THE LOGIC OF CAUSATION
Phase Two: Microanalysis
Chapter 15 – Some More Three-Item Syllogisms
1.Special Cases of Three-Item Syllogism
.
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.
pP | pP | pR | pR | qP | qP | qR | qR | ||||
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, forpQRP, 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. Heremqrel= #s 42, 58, 170, 186, whereas there it = #s 42, 46, 170, 174; similarly, herenprel= #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 |
prel | 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 |
qrel | 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 |
mqrel | 42, 58, 170, 186 | 74, 90, 202, 218 | 74, 76, 202, 204 | 98, 100, 226, 228 |
nprel | 149-150, 157-158 | 147-148, 155-156 | 147-148, 211-212 | 135-136, 199-200 |
prelqrel | 190 | 220 | 220 | 232 |
wrel | 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 |
crel | 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 forprel,qrel,prelqrelandwrel, 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-cQmeansnot-m+not-n+not-pQ+not-qQ, which does not implynot-cabs. 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. |
1st | QR | PQ | PR | ||
122 | mq | mqR | inconsistent | None | 0 |
123 | mq | npR | not-cQ | 147-148 | 2 |
124 | mq | pRqR | inconsistent | None | 0 |
127 | mq | pR | not-cQ | 147-148, 155-156 | 4 |
128 | mq | qR | inconsistent | None | 0 |
132 | np | mqR | not-cQ | 74, 202 | 2 |
133 | np | npR | inconsistent | None | 0 |
134 | np | pRqR | inconsistent | None | 0 |
137 | np | pR | inconsistent | None | 0 |
138 | np | qR | not-cQ | 74, 90, 202, 218 | 4 |
142 | pq | mqR | not-cQ | 76, 204 | 2 |
143 | pq | npR | not-cQ | 211-212 | 2 |
144 | pq | pRqR | not-cQ | 220 | 1 |
147 | pq | pR | not-s | 151-152, 159-160, 211-212, 215-216, 219-220, 223-224 | 12 |
148 | pq | qR | not-s | 76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252 | 12 |
172 | p | mqR | not-cQ | 74, 76, 202, 204 | 4 |
173 | p | npR | not-cQ | 211-212 | 2 |
174 | p | pRqR | not-cQ | 220 | 1 |
177 | p | pR | not-s | 151-152, 159-160, 211-212, 215-216, 219-220, 223-224 | 12 |
178 | p | qR | not-s | 74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252 | 16 |
182 | q | mqR | not-cQ | 76, 204 | 2 |
183 | q | npR | not-cQ | 147-148, 211-212 | 4 |
184 | q | pRqR | not-cQ | 220 | 1 |
187 | q | pR | not-s | 147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224 | 16 |
188 | q | qR | not-s | 76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252 | 12 |
2nd | RQ | PQ | PR | ||
222 | mq | mqR | not-cQ | 74, 202 | 2 |
223 | mq | npR | inconsistent | None | 0 |
224 | mq | pRqR | inconsistent | None | 0 |
227 | mq | pR | inconsistent | None | 0 |
228 | mq | qR | not-cQ | 74, 90, 202, 218 | 4 |
232 | np | mqR | inconsistent | None | 0 |
233 | np | npR | not-cQ | 147-148 | 2 |
234 | np | pRqR | inconsistent | None | 2 |
237 | np | pR | not-cQ | 147-148, 155-156 | 4 |
238 | np | qR | inconsistent | None | 0 |
242 | pq | mqR | not-cQ | 76, 204 | 2 |
243 | pq | npR | not-cQ | 211-212 | 2 |
244 | pq | pRqR | not-cQ | 220 | 1 |
247 | pq | pR | not-s | 151-152, 159-160, 211-212, 215-216, 219-220, 223-224 | 12 |
248 | pq | qR | not-s | 76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252 | 12 |
272 | p | mqR | not-cQ | 76, 204 | 2 |
273 | p | npR | not-cQ | 147-148, 211-212 | 4 |
274 | p | pRqR | not-cQ | 220 | 1 |
277 | p | pR | not-s | 147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224 | 16 |
