14b Main Three-Item Syllogisms cont'd - Logic Philosophy Spirituality

THE LOGIC OF CAUSATION

Phase Two: Microanalysis

Chapter 14–Main Three-ItemSyllogisms

Putting the data in the above table together in various combinations, we can now ascertain the moduses of resulting conclusions. As already said, when the premises have no common modus, they are “inconsistent”. When some resulting modus(es) fall under causation (c) and some other(s) under non-causation (not-c), we must admit that there is “no conclusion”. In all other cases, there is a conclusion, namely the determination (whatever it be, at least causation or non-causation) which includesallthe resulting moduses.

The following table lists all these results. Note well that all weak determinations mentioned in it are intended asabsolute, though not so specified. Syllogism with relative weaks will be considered later.

Table 14.4.Moduses of conclusions of all syllogisms with strong or absolute weak positive premises, generic or joint.

	Major	Minor	Conclusion	Common moduses	No.
	First Figure
Mood	QR	PQ	PR
111	mn	mn	mn	130	1
112	mn	mq	mq	138	1
113	mn	np	np	146	1
114	mn	pq	pq	154	1
115	mn	m	m	130, 138	2
116	mn	n	n	130, 146	2
117	mn	p	p	146, 154	2
118	mn	q	q	138, 154	2
121	mq	mn	mq	132	1
122	mq	mq	mq	140	1
123	mq	np	no conclusion	147-148, 162, 164, 178-180	7
124	mq	pq	not-n	155-156, 170, 172, 186-188	7
125	mq	m	mq	132, 140	2
126	mq	n	no conclusion	132, 147-148, 162, 164, 178-180	8
127	mq	p	no conclusion	147-148, 155-156, 162, 164, 170, 172, 178-180, 186-188	14
128	mq	q	not-n	140, 155-156, 170, 172, 186-188	8
131	np	mn	np	194	1
132	np	mq	no conclusion	74, 78, 134, 142, 198, 202, 206	7
133	np	np	np	210	1
134	np	pq	not-m	90, 94, 150, 158, 214, 218, 222	7
135	np	m	no conclusion	74, 78, 134, 142, 194, 198, 202, 206	8
136	np	n	np	194, 210	2
137	np	p	not-m	90, 94, 150, 158, 210, 214, 218, 222	8
138	np	q	no conclusion	74, 78, 90, 94, 134, 142, 150, 158, 198, 202, 206, 214, 218, 222	14

141	pq	mn	pq	196	1
142	pq	mq	not-n	76, 80, 136, 144, 200, 204, 208	7
143	pq	np	not-m	211-212, 226, 228, 242-244	7
144	pq	pq	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	49
145	pq	m	not-n	76, 80, 136, 144, 196, 200, 204, 208	8
146	pq	n	not-m	196, 211-212, 226, 228, 242-244	8
147	pq	p	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	56
148	pq	q	no conclusion	76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 144, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
151	m	mn	m	130, 132	2
152	m	mq	mq	138, 140	2
153	m	np	no conclusion	146-148, 162, 164, 178-180	8
154	m	pq	not-n	154-156, 170, 172, 186-188	8
155	m	m	m	130, 132, 138, 140	4
156	m	n	no conclusion	130, 132, 146-148, 162, 164, 178-180	10
157	m	p	no conclusion	146-148, 154-156, 162, 164, 170, 172, 178-180, 186-188	16
158	m	q	not-n	138, 140, 154-156, 170, 172, 186-188	10
161	n	mn	n	130, 194	2
162	n	mq	no conclusion	74, 78, 134, 138, 142, 198, 202, 206	8
163	n	np	np	146, 210	2
164	n	pq	not-m	90, 94, 150, 154, 158, 214, 218, 222	8
165	n	m	no conclusion	74, 78, 130, 134, 138, 142, 194, 198, 202, 206	10
166	n	n	n	130, 146, 194, 210	4
167	n	p	not-m	90, 94, 146, 150, 154, 158, 210, 214, 218, 222	10
168	n	q	no conclusion	74, 78, 90, 94, 134, 138, 142, 150, 154, 158, 198, 202, 206, 214, 218, 222	16
171	p	mn	p	194, 196	2
172	p	mq	no conclusion	74, 76, 78, 80, 134, 136, 142, 144, 198, 200, 202, 204, 206, 208	14
173	p	np	not-m	210-212, 226, 228, 242-244	8
174	p	pq	no conclusion	90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
175	p	m	no conclusion	74, 76, 78, 80, 134, 136, 142, 144, 194, 196, 198, 200, 202, 204, 206, 208	16
176	p	n	not-m	194, 196, 210-212, 226, 228, 242-244	10

