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Theory Interpretation, Bertrand Russell and Analysis of a Large Corpus of Sentences of a Theory

Bertrand Russell's view that one can form an interpretation of a theory of logic by analysing a large corpus of sentences of that theory is still valid today. The modern-day way of explaining this is through the use of model theory.

Model theory is a branch of mathematical logic that deals with the study of formal languages and their interpretations, or models. In this approach, a theory of logic is represented by a set of sentences that can be evaluated as true or false in different models. A model is a structure that assigns meanings to the symbols of the language, thereby providing an interpretation of the theory.

To understand a theory of logic, one can analyse its sentences in the context of different models. By doing so, one can determine the conditions under which the sentences are true or false, and gain insight into the meaning and validity of the theory. Through model theory, one can gain a deeper understanding of the meaning and validity of a theory by analysing its sentences in the context of different models.

Russell explored his thesis in two primary works, "The Principals of Mathematics" and "Principia Mathematica" (with Whitehead).