Definition of "irreducibility"

I gave them account of what I had seen of the case, of my opinion concerning the irreducibility of the rupture, and that it had no share in the present complaint; at the same time desiring my colleague to examine for himself.

1779, Percivall Pott, The Chirurgical Works of Percivall Pott, volume 3, page 305

There is plebs in bodies, in souls, in individuals, in the proletariat, in the bourgeoisie, but everywhere in a diversity of forms and extensions, of energies and irreducibilities.

1997, John S. Ransom, Foucault's discipline: the politics of subjectivity, page 130