The incomplete universe : totality, knowledge, and truth
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Bibliographic Information
The incomplete universe : totality, knowledge, and truth
MIT Press, c1991
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Note
"A Bradford book."
Includes bibliographical references (p. [155]-162) and index
Description and Table of Contents
Description
The central claim of this powerful philosophical exploration is that within any logic we have, there can be no coherent notion of all truth or of total knowledge. Grim examines a series of logical paradoxes and related formal results to reveal their implications for contemporary epistemology, metaphysics, and the philosophy of religion. He reaches the provocative conclusion that, if the universe is thought of in terms of its truths, it is essentially open and incomplete. The Incomplete Universe includes detailed work on the liar paradox and recent attempts at solution, Kaplan and Montague's paradox of the knower, the Goedel theorems and related incompleteness phenomena, and new forms of Cantorian argument. The emphasis throughout is philosophical rather than formal, with an eye to connection's with possible worlds, the notion of omniscience, and the opening lines of the Tractatus: "The world is all that is the case. "
Table of Contents
- Introduction - some philosphical fragments. Part 1 Apparent lessons of the liar: totality, truth and the liar
- possible worlds
- the divine liar
- possible ways out
- truth-value gaps, many-valued logics, and strengthened liars
- the propositional response
- accepting inconsistency
- the appeal to hierarchy
- barwise and etchemendy
- conclusion. Part 2 Truth, omniscience, and the paradox of the knower: the paradox of the knower
- the argument
- the power of the paradox
- possible ways out
- propositions and the strengthened knower
- redundancy theories and operators
- hierarchy
- conclusion. Part 3 Epistemic incompleteness: some ideal knowers and the standard Godel result
- beyond standard systems
- expressive incompleteness
- a cantorian generalization of Godel's incompleteness theorem
- conclusion. Part 4 Classes and quantification - the cantorian argument: there is no set of all truths
- extensions and applications
- alternative set theories - a possible way out?
- the problem without power sets
- the appeal to quantification
- a self-reflective problem for the central thesis?
- conclusion. Part 5 Concluding notes: philosophical fragments
- within any logic we have ...
- some twilight speculations.
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