In this case, it refers to "the present," and the subject of would show is "a candid examination of past experience." This sentence means:
We assume that the present is a better guide to the future than a frank look at
the past tells us it is.
That is, in the past until now, we have not been able to make good predictions about the future based on information we have in the present. However, we are assuming for what we are doing now that we are able to make accurate predictions about the future from the information we have in the present.
I hope that these definitions in particular will be helpful (from Oxford Dictionaries):
Demonstrate or prove:
"Experts say this shows the benefit of regular inspections"
[WITH CLAUSE]: "the figures show that the underlying rate of inflation
continues to fall"
Until now or until the point in time under discussion:
"Hitherto part of French West Africa, Benin achieved independence in 1960"