What do you believe is true even though you cannot prove it?
Progress.
The enterprise that employs me, seeking to understand and apply insight into how the world works, is ultimately based on the belief that this is a good thing to do. But it's something of a leap of faith to believe that that will leave the world a better place—the evidence to date is mixed for technical advances monotonically mapping onto human advances.
Naturally, this question has a technical spin for me. My current passion is the creation of tools for personal fabrication based on additive digital assembly, so that the uses of advanced technologies can be defined by their users. It's still no more than an assumption that that will lead to more good things than bad things being made, but, like the accumulated experience that democracy works better than monarchy, I have more faith in a future based on widespread access to the means for invention than one based on technocracy.