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THE LOGIC OF CAUSATION

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THE LOGIC OF CAUSATION

Phase Two: Microanalysis

Chapter 14 Main Three-Item Syllogisms

1. Applying Microanalysis to Syllogism.

2. The Moduses of Premises.

3. The Moduses of Conclusions

4. Dealing with Vaguer Propositions

3. The Moduses of Conclusions.

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 includes all the resulting moduses.

The following table lists all these results. Note well that all weak determinations mentioned in it are intended as absolute, 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 that many 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 item or its negation, or the minor, middle or major item or its negation, or again some 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 (wabs = pabs or qabs), or absolute causation (cabs = s or wabs = m or n or pabs or qabs). What we shall find is that no conclusion arises 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 forms s, wabs or cabs. 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

wabs = pabs or qabs

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

cabs =

m or n

or pabs or qabs

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 of s, wabs, cabs). 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

wabs

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

wabs

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

wabs

wabs

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

cabs

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

cabs

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

wabs

cabs

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

cabs

wabs

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

cabs

cabs

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.

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2016-06-13T10:43:33+00:00