By Sigurd Arild
According to Hume, there are two kinds of propositions: Relations between ideas and matters of fact.
Relations between ideas are simple and can, given the scarcest of knowledge, be proven without having to rely on personal experience or outside observation. For example, five plus seven will always equal 12, and in theory you could figure that out in your mind, even if you only had knowledge of smaller numbers and their operations. Out of 2 + 2 = 4 you could in principle deduce that 5 + 7 = 12, using your intuition and the capacities of your own psyche, without having to check with the external world.
So not many people argue over the type of propositions that Hume calls relations between ideas. They can easily be demonstrated to be true within the rules by which they operate, such as e.g. arithmetic.
However, with matters of fact, things are not so simple. To reason about those, we require experience and observations of the external world. If you were to say that the moon would keep orbiting the earth tomorrow and not, say, spin off into space, you would have to have some experience of the earth, the moon and so on. There is nothing in mathematics or logic itself that will allow you to predict that the moon will keep circling the earth.
Sure enough, science says that the moon will keep orbiting the earth tomorrow; Neil deGrasse Tyson probably thinks so, and you wouldn’t want to get into an argument with him, right? But here’s the thing: The foundations by which science has calculated that the moon will stay in orbit tomorrow were obtained by recourse to experience and observation; they were not magically deduced in a vacuum. In theory, there could be a universe where moons did not keep their orbits, or where gravity took a break every now and then. It would involve no breach of the rules of logic or mathematics if that was so. Only observation and experience would be upset if that were to happen.
With matters of fact, everything you say about the future is based on induction: You tacitly assume that things in the future will work in the same way as they did in the past. But how can you prove that?
Logic does not disallow a universe where things work in one way at one moment and then in another way the next. There’s no logical contradiction involved in postulating a universe where gravity only works some of the time.
How about observation and experience? That doesn’t work either. Sure, you could say, “the moon has kept circling the earth for thousands of years, so that’s what it will also do tomorrow.” But that doesn’t tell us anything about the future. Again there’s no logical contradiction involved in postulating a universe where gravity functions like clockwork for thousands of years only to suddenly one day go ‘pop.’
So if you think about it, you can’t really justify your belief that the moon will keep orbiting the earth tomorrow.
So why do you believe it? According to Hume, you believe it because you have observed the play of cause and effect so many times. If you were an infant observing the moon for the first time, you wouldn’t form beliefs about where the moon would be tomorrow. And that’s because an infant has no accumulated experiences and observations about the moon to fall back on.
But even the adult you, who’s firmly expecting the moon to keep orbiting the earth, have never observed anything about the moon or about the earth that necessitates the two of them staying together. That the moon will keep orbiting the earth in the future is no experience that you’ve had – that’s simply you having seen it a thousand times before. So really, it’s not reason or logic, but habit that has led you into forming this belief.
Inductivists sometimes try and get around Hume’s critique by multiplying their data. “If the dataset just gets big enough, then eventually there will come a point where we can regard our hypothesis as proven,” they assert. But Hume is here to tell you that that will never happen: No manner how many times you observe the trajectory of the moon, those observations still won’t tell you anything about where the moon will be tomorrow. The challenge of predicting the future based on observations made in the past is not quantitative, it’s qualitative.
Luckily, there’s another way to go about it. And that’s to say that data, in itself, doesn’t prove anything. All data does is inform your beliefs about reality, so that you can hold slightly less silly beliefs. Your beliefs are still unjustified, but really data’s the difference between being totally lost in the dark and then being lost in the dark in an informed and well-reasoned manner. You still can’t prove that the moon will keep circling the earth, but if one day the moon suddenly trails off into space, you certainly can point your finger at all those annoying inductivists who thought they were justified in their beliefs.