The Nebulous Space Between Proof by Contradiction and Occam's Razor
There are sizable parts of our understanding of the universe in which proof and disproof become a little less rigorous than is the case within the heavily worked core of physics and mathematics. For example, the question of faster than light transmission of information or the various proposed methods of faster than light travel that involve large amounts of negative energy, the most modern unobtanium. FTL of any sort appears implausible because any significant application can be used to engineer temporal paradoxes, ranging from receiving the reply to a missive before it was composed, very useful in breaking all bounds of computation, all way up to preventing your grandfather from marrying, very useful in breaking causality.
Causality (probably) doesn't yet emerge naturally from low-level physics. One can't definitely rule out that spacetime and thermodynamics as presently understood can coexist with temporal paradoxes and infinite computation in finite time, but Occam's Razor suggests that it is far more likely that FTL is impossible. It would require grand new epicycles atop what is known and proven of physics, and if anything, the lesson of physics to date is that the appearance of simplicity and symmetry in theory and mathematics is a strong heuristic for being on the right path.
Or consider Roko's basilisk, the more widely propagated example of malign acausal trade. Acausal gunboat diplomacy, perhaps. Acausal trade is not a completely ridiculous thought experiment, but it is one in which people seem to find it easy to slide off the edge of the map into lines of thought that are little better than speculation, untied to reality. The important problem axioms are whether or not a copy of you is you in an ethical sense (versus being a distinct entity that happens to be identical), and whether or not we live in an Everett-style many worlds multiverse. Occam's Razor is somewhat hard to deploy against the many worlds interpretation of quantum mechanics, because it does make many thorny issues conceptually simpler at the all-important mathematical level of physical theory, and it is not notably more or less strange and complicated than other interpretations that achieve the same goal. But as soon as one starts to think that a copy of you is also you, additional complications spring forth in great numbers, Roko's basilisk just a small part of it.
The many worlds, if real, are in no way threatening if even perfect copies of the self are their own individuals with their own lives and responsibilities. Terrible things will happen and have happened (insofar as tense has meaning) outside our light-cone. We are ethically responsible for none of it. Once it is posited that a copy of you is you, however, now every sentient entity is ethically entangled with every sufficiently close copy. Every sentient entity is burdened with considerable obligations that would make no sense to undertake absent this connection. This gives rise to a towering and not terribly consistent set of epicycles balanced poorly atop the usual business of ethics, a situation that bears considerable resemblance to the cloud of new physics that would be needed to support FTL. Occam's Razor is here a useful tool, a way to look back along the chain of thought and suggest that identification of ethical obligation or selfhood between copies with no possible connection to one another is problematic.
These two examples are high-minded versions of a class of problem that software engineers face day in and day out, precisely because the edges of current knowledge and practice are never very far away in any system running at large scale. Decisions are made in a context of some uncertainty regarding the outcome. All sorts of propositions about system behavior must be assessed in some way prior to making potentially expensive choices, but it is rarely practical and cost effective to extend the bounds of what is rigorously known to encompass the new and interesting area before taking action. Therefore one conducts thought experiments to see if ridiculous and contradictory suppositions arise from the axioms, or whether the results would require the rules of the so far unknown space of operation to be far more complicated than Occam's Razor would suggest they should be, given what is known to date.
It isn't perfect, particularly when the corpus of what is presently known is small, as is the case for less experienced engineers. But it works pretty well as a heuristic for anyone with a fair grasp of the way in which computation and programming works at the root, underneath all the pretty syntax.