Mistakes are ubiquitous. Error is always with us. The whole purpose of creating new knowledge is to correct errors. We cannot have certainty - about anything, ever. But at the same time this does not mean that all claims to truth are on equal footing. Relativism - the idea that all claims to truth are equal (that everyone's opinion has equal value) is false. Science, mathematics, philosophy and morality uncover objective truth about reality. It's just that objective truth does not mean what most people think it means.
If something is objectively true, this does not mean it is certainly true. Pause for a moment. What does "certain" mean? If I'm "certain" - what does that mean? It just means I feel some way. I feel certain. Certainty is an emotion! It's a feeling you get (or at least a feeling some people seem to want to have). But a feeling - the feeling that you are definitely, without a doubt correct is no guarantee that you are. You should have doubts. Doubt is good. Someone without doubt is dogmatic. And dogmatism only ever leads to evil.
Do you remember the time when you were certain that through any two points a only a single line can be drawn? Perhaps you still are, depending on how much maths you remember. So try it now: draw two random points anywhere on a piece of paper and draw a straight line through those two points. Can you draw more than one line through those two points? Have you tried? Well think a bit. It's said only one line can be drawn through those two points. Indeed Euclid who first laid down our mathematical foundations of geometry provided a rock solid mathematical proof of this. And this is what you are taught in school geometry class.
So there's a proof. But are you certain of so simple a truth? Most people are certain at least for some time that only one such straight line can be drawn.
Now bend the piece of paper. Or wrap the paper around a ball. Suddenly infinitely more straight lines can be drawn. Your prior certainty is undermined by a simple change of perspective.
But maybe you have objections now. You still refuse to accept this. "That's cheating" or some such. "The line is bent". The point here is: do you doubt it? Should you doubt it? Did you misunderstand the instruction as I first posed it to "draw a straight line through those two points"? Could I have phrased it in such a way as not to be misunderstood by you?
Karl Popper once said "It is impossible to speak in such a way that you cannot be misunderstood".
So it is with all knowledge. We always have doubts. We can always misunderstand. We can never be certain.
So when someone says "I know X" where "X" is any claim at all, what they're not - in actuality saying is: "I am certain that X is the case" or even: "I am justified in believing that X". No, what they actually mean is "The best idea I have at the moment is X and I've got no good criticism of X". When people say they know X they're not saying they can't (actually!) change their mind. Yes, of course: some people are dogmatists and claim not to doubt "X" when "X" is either something really obvious or something that is really important to them. But their thinking these things does not change the true structure of knowledge - or that they are, in fact, actually fallible humans. People are always fallible. We should know that even if they claim to have no doubts: we should doubt that very claim. Or better yet: understand that if they thought better about things then they would, like us, understand that although knowledge is genuinely possible the feeling that one is "certain" is no guarantee at all that one is in possession of the final, ultimate truth. That final, ultimate truth is something we aim for - but it's not something we can ever know to have obtained.
The "Justified True Belief" mistake handed down to us from Plato remains deeply ingrained in our language and ways of thinking about knowledge. But it's just that - a mistake. Knowledge isn't anything to do with being "justified true" (which is to say: in some way finally shown to be not possibly false) or even about the beliefs of people. Knowledge instead is very much a real thing: abstract and yet instantiated in physical objects. In other words: physical structures are arranged in particular ways in order to "code" the knowledge. So, for example brains encode knowledge, but so too do computers and even telescopes. All those structures encode causal relationships between objects so that something useful can be done with information.
Popper understood that knowledge is real and possible. But many people think he rejected knowledge because they think his entire philosophy is about falsificationism. So they think that Popper's philosophy says something like: you can be sure about those things you have falsified but not about anything else. Or something like that. But this is wide of the mark completely. Popper did not think you could be sure (as in certain, or absolutely 100% without any doubts for all time satisfied) that anything was true. Or false. No. He didnt believe in "confidence levels" at all. Everything we know is always conjectural - which is to say "tentative". It contains truth, but it's not the final truth. Knowledge claims are explanations about what is true. Falsification - or refutation broadly - rules out some explanations (theories, ideas, hypotheses) as being good explanations. David Deutsch sharpened up this idea even more: an experimental refutation makes a theory almost impossible to vary in such a way as to account for the refutation. In other words: if your favourite beautiful theory is slain by an ugly fact, then if the theory is any good, you shouldn't be able to just change it a little bit in order to now explain what went wrong. For example if you think eating a kilogram of grass cures the common cold, and someone tries and it doesn't work (so your theory is falsified) then if you come back with "oh - actually it's probably more like 1.1kg - try again" - this is called an "ad-hoc" modification - making your theory "easy to vary" and so we can reject the "grass cures the cold" theory and all infinite variants of it on that basis. We don't have to keep testing it. And it's fair for us to say "We know that grass doesn't cure the common cold". Does this mean we're sure it doesn't? That we're certain one day someone won't come along and show how if you isolate some chemical in grass and add it to some other chemical in alcohol and take it as a pill that this won't kill cold viruses? No. We can never be sure. But we've no reason whatever to think this is, or ever will be, the case.
