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THE LOGIC OF CAUSATION

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THE LOGIC OF CAUSATION

Phase Two: Microanalysis

Chapter 15 – Some More Three-Item Syllogisms

1. Special Cases of Three-Item Syllogism

2. Dealing with Negatives

.

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, involving weak 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 involve only three items, even though one or more propositions in them are of relative weak determination. 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, for pQRP, 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 (m and n) are carried over from Table 14.3. Notice the differences between the results below and those for relatives in Table 13.1. Here mqrel = #s 42, 58, 170, 186, whereas there it = #s 42, 46, 170, 174; similarly, here nprel = #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 for prel, qrel, prelqrel and wrel, 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 form p or q or pq has absolute form PR; a similar conclusion of relative form P(Q)R is not implied by it. A conclusion of the form not-cQ means not-m + not-n + not-pQ + not-qQ, which does not imply not-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

qQ

170, 186

2

127

mqP

p

qQ

170, 186

2

128

mqP

q

qQ

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

qQ

106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254

12

187

qP

p

qQ

106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254

12

188

qP

q

qQ

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

qQ

170, 186

2

327

mqP

p

qQ

170, 186

2

328

mqP

q

qQ

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

qQ

106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254

12

387

qP

p

qQ

106, 110, 122, 126, 170, 174, 186, 190, 234, 238, 250, 254

12

388

qP

q

qQ

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 conclusion w in 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 form not-s, which (remember) means ‘not strong causation’, implying both not-m + not-n; it can also be read as the disjunction wabs or not-cabs.

Next Section (continuation of same chapter)

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2016-06-13T10:43:55+00:00