Depicting Falsifiability in Algebraic Modelling

Achim Schlather and Martin Schlather ()
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Achim Schlather: Institute of Mathematics, University of Jena, 07743 Jena, Germany
Martin Schlather: Institute of Mathematics, University of Mannheim, 68131 Mannheim, Germany

J, 2025, vol. 8, issue 3, 1-23

Abstract: This paper investigates how algebraic structures can encode epistemic limitations, with a focus on object properties and measurement. Drawing from philosophical concepts such as underdetermination, we argue that the weakening of algebraic laws can reflect foundational ambiguities in empirical access. Our approach supplies instruments that are necessary and sufficient towards practical falsifiability. Besides introducing this new concept, we consider, exemplarily and as a starting point, the following two fundamental algebraic laws in more detail: the associative law and the commutative law. We explore and analyze weakened forms of these laws. As a mathematical feature, we demonstrate that the existence of a weak neutral element leads to the emergence of several transversal algebraic laws. Most laws are individually weaker than the combination of associativity and commutativity, but many pairs of two laws are equivalent to this combination. We also show that associativity and commutativity can be combined to a simple, single law, which we call cyclicity. We illustrate our approach with many tables and practical examples.

Keywords: magma; hemi-associativity; hemi-commutativity; epistemic limitation; measurement (search for similar items in EconPapers)
JEL-codes: I1 I10 I12 I13 I14 I18 I19 (search for similar items in EconPapers)
Date: 2025
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