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Symbolic Logic

  Symbolic logic was principally the work of Gottlob Frege (1848 - 1925), building on the ideas of , George Boole (1815 - 1864) (see Boolean logic). Apart from the symbols used by Boole, a second type of symbol is now used, the quantifier. The commonly used quantifiers translate the phrases ‘for every’ and ‘there is a’, and are known as universal and existential quantifiers respectively. With these additions, symbolic logic becomes the language of mathematics. Indeed, those who held to the school of logicism dominated by the work of , Bertrand Russell (1872 - 1970) believed that mathematics was in fact just the study of a branch of symbolic logic.

Symbolic logic has had such a great impact on mathematics because it provides a notation which is extremely flexible yet, to the initiated, simple to use. All the different ideas expressed throughout mathematics can be written in this language with only a few different ‘words’. However, like any language, it takes a long time to become familiar with it, to use it in its full expressiveness and even to think in it. Symbolic logic has had the unfortunate consequence of giving mathematics a completely incomprehensible appearance to the non-mathematician: it is written in a language as foreign to the average English speaker as Russian or Greek. All fields have their own technical vocabulary; mathematics has perhaps the most developed and alien one of all. SMcL

Further reading G. Boole, The Laws of Thought (1854); , J.N. Crossley et al., What Is Mathematical Logic?.



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