Attempting to reason with a child of this age is FUTILE. I'll be vilified by child-protection advocates for this answer, but here goes: bite back! Clearly, the child has little or no idea of the painful effect of his actions -- NOT HIS FAULT, he's simply not at a stage of development where these effects register to him as such. He may bite out of frustration, to combat boredom, for personal entertainment, or simply as a world-exploration experiment. After all, the huge reaction we give to his tiny action must be fascinating and empowering. He finds he, with so little apparent ability to modify his world, can make a huge change to it with one teensy stunt.
Turn each incident into a game, a game that to him you clearly enjoy and look forward to repeating. As soon as he bites, say "Ohhh, the BITING game, what fun! MY TURN!" You then proceed to return the favor, in the same manner as it was paid (bite the same spot on his body where he bit you, and in the same way). Obviously, you bite back with the most GENTLE pressure you feel will still register to him as a bite, i.e. JUST ENOUGH to cause a negative reaction on his part. This will require experimentation to assess his pain threshold: start gently, and ramp up the pressure until he reacts with aversion.
He will likely react with surprise, astonishment and shock. He may wail and burst into tears. You then say, "Oh, I hurt you! I'm so sorry. I apologise. That wasn't very nice of me to do that." Alternatively, if he laughs and seems to enjoy it, laugh with him, but be aware that you may not have bitten with enough pressure to register to him as pain. Adjust your subsequent bite pressure accordingly. Then, if he bites again, simply repeat the exercise in exactly the same way.
This is a great learning opportunity for both of you. He will find out at least one effect of his actions towards other people, and you will learn how he reacts to direct, relevant and appropriate feedback on his actions.