Wittgenstein's Tractatus and Logical Positivism

Logical Positivism, while now seen as mainly being of historical interest, was in the earliest years of the 20th Century, seen as an important philosophical movement, propounded mainly by a group that became known as the first Vienna Circle.  The Vienna Circle met at a cafe called Cafe Central.  The circle was interrupted by the First World War, but resumed afterwards.  Logical Positivism rejected all forms of metaphysics and a priori propositions, instead advocating a single, rational language of science that would evolve to become more precise as uncertainties and idiosyncrasies emerged.

This Circle was heavily influenced by the early work of Ludwig Wittgenstein, whose Tractatus Logico-Philosophicus, or the Tractatus for short.

The Tractatus consisted of seven main statements, each of which is supposed to be self-evident.  Each of these seven propositions have a number of sub-statements that relate to the 'parent' statement.

The main seven statements are:

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.
5. Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)
6. The general form of truth-function is: [, , N()].  This is the general form of proposition.
7. Whereof one cannot speak, thereof one must be silent.

There were many criticisms of Logical Positivism, one of the earliest came from Karl Popper, who argued that the Logical Positivist's requirement that a statement be scientifically verifiable was too strong.  Popper argued that instead, it should be possible to use a criterion of falsifiability.  

As an example of falsifiability, the statement 'All pigeons are grey.' can be proven as false by observing one brown pigeon.  However, the statement 'Grey pigeons do exist.' is not falsifiable, therefore stands as a valid statement.

Wittgenstein himself heavily criticised the Tractatus in his later work, and even some of its staunchest defenders later admitted that Logical Positivism was flawed.  Nevertheless, the movement was considered influential between the late 1920s and early 1930s and deserves to be remembered, albeit for historical reasons, rather than as a current branch of philosophy.