278 | p | qR | not-s | 76, 92, 106, 108, 122, 124, 204, 220, 234, 236, 250, 252 | 12 |
282 | q | mqR | not-cQ | 74, 76, 202, 204 | 4 |
283 | q | npR | not-cQ | 211-212 | 2 |
284 | q | pRqR | not-cQ | 220 | 1 |
287 | q | pR | not-s | 151-152, 159-160, 211-212, 215-216, 219-220, 223-224 | 12 |
288 | q | qR | not-s | 74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252 | 16 |
3rd | QR | QP | PR | ||
322 | mq | mqR | inconsistent | None | 0 |
323 | mq | npR | inconsistent | None | 0 |
324 | mq | pRqR | inconsistent | None | 0 |
327 | mq | pR | inconsistent | None | 0 |
328 | mq | qR | inconsistent | None | 0 |
332 | np | mqR | inconsistent | None | 0 |
333 | np | npR | inconsistent | None | 0 |
334 | np | pRqR | inconsistent | None | 0 |
337 | np | pR | inconsistent | None | 0 |
338 | np | qR | inconsistent | None | 0 |
342 | pq | mqR | p + not-pQ | 226, 228 | 2 |
343 | pq | npR | q + not-qQ | 136, 200 | 2 |
344 | pq | pRqR | not-cQ | 232 | 1 |
347 | pq | pR | q + not-qQ | 136, 151-152, 168, 183-184, 200, 215-216, 232, 247-248 | 12 |
348 | pq | qR | p + not-pQ | 106, 108, 110, 112, 226, 228, 230, 232, 234, 236, 238, 240 | 12 |
372 | p | mqR | p + not-pQ | 226, 228 | 2 |
373 | p | npR | q + not-qQ | 136, 200 | 2 |
374 | p | pRqR | not-cQ | 232 | 1 |
377 | p | pR | q + not-qQ | 136, 151-152, 168, 183-184, 200, 215-216, 232, 247-248 | 12 |
378 | p | qR | p + not-pQ | 106, 108, 110, 112, 226, 228, 230, 232, 234, 236, 238, 240 | 12 |
382 | q | mqR | p + not-pQ | 226, 228 | 2 |
383 | q | npR | q + not-qQ | 136, 200 | 2 |
384 | q | pRqR | not-cQ | 232 | 1 |
387 | q | pR | q + not-qQ | 136, 151-152, 168, 183-184, 200, 215-216, 232, 247-248 | 12 |
388 | q | qR | p + not-pQ | 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. |
1st | QR | PQ | PR | ||
122 | mqP | mq | inconsistent | None | 0 |
123 | mqP | np | inconsistent | None | 0 |
124 | mqP | pq | 170, 186 | 2 | |
127 | mqP | p | 170, 186 | 2 | |
128 | mqP | q | 170, 186 | 2 | |
132 | npP | mq | inconsistent | None | 0 |
133 | npP | np | inconsistent | None | 0 |
134 | npP | pq | pQ | 150, 158 | 2 |
137 | npP | p | pQ | 150, 158 | 2 |
138 | npP | q | pQ | 150, 158 | 2 |
142 | pPqP | mq | inconsistent | None | 0 |
143 | pPqP | np | inconsistent | None | 0 |
144 | pPqP | pq | pQqQ | 190 | 1 |
147 | pPqP | p | pQqQ | 190 | 1 |
148 | pPqP | q | pQqQ | 190 | 1 |
172 | pP | mq | inconsistent | None | 0 |
173 | pP | np | inconsistent | None | 0 |
174 | pP | pq | pQ | 150-152, 158-160, 182-184, 190-192 | 12 |
177 | pP | p | pQ | 150-152, 158-160, 182-184, 190-192 | 12 |
178 | pP | q | pQ | 150-152, 158-160, 182-184, 190-192 | 12 |
182 | qP | mq | inconsistent | None | 0 |
183 | qP | np | inconsistent | None | 0 |
184 | qP | pq | 106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254 | 12 | |
187 | qP | p | 106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254 | 12 | |
188 | qP | q | 106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254 | 12 | |
2nd | RQ | PQ | PR | ||
222 | mqP | mq | not-cQ | 74, 202 | 2 |
223 | mqP | np | inconsistent | None | 0 |
224 | mqP | pq | not-cQ | 90, 218 | 2 |
227 | mqP | p | not-cQ | 90, 218 | 2 |
228 | mqP | q | not-cQ | 74, 90, 202, 218 | 4 |
232 | npP | mq | inconsistent | None | 0 |
233 | npP | np | not-cQ | 147-148 | 2 |
234 | npP | pq | not-cQ | 155-156 | 2 |
237 | npP | p | not-cQ | 147-148, 155-156 | 4 |
238 | npP | q | not-cQ | 155-156 | 2 |
242 | pPqP | mq | inconsistent | None | 0 |
243 | pPqP | np | inconsistent | None | 0 |
244 | pPqP | pq | pq + not-wQ | 220 | 1 |
