Here's the problem: I was quite sure my cup would hold 8oz of coffee even before the presented evidence became available. Does that mean any experiments conducted by me on my coffee cup are necessarily flawed by my prejudice? Do I have to prove that I don't actually believe the cup will hold about 8oz in order to prove that it does?
No, as long as the experiment is set up in such a way that the outcome will accurately reflect the holding capacity of the cup regardless of what you believe about the cup, which makes it an empirical problem rather than one about logic.
If the experiment is to keep pouring until the cup is full and recording how much volume of liquid it took to fill the cup, there are a couple of potential outcomes:
1. The capacity is what it seems and the liquid volume equals the cup's interior volume.
2. The cup has a barely visible leak and no matter how much you pour the cup will never fill.
3. The cup is made of an absorbing material so the poured volume exceeds the capacity of the cup.
4. There is a mirror inside the cup which makes it appear larger or smaller than it really is.
5. There is a dimensional vortex at the cup's bottom which captures some of the liquid.
And so on. Whatever the case, the experiment will accurately determine the actual properties of the cup regardless of your biases, as long as the cup's volume and the volume of poured liquid are recorded accurately.