Why are some collections of fermions considered bosons? I read that He-4 is a boson because the four fermions in it add up to an integer spin—of zero—hence a boson.
Whereas I thought that if the parts are fermions, so is the whole.
Is an electron pair a boson? Can multiple such pairs occupy the same quantum state?
If the total spin of the atoms in my body adds up to an integer number, is my body a boson? Is it a fermion otherwise? Does it oscillate between the two as atoms enter and leave my body? I hope this silly example helps to explain where my confusion lies:
When does this adding up of the spins of the constituent particles to figure out the nature of the compound stop? And why does it not stop at the level of the atom?
 A: There are two different definitions of bosons. Sometimes they are simply defined as particles with an integer spin, but sometimes they are defined as particles having symmetric wave functions. Under the second definition, if some object, e.g., an alpha-particle, consists of an even number of fermions, it is only approximately a boson. Commutation relations for such objects differ from the canonical commutation relations for bosons. See, e.g., Lipkin's book "Quantum Mechanics: New Approaches to Selected Topics".
A: When something is made up of an even number of fermions, it behaves like a boson. It is because such an object needs and even number of fermion ladder operators. Although fermion ladder operators anti-commute, such products of even numbers of fermion ladder operators, commute. Therefore they behave like bosons.
It is not really about the spin. Sometimes the spin would combine into something else other than zero, and it would still behaves like a boson. The only thing about the spin is the fact that fermions always have half-integer spins, while bosons have integer spins. This follows form the spin-statistics theorem.