177	p	p	no conclusion	90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	64
178	p	q	no conclusion	74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 142, 144, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 198, 200, 202, 204, 206, 208, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	70
181	q	mn	q	132, 196	2
182	q	mq	not-n	76, 80, 136, 140, 144, 200, 204, 208	8
183	q	np	no conclusion	147-148, 162, 164, 178-180, 211-212, 226, 228, 242-244	14
184	q	pq	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
185	q	m	not-n	76, 80, 132, 136, 140, 144, 196, 200, 204, 208	10
186	q	n	no conclusion	132, 147-148, 162, 164, 178-180, 196, 211-212, 226, 228, 242-244	16
187	q	p	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 147-148, 151-152, 155-156, 159-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	70
188	q	q	no conclusion	76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 140, 144, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	64
	Second Figure
Mood	RQ	PQ	PR
211	mn	mn	mn	130	1
212	mn	mq	mq	138	1
213	mn	np	np	146	1
214	mn	pq	pq	154	1
215	mn	m	m	130, 138	2
216	mn	n	n	130, 146	2
217	mn	p	p	146, 154	2
218	mn	q	q	138, 154	2
221	mq	mn	np	194	1
222	mq	mq	no conclusion	74, 78, 134, 142, 198, 202, 206	7
223	mq	np	np	210	1
224	mq	pq	not-m	90, 94, 150, 158, 214, 218, 222	7
225	mq	m	no conclusion	74, 78, 134, 142, 194, 198, 202, 206	8
226	mq	n	np	194, 210	2
227	mq	p	not-m	90, 94, 150, 158, 210, 214, 218, 222	8
228	mq	q	no conclusion	74, 78, 90, 94, 134, 142, 150, 158, 198, 202, 206, 214, 218, 222	14

231	np	mn	mq	132	1
232	np	mq	mq	140	1
233	np	np	no conclusion	147-148, 162, 164, 178-180	7
234	np	pq	not-n	155-156, 170, 172, 186-188	7
235	np	m	mq	132, 140	2
236	np	n	no conclusion	132, 147-148, 162, 164, 178-180	8
237	np	p	no conclusion	147-148, 155-156, 162, 164, 170, 172, 178-180, 186-188	14
238	np	q	not-n	140, 155-156, 170, 172, 186-188	8
241	pq	mn	pq	196	1
242	pq	mq	not-n	76, 80, 136, 144, 200, 204, 208	7
243	pq	np	not-m	211-212, 226, 228, 242-244	7
244	pq	pq	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	49
245	pq	m	not-n	76, 80, 136, 144, 196, 200, 204, 208	8
246	pq	n	not-m	196, 211-212, 226, 228, 242-244	8
247	pq	p	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	56
248	pq	q	no conclusion	76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 144, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
251	m	mn	n	130, 194	2
252	m	mq	no conclusion	74, 78, 134, 138, 142, 198, 202, 206	8
253	m	np	np	146, 210	2
254	m	pq	not-m	90, 94, 150, 154, 158, 214, 218, 222	8
255	m	m	no conclusion	74, 78, 130, 134, 138, 142, 194, 198, 202, 206	10
256	m	n	n	130, 146, 194, 210	4
257	m	p	not-m	90, 94, 146, 150, 154, 158, 210, 214, 218, 222	10
258	m	q	no conclusion	74, 78, 90, 94, 134, 138, 142, 150, 154, 158, 198, 202, 206, 214, 218, 222	16
261	n	mn	m	130, 132	2
262	n	mq	mq	138, 140	2
263	n	np	no conclusion	146-148, 162, 164, 178-180	8
264	n	pq	not-n	154-156, 170, 172, 186-188	8
265	n	m	m	130, 132, 138, 140	4
266	n	n	no conclusion	130, 132, 146-148, 162, 164, 178-180	10
267	n	p	no conclusion	146-148, 154-156, 162, 164, 170, 172, 178-180, 186-188	16
268	n	q	not-n	138, 140, 154-156, 170, 172, 186-188	10
271	p	mn	q	132, 196	2
272	p	mq	not-n	76, 80, 136, 140, 144, 200, 204, 208	8

