 108, 122, 124, 130, 132, 134, 138, 140, 142, 145-150, 151-160, 162, 164, 170, 172, 177-180, 185-188, 194, 198, 202, 204, 206, 209-224, 234, 236, 250, 252	66-68, 70-72, 74-76, 78-80, 82-84, 90, 92, 98-100, 106, 108, 114-116, 122, 124, 130-132, 134-136, 138-140, 142-144, 146-148, 151-152, 155-156, 159-160, 162-164, 178-180, 194-196, 198-200, 202-204, 206-208, 210-212, 215-216, 218-220, 223-224, 226-228, 234, 236, 242-244, 250, 252	66-68, 70-72, 74-76, 78-80, 82-84, 98-100, 102, 104, 106, 108, 110, 112, 114-116, 130-132, 134-136, 138-140, 142-144, 146-148, 151-152, 162-164, 167-168, 178-180, 183-184, 194-196, 198-200, 202-204, 206-208, 210-212, 215-216, 226-228, 230-232, 234, 236, 238, 240, 242-244, 247-248

Note that forp_rel,q_rel,p_relq_relandw_rel, a major premise of form R(P)Q and a minor premise of form P(R)Q, of the same weak determination, have the same alternative moduses. This is not surprising, since these weak forms involve the same items as causes (P, R) and effect (Q). A similar equation is not obtained where a strong determination is involved because in such case the items involved are in fact only RQ and PQ (without complements).

The following tables list a selection of syllogisms one or both of whose premises involve all three items. They ignore syllogisms with an exclusively strong premise (such as moods 111-118, 121, 125, 126, etc.), not because such syllogisms are impossible or uninteresting, but simply for brevity’s sake (the reader is invited to look into such cases as an exercise).

The conclusions are implicit in the common moduses of the premises. Once these common moduses, if any, are identified, the conclusion has to be sought in Table 12.4, if of absolute form PR, or in Table 13.1, if of relative form P(Q)R, these forms being those predicted in Table 15.1 above.

Forms without subscript are intended as absolute, those with a subscript as relative to the mentioned complement (P, Q or R). A conclusion of the formporqorpqhas absolute form PR; a similar conclusion of relative form P(Q)R is not implied by it. A conclusion of the formnot-c_Qmeansnot-m+not-n+not-p_Q+not-q_Q, which does not implynot-c_abs. Lone determinations are sometimes concluded, but these are of course relative and not absolute. Note well that the subsidiary item S is never mentioned here, since we have not performed four-item microanalysis yet.

Table 15.4.Moduses of conclusions for selected relative weak positive minor premises (subfigures j, n).

