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- W2997475504 abstract "Harmony and conservative extension are two criteria proposed to discern between acceptable and unacceptable rules. Despite some interesting works in this field, the exact relation between them is still not clear. In this article, some standard counterexamples to the equivalence between them are summarized, and a recent formulation of the notion of stability is used to express a more refined conjecture about their relation. Then Prawitz's proposal of a counterexample based on the truth predicate to this refined conjecture is shown to rest on dubious assumptions. As a consequence, two new counterexamples are proposed: one uses the extension of logic with a small amount of arithmetic, while the other uses the extension of a small fragment of arithmetic with a problematic operator defined by Peano. It is argued that both these new counterexamples work fine to reject the conjecture and that the last one works also as a rejection of harmony as a complete criterion of acceptability of rules." @default.
- W2997475504 created "2020-01-10" @default.
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- W2997475504 date "2019-12-01" @default.
- W2997475504 modified "2023-09-27" @default.
- W2997475504 title "Peano's Counterexample to Harmony" @default.
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- W2997475504 doi "https://doi.org/10.1111/theo.12217" @default.
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