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Showing more than Saying (the Tractatus in Pictures)




Wittgenstein does not, however, relegate all that is not inside the bounds of sense to oblivion. He makes a distinction between saying (sagen) and showing (zeigen) which is made to do additional work.

There are, beyond the senses (
Sinne) that can be formulated in sayable propositions, things that can only be shown. These show themselves in the form of (contingent) propositions, in the symbolist and logical propositions, and even in the unsayable (metaphysical, ethical, aesthetic) propositions of philosophy. 'What can be shown cannot be said.' But it is there, in language, even though it cannot be said.

- Anat Biletzski


Sketches from the most minimal metaphysics: "the most that can sensibly be said" about everything at once, and then some. I had wanted this post to be wordless, but you won't get much out of it if I don't do quite a lot of setup first. A version with the German original and both flawed English translations is here.



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Proposition 6.41


PARAPHRASING THE WHOLE TRACTATUS:
  1. Reality is the aggregation of everything real.
  2. What is real are facts. A fact is a specific configuration of existing fundamental things.
  3. When we think, we model a possible world. The structure of the model is logic.
  4. When we think properly, we are entertaining a premise with a determinate concept attached.
  5. Whether a statement is successful depends on whether its constituents are.
  6. All statements have the same structure. With one general formula (just one powerful function, the "N-operator", the denial of all propositions f[x]), you can derive the fundamental particles of language and, from there, all more complex statements. The formula of all language:

  7. There is more to all this than can be put in words.



TERMS
  • 'Sachverhalt': A 'state of affairs' or 'atomic fact'. (see Proposition 2.)
  • 'Gegenständ': An 'object' or 'simple': the merest constituents of reality.
  • 'Satz': A sentence (...or 'proposition').
  • 'Elementarsatz': A fundamental particle of language; a primitive concept. Mirror the Gegenstände.
  • 'Sinn': A 'sense', which here means a determinate proposition: the truth-conditions of a sentence.
  • 'sinnlos': 'Meaningless'. Lacking a single, totally clear propositional content. (e.g. tautologies and contradictions).
  • 'unsinnig': 'Senseless'. Total nonsense; a sentence which is too malformed to ever carry sense (e.g. metaphysics, ethics, the Tractatus)
  • 'Gedanke': A thought - but, again, he means only clear, 'sinnvoll' thoughts.



The following is not finished (the text after each section are key lines I still want to draw out). I'll use as little text as possible.



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SOME IMPORTANT BUT TENUOUS ASSUMPTIONS:


  1. The Context Principle:"A [word] has meaning only in a proposition. Every variable can be conceived as a propositional variable." - LW, 3.314

  2. The false (falsch) is not the nonsensical (Unsinnig) is not the senseless (Sinnlos): "Sense must be determinate." - LW, 3.23.

    Statements fail to express thoughts when
    1. any constituent of them lacks a truth-value, or
    2. is of indeterminate sense - that is, when any constituent is a pseudo-concept (e.g. "world"; "fact"; "God"; "object"; "the Good"; "beauty").
    The Tractatus fails in almost every line; under its own rules, it is plain nonsense. Compared to observation statements, logic is 'senseless', but philosophy is even less than that: nonsense. (6.54)


  3. The key argument (never presented as an argument, heaven forfend):

  4. Logic is Transcendental: "Logic is not a body of doctrine, but a mirror-image of the world." -LW, TLP 6.13

  5. Language is logical: Takes language to have a basic, reducible logical structure. (This is the bit that Russell vaunted as 'Logical Symbolism'.)

  6. So language is Transcendental (3 + 4)
    Hence language can lead to knowledge and end, at last, philosophy (or the Cartesian project, at least). In its logical structure, language bears recoverable "multiplicities" which relate directly to the external world.


