The problem of reconciling a reversible micro-dynamics with the second law of thermodynamics has been a scientific and conceptual challenge for centuries and it continues to animate heated debate even today. In my opinion, one key point lays in the interrelation between the physical, the mathematical and the philosophical aspects of the problem. In many treatments those domains of knowledge dangerously mix, generating confusion and misunderstanding. In this short work I will show how disentangling these three domains for the problem (...) at hand will give a better understanding of the enigma of irreversibility and opens up possibility for future research. (shrink)