By your definition the dollar is worth nothing. Absolutely nothing. Too bad it's not true.
The argument is dubious.
*sigh*
No, a dollar is worth exactly the amount of work you put in to earn it, it is also worth the amount of goods you can trade it for. The underlying value of the dollar, and any currency, is the amount of work you will spend to earn it. Currently, the work for a BTC is the electricity input. You don't do anything to mine BTC, your GPU does.
So, a bitcoin that I mine is worth the cost of the electricity used to find it (production cost). But, a dollar isn't worth the cost of the paper it is printed on (production cost), it is worth the amount of effort that I put into getting it from someone else (exchange cost).
Why is a bitcoin valued at the cost of production, while the dollar is valued at the exchange cost?