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## On Gupta-Belnap Revision Theories of Truth, Kripkean Fixed Points, and The Next Stable Set. (2001)

Venue: | in Bulletin of Symbolic Logic, 7, No.3 |

Citations: | 4 - 1 self |

### Citations

237 |
Admissible Sets and Structures
- Barwise
- 1975
(Show Context)
Citation Context ...es, and some partial results about the scope of such definitions. We give an explicit approach, mirroring the theory of monotone inductive definitions and the theory of the "next admissible set&q=-=uot; (cf. [2]-=-,[15]) that yields a reasonably complete account. (iii) A rapprochement with Kripke. We propose an approach (realistic variance) to introducing variance into revision sequences that solves many of the... |

218 | Outline of a theory of truth - Kripke - 1975 |

194 |
Elementary induction on abstract structures
- Moschovakis
- 1974
(Show Context)
Citation Context ...and some partial results about the scope of such definitions. We give an explicit approach, mirroring the theory of monotone inductive definitions and the theory of the "next admissible set"=-= (cf. [2],[15]-=-) that yields a reasonably complete account. (iii) A rapprochement with Kripke. We propose an approach (realistic variance) to introducing variance into revision sequences that solves many of the puzz... |

95 | Theory of Recursive Functions and E�ective Computability - Rogers - 1992 |

76 | The Revision Theory of Truth - Gupta, Belnap - 1993 |

55 |
Notes on naive semantics
- Herzberger
- 1982
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Citation Context ...h] has a transitive 2 end extension; (ii) The supremum of the infinite time Turing machine "eventually writable" ordinals using as oracle h; (iii) The starting point of the "Herzberger=-= Grand Loop" ([9]) based on-=- initial hypothesis h. (iv) The closure ordinal of arithmetical-in-h quasi-inductive definitions. Of course, from the viewpoint we are adopting it makes no sense to "average out" such truth ... |

53 |
Truth and Paradox
- Gupta
- 1982
(Show Context)
Citation Context ...], or [14]. x2. Revision Theories of Truth and Definability. Belnap and Gupta in their book develop a general theory of circular definitions. This arose out of their earlier theory of truth, (cf. [3],=-=[7]-=-) which construed the Tarskian Truth Biconditionals as being definitional of truth. Briefly: Let L be a first order language, and let L + be the language with a possibly infinite set of new predicate ... |

36 |
The truth is never simple
- Burgess
- 1986
(Show Context)
Citation Context ... -definable. [8] considered at 5D.7 the question of providing an axiomatisation of S # . One can deduce a negative answer to this (well at least directly for S ) from an earlier result of Burgess [4] who showed that the set of stable truths over N formed a complete 1 2 set. Kremer also solved this negatively as follows: (ii) For any 1 2 set of integers X , there is a finite set of positive de... |

20 |
Set Theory”, Pure and Applied Mathematics
- Jech
- 1978
(Show Context)
Citation Context ...e ~s . We express this by saying that s should be definable in a 1 2 -way in a code for the wellordered sequence hs jsi. (The set of such codes forms a 1 1 set of reals, see for example, [11],x40.) THEOREM 2.1. Let S be S # or S ; let be any 1 2 -definable (in the codes) limit rule (this includes any of H ; G ; B ). The class of S -definable reals is precisely that of the 1 2 reals;... |

16 | 2004: ‘Semantics and the Liar Paradox - Visser |

11 | Revision sequences and computers with an infinite amount of time
- Löwe
(Show Context)
Citation Context ...atural numbers augmented ¨ with a � predicate symbol . Let be � a formula with one free variable in this language. Let ��� be defined by � � � � ����� ����� ������ � � � � � ¨ The question arises (in =-=[13]-=-), what kinds of sets � � � of natural numbers are or definable � for � various as is allowed ��� � to vary? We may show that the strongly ��¢ ¤ definable sets � extend throughout regardless of the ��... |

10 |
Gupta's rule of revision theory of truth
- Belnap
- 1982
(Show Context)
Citation Context ...,[16], or [14]. x2. Revision Theories of Truth and Definability. Belnap and Gupta in their book develop a general theory of circular definitions. This arose out of their earlier theory of truth, (cf. =-=[3]-=-,[7]) which construed the Tarskian Truth Biconditionals as being definitional of truth. Briefly: Let L be a first order language, and let L + be the language with a possibly infinite set of new predic... |

8 |
paradox: An essay on the logic of truth
- Truth
- 1991
(Show Context)
Citation Context .... Again we hope to discuss the ramifications of these results elsewhere. For an introduction to both the Kripkean theory and to revision theories the reader may refer to the accounts of [17],[16], or =-=[14]-=-. x2. Revision Theories of Truth and Definability. Belnap and Gupta in their book develop a general theory of circular definitions. This arose out of their earlier theory of truth, (cf. [3],[7]) which... |

6 |
The Gupta-Belnap systems S# and S* are not Axiomatisable’, Notre Dame
- Kremer
- 1993
(Show Context)
Citation Context ...ch we leave here for the reader.) Antonelli ([1]) gives explicit revision theoretic sets of definitions D for each of the complete 0 n sets, i.e. for each level of the arithmetic hierarchy. Kremer ([=-=12-=-] x8) gives an argument of Gupta showing that this result can be extended to the inductive sets: (i) Inductively definable subsets of N are S # and S -definable. [8] considered at 5D.7 the question o... |

