A Note on Paradoxical Propositions from an Inferential Point of View

0546974 - FLÚ 2022 RIV GB eng C - Konferenční příspěvek (zahraniční konf.)
Pezlar, Ivo
A Note on Paradoxical Propositions from an Inferential Point of View.
The Logica Yearbook 2020. London: College Publications, 2021 - (Blicha, M.; Sedlár, I.), s. 183-199. ISBN 978-1-84890-376-0.
[Logica 2020. Hejnice (CZ), 15.06.2020-19.06.2020]
Grant CEP: GA ČR(CZ) GA19-12420S
Institucionální podpora: RVO:67985955
Klíčová slova: proof-theoretic semantics * constructive type theory * paradox * inductive definitions * Martin-Löf
Obor OECD: Philosophy, History and Philosophy of science and technology

In a recent paper by Tranchini (Topoi, 2019), an introduction rule for the paradoxical proposition ρ∗ that can be simultaneously proven and disproven is discussed. This rule is formalized in Martin-Löf’s constructive type theory (CTT) and supplemented with an inferential explanation in the style of Brouwer-Heyting-Kolmogorov semantics. I will, however, argue that the provided formalization is problematic because what is paradoxical about ρ∗ from the viewpoint of CTT is not its provability, but whether it is a proposition at all.
Trvalý link: http://hdl.handle.net/11104/0323342