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Incompleteness Books
Showing 1-4 of 4
Thinking about Gödel and Turing: Essays on Complexity, 1970-2007 (Hardcover)
by (shelved 1 time as incompleteness)
avg rating 4.33 — 24 ratings — published 2007
Gödel's Proof (Hardcover)
by (shelved 1 time as incompleteness)
avg rating 4.18 — 5,649 ratings — published 1958
An Introduction to Gödel's Theorems (Paperback)
by (shelved 1 time as incompleteness)
avg rating 4.33 — 61 ratings — published 2007
Gödel's Theorem: An Incomplete Guide to Its Use and Abuse (Paperback)
by (shelved 1 time as incompleteness)
avg rating 3.94 — 154 ratings — published 2005
“Thousands of incomplete writings are probably enough to represent the chaotic mind of mine!”
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“Instead of proving all possible theorems in an axiomatic system (which Kurt Gödel showed is not possible), professional mathematicians continue to use a formal presentation of mathematics to specify and prove many theorems that are amenable to the formalist paradigm. This has generated a vast corpus of formal theory.
Controversies continue unresolved. Some mathematicians continue to insist on giving explicit constructions of mathematical entities, and do not allow proof by contradiction. This is a valid approach in its own right with much to recommend it. In the end, however, the choice that is likely to lead to the greater conquests is the one that offers the greater power and at the moment, it is David Hilbert's formalism that continues to predominate, while steadily being expanded as mathematics expands."
-David Tall (2013, p. 246) thinks though Formalism (mathematics) may have Lost the Battle it Still may Win the War.”
― How Humans Learn to Think Mathematically: Exploring The Three Worlds Of Mathematics
Controversies continue unresolved. Some mathematicians continue to insist on giving explicit constructions of mathematical entities, and do not allow proof by contradiction. This is a valid approach in its own right with much to recommend it. In the end, however, the choice that is likely to lead to the greater conquests is the one that offers the greater power and at the moment, it is David Hilbert's formalism that continues to predominate, while steadily being expanded as mathematics expands."
-David Tall (2013, p. 246) thinks though Formalism (mathematics) may have Lost the Battle it Still may Win the War.”
― How Humans Learn to Think Mathematically: Exploring The Three Worlds Of Mathematics