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concept-script - Notation

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concept-script is a notation created in 1879 by Gottlob Frege.

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Frege initiated an ambitious program to use a precise notation which would help in the rigorous development of mathematics. Although his efforts were almost entirely focused on the natural numbers, he discussed possible applications to geometry, analysis, mechanics, physics of motion, and philosophy. The precise notation of Frege was introduced in Concept Script (Begriffschrift) in 1879. This was a two-dimensional notation whose powers he compared to a microscope. The framework in which he set up his Concept Script was quite simple -- we live in a world of objects and concepts, and we deal with statements about these in a manner subject to the laws of logic. Thus Frege had only one model in mind, the real world. Let us refer to this as the absolute universe. From this he was going to distill the numbers and their properties. The absolute universe approach to mathematics via logic was dominant until 1930 -- we see it in the work of Whitehead and Russell (1910-1913). His formal system with two-dimensional notation had the universal quantifier, negation, implication, predicates of several variables, axioms for logic, and rules of inference. The explicit universal quantifier, predicates of several variables and the rules of inference were new to formal systems!

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