Debajyoti Gangopadhyay

Developments of quantum mechanics during the first three decades of the last century led most fundamentally to different orders of difficulties in the spatio-temporal modes of description. And, as a consequence, ambiguities in the meaning of quantum mechanical are in sight for the first time. So the question (from logico-philosophical grounds) we were left as back as late 20s of the last century – a question methodologically prior to all other questions - How to talk about quantum particles [in a Language] which are not instantiation of spatio-temporal is or ONE of their particular kind? Though not popular among the physicists, philosophers often use the phrase failure of principles of Individuation or ontological priorities of individual to describe this situation. Within the intended scope of this volume, we need not give the technical details of this failure here. We are basically narrating here a non-technical story outline of the way quantum mechanical language messes with standard logic and set theory embedded with the concept of unambiguous is, and the possible consequences.

This article is intended mainly to develop an expository outline of an inherently inconsistent reasoning in the development of quantum mechanics during 1920s, which set up the background of proposing different variants of quantum logic a bit later. We will discuss here two of the quantum logical variants with reference to Hilbert space formulation, based on the proposals of Bohr and Schrödinger as a result of addressing the same kernel of difficulties and will give a relative comparison. Our presentation is fairly informal, as our goal here is to simply sketch the central ideas leaving further details for other occasions. Quanta 2022; 11: 28–41.

We will argue here, that one of the salient messages of standard quantum formalism implies a failure of Classical Theory of Knowledge (hereafter CTK) which is primarily based on the presumption that, our knowledge is predetermined by Nature. This failure provides pointers against the classically held ontological definiteness of future. Quantum formalism admits interpretation , that suggests, that there is no such thing as ‘universal global present’ in the sense of being able to confirm a complete set of facts of matter about it, unless this is coupled with a specific observation recipe.

As the process of formation of knowledge is a perennial concern of philosophical investigation, any systematic study of philosophy, irrespective of Eastern and Western origins, starts with a thorough assessment of our valid means of cognition. Needless to say, that our means of cognitions play a crucial role in scientific knowledge formation also. But the question of delimiting clearly the objective means of cognition from the subject of cognition continues to stimulate epistemological troubles. This has been dramatized after quantum mechanics. Founding fathers of quantum mechanics as well as the philosophers of science continued to reflect upon the enigmatic dividing line between subjective and objective. It was tried to give a purely logico-empirical objective foundation of the whole spectrum of our knowledge including the scientific. This attempt failed! Here we will give a brief overview of the problem area and the current standpoints - whether we have reached any reasonably better consensus nearly after 2000 years of debate on this.