I once saw a cartoon in which one guy says to another: “I’ve made a careful study of logic and it’s all a bunch of hooey.” It’s really impossible to do without logic so we might as well try to get it right. “Deductive” logic is what is usually taught in college classes and involves understanding syllogisms and the like. Very simply put, a deductive syllogism involves a major premise, like “All dogs are sweet”, followed by a minor premise like “Bozo is a dog”, and a conclusion “Therefore Bozo is sweet.” Of course, everything depends here on to both premises being correct. If both premises are accurate, then the conclusion follows conclusively. If even one is not, then the argument is said to be invalid.
“Inductive” logic is a horse of a different color. It is the bases of scientific investigation and technically can never provide absolutely conclusive results, only varying degrees of probability. Here the most interesting thinker to follow is John Stuart Mill who in the early 1800s was an outstanding and very influential thinker. In addition to his work in ethical theory as the “inventor” of Utilitarian moral theory, Mill wrote A Systems of Logic in which he laid out the basic principles behind inductive logic, the basis for all scientific reasoning based on high probabilities. The methods are five and they are usually referred to as “Mill’s Methods”. The focus is usually on determining the cause of a given phenomenon.
The first of Mill’s methods is that of “Agreement”. If there is agreement as to a common relevant circumstance among all or almost all of the instances involved in a given phenomenon as to a common relevant circumstance then that factor is the cause of the stated effect. For instance, if everyone at the dinner ate the pie and everyone got sick, the pie can be called the cause of the effect, namely their sickness.
The second of Mill’s methods is called the “Method of Difference.” If two instances of a phenomenon have every characteristic in common except for one, then that one is the cause of the difference between them. Here if everyone except for one guest ate the pie and got sick, and that guest did not get sick, the pie can safely be called the cause of the sickness.
The third of Mill’s methods is that of the combination of Agreement and Difference. By combining the first two methods one can reinforce the findings of each, making one’s conclusion doubly strong. This double method is often used in determining the caused of various complex diseases. Indeed, it is necessary.
The fourth of Mill’s methods is called the method of “Residues”, or ‘leftovers.” Here we are asked to isolate all the phenomena that all instances of the phenomenon in question share, and then any remaining factor will be the cause of the given effect. Thus, for instance, by subtracting the weight of a truck from the weight of the truck AND its cargo we can determine the weight of the cargo. This method can be used to determine the cause in a given single case and does not require multiple instances.
The fifth of Mill’s Methods is called the method of “Concomitant Variation”. This method is appropriate when the various phenomena involved cannot be completely removed from their respective instances. This method allows the scientist to track the degree of differences between the causal instances involved. When the degree of variation between the proposed cause and its effect remains constant, then we can say that the former is the cause of the latter. This method is used a lot with astronomical and biological phenomena where the key factors cannot be removed.
In all of the above cases it must be remembered that scientific explanations of causation are always only probable at best. Inductive knowledge, unlike deductive knowledge, is always open-ended, or more or less probable. Such is the logic of logic. Deductive logic works within “closed systems”, as it were, while Inductive logic works with respect to “open-ended” systems. The former, if done correctly, offers us “air-tight” reasoning, while the latter can only provide varying degrees of “likelihood.”