I have this epistemological thumb rule that I live with pretty consistently, and I think you do, too. The thumb rule is this: We should always affirm the obvious unless we have good reason to deny it. Put another way, we should assume the world is just as it appears to be unless we have good reason to think otherwise. And, in fact, I think that's what we almost always do even if we don't think about this thumb rule explicitly.
Obviousness is a function of intuition. Sometimes you hear people say that something is intuitively obvious. That just means it seems to be so, it appears to be so, it's hard to deny, it seems absurd to deny, it seems reasonable to affirm, it's self-evident, etc. Intuition, in this context, isn't a hunch or a feeling that something is true. Rather, it's a rational insight that occurs through reflection. In other words, you just think about something, and it automatically appears true to you. For example, the way I know that two plus two is four isn't through experimenting with it in the physical world; rather, I know it by thinking about it. I can just reflect on it and "see" that it's true.
I often bring up this point in the context of morality. I believe in objective morality because I think it's more reasonable to affirm the obvious than to deny the obvious, and the existence of morality seems intuitively obvious to me. That is, when I think about morality, and I'm perfectly honest with myself, I cannot bring myself to honestly deny it. Apart from any proof against it, it appears more reasonable to affirm than to deny. So I'm just honest with myself, and I affirm the reality of morality.
Whenever I've stated this principle in discussions with people who disagree with me, they'll always try to show how unreliable our rational intuitions are. They'll point out all the many cases in which our rational intuitions failed us. Newtonian physics is very intuitive, but relativity and quantum mechanics are often counter-intuitive. These are examples of where things appeared to be one way but turned out to be another way. Another example people have given me is the fact that the world appears to be flat when you stand outside and look at it. But we know it's round.
Counter-examples like these are not sufficient to undermine the thumb rule, and there are three reasons. First, the thumb rule explicitly makes room for exceptions. The thumb rule does not make intuition out to be infallible. Rather, it says we should affirm the obvious unless we have good reason to deny it. In the case of quantum mechanics, we do have good reason to deny what initially appeared to be so and to affirm what is counter-intuitive. Of course intuition can be infallible, like in cases where we apprehend necessary truths, but intuition in general is fallible since for many things we intuit, it's possible for them to be false.
Second, the only way we could have discovered that the world was different than it appeared to be is by using the thumb rule. How do we know the earth is round? By making observations and inferences. The same thing is true of relativity and quantum mechanics. Unless we generally affirmed the obvious, we could never have discovered that the earth is round or that objects moving at different speeds move through time at different rates. We discovered these things through observations, calculations, and inferences. It appears, based on these tools, that the earth is round, and quantum theory is true, and so is general and special relativity.
Third, the denial of the thumb rule is self-refuting. The only way we could have known that subatomic particles behave in counter-intuitive ways is by making observations and calculations. That is, we must rely on appearances and how things seem to be. If we did not adhere to the principle that we should affirm the obvious unless we have good reason to think otherwise, we never could have discovered that anything is different than it appeared to be. So any argument against the principle that we should affirm the obvious is necessarily a self-refuting argument since it depends on the very principle that it attempts to refute. That's the problem with trying to come up with counter-examples to show that rational intuition is unreliable. If you deny that the world is pretty much the way it appears to be, you could never come up with an example of where the world is actually different than it appears to be.
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