273	p	np	no conclusion	147-148, 162, 164, 178-180, 211-212, 226, 228, 242-244	14
274	p	pq	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
275	p	m	not-n	76, 80, 132, 136, 140, 144, 196, 200, 204, 208	10
276	p	n	no conclusion	132, 147-148, 162, 164, 178-180, 196, 211-212, 226, 228, 242-244	16
277	p	p	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 147-148, 151-152, 155-156, 159-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	70
278	p	q	no conclusion	76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 140, 144, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	64
281	q	mn	p	194, 196	2
282	q	mq	no conclusion	74, 76, 78, 80, 134, 136, 142, 144, 198, 200, 202, 204, 206, 208	14
283	q	np	not-m	210-212, 226, 228, 242-244	8
284	q	pq	no conclusion	90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
285	q	m	no conclusion	74, 76, 78, 80, 134, 136, 142, 144, 194, 196, 198, 200, 202, 204, 206, 208	16
286	q	n	not-m	194, 196, 210-212, 226, 228, 242-244	10
287	q	p	no conclusion	90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	64
288	q	q	no conclusion	74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 142, 144, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 198, 200, 202, 204, 206, 208, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	70
	Third Figure
Mood	QR	QP	PR
311	mn	mn	mn	130	1
312	mn	mq	np	146	1
313	mn	np	mq	138	1
314	mn	pq	pq	154	1
315	mn	m	n	130, 146	2
316	mn	n	m	130, 138	2
317	mn	p	q	138, 154	2
318	mn	q	p	146, 154	2

321	mq	mn	mq	132	1
322	mq	mq	no conclusion	147-148, 162, 164, 178-180	7
323	mq	np	mq	140	1
324	mq	pq	not-n	155-156, 170, 172, 186-188	7
325	mq	m	no conclusion	132, 147-148, 162, 164, 178-180	8
326	mq	n	mq	132, 140	2
327	mq	p	not-n	140, 155-156, 170, 172, 186-188	8
328	mq	q	no conclusion	147-148, 155-156, 162, 164, 170, 172, 178-180, 186-188	14
331	np	mn	np	194	1
332	np	mq	np	210	1
333	np	np	no conclusion	74, 78, 134, 142, 198, 202, 206	7
334	np	pq	not-m	90, 94, 150, 158, 214, 218, 222	7
335	np	m	np	194, 210	2
336	np	n	no conclusion	74, 78, 134, 142, 194, 198, 202, 206	8
337	np	p	no conclusion	74, 78, 90, 94, 134, 142, 150, 158, 198, 202, 206, 214, 218, 222	14
338	np	q	not-m	90, 94, 150, 158, 210, 214, 218, 222	8
341	pq	mn	pq	196	1
342	pq	mq	not-m	211-212, 226, 228, 242-244	7
343	pq	np	not-n	76, 80, 136, 144, 200, 204, 208	7
344	pq	pq	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	49
345	pq	m	not-m	196, 211-212, 226, 228, 242-244	8
346	pq	n	not-n	76, 80, 136, 144, 196, 200, 204, 208	8
347	pq	p	no conclusion	76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 144, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
348	pq	q	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	56
351	m	mn	m	130, 132	2
352	m	mq	no conclusion	146-148, 162, 164, 178-180	8
353	m	np	mq	138, 140	2
354	m	pq	not-n	154-156, 170, 172, 186-188	8
355	m	m	no conclusion	130, 132, 146-148, 162, 164, 178-180	10
356	m	n	m	130, 132, 138, 140	4
357	m	p	not-n	138, 140, 154-156, 170, 172, 186-188	10
358	m	q	no conclusion	146-148, 154-156, 162, 164, 170, 172, 178-180, 186-188	16
361	n	mn	n	130, 194	2
362	n	mq	np	146, 210	2
363	n	np	no conclusion	74, 78, 134, 138, 142, 198, 202, 206	8
364	n	pq	not-m	90, 94, 150, 154, 158, 214, 218, 222	8

