Deduction and Induction

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Philosophy 103: Introduction to Logic
Deductive and Inductive Arguments

Abstract: Deductive and inductive arguments are characterized and distinguished in some detail.

I. We have said that the central concern of logic is the evaluation of arguments. In general, arguments fall into two kinds: deductive and inductive.
	A. It is sometimes argued that in deduction the particular is inferred from the general, as in
		All organisms have RNA. (This fruit fly is an organism.) Therefore, this fruit fly has RNA.
	B. And it is sometimes said that in induction the general is inferred from the particular, as in
		A red-eyed fruit fly has RNA. A white-eyed fruit fly has RNA. A Hawaiian fruit fly has RNA. Therefore, all fruit flies have RNA.
	C. But these definitions are misleading for several reasons. Let us briefly note some of them.
		1. In some kinds of deduction, the general is inferred from the particular (e.g., induction by complete enumeration):
			Only Plato and Aristotle were the great Greek philosophers.
			Plato and Aristotle lived in Athens.
			Therefore, all the great Greek philosophers lived in Athens.
			a. In induction by complete enumeration all the members of a class are listed with some characteristic and then a summary statement is made about the whole class.
					Entity e¹ has property p¹
					Entity e² has property p^{2 ________________________}
					Entity eⁿ has property pⁿ
			This example is a deductive argument.
		2. In some kinds of induction, the particular is inferred from the general (with another particular premiss).
			All the great Greek philosophers wrote treatises on science.
			All philosophers named Aristotle wrote treatises on science.
			Therefore Aristotle was a great Greek philosopher.
			a. This argument is only probable even though all of the statements in it happen to be true. E.g., compare the substitution of "Thales" for "Aristotle."
			b. The argument is inductive even though it moves from general to specific.
		3. Finally you, yourself, might remember having difficulty in applying the definition as it was given in a science class or education class because it is sometimes difficult to distinguish between a general statement and a particular statement.
			a. Consider the following cases:
				1. The whale is a mammal.
				2. All persons whose name is Lee Archie in this classroom are silly persons.
				3. All present kings of France are bald.
				4. All ideal gasses are perfectly elastic.
			b. The point is that any specific statement can be written as a general statement or vice versa.
					Often, when we make a statement, we do not know how many, if any, members of the subject class exist. Consequently, it could be begging the question to say that the statement is specific or general.
II. The Difference between Deduction and Induction
	A. Deduction: an argument whose premisses are claimed to provide conclusive evidence for the truth of its conclusion.
		1. To take the classic example which must be mentioned at least once in this course…
			All men are mortal.
			Socrates is a man.
			Therefore, Socrates is mortal.
		2. Note how the grammatical structure of this argument form makes the conclusion necessarily follow--not with probability, but with certainty.
			All B is C. All A is B. All A is C.


		3. Thus, deductive arguments claim certainty--"claim" is used because some deductive arguments do not meet this claim and are called "invalid."
		4. In general deductive arguments fall into several types--these are not exhaustive categories.
			1. Necessary analytic inferences: Peter is Jon's brother, so Jon must be Peter's brother.
					(i.e., they follow from the truths of the meanings of words.)
			2. Mathematical inferences: Since there are more people in the world than there are hairs on you and my head, the population of the world is greater than the hairs on your head.
					(i.e., they follow from the truths of mathematics.)
			3. Logical inferences: If you work hard, then you will succeed, and if you succeed, then you will be happy; therefore, if you work hard, you will be happy.
					(i.e., they follow from the truths of logic.)
	B. Induction: arguments that establish the truth of the conclusion as probable or probably true.
		1. Inductive arguments can range in probability from very low to very high, but always less than 100%.
		2. Often (but not always!) it is the sort of inference which attempts to reach a conclusion concerning all the members of a class on the basis of the observations of only some of them.
			(e.g., I've seen many persons with creased earlobes who have heart attacks, so I conclude that (all) persons who have creased earlobes are prone to have heart attacks.
		3. These sorts of arguments are often said to be empirical because they depend on observing the world.
		4. Some examples of some kinds of inductive argument are (note how these categories can overlap):
			a. Extrapolations: to infer unknown information from known information.
					e.g., increasing voltage leads to increasing rpm
			b. Predictions: the future will be like the past.
					e.g., the stock market predictions
			c. Part to Whole: since some things are this way, that all must be this way.
			d. Analogies, hunches, and so forth.
		5. Unlike deductive arguments in which nothing can be added to make the inference more certain, premisses can be added to inductive argument to make them more probable.
			Bryan Skyrms provides an example similar to this one:
					George is a man. George is 85 years old. George cannot run a 4 minute mile.
			We can always add the premiss that George has arthritis, a broken leg, and so forth to make it more probable. However, when we note that George is a paraplegic, then the argument becomes deductive.
	C. Test yourself on the following examples.
		1. All throughout history people repeat the same mistakes, so we can conclude that mistakes will be made in the future.
		2. The whale is a mammal, so all killer whales are mammals.
		3. All killer whales are mammals, so the whale is a mammal.

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