Ok, so this isn't a philosophy blog, and I'm not planning on overloading it with posts that require three years of university as a philosophy major to understand. That being said there's aspects of philosophy that actually are relevant to real life (even though most people seem to think otherwise). So bear with me here, I promise this is interesting...
Imagine you're at a beach and you want to skip rocks. You know for a fact that if you get a good, thin stone and throw it so that it spins the right way, it'll bounce on the water. Let's examine this a little: implicit in this knowledge are a myriad of smaller facts that you must have known first. For example, you had to know that dropping something will cause it to fall; and you had to know that the rock should be spinning, and should be thin. You may keep breaking down your knowledge into smaller and smaller facts, but you will never reduce it to a fact that you did not discover through experience. The point is this: everything you know about the way the world works is a product of your past experience.
Whenever you draw from past experience you're relying on an idea. That is, if you know some A caused some B, then A will cause B in all present and future times. Assume that A implies the exact same scenario every time; so, if A, you throw the same rock, at the same angle, at the same place, with the same force etc, then you know that B, it will bounce on the water the same amount of times, every time.
But where did this idea come from? Obviously, you couldn't have drawn it from experience, because any inference from experience requires this idea. Maybe, through rational argument, you can arrive at the idea. Let's think about that: imagine the skipping rock again. Is there any inherent contradiction in the idea that the next time you skip the rock it will, say, fly into the air and hit a seagull? The answer should be no. The only reason you'd say you know that won't happen is because of past experience. But this relies on the idea itself (that if A caused B in the past, A will cause B in all present and future events). Since thinking the opposite of the idea doesn't imply a contradiction, the idea can't be deduced through rational deduction.
And there you have the problem of induction. Basically what it means is that there is no such thing as a fact drawn from experience. Even knowledge you would bet your life on, for example that the sun will rise tomorrow, can never be 100% certain. All knowledge relies on this idea that can't be proven through experience or through rational argument. In other words, it is an assumption. An important and unavoidable assumption, since, without it we can't really interact with the world, but an assumption nonetheless.
So what's the significance of this? None really in day to day life. Interesting to know, though, that you can never really prove you won't suddenly slip right through the concrete while walking down the sidewalk, or any other ridiculous thing you care to imagine. It's also the reason that, in science, everything must be called a theory. Take the theory of evolution: with the overwhelming evidence to support it, you might say there's a 99.99999% chance of it being true, but you can never say it's a fact. Facts from experience, if 100% chance of truth is your definition of a fact, don't actually exist.
*Basically everything I wrote here was stolen from David Hume's An Enquiry concerning Human Understanding*
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