Mood	Major	Minor	Conclusion	Common moduses	No.
1^st	QR	PQ	PR
122	mq	mq_R	inconsistent	None	0
123	mq	np_R	not-c_Q	147-148	2
124	mq	p_Rq_R	inconsistent	None	0
127	mq	p_R	not-c_Q	147-148, 155-156	4
128	mq	q_R	inconsistent	None	0
132	np	mq_R	not-c_Q	74, 202	2
133	np	np_R	inconsistent	None	0
134	np	p_Rq_R	inconsistent	None	0
137	np	p_R	inconsistent	None	0
138	np	q_R	not-c_Q	74, 90, 202, 218	4
142	pq	mq_R	not-c_Q	76, 204	2
143	pq	np_R	not-c_Q	211-212	2
144	pq	p_Rq_R	not-c_Q	220	1
147	pq	p_R	not-s	151-152, 159-160, 211-212, 215-216, 219-220, 223-224	12
148	pq	q_R	not-s	76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252	12
172	p	mq_R	not-c_Q	74, 76, 202, 204	4
173	p	np_R	not-c_Q	211-212	2
174	p	p_Rq_R	not-c_Q	220	1
177	p	p_R	not-s	151-152, 159-160, 211-212, 215-216, 219-220, 223-224	12
178	p	q_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252	16
182	q	mq_R	not-c_Q	76, 204	2
183	q	np_R	not-c_Q	147-148, 211-212	4
184	q	p_Rq_R	not-c_Q	220	1
187	q	p_R	not-s	147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224	16
188	q	q_R	not-s	76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252	12
2^nd	RQ	PQ	PR
222	mq	mq_R	not-c_Q	74, 202	2
223	mq	np_R	inconsistent	None	0
224	mq	p_Rq_R	inconsistent	None	0
227	mq	p_R	inconsistent	None	0
228	mq	q_R	not-c_Q	74, 90, 202, 218	4
232	np	mq_R	inconsistent	None	0
233	np	np_R	not-c_Q	147-148	2
234	np	p_Rq_R	inconsistent	None	2
237	np	p_R	not-c_Q	147-148, 155-156	4
238	np	q_R	inconsistent	None	0
242	pq	mq_R	not-c_Q	76, 204	2
243	pq	np_R	not-c_Q	211-212	2
244	pq	p_Rq_R	not-c_Q	220	1
247	pq	p_R	not-s	151-152, 159-160, 211-212, 215-216, 219-220, 223-224	12
248	pq	q_R	not-s	76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252	12
272	p	mq_R	not-c_Q	76, 204	2
273	p	np_R	not-c_Q	147-148, 211-212	4
274	p	p_Rq_R	not-c_Q	220	1
277	p	p_R	not-s	147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224	16
278	p	q_R	not-s	76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252	12
282	q	mq_R	not-c_Q	74, 76, 202, 204	4
283	q	np_R	not-c_Q	211-212	2
284	q	p_Rq_R	not-c_Q	220	1
287	q	p_R	not-s	151-152, 159-160, 211-212, 215-216, 219-220, 223-224	12
288	q	q_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252	16
3^rd	QR	QP	PR
322	mq	mq_R	inconsistent	None	0
323	mq	np_R	inconsistent	None	0
324	mq	p_Rq_R	inconsistent	None	0
327	mq	p_R	inconsistent	None	0
328	mq	q_R	inconsistent	None	0
332	np	mq_R	inconsistent	None	0
333	np	np_R	inconsistent	None	0
334	np	p_Rq_R	inconsistent	None	0
337	np	p_R	inconsistent	None	0
338	np	q_R	inconsistent	None	0
342	pq	mq_R	p + not-p_Q	226, 228	2
343	pq	np_R	q + not-q_Q	136, 200	2
344	pq	p_Rq_R	not-c_Q	232	1
347	pq	p_R	q + not-q_Q	136, 151-152, 168, 183-184, 200, 215-216, 232, 247-248	12
348	pq	q_R	p + not-p_Q	106, 108, 110, 112, 226, 228, 230, 232, 234, 236, 238, 240	12
372	p	mq_R	p + not-p_Q	226, 228	2
373	p	np_R	q + not-q_Q	136, 200	2
374	p	p_Rq_R	not-c_Q	232	1
377	p	p_R	q + not-q_Q	136, 151-152, 168, 183-184, 200, 215-216, 232, 247-248	12
378	p	q_R	p + not-p_Q	106, 108, 110, 112, 226, 228, 230, 232, 234, 236, 238, 240	12
382	q	mq_R	p + not-p_Q	226, 228	2
383	q	np_R	q + not-q_Q	136, 200	2
384	q	p_Rq_R	not-c_Q	232	1
387	q	p_R	q + not-q_Q	136, 151-152, 168, 183-184, 200, 215-216, 232, 247-248	12
388	q	q_R	p + not-p_Q	106, 108, 110, 112, 226, 228, 230, 232, 234, 236, 238, 240	12

Table 15.5.Moduses of conclusions for selected relative weak positive major premises (subfigures k, o).

