The Principles of Logical Atomism
Russell referred to his atomistic doctrine as contrary to the tier "of the people who more or less follow Hegel" (PLA 178).
The first principle of logical atomism is that the World contains "facts". The facts are complex structures consisting of objects ("Particulars"). This he defines as "objects' relations in terms of atomic facts "(PLA 199) is a fact, either from an object with a simple property or from different objects, in relation to each other more easily. In addition, there are judgments ("Beliefs"), which are in a relationship to the facts, and by this relationship either true or false.
According to this theory, even ordinary objects of daily life "are apparently complex entities". According to Russell, words like "this" and "that" are used to denote particulars. In contrast, ordinary names such as "Socrates" actually are definitive descriptions. In the analysis of "Plato talks with his pupils", "Plato" needs to be replaced with something like "the man who was the teacher of Aristotle".
In 1905, Russell had already criticized Alexius Meinong, whose theories led to the paradox of the simultaneous existence and non-existence of fictional objects. This theory of descriptions was crucial to logical atomism, as Russell believed that language mirrored reality.
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