Certainty is, by standard dictionary definition, knowing for 100% sure that it's absolutely impossible that you could have made a mistake. This contradicts fallibilism which says you can't get a 100% guarantee that any thought process contains no mistakes.
The practical consequences of certainty are things like refusing to debate, not listening to suggestions or criticism, rejecting new scientific theories, being passive-minded or dogmatic, treating forward-thinkers and outliers badly, and even executing heretics.
Fallibilism isn't skepticism. Ayn Rand and Leonard Peikoff, who clearly aren't skeptics, advocated fallibilism (they didn't do as good a job of advocating it as Karl Popper, but they did say it's correct and make their important claims compatible with it). Fallibilism is compatible with reaching conclusions, taking actions, and not being hesitant, wishy-washy, or endlessly unsure. We can make mistakes, and we should take that into account when deciding how to deal with life, but it shouldn't stop us from doing things. Fallibilism should lead to doing things in robust, resilient ways with margins of error, openness to suggestions and criticism if someone sees a mistake. It should lead to valuing free speech, debate, transparency, objectivity, and ongoing, active attempts to think and learn better.
The desire for certainty and skepticism are linked together. A major cause of skepticism is seeking infallible certainty but being disappointed by failing to get it. If you seek 100% certainty as a requirement of knowledge, then you will get a bad outcome: you'll fail and give up on knowledge or you'll think you succeeded and close your mind to debate and criticism. Accepting fallibilism helps avoid skepticism. This is why Ayn Rand said omniscience is not the standard of knowledge: you don't need perfection or certainty to have knowledge, and setting the criteria for knowledge so impossibly high will result in you thinking nothing is knowledge. Karl Popper had a similar opinion that infallibility is not a requirement for knowledge; there's nothing wrong with fallible or conjectural knowledge and in fact that is what all the scientific success in human history used (since infallibility is impossible, science must always have used fallible knowledge).
Why debate, or listen to a critic, if you're convinced that it's absolutely impossible that you're wrong? You already know in advance that he's wrong and you're right. Either you won't debate or you will view debates as public performances where the wrong and bad people can be corrected, attacked, mocked, or something else where you never consider listening to them and it's never a rational debate where you are open to being corrected yourself.
Certainty, as defined above, is rejected by both Critical Rationalism and Objectivism. Confusingly, Objectivism provided a different, non-standard definition of "certainty", which fits the dictionary poorly, and said that we can have that other type of certainty that doesn't contradict fallibilism. Objectivist-certainty, also called "contextual certainty", means reaching a conclusion while doing your best, and feeling confident enough to take actions using your conclusion, but knowing that you may change your mind if there's ever any new information, new evidence, new ideas, new arguments, new discoveries, etc.
Objectivist-certainty is called "knowledge", "conjectural knowledge", "fallible knowledge" or "tentative knowledge" in Critical Rationalism. Critical Rationalism, like Objectivism, says that infallibility or the standard dictionary definition of "certainty" is not a requirement to have knowledge.
Who is into infallibilism and standard-dictionary-certainty? Some academic philosophers who define knowledge as "justified, true belief" or similar. According to them, anything that turns out to be mistaken was never knowledge. The only way to have knowledge is to have absolute certainty that something is true, and that you'll never change your mind no matter what, otherwise maybe it isn't really knowledge. Popper and Rand both rejected this viewpoint.
Uncertainty
Why is it uncertain that I'm seeing a cat over there which exists? Because sometimes physicists, ontologists, epistemologists, vision researchers, logicians, or zoologists come up with a new discovery that requires rethinking a lot of what we thought we knew. Also, human sight and memory are both fallible, people hallucinate or get confused, people sometimes make mistakes about whether they are awake or dreaming, aliens with advanced technologies could interfere, or we could be living in a simulation and the computer programming controlling the simulation could interfere. These things aren't literally impossible.
Also, you simply don't have any 100% positive proof, and if you tried to you'd run into problems not only with logic and proof but also with physics. If you write the proof down on paper then (as David Deutsch explained in The Fabric of Reality) the correctness of the proof depends on your understanding of the physics of pen and paper. Even if you avoid writing, your understanding of the physics of brains could be mistaken, as could various aspects of your understanding of minds.
Would I raise any of those objections if you said you exist and contain water, you're reading this on a computer that exists and contains silicon, the computer is on a desk that exists and is made primarily of wood, and you can see your cat in the room with you, etc? No. I'd agree with you. I simply don't 100% rule out that anyone could ever come up with a reasonable disagreement. I would be open to debating the topic if someone disagreed.
