In general, people do not use deductive reason, but instead must use plausible reasoning. That is, almost always we deal with questions in which there is not enough information to permit deductive reasoning, yet a choice must be made. A simple example is making plans based on the weather. We don’t know what the weather will be, but we have to take part in activities (or not) regardless. Plausible reasoning is very subtle and this is why we all think everyone else is stupid. To explain what plausible reasoning is, it is best to compare it to deductive reasoning. Deductive reasoning follows two lines of logic: suppose that if A is true, the B is true. Then we can say two things if B is false, then A is false and if A is true then B is true. Plausible reasoning, by contrast uses the weaker statements if B is true then A is more probable and if A is false, then B is less probable. It is worth noting that B is only a logical consequence not necessarily a physical consequence. For instance B could be clouds in the sky and A could be rain. Even though the clouds are the physical cause of the rain, just because it is cloudy does not mean it is raining. The degree of plausibility is then decided in some one manner. In mathematics this is called our prior information in the real world it is referred to as common sense. In spite the name, common sense is a complicated process. Because the degree of plausibility changes based on our previous information, the reliability of the conclusion changes as we go through several stages. Eventually, our conclusions could become nearly as certain as if we had used only deductive reasoning.
The study of plausible reasoning, and especially it’s mathematical formalism is of prime interest. This is because the world is too complicated to analyse all at once. Therefore the method of science has been to separate into small pieces which can be separated. The small pieces generate mathematical models or physical theories which we then use to try to explain more and more aspects of our physical reality. Many different such models can be generated and plausible reasoning chooses between them. Specifically, the mathematical formalism can help us choose between very similar models. This formalism will also give us insight into how the human mind might work and finally it will teach us how to teach machines to think, atleast in some limited sense. So then, understanding probable reasoning will help us determine the laws which govern our world, help us determine how we think, and is the basis for legitimate artificial intelligence.
The study of plausblity reasoning has the same rules as probability theory. This is not accident, they are one and the same.
Note that these are my notes on Jayne’s Probability Theory.