Popper was never a skeptic in the philosophical sense of the word. Quite the opposite! Skeptics believe in the "Justified true belief" theory of knowledge. They rightly conclude one can never be absolutely certain about knowledge claims but then wrongly conclude this means knowledge is not possible. Popper was a critic of this idea - he rejected it completely. He threw it away root and branch and started from the ground up. The idea here is to divorce knowledge from being about "certainties" or "justified truth". Instead knowledge is possible because there is an objective difference between knowledge claims. None of them are final absolutes - but in almost all cases, always, where there are two (or more) competing claims, one of them is better than the others. The process of criticism rules out all but one of the ideas. The one that survives: we say "I know that". That claim comes to be called a part of our "knowledge" of the world. But it's always revisable, always improbable. Popper was no skeptic about knowledge - he was a critic. And these are quite different things. One assumes knowledge is not possible because certainty isn't. The other says almost exactly the opposite: the pursuit of knowledge and its objective growth and improvement is only possible because certainty isn't. (To unpack this: if we were able to be certain then this would mean we'd have direct access to final truth and this would mean the quest for knowledge would stop. We'd just "tap-in" to that ultimate source of truth and that would be that. Game over. We'd never improve anything because we'd have the final, complete answer (and all the answers). So the pursuit of knowledge would stop.) But happily, the pursuit of knowledge isn't like this at all. Knowledge is hard won. And it comes to us with much misconception. Almost all we know contains misconception - and we can never be sure which is misconception and which is true. But that doesn't matter. As long as our process of error correction keeps on sifting the misconceptions from the kernels of truth, so that we make progress - this is all we need to be able to say "we are creating knowledge" or "we are learning" and "making objective progress". We can't know we've got the final truth, ever: but what we can know is that our process of criticism: experimental falsification and other kinds of refutation - makes the ideas that survive this process objectively better than the ideas that do not.
The purpose of science is to correct our knowledge about physical reality. Here we see improvements most obviously perhaps - objective progress seems to be made all the time. New medical discoveries improve our health and lengthen our lives and cure disease previously a death sentence. Each new iPhone is better than the one which went before and each new car engine is more efficient than previous models. One great theory is overturned by another even better theory. New explanations replace old ones. The news ones are not certainly true - but just closer to the "ontological" truth than its rival(s). Karl Popper called this verisimilitude. This means "closeness to truth" - where by "truth" we mean the ontological truth. What does that mean?
Ontological truth is a description of what is really there. We do not have a method for finding a final, once and for all description of what is really there but this is a wonderful thing. It means that the quest for knowledge is infinite. We make progress: forever. We don't find a final fact about reality and just stop and say "well that's it. No more needs to be known about this. We now know everything there is to know about this." That day, happily, will never come - we can always improve things.
This means we must try to show which of our ideas are wrong and how. And so this is the best thing you can do to help progress along. You don't need to be a great philosopher, a quick thinking mathematician or a creative scientist - you just need to be a critic. Critics have a bad reputation. And they don't deserve it. There are two, equally important ways to be in the world when it comes to progress; you can be a creator and you can be a critic. We are all both of these at various times and both are absolutely essential to creating knowledge.
Creation can result in improvements - and that's great. Producing something new can be exhilarating. But that again is just a feeling. Just because you're excited about a new creation doesn't mean you've actually produced something of value. You can be wrong, remember? You might very well be right about your new creation - you'll earn fame or money or social cache - your new idea will spread: some new art more beautiful or incisive might make you rich or famous. Some new scientific theory to overturn an old theory could solve a problem previously a stumbling block to progress might improve the world. But sometimes new creations lead to dead ends. That's just part of the creative process - creating stuff that just doesn't do what you want it to: art that's just not that good - music no one will listen to, a painting everyone says is derivative. A scientific theory quickly slain by an experiment that shows it to be wrong. A computer game no one wants to play. Criticism is how we sift the good, the beautiful, the true, the useful - from the bad, the ugly, the false, the damaging.
And this is true for ideas generally and your own ideas personally. Criticise your own ideas and don't be upset when others criticise your ideas. They are not criticising you personally. You are not your ideas. You merely have ideas. You can discard ideas. And you can criticise criticisms. You can defend your ideas. That's good too. If you want to get better, as fast as possible - create, criticise and repeat. It's the way to make progress.