popper-logic-scientific-discovery

appendix *viii 399
with the same number of parameters. Jeffreys himself gives as examples
y = ax and y = ax 2 ; and he says of them: ‘laws involving the same number
of parameters can be taken as having the same prior probability.’ 7
But the number of laws having the same prior probability is infinite, for
Jeffreys’s own examples can be continued to infinity: y = ax 3 , y = ax 4 ,
... y = ax n , and so on, with n →∞. Thus for each number of paramenters,
the same problem would recur as for the whole sequence.
Moreover, Jeffreys himself recognizes, in the same § 3.0, 8 that a law,
a 1, say, may be obtained from a law a 2 with one additional parameter,
by assuming that parameter to be equal to zero; and that in this case,
p(a 1)