Logic is not a body of doctrine, but a mirrorimage of the world. Logic is transcendental. Mathematics is a logical method. The propositions of mathematics are equations, and therefore pseudopropositions. A proposition of mathematics does not express a thought.
Indeed in real life a mathematical proposition is never what one needs. Rather, one uses mathematical propositions only to make inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics. (In philosophy the question, 'What do we actually use this word or this proposition for?' repeatedly leads to valuable insights.)
The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics. If two expressions are joined by the sign of equality, they can be substituted for one another. But it must be manifest in the two expressions themselves whether this is the case or not. When two expressions can be substituted for one another, that characterizes their logical form.
It is a property of affirmation that it can be construed as double negation. It is a property of '1 + 1 + 1 + 1' that it can be construed as '(1 + 1) + (1 + 1)'.
Frege says that the two expressions have the same meaning but different senses. But the essential point about an equation is that it is not necessary in order to show that the two expressions connected by the sign of equality have the same meaning, since this can be seen from the two expressions themselves. And the possibility of proving the propositions of mathematics means simply that their correctness can be perceived without its being necessary that what they express should itself be compared with the facts in order to determine its correctness.
It is impossible to assert the identity of meaning of two expressions. For in order to be able to assert anything about their meaning, I must know their meaning, and I cannot know their meaning without knowing whether what they mean is the same or different. An equation merely marks the point of view from which I consider the two expressions, it marks their equivalence in meaning.
Intuition is needed to solve mathematical, but language itself provides the necessary intuition. The process of calculating serves to bring about that intuition. Calculation is not an experiment.
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)
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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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 The world does not depend on me.
 The relative position of logic and science.
 Mathematics is a method of logic.
 Logic is transcendental.
 One can describe all true logical propositions in ...
 We can do without logical propositions.
 Recognizing a Tautology.
 The propositions of logic are tautologies.
 The General Form of a Truth Function.
 The microcosm.
 The boundary of my language represents the boundar...
 Elemental Propositions.
 Propositions occur in each other only as bases of ...
 Expressions.
 Identity.
 Truth Functions do not Include the Concept All.
 How is this useful?
 Every truthfunction an be obtained by successivel...
 Occam's rule points out that unnecessary signs mea...
 Signs for logical operations are punctuation marks...
 Logic must be clearly constructed from its primiti...
 Logical objects or logical constants in Frege's an...
 All propositions are the result of truth operators...
 The structures of propositions relate internally t...
 Propositions of probability.
 All deduction is a priori.
 Logical Inference.
 A proposition is a truth function of elemental pro...
 The general propositional form is the variable: 'I...
 Tautology and Contradiction.
 Truth Value Tables and Propositions.
 The sense of a proposition.
 A variable is the sign of a formal concept.
 Formal Properties and Relations.
 Logical Form  What can be shown, cannot be said.
 A proposition exhibits matters of fact which both ...
 Every proposition must make sense on its own.
 A proposition can be true or false only by being a...
 A proposition must have just as many degrees of fr...
 A sentence must use old expressions to tell us som...

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