How can such specialized rigs and catches be used so that logic acts as the all inclusive the mirror of the world? Well, in that they all hook up in an infinitely fine grid to form that great mirror.
(~p) is true if 'p' is false. Therefore, in the case when the proposition (~p) is true, proposition (p) is false. How then can the prefixed tilde '~' make it agree with reality? In (~p) it is not '~' that negates, but rather what it is that all the signs in this notation that negate p have in common. And that is the common rule that governs the construction of (~p), (~~~p), (~p ∨ ~p), (~p.~p), etc. etc. ad inf. It is this common rule that mirrors negation.
We might say: What is common to all symbols that affirm both p and q is the proposition (p.q). What is common to all symbols that affirm either p or q is the proposition (p∨q). Similarly, we can say that two propositions are opposed to one another if they have nothing in common with one another. And we can also say that every proposition has only one negative, since there is only one proposition that lies completely outside if it. Thus, in Russell's notation as well, we see that (q:p∨~p) says the same thing as 'q', and that (p∨~p) says nothing.
Once a notation has been established, it will contain a rule governing the construction of all propositions that negate p, affirm p, affirm p or q, and so on. These rules are equivalent to the symbols and reflect their sense.
Our symbols themselves must show that compounds created by using '∨', '.', etc. can only be propositions. This is indeed the case, since the symbol in (p) and (q) itself presupposes '∨', '~', etc. If the sign 'p' in (p∨q) could not stand for a complex sign, then it would not make sense in isolation. But in that case, the signs (p∨p), (p.p), etc., which have the same sense as (p), could not make sense either. But if (p∨p) makes no sense, then neither can (p∨q).
Must the sign of a negative proposition be constructed from that of the positive proposition? (Such as: when 'a' does not stand in a certain relation to 'b' then this could say that (aRb) was not the case.) The positive proposition necessarily presupposes the existence of the negative proposition and vice versa.
This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus LogicoPhilosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)
Friday, April 4, 2008
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 Tractatus LogicoPhilosophicus 1
 Tractatus LogicoPhilosophicus 2
 Tractatus LogicoPhilosophicus 2.01
 Tractatus LogicoPhilosophicus 2.02
 Tractatus LogicoPhilosophicus 2.03 to 2.063
 Tractatus LogicoPhilosophicus 2.1
 Tractatus LogicoPhilosophicus 2.2
 Tractatus LogicoPhilosophicus 3
 Tractatus LogicoPhilosophicus 3.0
 Tractatus LogicoPhilosophicus 3.1
 Tractatus LogicoPhilosophicus 3.2
 Tractatus LogicoPhilosophicus 3.3
 Tractatus LogicoPhilosophicus 3.32
 Tractatus LogicoPhilosophicus 3.33
 Tractatus LogicoPhilosophicus 3.34
 Tractatus LogicoPhilosophicus 3.4 to 3.5
 Tractatus LogicoPhilosophicus 4
 Tractatus LogicoPhilosophicus 4.00
 Tractatus LogicoPhilosophicus 4.01 to 4.022
 Tractatus LogicoPhilosophicus 4.023 to 4.027
 Tractatus LogicoPhilosophicus 4.03
 Tractatus LogicoPhilosophicus 4.04
 Tractatus LogicoPhilosophicus 4.05 to 4.0621
 Tractatus LogicoPhilosophicus 4.1
 Tractatus LogicoPhilosophicus 4.12 to 4.1213
 Tractatus LogicoPhilosophicus 4.122 to 4.1252
 Tractatus LogicoPhilosophicus 4.126 to 4.128
 Tractatus LogicoPhilosophicus 4.2 to 4.28
 Tractatus LogicoPhilosophicus 4.3 to 4.442
 Tractatus LogicoPhilosophicus 4.45 TO 4.4661
 Tractatus LogicoPhilosophicus 4.5 to 4.53
 Tractatus LogicoPhilosophicus 5
 Tractatus LogicoPhilosophicus 5 to 5.101
 Tractatus LogicoPhilosophicus 5.05 to 5.156
 Tractatus LogicoPhilosophicus 5.11 to 5.132
 Tractatus LogicoPhilosophicus 5.133 to 5.143
 Tractatus LogicoPhilosophicus 5.2 to 5.254
 Tractatus LogicoPhilosophicus 5.3
 Tractatus LogicoPhilosophicus 5.4 to 5.44
 Tractatus LogicoPhilosophicus 5.45
 Tractatus LogicoPhilosophicus 5.46 to 5.472
 Tractatus LogicoPhilosophicus 5.473 to5.476
 Tractatus LogicoPhilosophicus 5.5 to 5.503
 Tractatus LogicoPhilosophicus 5.51
 Tractatus LogicoPhilosophicus 5.52
 Tractatus LogicoPhilosophicus 5.53 to 5.535
 Tractatus LogicoPhilosophicus 5.5351 to 5.5352
 Tractatus LogicoPhilosophicus 5.55 to 5.5571
 Tractatus LogicoPhilosophicus 5.6 to 5.621
 Tractatus LogicoPhilosophicus 5.63 to 5.641
 Tractatus LogicoPhilosophicus 6
 Tractatus LogicoPhilosophicus 6 to 6.01
 Tractatus LogicoPhilosophicus 6.1 to 6.1202
 Tractatus LogicoPhilosophicus 6.1203
 Tractatus LogicoPhilosophicus 6.121 to 6.124
 Tractatus LogicoPhilosophicus 6.125 to 6.1271
 Tractatus LogicoPhilosophicus 6.13 to 6.2331
 Tractatus LogicoPhilosophicus 6.234 to 6.3432
 Tractatus LogicoPhilosophicus 6.342 to 6.372
 Tractatus LogicoPhilosophicus 6.373 to 6.3751
 Tractatus LogicoPhilosophicus 6.5
 Tractatus LogicoPhilosophicus 7
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