7c Reductions in Figure 2 - Logic Philosophy Spirituality

THE LOGIC OF CAUSATION

Phase One: Macroanalysis

Chapter 7 –Reduction of Positive Moods.

1.Reduction.

First, note that six moods in subfigure 2d have inconsistent premises. Specifically, if the minor premise (which has form P(S)Q) involves a strong determination, then it conflicts with any weak determination of same polarity in the major premise (which has form R(P)Q).

For if the minor concerns complete causation, clause (i) of which means that (P + notQ) is impossible – it is incompatible with the major, which implies (P + notQ) is possible when it concerns partial causation (see clause (ii) of that). Similarly, if the minor concerns necessary causation, clause (i) of which means that (notP + Q) is impossible – it is incompatible with the major, which implies (notP + Q) is possible when it concerns contingent causation (see clause (ii) of that).

Additionally, we may directly reduce a number of moods in figure 2 to figure 1, by converting the major premise. This is feasible when the major premise involves only strong causation; i.e. subfigures 2a and 2b are thus reducible respectively to subfigures 1a and 1b. This is not feasible when the major premise involves weak causation, since its conversion results in negation of the complement; which means that subfigures 2c and 2d have to be evaluated relatively independently (i.e. within the same figure, even if possibly through some moods reduced to figure 1).

Summary of figure 2.

·18 valid moods:

211-218, 221, 226, 231, 235, 251, 253, 256, 261-262, 265.

·40 moods without conclusion(nil):

222, 224-225, 227-228, 233-234, 236-238, 241, 244-248, 252, 254-255, 257-258, 263-264, 266-268, 271, 273-278, 281-282, 284-288.

·6 impossible moods(**):

223, 232, 242-243, 272, 283.

Total of moods = 18 valid and 46 invalid = 64.

Table 7.4.Sources of validity or invalidity in figure 2.

This table may be read as follows:

yes= element of conclusion (m,n,porq) are implied by the given premises.

no= element of conclusion (m,n,porq) are not implied (which does not mean denied) by the given premises.

by= by any sort of reduction to (number of mood used) orMA(matricial analysis).

Elements of conclusions for which matricial analysis is required areshaded.

since= for given premises, if an element of conclusion is valid (yes), then its contrary element is invalid (no).

**= incompatible premises.

nil= no valid conclusion.

Ref.	Mood #	Elements of conclusion implied?
§1	211	m	n	p	q
major	mn	yes	yes	no	no
minor	mn	by	by	since	since
concl.	mn	111	111	m	n
§2	212	m	n	p	q
major	mn	yes	no	no	yes
minor	mq	by	since	since	by
concl.	mq	112	q	m	112
§2	213	m	n	p	q
major	mn	no	yes	yes	no
minor	np	since	by	by	since
concl.	np	p	113	113	n
§6	214	m	n	p	q
major	mn	no	no	yes	yes
minor	pq	since	since	by	by
concl.	pq	p	q	114	114
§11	215	m	n	p	q
major	mn	yes	no	no	no
minor	m	by	by	since	by
concl.	m	115	115	m	115
§11	216	m	n	p	q
major	mn	no	yes	no	no
minor	n	by	by	by	since
concl.	n	116	116	116	n
§17	217	m	n	p	q
major	mn	no	no	yes	no
minor	p	since	by	by	by
concl.	p	p	117	117	117
§17	218	m	n	p	q
major	mn	no	no	no	yes
minor	q	by	since	by	by
concl.	q	118	q	118	118

Ref.	Mood #	Elements of conclusion implied?
§3	221	m	n	p	q
major	mq	no	yes	no	no
minor	mn	by	by	by	since
concl.	n	MA	256	MA	n
§4	222	m	n	p	q
major	mq	no	no	no	no
minor	mq	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§5	223	m	n	p	q
major	mq	qof major premise and
minor	np	nof minor premise
concl.	**	are incompatible
§8	224	m	n	p	q
major	mq	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§13	225	m	n	p	q
major	mq	no	no	no	no
minor	m	by	by	by	by
concl.	*nil*	221	222	221	221
§14	226	m	n	p	q
major	mq	no	yes	no	no
minor	n	by	by	by	since
concl.	n	221	256	221	n
§19	227	m	n	p	q
major	mq	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	224	224	224	224
§20	228	m	n	p	q
major	mq	no	no	no	no
minor	q	by	by	by	by
concl.	*nil*	222	222	222	222

Ref.	Mood #	Elements of conclusion implied?
§3	231	m	n	p	q
major	np	yes	no	no	no
minor	mn	by	by	since	by
concl.	m	265	MA	m	MA
§5	232	m	n	p	q
major	np	pof major premise and
minor	mq	mof minor premise
concl.	**	are incompatible
§4	233	m	n	p	q
major	np	no	no	no	no
minor	np	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§8	234	m	n	p	q
major	np	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§14	235	m	n	p	q
major	np	yes	no	no	no
minor	m	by	by	since	by
concl.	m	265	231	m	231
§13	236	m	n	p	q
major	np	no	no	no	no
minor	n	by	by	by	by
concl.	*nil*	233	231	231	231
§20	237	m	n	p	q
major	np	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	233	233	233	233
§19	238	m	n	p	q
major	np	no	no	no	no
minor	q	by	by	by	by
concl.	*nil*	234	234	234	234

