On the alternatives to the ideal mathematical points-like separatedness

TL;DR

This paper critiques a fuzzy logic-based approach to modeling physical systems as an alternative to ideal point-based models, highlighting potential misconceptions and clarifying conceptual differences.

Contribution

It analyzes the limitations of fuzzy set models in representing physical phenomena and clarifies how this approach differs from traditional point-based models.

Findings

Fuzzy set models may be misleading in physical system representations

The approach challenges traditional notions of points, sets, and continuity

It questions the suitability of classical concepts for natural phenomena description

Abstract

In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a non-classical logic, in particular the fuzzy sets theory, with events represented as spatiotemporally blurred blobs. Here we point out and discuss a number of aspects of this imperfect symbolic description that might potentially be misleading. Besides that, we analyze its relation to various concepts used commonly to model physical systems, denoted by terms like: point, set, continuous, discrete, infinite, or local, clarifying further how our viewpoint is different and asking whether, in light of our main postulate, any of these notions, or their opposites, if exist, are in their usual meanings suitable to accurately describe the natural phenomena.