Developing a Fundamental Theoretical Definition for Athletic Injury

Metaphysics, Logic, and Mathematics

Abstract

Athletic injury remains inadequately conceptualised and poorly defined. Existing definitions are overly vague and lack conceptual and logical coherence, failing to provide sufficient frameworks for their formalisation and the development of more precise understandings, operationalisations (including mathematisation) and identifications of athletic injury and associated concepts. This undermines the critical scientific principles of predictability, falsifiability, and reproducibility. Furthermore, related concepts that are often integrated into various operational definitions of athletic injury, such as pain and athlete availability, are commonly conflated as fundamental criteria. To address these concerns, this article proposes a new theoretical definition of athletic injury, developed through a systematic process of metaphysical inquiry grounded in Aristotelian logic. This approach employs well-established tools such as thought experiments, boundary tests, and logical reasoning to test for conceptual and logical coherence in existing definitions, and to establish a set of necessary and sufficient conditions for an athletic injury to exist. Through this process, commonly conflated concepts (Symbebekós, ‘accidental properties’) are examined for logical independence and disentangled, and the development of a more refined conceptualisation and definition of athletic injury is achieved, capturing its fundamental essence (To ti ēn einai, ‘what it is to be’) as "Tissue damage and loss of physical function during sports participation, resulting from singular, sustained, or repetitive transfer of mechanical energy, where the damage experienced is not a normal part of the physical training and positive adaptation process, but exceeds the threshold of mechanical and physiological tolerance. This is dependent upon the nature and degree of tissue damage sustained." By introducing a demarcating threshold of tissue damage and loss of physical function to distinguish athletic injury from non-injury, this definition aligns athletic injury more closely to the definitions of (general) injury proposed by the World Health Organization and International Classification of Diseases. Furthermore, by grounding athletic injury in objectively measurable physical parameters that can be appropriately mathematised for inclusion in mathematical (e.g., predictive) models, and that also function within a unified physics-based framework, athletic injury can be mathematically defined as occurring when the damage (D) experienced by a tissue exceeds a critical damage threshold (Dc), i.e., D > Dc. Here, D = 0 corresponds to an undamaged state and D = 1 corresponds to complete tissue failure. This definition lays the foundation for a formalised linguistic system and semantic network for mathematical modelling (e.g. predictive modelling), defining athletic injury and related concepts within a mathematical framework with precisely defined relationships. This increase in precision significantly enhances the predictability, falsifiability, and reproducibility of athletic injury research, paving the way for advancements in assessment technologies and data analysis methods that improve the identification, measurement, and prediction of athletic injuries and associated concepts.