Mood	Major	Minor	Conclusion	Common moduses	No.
1^st	QR	PQ	PR
122	mq_P	mq	inconsistent	None	0
123	mq_P	np	inconsistent	None	0
124	mq_P	pq	q_Q	170, 186	2
127	mq_P	p	q_Q	170, 186	2
128	mq_P	q	q_Q	170, 186	2
132	np_P	mq	inconsistent	None	0
133	np_P	np	inconsistent	None	0
134	np_P	pq	p_Q	150, 158	2
137	np_P	p	p_Q	150, 158	2
138	np_P	q	p_Q	150, 158	2
142	p_Pq_P	mq	inconsistent	None	0
143	p_Pq_P	np	inconsistent	None	0
144	p_Pq_P	pq	p_Qq_Q	190	1
147	p_Pq_P	p	p_Qq_Q	190	1
148	p_Pq_P	q	p_Qq_Q	190	1
172	p_P	mq	inconsistent	None	0
173	p_P	np	inconsistent	None	0
174	p_P	pq	p_Q	150-152, 158-160, 182-184, 190-192	12
177	p_P	p	p_Q	150-152, 158-160, 182-184, 190-192	12
178	p_P	q	p_Q	150-152, 158-160, 182-184, 190-192	12
182	q_P	mq	inconsistent	None	0
183	q_P	np	inconsistent	None	0
184	q_P	pq	q_Q	106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254	12
187	q_P	p	q_Q	106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254	12
188	q_P	q	q_Q	106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254	12
2^nd	RQ	PQ	PR
222	mq_P	mq	not-c_Q	74, 202	2
223	mq_P	np	inconsistent	None	0
224	mq_P	pq	not-c_Q	90, 218	2
227	mq_P	p	not-c_Q	90, 218	2
228	mq_P	q	not-c_Q	74, 90, 202, 218	4
232	np_P	mq	inconsistent	None	0
233	np_P	np	not-c_Q	147-148	2
234	np_P	pq	not-c_Q	155-156	2
237	np_P	p	not-c_Q	147-148, 155-156	4
238	np_P	q	not-c_Q	155-156	2
242	p_Pq_P	mq	inconsistent	None	0
243	p_Pq_P	np	inconsistent	None	0
244	p_Pq_P	pq	pq + not-w_Q	220	1
247	p_Pq_P	p	pq + not-w_Q	220	1
248	p_Pq_P	q	pq + not-w_Q	220	1
272	p_P	mq	inconsistent	None	0
273	p_P	np	not-c_Q	147-148, 211-212	4
274	p_P	pq	not-s + not-q_Q	151-152, 155-156, 159-160, 215-216, 219-220, 223-224	12
277	p_P	p	not-s + not-q_Q	147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224	16
278	p_P	q	not-s + not-q_Q	151-152, 155-156, 159-160, 215-216, 219-220, 223-224	12
282	q_P	mq	not-s + not-c_Q	74, 76, 202, 204	4
283	q_P	np	inconsistent	None	0
284	q_P	pq	not-s + not-p_Q	90, 92, 106, 108, 122, 124, 218, 220, 234, 236, 250, 252	12
287	q_P	p	not-s + not-p_Q	90, 92, 106, 108, 122, 124, 218, 220, 234, 236, 250, 252	12
288	q_P	q	not-s + not-p_Q	74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252	16
3^rd	QR	QP	PR
322	mq_P	mq	inconsistent	None	0
323	mq_P	np	inconsistent	None	0
324	mq_P	pq	q_Q	170, 186	2
327	mq_P	p	q_Q	170, 186	2
328	mq_P	q	q_Q	170, 186	2
332	np_P	mq	inconsistent	None	0
333	np_P	np	inconsistent	None	0
334	np_P	pq	p_Q	150, 158	2
337	np_P	p	p_Q	150, 158	2
338	np_P	q	p_Q	150, 158	2
342	p_Pq_P	mq	inconsistent	None	0
343	p_Pq_P	np	inconsistent	None	0
344	p_Pq_P	pq	p_Qq_Q	190	1
347	p_Pq_P	p	p_Qq_Q	190	1
348	p_Pq_P	q	p_Qq_Q	190	1
372	p_P	mq	inconsistent	None	0
373	p_P	np	inconsistent	None	0
374	p_P	pq	p_Q	150-152, 158-160, 182-184, 190-192	12
377	p_P	p	p_Q	150-152, 158-160, 182-184, 190-192	12
378	p_P	q	p_Q	150-152, 158-160, 182-184, 190-192	12
382	q_P	mq	inconsistent	None	0
383	q_P	np	inconsistent	None	0
384	q_P	pq	q_Q	106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254	12
387	q_P	p	q_Q	106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254	12
388	q_P	q	q_Q	106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254	12

