It is customarily assumed that paracomplete and paraconsistent solutions to liar paradoxes require a logical system weaker than classical logic. That is, if a logic is not fragile to liar paradoxes, it must be logically weaker than classical logic. Defenders of classical logic argue that the losses of weakening it outweigh the gains. Advocates of paracomplete and paraconsistent solutions disagree. We articulate the notion of fragility with respect to the liar paradox and show that it can be disentangled from logical strength. Strength and resilience to paradox do not force a trade-off with respect to liars: there can be logics which are not weaker than classical logic and are solid to the liar.

中文翻译：

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 脆弱性和强度


通常认为，对说谎者悖论的准完备和准一致解决方案需要比经典逻辑弱的逻辑系统。也就是说，如果一种逻辑对于说谎者悖论并不脆弱，那么它在逻辑上一定比经典逻辑弱。古典逻辑的捍卫者认为，削弱古典逻辑的损失大于收益。准完备和准一致解决方案的拥护者不同意。我们阐述了关于说谎者悖论的脆弱性概念，并表明它可以与逻辑强度分开。对悖论的强度和适应能力不会迫使说谎者进行权衡：可能存在不弱于经典逻辑并且对说谎者来说是可靠的逻辑。