Can people make bad faith claims and waste time in debates? Yes. There are many ways to recognize and defend against that (though it remains a difficult problem sometimes and better strategies could be developed). The effective ways to deal with it don't require refusing to consider any criticism on certain topics where you feel certain. And the lack of certainty stuff is rarely what trolls actually bring up – it's too abstract, technical, unintuitive to many audience members, and unlikely to emotionally trigger most people.
Knowledge
What is knowledge? It's a subset of information or data. Information is basically anything that could be measured. A grain of sand or drop of water contains vast amounts of information because it contains vast numbers of atoms that could be measured in multiple different ways. Most information isn't knowledge. Knowledge is useful, it has purpose, it's goal-oriented, it solves problems, stuff like that. This is basically the standard dictionary meaning of "knowledge" (but not the "justified, true belief" meaning favored by some philosophers). Some dictionary definitions require that knowledge be contained in a mind, but others allow it to be in books, on computer disks, etc. The concept of being able to write down your knowledge and read it again later makes common sense, fits some dictionaries, and is the Critical Rationalist view.
Note: The definition of “information” that I’m using is in widespread use and has made it into dictionaries now but it's not the standard historical definition, which is more like “facts” or “knowledge”. The more modern definition of "information" that I’m using is more specific and includes non-knowledge. It’s connected with modern developments in physics, math, computer science, information theory and biology. People needed a word for, among other things, the information stored in computer disks or in genes.
I don't think a good, exact, technical, formal definition of knowledge is known. But that's OK. We don't need that to discuss knowledge or do science, and we might even be able to invent artificial general intelligence without it.
What can be accomplished with fallible, uncertain knowledge and no rigorous definition of exactly which information is and isn't knowledge? Everything scientists and philosophers have ever accomplished in human history, since they were all fallible and none of them had a way better definition of knowledge.
According to Critical Rationalism, the only known way of creating knowledge is through evolution. However, it seems problematic to define knowledge in terms of the output of evolution because maybe one day a different way of creating knowledge could be discovered. Humanity has had very poor results trying to come up with other knowledge creation methods so far, but that doesn't mean there are no others.
The physicist and Critical Rationalist David Deutsch hypothesized that knowledge is large structures in the multiverse whereas non-knowledge information forms much smaller multiverse structures. Even if this is correct, it isn't actionable: we can't see the whole multiverse and observe structure sizes. And it doesn't give an exact delineation of how large the structures have to be to count as knowledge, which is similar to me not giving an exact statement of how useful information has to be to count as knowledge.
Critical Rationalists view knowledge as something we keep trying to improve so an exact definition of the minimum cutoff doesn't necessarily seem very useful. We want ongoing progress, not to reach the bare minimum then stop. And we don't spend our time arguing that something isn't useful enough to count as "knowledge"; we aren't trying to do that type of gatekeeping. If anyone thinks an idea is knowledge, then it's above the cutoff; it can be discussed, debated, criticized, improved on, etc. The point of the cutoff is just to clarify that a grain of sand isn't full of knowledge; the cutoff isn't meant to be used against human beings. If people have dumb ideas, we criticize them as incorrect rather than trying to deny they meet the definition of "knowledge".
Are incorrect ideas knowledge? Broadly, yes. People try to come up with good, useful ideas, and while they make mistakes, that doesn't mean there is no knowledge present. Non-knowledge can be thought of like white noise, random junk data or arbitrary information. If a human thought something was a good idea, then it's not going to be anything like random noise; it will actually have a lot of order, structure, correctness and usefulness to it even if it's quite badly wrong with lots of big mistakes.
Objectivism also often views incorrect ideas as knowledge because they were correct in some limited context. Criticizing ideas changes the context but doesn't make them wrong in their original context that doesn't include the new information in the criticism. This is important to how imperfect people who make mistakes can make progress anyway. If each mistake totally invalidated each idea, then science would never have gotten anywhere because making scientific progress only using perfect ideas is way too unrealistic and infallibilist.
Is human knowledge ever true, correct or perfect? There is nothing that says it can't be. We can't absolutely, infallibly prove we're right and made no mistakes. But sometimes we may have made no mistakes. However, even if we had an idea that is the absolute perfect truth with zero errors, we would have no way to know that with certainty. We may be correct sometimes but we don't infallibly know which times those are. Karl Popper talked about the ancient philosopher Xenophanes making this point thousands of years ago.
Many people have contributed to the ideas discussed here including Karl Popper, Elliot Temple, David Deutsch, Claude Shannon (information theory), Charles Darwin, Richard Dawkins, Ayn Rand, Leonard Peikoff, Xenophanes and Socrates.
Messages