“Philosophical problems arise when language goes on holiday”
“The aim of philosophy is to erect a wall at the point where language stops anyway.”
Ludwig Wittgenstein (1889-1951)
Tractatus Logico-Philosophicus (1922) 
Premise: initially Wittgenstein claimed that this tractatus would solve all the philosophical dilemmas of the time, though he later changed his mind about the nature of language. Indeed he rejected the possibility of a universal language. Though rather than writing a ‘mea culpa’, he criticises a passage from St.Augustine. Contrary to the the Augustinian idea that language is fixed, Wittgenstein instead wrote in his ‘Philosophical investigation’ that words and meanings are actually incredibly flexible and context-based (this is where originates the ‘language games’ concept). Initially Wittgenstein also believed that propositions always had a reality/picture correspondence, but he was puzzled when the economist Piero Sraffa made a napolitan hand gesture to prove him wrong.
In the introduction Russell makes clear that Wittgenstein’s goal is to achieve a ‘logically perfect language’ without ambiguity or contradiction.
Russell gives an in-depth explanation of Wittgenstein’s truth function:
“The symbol he uses is (p, ξ, N(ξ)). The following is the explanation of this symbol:
p stands for all atomic propositions.
ξ stands for any set of propositions.
N(ξ) stands for the negation of all the propositions making up ξ.
The whole symbol (p, ξ, N(ξ)) means whatever can be obtained by taking any selection of atomic propositions, negating them all, then taking any selection of the set of propositions now obtained, together with any of the originals—and so on indefinitely. ”
-The seven propositions:
1) The world is everything that is the case
2) What is the case, the fact, is the existence of atomic facts
3) The logical picture of the facts is the thought.
4) The thought is the significant proposition. [could also be rendered: the thought is a proposition with a sense]
5) Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)
6) The general form the truth-function is: (p, ξ, N(ξ)). This is the general form of a proposition.
7) Whereof one cannot speak, thereof one must be silent.
In the preface, Wittgenstein credits Frege and Russell as two inspirations. Then he explains in a nutshell the thesis of his tractatus: “Its whole meaning could be summed up somewhat as follows: What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent. The book will, therefore, draw a limit… to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought). The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.”
Wittgenstein’s proposition’1 says “the world is everything that is the case”. Then, the world is the totality of facts, not of things. A better way to understand a fact is the ‘atomic fact’ (a combination of objects; atomic facts are independent of one another). It is the configuration of the objects that forms the atomic fact.
The world is facts in a logical space.
We make to ourserlves pictures of these facts. These pictures are models of reality. In this mental pictures the objects (elements) are all connected together, combined with one another. The picture “depicts reality by representing a possibility of the existence and non-existence of atomic facts”. If the picture agrees with reality then it is true otherwise wrong.
No picture can be said to be a priori true: it has to be compared with reality. Thought occurs when we have a logical picture of facts in mind.
One impression from reading Wittgenstein is the following: we could say that what is empirical is uncertain, while what is logical is tautological (such as proposition on 3.032 comparing geometry and physics). In proposition 3.05 he says “We could only know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).”- that is true of tautological systems, but not of empirical sciences.
For instance in 6.1 Wittegsntein says “the proposition of logic are tautologies” and in 6.11 “the propositions of logic therefore say nothing (they are the analytical propositions”).
Objects can only be described- we cannot talk about their inner essence.
Philosophy is filled with confusions because of the ambiguity of ordinary language. To avoid this error, a logical syntax (as used by Frege and Russell) is needed. A syntax where signs have their unique meaning. Signs should only have a descriptive purpose.
The danger of ordinary language is that of disguising thought.
Our propositions are just pictures (models) of reality. Propositions should be formulated in a simple way, so that when comparing their truthfulness with reality clear ‘yes or no’ answers can be given. Wittgenstein’s strict logicism resembles Wolfgang Pauli’s aphorism “it is not even wrong” (referring to the fact that vague propositions prove their ambiguity when the readers has no instruments to assess their truthfulness or falseness).
Propositions are useful because they provide a picture of a state of affairs. By context and by association with the mental pictures we already have, we can make sense of propositions.
For Wittgenstein “The possibility of propositions is based upon the principle of the representation of objects by signs”.
Without checking the truthfulness of a provision with reality, any proposition could be true.
In logic contradiction is shown by the structure that we have given. In logic there there tautological or contradicting conditions. However they tell us nothing about the state of affairs, they are not pictures of reality. They are without sense since a tautology is unconditionally true, while a contradiction is on “no condition true”.
Wittgenstein criticises the reliability of empiricism on the same lines as of Hume.
Probability also is a generalisation because it depends on our belief that through calculations we can give weight to what is uncertain or unknown in our picture of a state of affairs, but there may be circumstances with which we are not acquainted that might explain a certain phenomenon.
As proposition 5.473, Wittgenstein says “In a certain sense we cannot make mistakes in logic”: this is due to the fact that once having created a structure with arbitrary determinations and symbols, logical statements can be easily deduced one by one. At 6.1251 Wittgenstein also adds that there can never be surprises in logic.
At 5.6, Wittgenstein says “The limits of my language mean the limits of my world”. A few lines below, Wittgenstein seems to suggests language is not rich enough so that we can use it to express, describe our inner self (something that may be related to Wittgenstein’s concept of the ‘mystical’). The mystical seems to be what we experience but what is also inexpressible (it ‘shows itself’, but cannot be expressed because of the limits of language).
There a couple of statements in the Tractatus that contain strong arguments but seem to lack in evidence and in deductive logic (for instance 5.5421, 5.621, 5.632, 5.634, 5.641, 6.41, 6.431, 6.4311).
The propositions following proposition 6 are a criticism of classical mechanics and of induction (the law of causality is considered to be some sort of psychological need that we have to make sense of the world and harmonise the events that we witness). He then suggests that within the world it is impossible to make value judgments (so ethics cannot be ‘expressed’).
The problem of metaphysics in philosophy is that it is impossible to give precise and logical meaning to the typical signs (I guess Wittgenstein refers to words such as ‘absolute’, ‘immortal’, ‘trascendental’, etc) used in metaphysical discussions.
The 7th proposition is very well known, but Wittgenstein meant finding the limits of what can be expressed logically with our languages. However Wittgenstein made clear in his other writings and letters that what is really meaningful in life is indeed what cannot be expressed in words.
 “Tractatus Logico Philosophicus” by Ludwig Wittgenstein, LONDON KEGAN PAUL, TRENCH, TRUBNER & CO., LTD. NEW YORK: HARCOURT, BRACE & COMPANY, INC. 1922