365	n	m	n	130, 146, 194, 210	4
366	n	n	no conclusion	74, 78, 130, 134, 138, 142, 194, 198, 202, 206	10
367	n	p	no conclusion	74, 78, 90, 94, 134, 138, 142, 150, 154, 158, 198, 202, 206, 214, 218, 222	16
368	n	q	not-m	90, 94, 146, 150, 154, 158, 210, 214, 218, 222	10
371	p	mn	p	194, 196	2
372	p	mq	not-m	210-212, 226, 228, 242-244	8
373	p	np	no conclusion	74, 76, 78, 80, 134, 136, 142, 144, 198, 200, 202, 204, 206, 208	14
374	p	pq	no conclusion	90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
375	p	m	not-m	194, 196, 210-212, 226, 228, 242-244	10
376	p	n	no conclusion	74, 76, 78, 80, 134, 136, 142, 144, 194, 196, 198, 200, 202, 204, 206, 208	16
377	p	p	no conclusion	74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 142, 144, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 198, 200, 202, 204, 206, 208, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	70
378	p	q	no conclusion	90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	64
381	q	mn	q	132, 196	2
382	q	mq	no conclusion	147-148, 162, 164, 178-180, 211-212, 226, 228, 242-244	14
383	q	np	not-n	76, 80, 136, 140, 144, 200, 204, 208	8
384	q	pq	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	56
385	q	m	no conclusion	132, 147-148, 162, 164, 178-180, 196, 211-212, 226, 228, 242-244	16
386	q	n	not-n	76, 80, 132, 136, 140, 144, 196, 200, 204, 208	10
387	q	p	no conclusion	76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 140, 144, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256	64
388	q	q	no conclusion	91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 147-148, 151-152, 155-156, 159-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	70

If we compare the results of microanalysis listed in the above table with those obtained by macroanalysis (those listed in chapter 6, and again in Tables 7.3, 7.4 and 7.5, and those listed in Tables 9.4 and 9.5), we discover that they are in most cases apparently inconsistent! However, before making any hasty judgments, it is well to become aware thatmany apparent similarities between the cases treated are in fact superficial, so that differences in result should come as no surprise.

We could at this stage create a table listing all positive moods in the three figures in one column, the collected positive and negative conclusions by macroanalysis in a second column, and the above conclusions obtained by microanalysis in a third column. Then, in a fourth column, we would want to explain, case by case, why any eventual divergences occurred. However, it is still too early for such a systematic comparison between our approaches, for reasons that will become clear in the following comments.

In the above table, we are dealing with only three items, P, Q and R. The weak determinations considered are always absolute (involving 108 alternative moduses in the PQR matrix). It follows that even when one or both premises are weak, the syllogism is always in subfigure ‘a’[6].

We cannot, therefore, compare the conclusions obtained here to those previously found, when a subsidiary item (S) was specified and the minor item (P) was occasionally found as a complement in the major premise (as in subfigure ‘d’ and others). Here, when a weak determination (absolute) is affirmed or denied in premise(s) and/or in conclusion, the effective moduses might concern the subsidiary itemorits negation,orthe minor, middle or major item or its negation,or againsome other item entirely!

We must thus tread very carefully before making comparisons. It is ultimately only by developing four-item microanalysis, and thereby four-item syllogism, that mechanical comparisons with macroanalysis can safely be made. We will consequently abstain from such consistency checking for now, while acknowledging its ultimate importance. Let us rather at this stage continue to develop three-item syllogistic theory. Some of these developments will clarify the issue raised here, as we shall see.

4.Dealing with Vaguer Propositions.

We shall now deal with three-item syllogism with vague premises; that is, strong causation (s=m or n), absolute weak causation (w_abs=p_absor q_abs), or absolute causation (c_abs=s or w_abs=m or n or p_absor q_abs). What we shall find is thatno conclusionarises from any combination of such premises (with each other – we shall not bother to deal with combinations of vague premises with more precise premises, regarding them as practically unlikely to arise). This is an interesting result, though negative.

The following table merges the moduses of precise positive premises (given in Table 14.3, above), to obtain those of vague positive premises with formss,w_absorc_abs. Note well that each of these forms is fully convertible, i.e. is the same for two given items whatever their positions (QR and RQ have the same moduses, PQ and QP have the same moduses).

Table 14.5.Enumeration of three-item alternative moduses for vague positive premises, for any figure of syllogism.

