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The Syadvada System of Predication 133
and psychological state, the probabilities of each of the three answers to any given stimulus are constant. Let the probabilities of answering syddasti, syådavaktavyah and syātnāsti be p, q, and r, where p· q+r=1. If, after n trials, the probabilities of the 7 types of predication are P1, n, P2, n, etc. where P1, n, is the probability of syådasti, etc. then the vector [P1.; P2, n; P3, n; P4, n; P5, n; P6, n; P7, n;] is transformed into the vector [P1, n+1; P2, n+1; etc.] by multiplication by the matrix
So
P
0
7
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0
q
0
0
0
r
P
0
0
q
0
0
0 0
0
0 0
0 0
0
0
0
0
0
0
0
0
0
p+q o
0
0 qtr 0
P 1
p+r
0
0
q
P
0
9 0 r
Evidently this could be made a little more symmetrical by transposing row and column (3) and (4).
The latent roots of this matrix are:
1, p+q, q+r, p+r, p, q, r. Pin-p
r
P20
Pan (p+r)-p11μ
P4n-q"
P5n=(p+q)-p1—q1 Pen (q+r)-qa—μ¤1
Pa=1−(q+r)2~(r+p)¤—(q+r)2+p2+q2+r2.
Thus unless one of p,q, or r is zero the final predication will be syädasti nåsti ca avaktavyaśca. In many cases when the stimulus is far from the threshold, p or r will be unity. The subject will always, or never, say 'this is bitter", or "this is illuminated". It is unlikely that q will ever be unity. So in this case syādavaktavyah will almost always be at best a provisional predication. It is however possible that p or r (say r) should be small, but not zero. If so
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