# Logic I: Introduction to Symbolic Logic (PH126)

Consider the following two arguments. A. All Martians are green; Andres is a Martian; therefore Andres is green. B. Most Martians are green; Andres is Martian; therefore Andres is green. There is, clearly, a sense in which A is a good argument and B isn’t: it is impossible for both premises of A to be true while its conclusion is false – that is, it is impossible for all Martians to be green, and for Andres to be a Martian, and also for Andres to be, say, pink. B lacks this property: it is possible that most Martians are green, Andres is Martian, and he isn’t green. In this sense in A but not in B the truth of the premises guarantees the truth of the conclusion.

This property, which A has and B lacks, is what philosophers call ‘logical validity’, and it is the central notion of this module. Symbolic logic uses specially-designed formal languages to capture the idea of logical validity in virtue of logical form, and to develop methods for establishing the validity and invalidity of arguments. You will learn two such languages and a number of methods. And you will learn how to translate English sentences into formal language ones and vice versa. Learning to make such translations will increase your sensitivity to the subtleties of natural languages, and will provide you with the tools for articulating structural ambiguities and to capture the logical relationships between English sentences. With the methods for establishing validity and invalidity which you will learn, you will then be able to determine the validity or invalidity of English arguments. These skills are essential not only for reading and writing philosophy, but also for any aspect of life which involves reasoning and clear articulation of thoughts.

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#### CATS

This module is worth 15 CATS