Determ.	Major QR	Major RQ	Minor PQ	Minor QP
s=m or n	10, 12, 14, 25-30, 42, 44, 57-60, 74, 78, 89-90, 93-94, 130, 132, 134, 138, 140, 142, 145-150, 153-158, 162, 164, 170, 172, 177-180, 185-188, 194, 198, 202, 206, 209-210, 213-214, 217-218, 221-222	10, 12, 14, 25-30, 42, 44, 57-60, 74, 78, 89-90, 93-94, 130, 132, 134, 138, 140, 142, 145-150, 153-158, 162, 164, 170, 172, 177-180, 185-188, 194, 198, 202, 206, 209-210, 213-214, 217-218, 221-222	66-68, 70-72, 74-76, 78-80, 82-84, 98-100, 114-116, 130-132, 134-136, 138-140, 142-144, 146-148, 162-164, 178-180, 194-196, 198-200, 202-204, 206-208, 210-212, 226-228, 242-244	66-68, 70-72, 74-76, 78-80, 82-84, 98-100, 114-116, 130-132, 134-136, 138-140, 142-144, 146-148, 162-164, 178-180, 194-196, 198-200, 202-204, 206-208, 210-212, 226-228, 242-244
w_abs=p_absor q_abs	12, 14, 16, 27-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 132, 134, 136, 140, 142, 144, 147-152, 155-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256	12, 14, 16, 27-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 132, 134, 136, 140, 142, 144, 147-152, 155-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256	70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256	70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256
c_abs= m or n or p_absor q_abs	10, 12, 14, 16, 25-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 130, 132, 134, 136, 138, 140, 142, 144-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256	10, 12, 14, 16, 25-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 130, 132, 134, 136, 138, 140, 142, 144-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256	66-68, 70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 130-132, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 194-196, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256	66-68, 70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 130-132, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 194-196, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256

As the table below shows, no positive or negative conclusion is obtainable from two vague positive premises (any combination ofs,w_abs,c_abs). This means one has to go to a more precise level – of generics or joints – to obtain a conclusion in positive causative syllogism.

Note that the three figures yield the same moduses in each mood. This is because, as indicated above, the premises involved have the same moduses whatever the orientation of the items concerned (i.e. they are all fully convertible).

Table 14.6.Moduses of conclusions for selected vague positive premises.

Major	Minor	Conclusion
First Figure
QR	PQ	PR
Second Figure
RQ	PQ	PR
Third Figure
QR	QP	PR
For all three figures			Common moduses	No.
s	s	no conclusion	74, 78, 130, 132, 134, 138, 140, 142, 146-148, 162, 164, 178-180, 194, 198, 202, 206, 210	21
s	w_abs	no conclusion	74, 78, 90, 94, 134, 138, 140, 142, 146-148, 150, 154-156, 158, 162, 164, 170, 172, 178-180, 186-188, 198, 202, 206, 210, 214, 218, 222	33
w_abs	s	no conclusion	74, 76, 78, 80, 132, 134, 136, 140, 142, 144, 147-148, 162, 164, 178-180, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 226, 228, 242-244	33
w_abs	w_abs	no conclusion	74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 140, 142, 144, 147-148, 150-152, 155-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	93
s	c_abs	no conclusion	74, 78, 90, 94, 130, 132, 134, 138, 140, 142, 146-148, 150, 154-156, 158, 162, 164, 170, 172, 178-180, 186-188, 194, 198, 202, 206, 210, 214, 218, 222	36
c_abs	s	no conclusion	74, 76, 78, 80, 130, 132, 134, 136, 138, 140, 142, 144, 146-148, 162, 164, 178-180, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 226, 228, 242-244	36
w_abs	c_abs	no conclusion	74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 132, 134, 136, 140, 142, 144, 147-148, 150-152, 155-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	96
c_abs	w_abs	no conclusion	74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 138, 140, 142, 144, 146-148, 150-152, 154-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	96
c_abs	c_abs	no conclusion	74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 130, 132, 134, 136, 138, 140, 142, 144, 146-148, 150-152, 154-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256	100

This table is interesting in that it shows that no causative conclusion can be drawn from vague causative premises in any of the three figures. In particular, it answers one of our first questions, teaching us that, generally speaking, if P causes Q and Q causes R, it does not follow that P causes R.

[6]See chapter 5 for the list of subfigures.

You can purchase a paper copy of this book at The Logician’s secure online Bookshop.