David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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odel’s incompleteness results apply to formal theories for which syntactic constructs can be given names, in the same language, so that some basic syntactic operations are representable in the theory. It is now customary to derive these results from the ﬁxed point theorem (also known as the reﬂection theorem), which asserts the existence of sentences that “speak about themselves”. Let T be the theory and, for each wﬀ φ, let pφq be the term that serves as its name. Then the theorem says that, for any wﬀ α(v) (with one free variable), there exists a sentence β for which: T ` β ↔ α(pβq) β is sometimes called the ﬁxed point of α(v). All that is needed for the ﬁxed point theorem is..
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Paolo Cotogno (2009). A Brief Critique of Pure Hypercomputation. Minds and Machines 19 (3):391-405.
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