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"Postulate 2. To every observable in classical mechanics there corresponds a linear, Hermitian operator in quantum mechanics. "

"Postulate 6. The total wavefunction must be antisymmetric with respect to the interchange of all coordinates of one fermion with those of another. Electronic spin must be included in this set of coordinates. The Pauli exclusion principle is a direct result of this antisymmetry principle."

What hermitian operator or observable does the pauli exclusion principle fall under? Is it position?

If nature had no position basis. Does it mean there was also no pauli exclusion principle?

One may wonder why I asked this. This is just to have versatile understanding of it from different points of views to get better handle of the concepts.