My point was the fact that a resource is finite does not mean you can't grow it. If I am a child with a second-grade education- I have a finite amount of knowledge, but there are "tricks" (aka education, development) that I can do to increase my knowledge. If I have a pond in my backyard, there is a finite amount of water it can hold, but if I dredge out a few more hectares, it will store even more groundwater and its capacity has increased while still remaining finite (I cannot drink from it forever).
I understand your point about the meaning of 'finite'. My point simply is that those who primarily viewed willpower as a limited resource, finite and exhaustible, did not perform as well as those who believed that exercising willpower increases it. It is not about the nuances of a certain word but how certain attitudes affect performance.
Dweck wrote a popular book 'Mindset'
where she contrasts 'fixed' mindset with 'growth' mindset.
Perhaps 'fixed' makes more sense than 'finite' here.
More information at http://mindsetonline.com/