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"Fluxions" adapted from Library of Congress, P&P Online, LC-USZ62-95311Philosophy 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, for the purposes of this course arguments will fall into two kinds: deductive and inductive. (As noted before there are other kinds of logic not fitting well into either category: e.g., modal logics, logic of commands, some multi-value logics, to name a few.)
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 p2
________________________
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. (Note that interpretation of this example does not obviate the claim that the argument is an invalid deductive argument, if someone mistakenly claims the conclusion follows with necessity. Apart from the psychological aspects the argument is inductive because the conclusion follows with some probability.)
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" means "All whales are mammals."
2. "All persons whose name is Lee Archie in this classroom are silly persons" means "Lee Archie is a silly person."
3. "All present kings of France are bald" fails to have a reference.
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. (This definition is a bit of a kludge since we want to retain a meaning to the phrase "invalid deductive argument" which might be, in some cases, a correct inductive argument.)  In the beginning, it's probably best to think of a good or valid deductive argument as one in which the conclusion follows from the premiss(es) with logical necessity. 
1. The "claim" part of the definition is a kludge since the psychological aspect of the process is strictly speaking  irrelevant to the logical aspect of  rules of inference or entailment.
2. 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.
3. Note how the grammatical structure of this argument form makes the conclusion necessarily follow--not with probability, but with certainty.
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All B is C.
All A is B.
All A is C.

4. Thus, deductive arguments claim certainty--"claim" is used because some deductive arguments do not meet this claim and are called "invalid."
5. In general deductive arguments fall into several types--these are examples, not exhaustive categories:
a. 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.)
b. Mathematical inferences: Since there are more people in the world than there are hairs on your 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.)
c. 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. So, informally at least, an inductive argument claims its conclusion follows with some degree of probability.  The word "claims" is included in this version of the definition if we want to use the meaningful phrase "incorrect inductive argument."
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 of a certain kind are this way, all things of that kind are this way.
d. Analogies, hunches, and so forth.
5. Unlike deductive arguments in which nothing can be added to make the inference more certain, almost always  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. (Bryan Skyrms, Choice and Chance, 4th ed. (Stamford, CT: Wadsworth, 2000), 18.) However, when we note that George is a paraplegic, then the argument becomes deductive. 
C. Test yourself on the distinction between induction and deduction in the following example exercises:.
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.

4. Dumbbell training is inherently safe.  I've never observed a torn muscle or any other serious injury resulting from the proper use of dumbbells. (Bill Philips and Michael D'Orso, Body for Life (New York: Harper Collins, 1999), 123.)

5. All human beings have the ability to think rationally and realistically. We all can realize, "Even if I am probably correct, there is still room for questioning." Thus we can allow discussion, disconfirmation, and new evidence to change our minds. (James O. Prochaska, et at., Changing for Good (New York: William Morrrow, 1994), 182.)

6. Most psychohistorians reject non-psychoanalytic psychologies for use in historical research because of their ahistorical non-developmental character and because they are either so simplistic that they explain only elementary traits or so locking in structural coherence as to be unusable by historians. (Peter Loewenberg, Decoding the Past: the Psychohistorical Approach (New York: Alfred A. Knopf, 1983), 19.)

7. In logic we are concerned with propositions rather than beliefs, since logic is not interested in what people do in fact believe, only in the conditions which determine the truth or falsehood of possible beliefs. (Bertrand Russell, The Analysis of Mind (London: Routledge, 1989), 204.)

8. Many of those children whose conduct have been most narrowly watched, become the weakest men, because their instructors only instill certain notions into their minds, that have no other foundation than their authority and if they be loved or respected, the mind is cramped in its exertions and wavering in its advances. (Mary Wollstonecraft, Vindication of the Rights of Woman (1792 London: T. Fisher Unwin, 1891), 45.)

9. Given the view that species evolve into one another, then members of one species must somehow give rise to members of another species.  It follows that members of the second species must somehow derive as variants of members of the first. (Stuart A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution (Oxford: Oxford University Press, 1993), 6.)

10. Astronomers infer the existence of dark matter because it would provide the unseen glue that keeps galaxies intact and galaxy clusters from disassembling. But dark matter has never been convincingly detected directly. (Ron Cowen, "PAMELA Spots the Dark Stuff, Maybe," Science News (2008)  vol. 174:3, 8.)

Recommended Sources

Defining Deduction and Induction  A reprint from Ron Yezzi, Practical Logic (Mankato: G. Bruno & Company, 1992) outlining some of the problems of distinguishing between deductive and inductive arguments.
Four Varieties of Inductive Argument  Statistical syllogism, generalization, analogy, and simple induction are discussed by John L. King.
Inductive Logic A discussion of inductive logic with an emphasis on probability and likelihood in the Stanford Encyclopedia of Philosophy by James Hawthorne.

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