You cannot be completely certain.

Even when you think you are completely certain, you are not completely certain. If you think you are completely certain of something, you are misunderstanding the meaning of certainty.

If you are ever actually completely certain then there is nothing that could ever change your mind. No mountain of evidence can convince you otherwise. If you are certain, then any contradictory sensory input must be a problem with the sensors. If you think your are certain then you must disregard your eyes and your ears when they tell you otherwise. Even if Zeus came down from the heavens and set you straight on international television, you would more readily believe that everyone in the world had a simultaneous identical hallucination – a vanishingly tiny but nonzero probability – than you would believe that you were wrong.

That’s complete certainty.

If the universe turned out to be a simulation, and the Lords of the Matrix stopped existence and showed you that your certainty was based in falsehood after showing you insurmountable evidence that they control all creation, you would conclude yourself insane instead of considering that you might be incorrect.

That’s complete certainty. Complete certainty is an unwillingness to ever even consider alternatives, no matter what happens. Complete certainty is saying that there is no way the world could be that could convince you otherwise.

Complete certainty is pre-emptive insanity. If you claim certainty, you are willing to pronounce yourself insane when reality proves you wrong, instead of agreeing with your own senses.

We can be very very sure of things, but no matter how certain we are, there is always a chance that we’re wrong. We think it’s trivially obvious that $1 + 1 = 2$, but there’s always a possibility that we’ll wake up tomorrow and find that $1 + 1 = 3$. Not that the symbols have changed, but that $•$ near $•$ is $•••$.

If you ever wake up and find that $1 + 1 = 3$, there’s a good chance you’ve gone insane. However, there’s also a tiny chance that you always were insane, that your stored memories of $1 + 1$ equalling $2$ were fake. There’s a chance that logic isn’t static.

There’s not a very appreciable chance that logic isn’t static, but if it isn’t, you’d better be prepared to live in a crazier universe.

There is an allegory of a philosopher who hid on a mountain trying to deduce everything that was certainly true. After quite some time, the philosopher descendent the mountain with only the phrase

I think, therefore I am

There is some entity you, who is processing this. Of that, perhaps, you can be certain, though even there I would tread cautiously.

And for everything else? Certainty is naught but insanity in another guise.