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THE
LOGIC OF CAUSATION
©
Avi Sion, 2003. All rights reserved.
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.
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.
You can purchase a paper copy of this book 
at The Logician's secure online Bookshop.
|
