knowledge by inductive reasoning
Inductive reasoning is where you reason from the specific to the general, unlike deductive where you reason from the general to the specific. Inductive reasoning depends on assumptions such as that the future will be like the past and that the universe is uniform. The scientific method is based on induction. It assumes that the future will be like the past. Experiments are performed and repeated over and over, and when a large enough sampling is taken, scientists conclude that the results that have been reached so far will also be manifest in the future. So, for example, if things always fall when we drop them, and they’ve always done that in the past, then they will probably also do that tomorrow.
As David Hume and many others before him have pointed out, the assumptions of the scientific method cannot be proved by the scientific method. How would you go about proving that the future will be like the past? The temptation is to say, “Well, the scientific method has always worked in the past, so surely it will work tomorrow,” but that begs the question because whether or not the future will be like the past is the thing we’re trying to prove. So the only way the scientific method can give us true information is if we assume the future will be like the past. It’s not even provable in principle. The scientific method is the least reliable way we can know things because it depends on the previous ways we can know things. It depends on the reliability of our sensory experience to give us true information about the world, and it depends on our intuitive knowledge of the uniformity of nature. No conclusion can be more reliable than the premises upon which it rests.
That’s why scientism is self-refuting. Scientism is the belief that scientific knowledge is the only knowledge we can have. If something is not demonstrated by the scientific method, then it can’t be known. That’s a self-refuting claim because the claim itself cannot be demonstrated by the scientific method.
It seems like we are well-justified in trusting inductive reasoning in general and the scientific method in particular to give us true information. What is remarkable is the fact that it seems we can be more certain about our knowledge of immaterial things than about material things since our knowledge at the intuitive level—the most reliable level—is full of knowledge about immaterial things like logic, minds, propositions, numbers, etc.
There are other ways we know things (e.g. knowledge by analogy is how we know solipsism is false), but those are the four major ways as I see it. Of course epistemology is a fairly broad area of philosophy.