brain would in itself be an admission of ignorance regarding intelligence and the nature of the mind, like trying to build a jet airliner by copying a living bird precisely, feather by feather, with no theoretical understanding of aeronautical engineering. Human thinking is symbol processing In 1963, Allen Newell and Herbert A. Simon proposed that "symbol manipulation" was the essence of both human and machine intelligence. They wrote: "A physical symbol system has the necessary and sufficient means of general intelligent action." This claim is very strong: it implies both that human thinking is a kind of symbol manipulation (because a symbol system is necessary for intelligence) and that machines can be intelligent (because a symbol system is sufficient for intelligence). Another version of this position was described by philosopher Hubert Dreyfus, who called it "the psychological assumption": "The mind can be viewed as a device operating on bits of information according to formal rules." The "symbols" that Newell, Simon and Dreyfus discussed were word-like and high levelsymbols that directly correspond with objects in the world, such as <dog> and <tail>. Most AI programs written between 1956 and 1990 used this kind of symbol. Modern AI, based on statistics and mathematical optimization, does not use the high-level "symbol processing" that Newell and Simon discussed. Arguments against symbol processing These arguments show that human thinking does not consist (solely) of high level symbol manipulation. They do not show that artificial intelligence is impossible, only that more than symbol processing is required. Gödelian anti-mechanist arguments In 1931, Kurt Gödel proved with an incompleteness theorem that it is always possible to construct a "Gödel statement" that a given consistent formal system of logic (such as a high-level symbol manipulation program) could not prove. Despite being a true statement, the constructed Gödel statement is unprovable in the given system. (The truth of the constructed Gödel statement is contingent on the consistency of the given system; applying the same process to a subtly inconsistent system will appear to succeed, but will actually yield a false "Gödel statement" instead.) More speculatively, Gödel conjectured that the human mind can correctly eventually determine the truth or falsity of any well-grounded mathematical statement (including any possible Gödel statement), and that therefore the human mind's power is not reducible to a mechanism. Philosopher John Lucas (since 1961) and Roger Penrose (since 1989) have championed this philosophical anti-mechanist argument. Gödelian anti-mechanist