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In the first half of the 20th Century two systems were developed which proposed that every sentence (in any language) could be translated into them. Russell and Whitehead in 1913 published the "Principia". In this book Russell and Whitehead laid out a system in which any sentence could be converted into a symbolic sentence, using a quantifier and a limited number of functions, which would give an absolutly clear meaning to any sentence. For Example the sentence "All computers are good" would be translated into the symbolic sentence - Ux (Cx->Gx), where U is the universal quantifier (i.e. meaning for EVERY ONE of these), and -> is the function If...Then. So the clarified statement is read "For Every X (if X is a Computer, then X is Good)". For particular statements, that is about ONE or a LIMITED number of things, as in the statement "This computer is good", the translation would appear like this - Ex (Cx + Gx). Reading this symbolic statement becomes "There exists an X (where X is a computer and X is good)". Using all of the functions, and with the proper amount of work by the Logician (you, that is!), every sentence uttered may be rendered, regardless of its complexity, into this system. Alan Turing in 1937 published his paper "On computable Numbers". In this paper he showed that all sentences in any language can be converted in to a sequence of numbers using only 0 and 1. Using a machine to carry out the translation of sentences the state of translations would move the machine from one state to another. This machine, the famous Turing Machine, was conceived by Turing as the penultimate translation device and showed us not only that a machine could be constructed in this fashion, but indicate something about how things are carried out by us (humans) ourselves. |
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