Abstract
Some truth theories allow to represent and prove generalized statements as “all that you said is true” or “all theorems of \({\mathbf {PA}}\) are true” in the sense of deflationism.
I swear, in the kingdom of generalities, you could be imperius rex. (Haruki Murakami “A Wild Sheep Chase”)
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Notes
- 1.
We note that this is the same reason why unrestricted form of the coinductive datatype implies a contradiction in Martin-Löf’s intuitionistic type theory.
- 2.
Contrary, \((\mathbf {Tr}(A)\rightarrow \mathbf {Tr}(B))\rightarrow (\mathbf {Tr}(A\rightarrow B))\) is not problematic. Merging two streams is a typical guarded correcursive function.
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Yatabe, S. (2017). Truth as a Logical Connective. In: Otake, M., Kurahashi, S., Ota, Y., Satoh, K., Bekki, D. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2015. Lecture Notes in Computer Science(), vol 10091. Springer, Cham. https://doi.org/10.1007/978-3-319-50953-2_13
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