What is inductive reasoning? Well, we use it a lot in the field of science. Whenever we observe something in the world, we are likely to categorize it and organize it in such a way that we can understand what it is. We no only observe things for identification, but we also may discover causal relationships. After we have observed a cause and effect relationship or a repeated occurrence, we are likely to create a rule to say that the same causal relationship or event will happen in the future. We know that if you throw an apple up in the air, it will come back down. How do we know this? From repeated observations of this phenomenon happening in the past. We not only generalize for what will happen in the future in regards to time, but we also generalize based on identification. For example:
I observed a swan and noted that it was white. I observed another swan and noted it was white. Up until this point, we have only observed swans that are white. Therefore, if we see a swan, we know it will be white. However, one day it may be possible that we see a black swan. Thus, the generalization becomes faulty.
Induction works not because it is necessarily the "truth" but because it works for our purpose of moving forward in search of the truth. When we observe things in science they may always be subject to change in some shape or form.
Can we know anything to be certain?
Past our own personal experience, it is hard to say whether we can truly "know" anything to be true. Regardless, we must have faith or at least be practical in order to function and be a product of society. The philosopher C. D. Broad said that "induction is the glory of science and the scandal of philosophy."
Oh yes, I forgot to mention one more thing. Deductive reasoning may shed some light on where we can know something to be certain. In deductive reasoning, although many times hinging on the research from inductive reasoning, is more of a structure to lead to truth. In a deductive argument, the conclusion HAS to be true so long as the supporting premises are true. The most basic deductive argument is modus ponens.
1. If P then Q
2. (Assert) P
1. If it is raining then the streets are wet.
2. It is raining.
Therefore, the streets are wet.
As you can see, so long as the statements are true, the conclusion that follows has to be true. The question still remains, if it is raining will the streets really be wet? Again, the problem of induction sneaks its way in! Anyway, there you have it! Now go ponder about life until someone asks what you are thinking about.