6 |
Semantics and the liar paradox, in: Handbook of Philosophical Logic, edited by D
- Visser
- 1989
(Show Context)
Citation Context ...icate. Indeed there are several accounts of semantical approaches to this problem and that of the Tarskian Liar which broadly speaking split the semantical theories into these two camps (for example, =-=[17]-=-,[16]). The tenor of the results here is threefold. (i) Revision theories of truth are complicated. Revision theories of truth (one should speak of theories as there are a class of theories based upon... |

5 | Alternative revision theories of truth - Chapuis - 1996 |

4 |
A Guide to Truth Predicates in the Modern Era
- Sheard
- 1994
(Show Context)
Citation Context .... Indeed there are several accounts of semantical approaches to this problem and that of the Tarskian Liar which broadly speaking split the semantical theories into these two camps (for example, [17],=-=[16]-=-). The tenor of the results here is threefold. (i) Revision theories of truth are complicated. Revision theories of truth (one should speak of theories as there are a class of theories based upon vari... |

4 | On Revision Operators
- Welch
- 2003
(Show Context)
Citation Context ...able truth sets that are also Kripkean fixed points. The results here are all of a technical nature (although some are of a "soft" variety) and so no proofs will be given. These will appear =-=elsewhere [18]-=-. There is also little discussion of the philosophical issues involved, or proposed. Again we hope to discuss the ramifications of these results elsewhere. For an introduction to both the Kripkean the... |

3 | A revision-theoretic analysis of the arithmetical hierarchy
- Antonelli
- 1994
(Show Context)
Citation Context ...= h, then '(x) is stably false in 1. That is, for all sufficiently large hM; s i j= :'[x] ([8] 5D.18 actually defines the analogous version for S # which we leave here for the reader.) Antonelli ([1=-=-=-]) gives explicit revision theoretic sets of definitions D for each of the complete 0 n sets, i.e. for each level of the arithmetic hierarchy. Kremer ([12] x8) gives an argument of Gupta showing that... |

3 |
Recursion on abstract structures, The handbook of computability theory
- HINMAN
- 1999
(Show Context)
Citation Context ...rue these as "eventually writable" for some generalised computation over the structure M (much as can be done for ordinary computations over suitable structures - see, for example Hinman's a=-=rticle in [10].) In a se-=-nse to name this (or the realistically varied theory of the previous section) a "generalisation" of the Kripkean supervaluation theory is a misnomer, since not all j vF fixed points occur as... |

3 |
The Liar Speaks the Truth. A Defense of the Revision Theory of Truth
- Yaqub
- 1993
(Show Context)
Citation Context ...ecisely that of a ¡�¢ ¤ complete set. (This answers Problem 32 of [12]). 3. Fully varied sequences. Stronger, and as we shall see, much more complex semantical systems are afforded by Yaqūb sequences =-=[20]-=- and the fully varied (fv) sequences suggested by Belnap & Gupta [8], p.168) and discussed in Chapuis [5]. The authors are only considering sequences based on the revision function ��� - the evaluatio... |

2 |
The revision theory of truth, M.I.T
- GUPTA, BELNAP
- 1993
(Show Context)
Citation Context ... s 0 = h, and 1 is officially at least the length of all the ordinals. The gap in this brief sketch is what to do at limit stages of this process. A number of views have been expressed (summarised in =-=[8]), as the theory evo-=-lved, but in all cases some kind of "bootstrapping policy" or "limit rule", let us call it here , is invoked to tell us how how to handle limits and to define the sequence of exten... |

2 |
Revision sequences and computers with an infinite amount of time
- OWE
(Show Context)
Citation Context ...natural numbers N augmented with a predicate symbol _ s. Let '(v 0 ) be a formula with one free variable in this language. Lets' be defined bys' (s) = fn j hN; si j= '( _ n)g: The question arises (in =-=[1-=-3]), what kinds of sets of natural numbers are S or S # definable for various as ' is allowed to vary? We may show that the strongly definable sets extend throughout 1 2 regardless of the choice of ... |

2 |
The liar speaks the truth. a defense of the revision theory of truth
- UB
- 1993
(Show Context)
Citation Context ...cisely that of a complete 1 2 set. (This answers Problem 32 of [12]). x3. Fully varied sequences. Stronger, and as we shall see, much more complex semantical systems are afforded by Yaqub sequences [=-=20-=-] and the fully varied (fv) sequences suggested by Belnap & Gupta [8], p.168) and discussed in Chapuis [5]. The authors are only considering sequences based on the revision functions - the evaluation ... |

1 |
Minimality in the 2 -degrees
- FRIEDMAN
- 1974
(Show Context)
Citation Context ...on of strongly revision theoretically definable over N, in the sense of 2.3 (ii), with that of " 1 2 -definable". The theory of the latter reducibility is known to be independent of ZF (cf. =-=Friedman [6]-=-). Remark: 5 Similar considerations to that of the theorem show that if, for example, L is the language of Arithmetic (or any recursive language that has REVISION THEORIES OF TRUTH AND KRIPKEAN FIXED ... |

1 | Barwise,\Admissible Sets and Structures - Jon |

1 | P.Burgess,The Truth is never simple - John - 1986 |

1 | Two theorems concerning stability in \Truth or Consequences: Essays in honor of Nuel Belnap - Gupta - 1990 |

1 | Revision Sequences and Computers with an In Amount of Time - owe - 1999 |

1 | Eventually In Time Turing Degrees: in time decidable reals - Welch - 2000 |