#artificial-intelligence #geb #goedel-escher-bach #hofstadter
What is a legal method of procedure, and what is an illegal one? Since mathematical reasoning had always been done in "natural language" (e.g., French or Latin or some language for normal communication), there was always a lot of possible ambiguity. Words had different meanings to different people, conjured up different images, and so forth. It seemed reasonable and even important to establish a single uniform notation in which all mathematical work could be done, and with the aid of which any two mathematicians could resolve disputes over whether a suggested proof was valid or not. This would require a complete codification of the universally acceptable modes of human reasoning, at least as far as they applied to mathematics. This was the goal of Principia Mathematica, which purported to derive all of mathematics from logic, and, to be sure, without contradictions! It was widely admired, but no one was sure if (1) all of mathematics really was contained in the methods delineated by Russell and Whitehead, or (2) the methods given were even self-consistent. Was it absolutely clear that con tradictory results could never be derived, by any mathematicians what soever, following the methods of Russell and Whitehead
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- owner: piotr.wasik - (no access) - Douglas Hofstadter "Goedel, Escher, Bach", p23
- owner: naraypv - (no access) - Gödel, Escher, Bach_ An Eternal Golden Braid-Basic Books (1994).pdf, p31
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