منابع مشابه
A Fundamental Flaw in an Incompleteness Proof by George Boolos
This paper addresses a proof of incompleteness published by George Boolos. An analysis of this proofs demonstrates that there is an elementary error in the proof; the proof relies on the unproven assumption that the formal system can selfreference its own formulas.
متن کاملFrege, Boolos, and Logical Objects
∗This paper was published in the Journal of Philosophical Logic, 33/1 (2004): 1–26. The authors would like to thank C.A. Anderson, Thomas Hofweber, Jeffrey Kegler, and Kai Wehmeier for their comments on this paper. The paper was presented in its current form at the Seminar für Philosophie, Logik, und Wissenschaftstheorie, Universität München. We gratefully acknowledge the audience feedback. †An...
متن کاملBoolos-style proofs of limitative theorems
In his famous paper announcing the incompleteness theorem, Gödel remarked that, though his argument is analogous to the Richard and the Liar paradoxes, “Any epistemological antinomy could be used for a similar proof of the existence of undecidable propositions.” ([7] Note 14). It is interesting that, despite the fact that the soundness of arguments like Gödel’s one built on self–reference (or d...
متن کاملGeorge
not much worried whether they be right or wrong. His desire to be the center of attraction may lead him to do things considered irrational when viewed from other angles. If he is in the upper 10 per cent of his class at school, it might be well to advance him to the next grade, provided he is sufficiently interested to show that he is capable of doing the work. If convenient, the teacher should...
متن کاملThe Curious Inference of Boolos in Mizar and OMEGA!
We examine Boolos’ curious inference and formalize it in a system based on set theory (Mizar) and a system based on classical higher-order logic (OMEGA). The Boolos example is interesting because while it can in principle be proven using a complete first-order calculus, it is impractical to do so. In our case study we are interested in aspects such as how natural and at what level of granularit...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1999
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1039096302