Gettiers in software engineering (2019)

As long as "your assumptions" includes "I know what I am doing", then OK.

But most people tend not to include that in the "your assumptions" list, and frequently it is the source of the bug.

What if you never believed that in the first place?

Then you're good to ignore that as a possible source of the problem.

Then, to be consistent, you should not trust either your deductions or even your choice of axioms.

In other words, it looks like a form of solipsism.

You can not know what you are doing and still trust in logic.

But what world it would be if you could flip a coin on any choice and still survive! If the world didn't follow any self-consistent logic, like a Roger Zelazny novel, that would be fantastic. Not sure that qualifies as solipsism, but still. Would society even be possible? Or even life?

Here, as long as you follow cultural norms, every choice has pretty good outcomes.

I trust things to varying degrees until I test them. Then I trust them more or less.

In certain geographic regions of the planet at least.

Logic will only tell you what follows from your choice of axioms, not how to choose them, and only if you can trust your ability to apply it correctly. Absent that, your only option appears to be to put your trust in other people - which is, I suppose, what you are saying in your final paragraph.