Table 15.6.Moduses of conclusions for selected relative weak positive premises (subfigures l, p).

Mood	Major	Minor	Conclusion	Common moduses	No.
1^st	QR	PQ	PR
122	mq_P	mq_R	inconsistent	None	0
123	mq_P	np_R	inconsistent	None	0
124	mq_P	p_Rq_R	inconsistent	None	0
127	mq_P	p_R	inconsistent	None	0
128	mq_P	q_R	inconsistent	None	0
132	np_P	mq_R	inconsistent	None	0
133	np_P	np_R	inconsistent	None	0
134	np_P	p_Rq_R	inconsistent	None	0
137	np_P	p_R	inconsistent	None	0
138	np_P	q_R	inconsistent	None	0
142	p_Pq_P	mq_R	inconsistent	None	0
143	p_Pq_P	np_R	inconsistent	None	0
144	p_Pq_P	p_Rq_R	inconsistent	None	0
147	p_Pq_P	p_R	inconsistent	None	0
148	p_Pq_P	q_R	inconsistent	None	0
172	p_P	mq_R	inconsistent	None	0
173	p_P	np_R	inconsistent	None	0
174	p_P	p_Rq_R	inconsistent	None	0
177	p_P	p_R	p-alone_Q	151-152, 159-160	4
178	p_P	q_R	inconsistent	None	0
182	q_P	mq_R	inconsistent	None	0
183	q_P	np_R	inconsistent	None	0
184	q_P	p_Rq_R	inconsistent	None	0
187	q_P	p_R	inconsistent	None	0
188	q_P	q_R	q-alone_Q	106, 122, 234, 250	4
2^nd	RQ	PQ	PR
222	mq_P	mq_R	not-c_Q	74, 202	2
223	mq_P	np_R	inconsistent	None	0
224	mq_P	p_Rq_R	inconsistent	None	0
227	mq_P	p_R	inconsistent	None	0
228	mq_P	q_R	not-c_Q	74, 90, 202, 218	4
232	np_P	mq_R	inconsistent	None	0
233	np_P	np_R	not-c_Q	147-148	2
234	np_P	p_Rq_R	inconsistent	None	0
237	np_P	p_R	not-c_Q	147-148, 155-156	4
238	np_P	q_R	inconsistent	None	0
242	p_Pq_P	mq_R	inconsistent	None	0
243	p_Pq_P	np_R	inconsistent	None	0
244	p_Pq_P	p_Rq_R	not-c_Q	220	1
247	p_Pq_P	p_R	not-c_Q	220	1
248	p_Pq_P	q_R	not-c_Q	220	1
272	p_P	mq_R	inconsistent	None	0
273	p_P	np_R	not-c_Q	147-148, 211-212	4
274	p_P	p_Rq_R	not-c_Q	220	1
277	p_P	p_R	not-s	147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224	16
278	p_P	q_R	not-c_Q	220	1
282	q_P	mq_R	not-c_Q	74, 76, 202, 204	4
283	q_P	np_R	inconsistent	None	0
284	q_P	p_Rq_R	not-c_Q	220	1
287	q_P	p_R	not-c_Q	220	1
288	q_P	q_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252	16
3^rd	QR	QP	PR
322	mq_P	mq_R	inconsistent	None	0
323	mq_P	np_R	inconsistent	None	0
324	mq_P	p_Rq_R	inconsistent	None	0
327	mq_P	p_R	inconsistent	None	0
328	mq_P	q_R	inconsistent	None	0
332	np_P	mq_R	inconsistent	None	0
333	np_P	np_R	inconsistent	None	0
334	np_P	p_Rq_R	inconsistent	None	0
337	np_P	p_R	inconsistent	None	0
338	np_P	q_R	inconsistent	None	0
342	p_Pq_P	mq_R	inconsistent	None	0
343	p_Pq_P	np_R	inconsistent	None	0
344	p_Pq_P	p_Rq_R	inconsistent	None	0
347	p_Pq_P	p_R	inconsistent	None	0
348	p_Pq_P	q_R	inconsistent	None	0
372	p_P	mq_R	inconsistent	None	0
373	p_P	np_R	inconsistent	None	0
374	p_P	p_Rq_R	inconsistent	None	0
377	p_P	p_R	p-alone_Q	151-152, 183-184	4
378	p_P	q_R	inconsistent	None	0
382	q_P	mq_R	inconsistent	None	0
383	q_P	np_R	inconsistent	None	0
384	q_P	p_Rq_R	inconsistent	None	0
387	q_P	p_R	inconsistent	None	0
388	q_P	q_R	q-alone_Q	106, 110, 234, 238	4

