General evidence can prove generalizations. Specific evidence is required for specific propositions. The scope of sensory data that can tie a statement to reality (serve as evidence) varies with the scope of the statement.
If I make the statement, "All men have heads," then the scope of potential, direct evidence for this statement (and counterexamples) is all men. I can observe a few random men and have a sensory basis to at least hypothesize that "All men have heads," is true. (Exactly when I can logically say that a generalization is proven, is the subject of the epistemology of induction. While the principles of general induction are not yet fully known, the philosophy of Objectivism and the principles of modern science/technology show that induction works. I recommend Dr. Peikoff's course, Objectivism Through Induction.)
If, on the other hand, I make the statement that "Julius Oglethorpe III lives at 10 Warkworth Terrace in Cambridge, England," then I can't gain a basis for hypothesizing that statement (let alone proving it) by observing a few random men. I need evidence that pertains to the specific statement at hand. To hypothesize, I need to see effects of the fact that Julius Oglethorpe III exists, or the fact that 10 Warkworth Terrace exists. To prove this statement, I need to see a set of facts that all evidence shows can only come from the fact that a man with this name lives at this address.
In both cases, the evidence that warrants the hypothesis or conclusion reduces to sensory data. But the evidence for the specific statement is much more specific than that for the general statement.
[Note: This short article was derived from a longer comment I made at "The Christian Egoist" blog: D'Souza vs. Bernstein: Is Either Good for Mankind?]
Proceeding from Axioms in Objectivism - YouTube Edition
The Proof of Free Will (Libertarian Volition)
Taking Philosophy Seriously...
A Refutation of the Argument from Design