Induction
Most of the inferences we make every day are inductive: there is only a certain likelihood that our conclusions are true. Furthermore, most of the time we are not even aware that we are making such inferences.
For example, every time you take a step on the way to the refrigerator, you are engaging in an inference something like this: “When I have taken steps in the past, the floor has always been there, and my steps take me where I intend to go. I have no reason to suspect that this step will be into empty space or that it will suddenly take me to the surface of some planet orbiting Antares. Therefore, this step will propel me across the floor toward the refrigerator.”
Of course we do not consciously think about our steps like this! Things have just always worked out for us so consistently and so often that we don’t give our everyday walking a second thought. But we perform inferences like this when we drive cars, cook food, and engage in scientific experiments. We reason from our past experiences to the way things will work in the future.
Now, we might say, “But it is certain that when I take a step the floor will continue to be there. Of course that is reliable.” But this is a mistake! It is not certain that our steps will take us across the floor to our intended destination, and a moment of reflection will reveal this fact. Genuine certainty is impossible whenever we are reasoning inductively. It is only likely that our good inductive conclusions are true.
Next we might say that this level of likelihood is just as good as being certain. After all, it is the case that our steps work the same way that we really don’t think about them any more. But there are plenty of people that have had the floor collapse out from under them, and these people recognize that the “fact” of the floor always being there is not the same thing as certainty! Saying “1 + 1 = 2” is not making the same sort of inference as saying, “The floor has always been there, so it will be there when I take this next step.”
But, induction works pretty well the vast majority of the time! Most of the time the floor is there, when we turn the steering wheel to the right the car turns to the right, and when we add salt to our soup that makes the soup taste salty. But none of these inferences is certain, and there are many contexts in which we demand certainty.