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Paragraphs 1 --> 2



1. The world is all that is the case.
1. & 1.11 & 1.2



1.13:







2. What is the case is the existence of states of affairs








 

 
NB: Those birth descriptions are highly metaphorical; "objects" are supposed to be infinitesimal, "atomic" in the Greek sense. "Redness". The simplest possible units of what constitute facts. Looking more closely at a Gegenstand:



"A picture is a model of reality." - 2.12
2.141 - A picture is a fact.
2.172 - A picture cannot depict its pictorial form: it displays it.
2.19 - Logical pictures can depict the world.
2.223 - In order to tell whether a picture is true or false we must compare it with reality.
2.224 - It is impossible to tell from the picture alone whether it is true or false.




3. A logical picture of facts is a thought.



3.01 - The totality of true thoughts is a picture of the world.
3.1 - In a proposition a thought finds an expression that can be perceived by the senses.
3.3 - Only propositions have sense; only in the nexus of a proposition does a name have meaning.
3.332 - No proposition can make a statement about itself, because a propositional sign cannot be contained in itself.




4. A thought is a proposition with a sense.




4.001
4.003 - Most of the propositions and questions to be found in philosophical works are not false but nonsensical.
4.0031 - All philosophy is a 'critique of language'. The apparent logical form of a proposition need not be its real one.
4.11 - The totality of true propositions is the whole of natural science
4.461 - Propositions show what they say; tautologies and contradictions show that they say nothing.
4.464 - A tautology's truth is certain, a proposition's possible, a contradiction's impossible.



5. A proposition is a truth-function of elementary propositions.



5.3 - All propositions are results of truth-operations on elementary propositions.
5.6 - The limits of my language mean the limits of my world.
5.61 - We cannot think what we cannot think; so what we cannot think we cannot say either.
5.621 - The world and life are one.
5.63 - I am my world. (The microcosm.)
5.632 - The subject does not belong to the world but it is a limit of the world



6. The general forms of truth-functions and propositions are the same:




6.13 - Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.
6.2 - Mathematics is a logical method.
6.21 - A proposition of mathematics does not express a thought.
6.41 - The sense of the world must lie outside the world.
6.431 - At death the world does not alter, but comes to an end.
6.4311 - Death is not an event in life: we do not live to experience death.
6.44 - It is not how things are in the world that is mystical, but that it exists.









7. Whereof we cannot speak, thereof we must be silent.


Note that all of the things in these diagrams can in fact easily be said: they all fit into a set of propositions (albeit a self-refuting set): it's called Tractatus Logico-Philosophicus. Drawing is only a kind of saying; the kind of reference that he means by zeigen is far less concrete and more important than this.
2.12 - A picture is a model of reality.
2.141 - A picture is a fact.
2.172 - A picture cannot depict its pictorial form: it displays it.
2.19 - Logical pictures can depict the world.
2.223 - In order to tell whether a picture is true or false we must compare it with reality.
2.224 - It is impossible to tell from the picture alone whether it is true or false.
3 - A logical picture of facts is a thought.
3.01 - The totality of true thoughts is a picture of the world.
3.1 - In a proposition a thought finds an expression that can be perceived by the senses.
3.3 - Only propositions have sense; only in the nexus of a proposition does a name have meaning.
3.332 - No proposition can make a statement about itself, because a propositional sign cannot be contained in itself.
4 - A thought is a proposition with a sense.
4.001 - The totality of propositions is language.
4.003 - Most of the propositions and questions to be found in philosophical works are not false but nonsensical.
4.0031 - All philosophy is a 'critique of language'. The apparent logical form of a proposition need not be its real one.
4.11 - The totality of true propositions is the whole of natural science
4.461 - Propositions show what they say; tautologies and contradictions show that they say nothing.
4.464 - A tautology's truth is certain, a proposition's possible, a contradiction's impossible.
5.3 - All propositions are results of truth-operations on elementary propositions.
5.6 - The limits of my language mean the limits of my world.
5.61 - We cannot think what we cannot think; so what we cannot think we cannot say either.
5.621 - The world and life are one.
5.63 - I am my world. (The microcosm.)
6.13 - Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.
6.2 - Mathematics is a logical method.
6.21 - A proposition of mathematics does not express a thought.

6.431 - At death the world does not alter, but comes to an end.
6.4311 - Death is not an event in life: we do not live to experience death.
6.44 - It is not how things are in the world that is mystical, but that it exists.

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