Ref.	Mood #	Elements of conclusion implied?
§7	241	m	n	p	q
major	pq	no	no	no	no
minor	mn	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§9	242	m	n	p	q
major	pq	pof major premise and
minor	mq	mof minor premise
concl.	**	are incompatible
§9	243	m	n	p	q
major	pq	qof major premise and
minor	np	nof minor premise
concl.	**	are incompatible
§10	244	m	n	p	q
major	pq	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	MA	MA	MA	MA
§23	245	m	n	p	q
major	pq	no	no	no	no
minor	m	by	by	by	by
concl.	*nil*	241	241	241	241
§23	246	m	n	p	q
major	pq	no	no	no	no
minor	n	by	by	by	by
concl.	*nil*	241	241	241	241
§25	247	m	n	p	q
major	pq	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	244	244	244	244
§25	248	m	n	p	q
major	pq	no	no	no	no
minor	q	by	by	by	by
concl.	*nil*	244	244	244	244

Ref.	Mood #	Elements of conclusion implied?
§12	251	m	n	p	q
major	m	no	yes	no	no
minor	mn	by	by	by	since
concl.	n	161	161	161	n
§15	252	m	n	p	q
major	m	no	no	no	no
minor	mq	by	by	by	by
concl.	*nil*	162	162	162	162
§16	253	m	n	p	q
major	m	no	yes	no	no
minor	np	by	by	by	since
concl.	n	163	163	163	n
§24	254	m	n	p	q
major	m	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	164	164	164	164
§27	255	m	n	p	q
major	m	no	no	no	no
minor	m	by	by	by	by
concl.	*nil*	165	165	165	165
§28	256	m	n	p	q
major	m	no	yes	no	no
minor	n	by	by	by	since
concl.	n	166	166	166	n
§29	257	m	n	p	q
major	m	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	167	167	167	167
§30	258	m	n	p	q
major	m	no	no	no	no
minor	q	by	by	by	by
concl.	*nil*	168	168	168	168

Ref.	Mood #	Elements of conclusion implied?
§12	261	m	n	p	q
major	n	yes	no	no	no
minor	mn	by	by	since	by
concl.	m	151	151	m	151
§16	262	m	n	p	q
major	n	yes	no	no	no
minor	mq	by	by	since	by
concl.	m	152	152	m	152
§15	263	m	n	p	q
major	n	no	no	no	no
minor	np	by	by	by	by
concl.	*nil*	153	153	153	153
§24	264	m	n	p	q
major	n	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	154	154	154	154
§28	265	m	n	p	q
major	n	yes	no	no	no
minor	m	by	by	since	by
concl.	m	155	155	m	155
§27	266	m	n	p	q
major	n	no	no	no	no
minor	n	by	by	by	by
concl.	*nil*	156	156	156	156
§30	267	m	n	p	q
major	n	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	157	157	157	157
§29	268	m	n	p	q
major	n	no	no	no	no
minor	q	by	by	by	by
concl.	*nil*	158	158	158	158

Ref.	Mood #	Elements of conclusion implied?
§18	271	m	n	p	q
major	p	no	no	no	no
minor	mn	by	by	by	by
concl.	*nil*	241	231	231	231
§21	272	m	n	p	q
major	p	pof major premise and
minor	mq	mof minor premise
concl.	**	are incompatible
§22	273	m	n	p	q
major	p	no	no	no	no
minor	np	by	by	by	by
concl.	*nil*	233	233	233	233
§26	274	m	n	p	q
major	p	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	234	234	234	234
§31	275	m	n	p	q
major	p	no	no	no	no
minor	m	by	by	by	by
concl.	*nil*	241	231	231	231
§32	276	m	n	p	q
major	p	no	no	no	no
minor	n	by	by	by	by
concl.	*nil*	233	231	231	231
§33	277	m	n	p	q
major	p	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	233	233	233	233
§34	278	m	n	p	q
major	p	no	no	no	no
minor	q	by	by	by	by
concl.	*nil*	234	234	234	234

Ref.	Mood #	Elements of conclusion implied?
§18	281	m	n	p	q
major	q	no	no	no	no
minor	mn	by	by	by	by
concl.	*nil*	221	241	221	221
§22	282	m	n	p	q
major	q	no	no	no	no
minor	mq	by	by	by	by
concl.	*nil*	222	222	222	222
§21	283	m	n	p	q
major	q	qof major premise and
minor	np	nof minor premise
concl.	**	are incompatible
§26	284	m	n	p	q
major	q	no	no	no	no
minor	pq	by	by	by	by
concl.	*nil*	224	224	224	224
§32	285	m	n	p	q
major	q	no	no	no	no
minor	m	by	by	by	by
concl.	*nil*	221	222	221	221
§31	286	m	n	p	q
major	q	no	no	no	no
minor	n	by	by	by	by
concl.	*nil*	221	241	221	221
§34	287	m	n	p	q
major	q	no	no	no	no
minor	p	by	by	by	by
concl.	*nil*	224	224	224	224
§33	288	m	n	p	q
major	q	no	no	no	no
minor	q	by	by	by	by
concl.	*nil*	222	222	222	222

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