Why are the commutators for spin taken as postulates?

I am reading an Introduction to Quantum Mechanics by Griffiths and he says "The algebraic theory of spin is a carbon copy of the theory of orbital angular momentum", then states in the footnote that the commutation relations are postulates. This seems like a huge assumption to me that they are identical to the commutations for angular momentum. What justifies this assumption? Why can we not derive the commutation relations for spin?

• FWIW, the angular momentum operator ${\bf J}$ generates 3D rotations, and constitutes a representation of the Lie algebra $so(3)$ for 3D rotations. Commented Jan 2, 2020 at 21:01
• This question seems a duplicate of physics.stackexchange.com/questions/184027/… Commented Jan 2, 2020 at 22:01

They don't have to be postulated and follow from the main postulates of the Quantum Mechanics. Whenever you have a quantum state (i.e. wave function) different observers that are related to each other by rotations can observe the state and compute amplitudes with values independent of observer. The physical object is independent of the observer too, but its description naturally differs for two observers. Nevertheless the norm of the state has to remain invariant under such coordinate rotations therefore the rotations have to be represented by a unitary (or anti-unitary) operator. Representation theory tells us that $$SU(2)$$ is a unitary representation (double-cover) of $$SO(3)$$ and hence is appropriate for describing the spin (intrinsic angular momentum).