247 | pPqP | p | pq + not-wQ | 220 | 1 |
248 | pPqP | q | pq + not-wQ | 220 | 1 |
272 | pP | mq | inconsistent | None | 0 |
273 | pP | np | not-cQ | 147-148, 211-212 | 4 |
274 | pP | pq | not-s + not-qQ | 151-152, 155-156, 159-160, 215-216, 219-220, 223-224 | 12 |
277 | pP | p | not-s + not-qQ | 147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224 | 16 |
278 | pP | q | not-s + not-qQ | 151-152, 155-156, 159-160, 215-216, 219-220, 223-224 | 12 |
282 | qP | mq | not-s + not-cQ | 74, 76, 202, 204 | 4 |
283 | qP | np | inconsistent | None | 0 |
284 | qP | pq | not-s + not-pQ | 90, 92, 106, 108, 122, 124, 218, 220, 234, 236, 250, 252 | 12 |
287 | qP | p | not-s + not-pQ | 90, 92, 106, 108, 122, 124, 218, 220, 234, 236, 250, 252 | 12 |
288 | qP | q | not-s + not-pQ | 74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252 | 16 |
3rd | QR | QP | PR | ||
322 | mqP | mq | inconsistent | None | 0 |
323 | mqP | np | inconsistent | None | 0 |
324 | mqP | pq | 170, 186 | 2 | |
327 | mqP | p | 170, 186 | 2 | |
328 | mqP | q | 170, 186 | 2 | |
332 | npP | mq | inconsistent | None | 0 |
333 | npP | np | inconsistent | None | 0 |
334 | npP | pq | pQ | 150, 158 | 2 |
337 | npP | p | pQ | 150, 158 | 2 |
338 | npP | q | pQ | 150, 158 | 2 |
342 | pPqP | mq | inconsistent | None | 0 |
343 | pPqP | np | inconsistent | None | 0 |
344 | pPqP | pq | pQqQ | 190 | 1 |
347 | pPqP | p | pQqQ | 190 | 1 |
348 | pPqP | q | pQqQ | 190 | 1 |
372 | pP | mq | inconsistent | None | 0 |
373 | pP | np | inconsistent | None | 0 |
374 | pP | pq | pQ | 150-152, 158-160, 182-184, 190-192 | 12 |
377 | pP | p | pQ | 150-152, 158-160, 182-184, 190-192 | 12 |
378 | pP | q | pQ | 150-152, 158-160, 182-184, 190-192 | 12 |
382 | qP | mq | inconsistent | None | 0 |
383 | qP | np | inconsistent | None | 0 |
384 | qP | pq | 106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254 | 12 | |
387 | qP | p | 106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254 | 12 | |
388 | qP | 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. |
1st | QR | PQ | PR | ||
122 | mqP | mqR | inconsistent | None | 0 |
123 | mqP | npR | inconsistent | None | 0 |
124 | mqP | pRqR | inconsistent | None | 0 |
127 | mqP | pR | inconsistent | None | 0 |
128 | mqP | qR | inconsistent | None | 0 |
132 | npP | mqR | inconsistent | None | 0 |
133 | npP | npR | inconsistent | None | 0 |
134 | npP | pRqR | inconsistent | None | 0 |
137 | npP | pR | inconsistent | None | 0 |
138 | npP | qR | inconsistent | None | 0 |
142 | pPqP | mqR | inconsistent | None | 0 |
143 | pPqP | npR | inconsistent | None | 0 |
144 | pPqP | pRqR | inconsistent | None | 0 |
147 | pPqP | pR | inconsistent | None | 0 |
148 | pPqP | qR | inconsistent | None | 0 |
172 | pP | mqR | inconsistent | None | 0 |
173 | pP | npR | inconsistent | None | 0 |
174 | pP | pRqR | inconsistent | None | 0 |
177 | pP | pR | p-aloneQ | 151-152, 159-160 | 4 |
178 | pP | qR | inconsistent | None | 0 |
182 | qP | mqR | inconsistent | None | 0 |
183 | qP | npR | inconsistent | None | 0 |
184 | qP | pRqR | inconsistent | None | 0 |
187 | qP | pR | inconsistent | None | 0 |
188 | qP | qR | q-aloneQ | 106, 122, 234, 250 | 4 |
2nd | RQ | PQ | PR | ||
222 | mqP | mqR | not-cQ | 74, 202 | 2 |
223 | mqP | npR | inconsistent | None | 0 |
224 | mqP | pRqR | inconsistent | None | 0 |
227 | mqP | pR | inconsistent | None | 0 |
228 | mqP | qR | not-cQ | 74, 90, 202, 218 | 4 |
232 | npP | mqR | inconsistent | None | 0 |
233 | npP | npR | not-cQ | 147-148 | 2 |
234 | npP | pRqR | inconsistent | None | 0 |
