Logic Notebook 1867-1880

In arithmetic [...] now suppose

then it does not follow that every x is z and therefore not that [...] This seems to be a downright exception. So this very valuable formula, [...] which it seems hopeless to get any developments, must be dispensed [...].

In arith if [...]

But this is not [...] here

This objection is so serios that I am going to [...] it by a new [...] [...] This is to mean 'is one [...]' [...] Every a is 6. or [...] [...] [...]

64r

a , b =, 0

This might be interesting and indeed would be, but does not look hopeful for the present purpose at all.

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In return, then; we must get along without the rule that if

L (exp. x) =, M (exp. y)

L (exp. x,a) =, M (exp. y,a)

This holds with arithmetical but not with logical.

Log (lower exp. e) a has several values Let the sum of them

Addition (exp.,) Log (exp. a, lower exp. e) = L (exp.a, lower exp.r)

then this is a particular value of Log (lower exp. e a)

Then if a = L (exp. b) b, L (exp.a, lower exponential r) =, b

1-x is other than every x and may be denoted by n^x Then the fundamental formula or the calculus becomes x, n^x =, 0 =, n' G' = 0 log1 = 0

x, logx = 0 logx^x, x^x = 1

n^x, n^n^x =, n^x, x n^x + n^n^x = 1

[...]