As tempted as I am to simply ask you "cash or charge?", I think I'll save the time and just give you a short snippet from a typical introductory text in logic, the kind you might encounter as a freshman in college, on the understanding that you'll simply dismiss it if it proves inconvenient to you. Or perhaps you'll take it as a starting point for your own voyage of discovery - your choice.
The preceding chapters have dealt with deductive arguments, which are valid if their premisses establish their conclusions demonstratively, but invalid otherwise. There are very many good and important arguments, however, whose conclusions cannot be proved with certainty. Many causal connections in which we rightly place confidence can be established only with probability - though the degree of probability may be very high. Thus we can say without reservation that smoking causes cancer, but we cannot ascribe to that knowledge the kind of certainty that we ascribe to our knowledge that the conclusion of a valid deductive argument is entailed by its premisses. On that deductive standard, one distinguished medical investigator observes, "No one will ever be able to prove that smoking causes cancer, or that anything causes anything. Theoretically, you can never prove anything. " Deductive certainty is, indeed, too high a standard to impose when evaluating our knowledge of facts about the world.In this and the following chapters we turn to the analysis of arguments that are not claimed to demonstrate the truth of their conclusions as following necessarily from their premisses, but are intended merely to support their conclusions as probable, or probably true. Arguments of this latter kind are generally called inductive, and they are radically different from the deductive variety. The fundamental distinction between deduction and induction was discussed at some length in our opening chapter. Part Three of this book has been devoted to deduction; Part Four will be devoted to induction. Of all inductive arguments there is one type that is most commonly used: argument by analogy. Two examples of analogical arguments are these:
Some people look on preemployment testing of teachers as unfair - a kind of double jeopardy. "Teachers are already college graduates," they say. "Why should they be tested?" That's easy. Lawyers are college graduates and graduates of professional school, too, but they have to take a bar exam. And a number of other professions ask prospective members to prove that they know their stuff by taking and passing examinations: accountants, actuaries, doctors, architects. There is no reason why teachers shouldn't be required to do this too.We may observe a very great similitude between this earth which we inhabit, and the other planets, Saturn, Jupiter, Mars, Venus, and Mercury. They all revolve round the sun, as the earth does, although at different distances and in different periods. They borrow all their light from the sun, as the earth does. Several of them are known to revolve around their axis like the earth, and by that means, must have a like succession of day and night. Some of them have moons, that serve to give them light in the absence of the sun, as our moon does to us. They are all, in their motions, subject to the same law of gravitation, as the earth is. From all this similitude, it is not unreasonable to think that those planets may, like our earth, be the habitation of various orders of living creatures. There is some probability in this conclusion from analogy.
Most of our own everyday inferences are by analogy. Thus I infer that a new computer will serve me well on the grounds that I got very good service from a computer earlier purchased from the same manufacturer. If a new book by a certain author is called to my attention, I infer that I will enjoy reading it on the basis of having read and enjoyed other books by that author. Analogy is at the basis of most of our ordinary reasonings from past experience to what the future will hold. Not an explicitly formulated argument, of course, but something very much like analogical inference is presumably involved in the conduct of the burned child who shuns the fire.
None of these arguments is certain or demonstratively valid. None of their conclusions follows with logical necessity from their premisses. It is logically possible that what is appropriate for judging the employability of lawyers and doctors is not appropriate for judging the employability of teachers. It is logically possible that earth may be the only inhabited planet, that the new computer may not work well at all, and that I may find my favorite author's latest book to be intolerably dull. It is even logically possible that one fire may burn and not another. But no argument by analogy is intended to be mathematically certain. Analogical arguments are not to be classified as either valid or invalid. Probability is all that is claimed for them.
Good grief, I saw through hume decades ago, and your still caught in that trap? Whewell, and every other philosopher who accepted the a priori superstition were complete failures in the field of epistemology (the very worst, of course is Kant). Mill is so full of errors one hardly knows where to begin.
If you wanted to impress me with your knowledge of philosophers you should have picked Aristotle, Bacon (very sadly, he made major contributions to philosophy most do not even know exist), John Locke, and Ayn Rand.
I did not learn philosophy from philosophers. By the time I was nineteen, I had already developed a system of logic that I only later discovered Boole had already developed. (When I was nineteen no one was yet aware of how significant boolean algebra would be in the field of computers, which was not yet a field.) By the time I was thirty, my philosophy was fully developed. My study of philosophers has only been to discover how the principles I know are true were articulated by others. What I discovered is that most philosophers were mostly wrong, and that the field of philosophy has all but been destroyed by philosophers.
I am guessing you are an amateur philosopher, because you do exhibit flashes of clear thought. Most professional philosopher, that is, those who "teach" philosophy in some capacity, have completely surrendered their minds to one form of irrationality or another.
Like most amateurs, you have been entertaining, but not very enlightening, of course.
Hank
What! No Aristotle? It's not even a game without an opponent!