(It can help to start with the short piece on deduction.)
Induction is a process we can use to create rules which we might then put to use via deduction. We need it because in a messy world, there are limits to the clearly correct statements we have to work with. Induction does not provide the certainty that deduction can, but it can operate from less certain evidence.
Aristotle articulated induction as reasoning from the specific to the general. That is from examples to a rule. (Once we have a rule, we can then use it in deduction.) We find evidence, examples of something and create a rule, or prediction from it.
The sun rises in the east in the mornings I have checked, therefore the sun rises in the east every morning.
At once I think we can see the power and the peril of induction. The results of this example are almost certainly good enough for the rest of my life. Yet at the same time we can be fairly confident that one day, the rule will break down.
This is one problem with induction - a pattern may be real and may continue, but may not be forever. What risks are involved in relying on the pattern is definitely something to keep in mind. (There are deeper philosophical problems with induction, but they are of less concern in ordinary life.)
Another difficulty is that of sampling - what if the pattern we see is because we have collected a biased set of examples? If I look outside the building every day at the same time I could easily conclude that all delivery vans are red, where in reality Royal Mail delivers at the same time every morning and UPS come later.
Finally, as the saying goes, correlation is not causation. Just because two things do in fact occur together doesn't mean one is causing the other. A now famous study found a correlation between Nobel Prizes per capita and chocolate consumption. We can be fairly sure some other forces are at work here, likely causing both phenomena.
Despite these problems, induction is a vital way of thinking about a complex and uncertain world. We need a method of giving us some clue what to expect and induction is a good one, with flaws that can often be addressed. Another method which was also articulated by Aristotle is at once more dangerous and yet more powerful - analogy.
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