ENPages That Need Review
Logic Notebook 1867-1880
7
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
5
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
4
Nov. 12
E is a non relative term Ex is to be regarded as signifying the C's among all the x's
[...]
perhaps rather if the x's exist.
I will now note all the exceptions, in reference to these exponents.
In arithmetic [...] now in logic no sense has been attached to (E^x)^4 which is of course different from E^x^4 Therefore this signification may be gone [...] If [...] but [...] is indeterminate for it may be that [...]
Hence we might write [...]
0
Nov 11
Then my first developement formula will be
[Dr?]
where, however C may [Dr?] alpha. C will infact itself be of the same form. So that the formula should be written
[Dr?]
How I reserve this important matter for the future study. I ought somehow to get from it something answering to [Dr?] theorem.
Thus [Dr?] [Dr?]
Here are only two equations for the determination of three unknown quantities. But returning to Qx I can first separate his into a series of terms for
Logic Notebook 1867 Oct-Nov
6
For example, if I were to [let?] the exponent express the [ground?] of [relat?on] [?] the other letter the [cesse???] of the relation fixing the meanin of [ale???] 1 could be the relation identical with [A?] whatever in identical with any a [Ser?] us see how how our fundamental equations would appearx^l + y^l = (x+y)^l How the inverse should be [expressed?] would require further consideration l,v^1,(1-v^l)=o The invers would be simply this if a = b then [v?], b = a^-l [My?] [anal???] so far are but remote. Still I hope they will develope into something.
2
When I conceive a things as say "three" or say 'necessary' I necessarity have some concrete object in my imagination.I have some concrete [which]- 'the necesary' By saying that I have the necesary in my mind, it is not meant that I have simply the chapter necessity. For what I am thinking is no- necessity but the necessary. Then I must have something which i recognize as a general sign of the necessary. But which should that particular feeling which is a sign of the necessary be a sign of that any more than of anything else? Because [?] my constitution very true.
0
Oct 2
Of the Effect of a Change of Information
Suppose it is learned that Any S is P Not P is not S Some P is S Then S receives an addition to its comprehension not S to its extension P an addition to its extension Any S is not P not P receives an addition to its extension not S receives an addition to its extension Also S receives an indefinite addition to its extension
If are looking at an S find it to be P. Some S is P This adds to the extension of P - supposing we know what S Any S is not P This adds to the comprehension of S - supposing we know something of not P