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judgments. Both these, however, occur as limiting cases, and they can only be applied 
with confidence under extreme circumstances, such as probably never occur in human 
afiairs. [Edinburgh Memoir, pp. 630-645.) 
5thly. I have, in efiect, remarked that there is reason to suppose that all questions 
in the theory of probabilities can ultimately be reduced to questions in which the imme- 
diate subjects of probability are logical, i. e. involve no other essential relations than 
those of genus and species, whole and part. This is a question of theoretical rather 
than of practical interest. For instance, whether the formula of the arithmetical mean, 
which is the basis of the theory of astronomical observations, is self-evident, or whether 
it rests upon an ultimate logical basis, or whether, as I am inclined to believe, it may 
lawfully be regarded in either of these distinct but not confiicting lights, the super- 
structure remains the same. 
