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Classical recapture and maximality
Philosophical Studies Pub Date : 2020-08-18 , DOI: 10.1007/s11098-020-01517-9
Lucas Rosenblatt

The idea of classical recapture has played a prominent role for non-classical logicians. In the specific case of non-classical theories of truth, although we know that it is not possible to retain classical logic for every statement involving the truth predicate, it is clear that for many such statements this is in principle feasible, and even desirable. What is not entirely obvious or well-known is how far this idea can be pushed. Can the non-classical theorist retain classical logic for every non-paradoxical statement? If not, is she forced to settle for a very weak form of Classical Recapture, or are there robust versions of classical recapture available to her? These are the main questions that I will address in this paper. As a test case I will consider a paracomplete account of the truth-theoretic paradoxes and I will argue for two claims. First, that it is not possible to retain the law of excluded middle for every non-paradoxical statement. Secondly, that there are no robust versions of classical recapture available to the paracomplete logician.

中文翻译:

经典重获和最大化

经典重获的思想在非经典逻辑学家中发挥了突出的作用。在非经典真理论的特定情况下,虽然我们知道不可能为每个涉及真谓词的陈述保留经典逻辑,但很明显,对于许多这样的陈述,这在原则上是可行的,甚至是可取的。不完全明显或众所周知的是,这个想法可以推进到什么程度。非经典理论家能否为每个非悖论陈述保留经典逻辑?如果不是,她是否被迫接受一种非常弱的古典重获形式,或者是否有强大的古典重获形式可供她使用?这些是我将在本文中解决的主要问题。作为一个测试案例,我将考虑对真理论悖论的超完备说明,我将论证两个主张。首先,不可能为每个非悖论陈述保留排中律。其次,准完全逻辑学家没有可用的经典重获的稳健版本。
更新日期:2020-08-18
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