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THE LOGIC OF CAUSATION

© Avi Sion, 1999, 2000; 2003, 2005; 2008, 2010  All rights reserved.

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THE LOGIC OF CAUSATION

Phase Two: Microanalysis

Appendix – Grand Matrices

For a fuller account of this topic, see Chapter 12.

1. Catalogue of moduses for the four conjunctions of two items (P, R).

Row

Items

**

Possible moduses, labeled 2-15

label

P

R

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

a

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

b

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

c

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

d

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

** Column labeled No. 1 is an impossible modus.

2. Catalogue of moduses for the eight conjunctions of three items (P, Q, R).

Items

**

Possible moduses, labeled 2-16

P

(Q)

R

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



** Column labeled No. 1 is an impossible modus.

Same table continued.

Items

Moduses, labeled 17-32

P

(Q)

R

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 33-48

P

(Q)

R

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 49-64

P

(Q)

R

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1


Table 3 continued.

Items

Moduses, labeled 65-80

P

(Q)

R

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 81-96

P

(Q)

R

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 97-112

P

(Q)

R

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 113-128

P

(Q)

R

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1


Table 3 continued.

Items

Moduses, labeled 129-144

P

(Q)

R

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 145-160

P

(Q)

R

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 161-176

P

(Q)

R

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 177-192

P

(Q)

R

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1


Table 3 continued.

Items

Moduses, labeled 193-208

P

(Q)

R

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 209-224

P

(Q)

R

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 225-240

P

(Q)

R

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



Same table continued.

Items

Moduses, labeled 241-256

P

(Q)

R

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

0

0

0

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1



You can purchase a paper copy of this book Books by Avi Sion in The Logician Bookstore at The Logician’s secure online Bookshop.

2016-06-13T10:53:07+00:00