Switch to: References

Citations of:

A Note on Priest's Finite Inconsistent Arithmetics

J. B. Paris & N. Pathmanathan

Journal of Philosophical Logic 35 (5):529-537 (2006)

Add citations

You must login to add citations.

Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.details We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...) Download Export citation Bookmark 9 citations
On LP -models of arithmetic.J. B. Paris & A. Sirokofskich - 2008 - Journal of Symbolic Logic 73 (1):212-226.details We answer some problems set by Priest in [11] and [12], in particular refuting Priest's Conjecture that all LP-models of Th(N) essentially arise via congruence relations on classical models of Th(N). We also show that the analogue of Priest's Conjecture for I δ₀ + Exp implies the existence of truth definitions for intervals [0,a] ⊂ₑ M ⊨ I δ₀ + Exp in any cut [0,a] ⊂e K ⊆ M closed under successor and multiplication. Download Export citation Bookmark 7 citations
Is there an inconsistent primitive recursive relation?Seungrak Choi - 2022 - Synthese 200 (5):1-12.details The present paper focuses on Graham Priest’s claim that even primitive recursive relations may be inconsistent. Although he carefully presented his claim using the expression “may be,” Priest made a definite claim that even numerical equations can be inconsistent. His argument relies heavily on the fact that there is an inconsistent model for arithmetic. After summarizing Priest’s argument for the inconsistent primitive recursive relation, I first discuss the fact that his argument has a weak foundation to explain that the existence (...) Download Export citation Bookmark
On elimination of quantifiers in some non‐classical mathematical theories.Guillermo Badia & Andrew Tedder - 2018 - Mathematical Logic Quarterly 64 (3):140-154.details Elimination of quantifiers is shown to fail dramatically for a group of well‐known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by moving to more extensional underlying logics can we get the property back. Download Export citation Bookmark
Wittgenstein on Incompleteness Makes Paraconsistent Sense.Francesco Berto - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 257--276.details I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) Download Export citation Bookmark 7 citations
Can Gödel's Incompleteness Theorem be a Ground for Dialetheism?Seungrak Choi - 2017 - Korean Journal of Logic 20 (2):241-271.details Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest’s argument for Dialetheism from Gödel’s theorem is unconvincing as the lesson of Gödel’s proof (or Rosser’s proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest’s inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying Gödel sentence to the inconsistent and complete theory of arithmetic. We argue, (...) Download Export citation Bookmark 3 citations
Axioms for finite collapse models of arithmetic.Andrew Tedder - 2015 - Review of Symbolic Logic 8 (3):529-539.details The collapse models of arithmetic are inconsistent, nontrivial models obtained from ℕ and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom system for (...) Download Export citation Bookmark 4 citations
The Scope of Gödel’s First Incompleteness Theorem.Bernd Buldt - 2014 - Logica Universalis 8 (3-4):499-552.details Guided by questions of scope, this paper provides an overview of what is known about both the scope and, consequently, the limits of Gödel’s famous first incompleteness theorem. Download Export citation Bookmark 1 citation
New arguments for adaptive logics as unifying frame for the defeasible handling of inconsistency.Diderik Batens - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 101--122.details Download Export citation Bookmark 1 citation

1