Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?
Bhupinder Singh Anand
Abstract
Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general, scientific, discourse cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic is verifiably complete. We show how some paradoxical concepts of Quantum mechanics can be expressed, and interpreted, naturally under a constructive definition of mathematical truth.
Create a lesson
Related papers
On the Rank Condition for Perfect Cuboids
Valery Asiryan
A Local Proof of Langlands's First Main Lemma for Local Epsilon Factors over Nonarchimedean Local Fields
Fukuhiro Ueda
The first type of power mean bounds for the Gaussian hypergeometric function
Zhen-Hang, Yang, Jing-Feng Tian
On a new class of q-fractional integral operators involving multivariate q-Mittag-Leffler functions
Min-Jie Luo, Qing-Hui Peng, Ravinder Krishna Raina
Partition-theoretic density formulas: radial Tauberian theory and non-radial instability
Mohammad F. Marashdeh
Octonionic Kittaneh Numerical Radius Inequalities
K. Mahesh Krishna