Vague Objects in Quantum Mechanics?

Peter J. Lewis

Thomas Bittner

The successful application of quantum probability in cognitive science has been persistently challenged by the foundational 'why quantum?' question. In this paper, a novel answer is proposed through the development of an ontological grounding for the quantum-like structures observed in human judgment. It is argued that these cognitive structures may be a direct reflection of an objective, information-theoretic vagueness inherent in the macroscopic world. To formalize this, 'Quantized Mereology' is developed - a framework inspired by Rovelli's Relational Quantum Mechanics (RQM), where determinate mereological facts about vague entities like forests and clouds are established relationally through an act of judgment. The framework uses a real-valued Hilbert space as a precise object language, which is given meaning by a partition-theoretic meta-language. A key contribution is a defense of the real-valued structure, in which it is argued that the physical constraints necessitating complex numbers in microphysics constitute a category error when applied to the conceptual systems modeled herein. The result is a generative model for objective vagueness that provides a candidate ontological foundation for quantum cognition.

Pankaj Sharan

Christian Alafaci

While classical accounts of identity (‘classical’ here pertaining to both logics and physics) are generally well understood, the advent of quantum theory, specifically quantum statistics, has cast shadow over these conceptions. Dealing with the consequently surfacing problems is a philosophically rich and interesting enterprise. I begin this thesis by providing an exegesis of the roles played by, and features of, identity in logics, classical physics, and quantum physics. Therein I consider how under a quantal description of reality, classical notions of identity and individuality break down. In the second chapter, I address how this problem has launched an arc of thought in analytic metaphysics and formal philosophy motivating the development of non-standard formal frameworks with which philosophical sense can be made of quantal objects. Among these, I explore and critically evaluate quaset theory, quasi-set theory, and non-reflexive Schr¨odinger logics, identifying some significant problems with quaset theory that arise in defining cardinality and later, pointing out a problem with Schr¨odinger logics in their modelling of the continuity between quantal and classical treatments of the world. The queer character of identity in the quantal regime motivates a turn to vagueness which I introduce in the third chapter, providing a brief outline of vagueness and the sorites paradox. Further, I reflect on the fundamental nature of vagueness, outlining and evaluating the semantic and ontic conceptions thereof. In the final chapter, I proceed to explicate and assess notions that identity and quantal objects can be vague. I shall discuss accounts according to which the vagueness of identity and quantum objects is posited as a feature of nature emerging in quantum systems — the ontic vagueness of identity — finding that these ideas are flawed and/or rely on misinterpretations of vagueness. Finally, I present an argument which suggests how the vagueness of identity can arise as an artifact of the differing treatments of identity in the quantal and classical regimes in which the vagueness involved can be semantic rather than ontic.

Pankaj Sharan

Hanoch Ben‐Yami

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning.