Is (P OR Q) logically equivalent to (Q OR P)?

This is the opening gambit used by abb3w [1] to assess an individual's grounding in logic and science, and the reference point he uses to know exactly how to debate one of his detractors.

The statement is the first of the Robbins axioms, from which we get the foundation of Boolean logic. abb3w [2] went through the whole schtick once, here (Fark Link) (starting with Samurai_Goat [3] yelling "Huuuaaaaahhhh!").

These axioms are the foundation of all science, and therefore cannot be proven, and must be taken on faith. Not much faith, but faith nonetheless. They describe that evidence is a reflection of reality.

Is the phrase "would you like a pear or a quince?" logically equivalent to the phrase "would you like a quince or a pear?"
Both questions provide for three answers: a pear, a quince, or both a pear and a quince.

I was told there would be no math.

The next three axioms are:

  • 'P OR (Q OR R)' = '(P OR Q) OR R'
  • 'NOT P' = 'P NOR P'
  • 'P NOR Q' = 'NOT (P OR Q)'

Note that once we have the first two principles, we can start making (not very interesting) inferences, such as (P NOR Q) NOR (P NOR R) = P OR (Q AND R).

We can prove God does not exist to the same degree we can prove your brains are not made of cauliflower.