Earlier quoted context omitted.
You can demonstrate the presence of a vulnerability in closed source software but there's no way to demonstrate (or even provide evidence of) the absence of any vulnerabilities.
That's identically true of open-source software. To put it in the theoretical terms you're probably most comfortable with: the programming language used to represent a computer program has nothing fundamentally to do with whether it can be verified. Obviously some languages are easier to verify programs in than others, but the gap between assembly and C in ordinary compiled programs is surprisingly small. Open vs. cl…
I would guess that programs in a Turing-incomplete language will be easier to verify than ones in a Turing complete one.