And the classic answer is that you can’t be certain of anything except that you think and that you exist. Everything else may be doubted by imagining that you’ve been wired up to a V-R machine since birth. But perhaps the answer really depends on what sort of thing you’re doing. For day-to-day purposes I think I can be certain that I’m sitting on a chair, Africa exists, 132=169, and so on; I can rule out the V-R possibility. It’s only when I do some philosophy that I can doubt these things. And that sort of oscillation between the sceptical mode and the trusting mode characterises good science. Scientific revolutions like the discovery of Relativity Theory depend on trusting almost nothing we took for granted. But then to build up knowledge we have to take a lot of things for granted. You have to be careful who and what you trust; sometimes you should trust almost nothing. But most of the time you do need to put your trust in things in order to make any progress in life. So, yes, we can be certain of lots of things, but only some of the time.
I'd read all her novels by the time I was 16, and then at college I discovered her Philosophy. It was the first time I had come across this idea of getting closer to the truth by perfecting your concepts and it had a big impact on me. Some of her ideas are quite mystical and I still find them mysterious and difficult.