237 | npP | pR | not-cQ | 147-148, 155-156 | 4 |
238 | npP | qR | inconsistent | None | 0 |
242 | pPqP | mqR | inconsistent | None | 0 |
243 | pPqP | npR | inconsistent | None | 0 |
244 | pPqP | pRqR | not-cQ | 220 | 1 |
247 | pPqP | pR | not-cQ | 220 | 1 |
248 | pPqP | qR | not-cQ | 220 | 1 |
272 | pP | mqR | inconsistent | None | 0 |
273 | pP | npR | not-cQ | 147-148, 211-212 | 4 |
274 | pP | pRqR | not-cQ | 220 | 1 |
277 | pP | pR | not-s | 147-148, 151-152, 155-156, 159-160, 211-212, 215-216, 219-220, 223-224 | 16 |
278 | pP | qR | not-cQ | 220 | 1 |
282 | qP | mqR | not-cQ | 74, 76, 202, 204 | 4 |
283 | qP | npR | inconsistent | None | 0 |
284 | qP | pRqR | not-cQ | 220 | 1 |
287 | qP | pR | not-cQ | 220 | 1 |
288 | qP | qR | not-s | 74, 76, 90, 92, 106, 108, 122, 124, 202, 204, 218, 220, 234, 236, 250, 252 | 16 |
3rd | QR | QP | PR | ||
322 | mqP | mqR | inconsistent | None | 0 |
323 | mqP | npR | inconsistent | None | 0 |
324 | mqP | pRqR | inconsistent | None | 0 |
327 | mqP | pR | inconsistent | None | 0 |
328 | mqP | qR | inconsistent | None | 0 |
332 | npP | mqR | inconsistent | None | 0 |
333 | npP | npR | inconsistent | None | 0 |
334 | npP | pRqR | inconsistent | None | 0 |
337 | npP | pR | inconsistent | None | 0 |
338 | npP | qR | inconsistent | None | 0 |
342 | pPqP | mqR | inconsistent | None | 0 |
343 | pPqP | npR | inconsistent | None | 0 |
344 | pPqP | pRqR | inconsistent | None | 0 |
347 | pPqP | pR | inconsistent | None | 0 |
348 | pPqP | qR | inconsistent | None | 0 |
372 | pP | mqR | inconsistent | None | 0 |
373 | pP | npR | inconsistent | None | 0 |
374 | pP | pRqR | inconsistent | None | 0 |
377 | pP | pR | p-aloneQ | 151-152, 183-184 | 4 |
378 | pP | qR | inconsistent | None | 0 |
382 | qP | mqR | inconsistent | None | 0 |
383 | qP | npR | inconsistent | None | 0 |
384 | qP | pRqR | inconsistent | None | 0 |
387 | qP | pR | inconsistent | None | 0 |
388 | qP | qR | q-aloneQ | 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. |
1st | QR | PQ | PR | ||
s | wR | not-s | 74, 90, 147-148, 155-156, 202, 218 | 8 | |
w | wR | 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 | wR | 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 | |
wP | s | inconsistent | None | 0 | |
wP | w | wQ | 106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254 | 23 | |
wP | c | wQ | 106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254 | 23 | |
wP | wR | wQ | 106, 122, 151-152, 159-160, 234, 250 | 8 | |
2nd | RQ | PQ | PR | ||
s | wR | not-s | 74, 90, 147-148, 155-156, 202, 218 | 8 | |
w | wR | 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 | wR | 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 | |
wP | s | not-s | 74, 76, 147-148, 202, 204, 211-212 | 8 | |
wP | 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 | |
wP | 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 | |
wP | wR | 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 | |
3rd | QR | QP | PR | ||
s | wR | inconsistent | None | 0 | |
w | wR | 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 | wR | 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 | |
wP | s | inconsistent | None | 0 | |
wP | w | wQ | 106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254 | 23 | |
wP | c | wQ | 106, 110, 122, 126, 150-152, 158-160, 170, 174, 182-184, 186, 190-192, 234, 238, 250, 254 | 23 | |
wP | wR | wQ | 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 disjunctionwabsor not-cabs.
Next Section(continuation of same chapter)