We can similarly look into syllogisms involving vague positive premises, absolute or relative weak. The following table gives some examples.

Table 15.7.Moduses of conclusions for selected combinations of relative weak and absolute vague positive premises (various subfigures).

Fig.	Major	Minor	Conclusion	Common moduses	No.
1^st	QR	PQ	PR
	s	w_R	not-s	74, 90, 147-148, 155-156, 202, 218	8
	w	w_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	31
	c	w_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	31
	w_P	s	inconsistent	None	0
	w_P	w	w_Q	106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254	23
	w_P	c	w_Q	106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254	23
	w_P	w_R	w_Q	106, 122, 151-152, 159-160, 234, 250	8
2^nd	RQ	PQ	PR
	s	w_R	not-s	74, 90, 147-148, 155-156, 202, 218	8
	w	w_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	31
	c	w_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	31
	w_P	s	not-s	74, 76, 147-148, 202, 204, 211-212	8
	w_P	w	not-s	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	31
	w_P	c	not-s	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	31
	w_P	w_R	not-s	74, 76, 90, 92, 106, 108, 122, 124, 147-148, 151-152, 155-156, 159-160, 202, 204, 211-212, 215-216, 218-220, 223-224, 234, 236, 250, 252	31
3^rd	QR	QP	PR
	s	w_R	inconsistent	None	0
	w	w_R	w	106, 108, 110, 112, 136, 151-152, 168, 183-184, 200, 215-216, 226, 228, 230, 232, 234, 236, 238, 240, 247-248	23
	c	w_R	w	106, 108, 110, 112, 136, 151-152, 168, 183-184, 200, 215-216, 226, 228, 230, 232, 234, 236, 238, 240, 247-248	23
	w_P	s	inconsistent	None	0
	w_P	w	w_Q	106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254	23
	w_P	c	w_Q	106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254	23
	w_P	w_R	w_Q	106, 110, 151-152, 183-184, 234, 238	8

Note that some combinations are inconsistent. Some moods yield conclusionwin relative (which implies absolute) form, and some only in absolute form. In other cases, though the number of common moduses may vary considerably, there is no conclusion other than the formnot-s, which (remember) means ‘not strong causation’, implying bothnot-m + not-n; it can also be read as the disjunctionw_absor not-c_abs.

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