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Showing 1 to 7 of 7 for “"Incompleteness theorems"”.
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Godel's incompleteness theorems
<p>"Incompleteness or inconsistency? Kurt Godel shocked the mathematical community in 1931 when he proved any effectively generated, sufficiently complex, and sound axiomatic system could not be both consistent and complete. This thesis will explore two formal languages of logic and their …
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Mathematics, cognition, and you!
… claims that come in such forms as lemmas, theorems, or conjectures. These proofs can be accomplished through a variety of means including (though not limited to) logical deduction, geometric intuition, diagramming, or computer assistance. What is common to each of these is the …
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A Possible and Necessary Consistency Proof
After Gödel's incompleteness theorems and the collapse of Hilbert's programme Gerhard Gentzen continued the quest for consistency proofs of Peano arithmetic. He considered a finitistic or constructive proof still possible and necessary for the foundations of mathematics. For a proof to be …
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Modal logics of provability
Gödel proved his Incompleteness theorems for any theory 'strong' enough to represent recursive functions. In the process he showed that the provability predicate can be represented in such theories. Modal logics of provability are modal logics which attempt to express the concept of 'provability' …
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Beyond the material : rethinking the limits of reality through philosophy, science, and anthropology : is there something else?
… vulnerability to Hempel’s dilemma and Gödel’s incompleteness theorems. Then, developments in quantum physics are shown to challenge materialism’s core axioms, revealing fractures in its claim to provide a complete ontology. The second half turns to anthropological case studies, demonstrating …
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Carnap and the Ontology of Mathematics
… non-standard models, which relies on Gödel's incompleteness theorems and targets Carnap's claim that mathematics is analytic. I show that my reconstruction of Beth's argument is more charitable to the text than competing interpretations in the secondary literature, and argue that it is also …
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Gödel's incompleteness theorem
… aim of the thesis is to state and prove Gödel's Incompleteness Theorem for number theory"--Document.</p>