TY - JOUR

T1 - Analysis of Penrose’s Second Argument Formalised in DTK System

AU - Corradini, Antonella

AU - galvan, sergio

PY - 2021

Y1 - 2021

N2 - This article aims to examine Koellner’s reconstruction of Penrose’s
second argument a reconstruction that uses the DTK system to
deal with Gödel’s disjunction issues. Koellner states that Penrose’s argument
is unsound, because it contains two illegitimate steps. He contends
that the formulas to which the T-intro and K-intro rules apply are both
indeterminate. However, we intend to show that we can correctly interpret
the formulas on the set of arithmetic formulas, and that, as a consequence,
the two steps become legitimate. Nevertheless, the argument remains partially
inconclusive. More precisely, the argument does not reach a result
that shows there is no formalism capable of deriving all the true arithmetic
propositions known to man. Instead, it shows that, if such formalism exists,
there is at least one true non-arithmetic proposition known to the human
mind that we cannot derive from the formalism in question. Finally, we
reflect on the idealised character of the DTK system. These reflections
highlight the limits of human knowledge, and, at the same time, its irreducibility
to computation.

AB - This article aims to examine Koellner’s reconstruction of Penrose’s
second argument a reconstruction that uses the DTK system to
deal with Gödel’s disjunction issues. Koellner states that Penrose’s argument
is unsound, because it contains two illegitimate steps. He contends
that the formulas to which the T-intro and K-intro rules apply are both
indeterminate. However, we intend to show that we can correctly interpret
the formulas on the set of arithmetic formulas, and that, as a consequence,
the two steps become legitimate. Nevertheless, the argument remains partially
inconclusive. More precisely, the argument does not reach a result
that shows there is no formalism capable of deriving all the true arithmetic
propositions known to man. Instead, it shows that, if such formalism exists,
there is at least one true non-arithmetic proposition known to the human
mind that we cannot derive from the formalism in question. Finally, we
reflect on the idealised character of the DTK system. These reflections
highlight the limits of human knowledge, and, at the same time, its irreducibility
to computation.

KW - Disjunction

KW - Penrose

KW - Disjunction

KW - Penrose

UR - http://hdl.handle.net/10807/200127

U2 - 10.12775/LLP.2021.019

DO - 10.12775/LLP.2021.019

M3 - Article

SN - 2300-9802

VL - 2021

SP - 1

EP - 30

JO - Logic and Logical Philosophy

JF - Logic and Logical Philosophy

ER -