1. Induction is the process of discovering truths through generalization. Unlike in deductive reasoning, where the conclusion is merely a rearrangement of information already contained in the premises, an inductive conclusion contains new information supported (but not guaranteed) by the premises.
All known living things are composed of cells. Therefore, this new organism I just discovered is probably composed of cells as well.1
Every movie theater in which I have watched a movie was overheated; therefore, all movie theaters must be overheated.
2. When using inductive reasoning, it is always possible that true premises could produce a false conclusion. This is because inductive truths are creatures of probability rather than logical necessity. As a result, induction can create new knowledge, but that new knowledge can never be completely certain. For example, the more living things I discover that contain cells, the more I am justified in assuming that the next one I discover will also be composed of cells. But no matter how many organisms I consider, it is always conceivable that the next one will actually have some other, completely different, structure. The movie theater example above is clearly a case where the premises are too incomplete to lead to a correct conclusion—I am sure that chilly movie theaters exist.
3. People “beg the question” when they create arguments in which the premises assume that the conclusion is true, or when the conclusion is somehow contained within the premises. Sometimes the presence of the conclusion in the premises is obvious, but sometimes it is present only in a disguised form that makes it harder to notice.
Example of begging the question: People should feel guilty for stealing from others. People feel guilty for committing acts that are immoral. Therefore, stealing is immoral. (This begs the question because the first premise assumes that stealing is immoral; otherwise, there would be no reason for people to feel guilty about it.)2
Using induction to predict the future begs the question because the only way to justify the process of induction is a further use of induction. One could attempt to argue that induction has been a valid means of predicting all past futures, so it will most likely be valid for future futures as well, but this would be using induction to justify itself.
4. It would certainly be nice if there was a logically valid foundation for induction, but then we would have to seek a logically valid foundation for the foundation, and a more basic foundation for that foundation of the foundation, and so forth. Eventually, there has to be a most basic level at which there is no simpler justification possible. If the principle of induction is that most simple level, I could live with that.
I would be even more satisfied with induction’s lack of foundation if I was sure that I was not just accepting induction out of habit. One of the challenges of philosophy is to distinguish between beliefs too fundamental to be justified and beliefs that only appear fundamental but are actually misconceptions. The difference is often subtle. Because I have been steeped in a culture of inductive reasoning for my whole life, induction to me appears truly fundamental. However, I question this assumption, given that entire human civilizations—for example the ancient Greeks—have succeeded even as they rejected inductive logic as a way to gain knowledge. Despite this source of doubt, I see no way for the modern world to proceed without induction, unjustifiable as it may be.3
1. This is something of a matter of definition. Viruses, for example, have most characteristics of living beings.
2. Take out the word “should” and this series is closer to the logical fallacy of affirming the consequent. It can be more difficult than it seems to beg the question because it’s not a break in formal logic, but often a trick of language usage.
3. I don’t think you use induction out of habit and I doubt any civilization rejected it in any meaningful way. The process has almost certainly been ingrained in our nervous systems by evolution and is no more extractable than is our ability to coordinate physical movement.