Theology is the actual "Queen of the Sciences". Nothing can possibly make sense or be true without it.
True in the sense that nothing can be known absolutely unless it is revealed by an omniscient source. However, I'm quite sure our non-believing friends have accommodated themselves to the idea that nothing will ever be known absolutely.
Maybe few have looked at this in detail, and maybe there's not much to discuss. I'll just press on and finish the argument in brief, and then people can discuss it as they see fit.
Of the three types of inference, only one (deduction) is "truth preserving". That is, if a cause is known to be true and a rule is known to be true, the consequent effect is also known to be true. "Known to be true" is a loaded phrase that can be compromised by the procedural difficulties
@Loudmouth mentioned, but in terms of abstract logic, it holds. Such does not hold for the other 2. An effect and a rule can be known, but it is always possible that other rules will produce the same effect, and hence multiples causes are possible. A cause and effect can be known, and yet multiple possible rules proposed.
It is this last one (induction) that poses the problem for science. Science searches for rules to explain cause and effect, which means it uses induction. Induction, however, is not truth preserving. Science, must, therefore, rely on pragmatic means (levels of confidence) rather than deterministic rules of logic to arrive at a theory as best it can. On the flip side, though, a falsification test is deductive. Using a rule, the effect is predicted for a known cause. Therefore, while a theory can't be proved, a falsification test can conclusively disprove it. The best the remaining theories can claim, then, is that no falsification test has yet been found.
This was further elaborated by Godel with his incompleteness theorem. Some will argue the theorem can only be applied narrowly to mathematics, but given the prevalence of mathematics in science, it essentially applies to all quantitative science (with qualitative science being the much weaker brother). Godel's theorem shows that no axiomatic system can be made complete, and further that no defined system can prove its consistency from within that system.
That is the longer, unpacked version of Loudmouth's quote from Popper.