Part III: Inductive and Abductive Arguments

If you find that an argument is deductively valid, you have a kind of ironclad guarantee: You can be absolutely sure that the conclusion is true if the premises are true. Of course, you cannot be certain that the conclusion of the argument is true, since a deductively valid argument may have one or more false premises.

How can we know whether the premises are true? Perhaps when we analyze an argument and consider the first premise, p1, we find that we have good reasons to believe that p1 is true. Then we can identify those reasons as premises of a different argument—an argument that has p1 as its conclusion. But then we need to critically analyze that argument too by considering our reasons for accepting its premises as true… Even deductive arguments rarely if ever make their conclusions certain, since we rarely have deductive certainty about the premises. Maybe we never have such certainty.

But we may have good reasons for believing something even when we do not have certainty that it is true. Many good arguments give a somewhat weaker guarantee concerning the truth of their conclusions, and we often cannot afford to wait for deductive certainty before making a decision. For example, consider the following:

[CARTOON Sorry! I don’t have permission to post this yet.]:

Frame one, three people sitting at a counter with coffee cups.

Frame one: the person on the left takes a sip of coffee.

Frame two: the person on the left drops the cup and looks sick and drops the cup, the person on the right takes a sip of coffee.

Frame three: The person on the left keels over, the person on the right looks sick and drops his cup.

Frame four: Person on the right keels over, the person in the middle looks curiously at the contents of his coffee cup.]

Caption: “Dick should not drink the coffee.”

(Source: Richard L. Epstein, Critical Thinking, Illustrated by Alex Raffi. P. 60. Wadsworth Publishing Company.)

Dick does not have deductive proof that the coffee caused his companions to keel over. It is possible that there is some other explanation for their troubles. But obviously Dick has some good reasons to believe that he should avoid drinking the coffee. Dick might reason as follows:

(1) Other people around me keeled over after drinking this coffee.

(2) The best explanation for them keeling over is that there is something wrong with the coffee.

(3) Therefore it is likely that I would also keel over after drinking this coffee.

The argument is not deductively valid: the other two people may have been ready to keel over anyway, and maybe they would have done it even if they had not tasted the coffee. We can imagine an objector who might say “I’m not going to believe anything unless I have a deductively valid argument that proves that it’s true.” Maybe we should let such fanatical logicians make their own choices about whether to drink the coffee. In a dangerous world, such fanatics will not be long lived.

Nondeductive arguments to not guarantee the truth of their conclusion given the truth of the premises. But when nondeductive arguments are strong, the truth of their premises makes the truth of the conclusion probable. In this lesson we will consider two different forms of nondeductive inference. We will also discuss the evaluation of philosophical arguments.

Objectives

-Distinguish simple deductive arguments from simple nondeductive arguments.

-Recognize some species of good nondeductive arguments.

-Evaluate the strength of inductive and abductive arguments.

-Effecively use key concepts of nondeductive inference.

-Generate abductive hypotheses in simple contexts, and evaluate their relative strength.

Pre-Text: In the previous section, we defined two kinds of nondeductive argument: Inductive arguments and Abductive arguments. Most scientific arguments are nondeductive arguments of these two types.

Inductive Argument (or ‘induction’): A nondeductive argument in which characteristics of individuals not in a sample are inferred from the characteristics of individuals in a sample.

Abductive argument (or ‘abduction’): A form of nondeductive inference, also called “inference to the best explanation” in which a hypothesis is supported on the ground that it is the best explanation for some observed phenomenon.

Here is an example of an inductive argument, from the previous section:

Example:

(1) 95% of all examined fish from the Otsoga river contained dangerous levels of mercury.

(2) This fish came from the Otsoga river.

(3) Therefore, this fish (probably) contains dangerous levels of mercury.

Is this a good argument? Maybe it’s good enough to make you hesitate if you were about to sit down to a nice fish dinner. 95% seems like pretty good evidence.

If 95% of examined fish contained mercury, you might conclude that there is a 95% chance that any fish you catch in the Otsoga will contain mercury. Of course, this leaves a 5% chance that any particular fish will not contain mercury, so the conclusion of the argument is only probable, not certain. Sometimes probable conclusions are all we can get. And often it’s all we need.

But even an apparently strong inductive argument may contain problems:

What if all the fish examined in the study came from a pool next to a chemical plant, but you caught your fish upstream from the chemical plant?

What if all the examined fish were bottom-feeding carp, but the one you caught was a trout? [Trout rarely contain poisons because they cannot survive in polluted water. Carp and catfish, on the other hand, are much more likely to contain pollution and poisons.]

Either of these would probably undermine your confidence that you have a poisoned fish. Either of these would suggest that the fish examined in the sample are not representative of the whole population, or that your fish may not be an average representative of the sampled population. Even so, given the risk of mercury poisoning caution might recommend that you should not eat this fish!

Inductive arguments may be strong or weak, but they are never valid. Inductive arguments are strong when the examined sample is representative of the larger population, and when the examined sample is appropriately large. If the sample is biased, or unrepresentative, and when the sample is small, inductive arguments will be weaker.

Many scientific arguments are inductions. But there is another type of argument that is often used in the sciences. This argument form is called “inference to the best explanation,” or abduction. Here is an example of an abductive argument given by Aristotle:

“The world must be spherical in shape. For the night sky looks different in the northern and southern regions, and this would be so if the earth were spherical.” -Aristotle, Physics.

To put this argument in standard form, we might interpret it as follows:

(1) The night sky looks different in the northern and southern regions.

(2) The best explanation for this fact is that the earth is round.

(3) Therefore (probably) the earth is spherical in shape.

Is this an appropriate interpretation of Aristotle’s argument? Aristotle never explicitly says that the “spherical earth” hypothesis is the best explanation for his observations. But we can interpret him as offering this kind of argument if this seems the best way to capture his intentions.

If we interpret the argument as an abduction, is it a strong or weak abductive argument? Of course we know that the conclusion is true. But looking back, we might regard Aristotle’s inference as a shrewd and daring guess. The fact that the night sky looks different in north and south is not by itself very strong evidence for the claim that the earth is spherical.

THINK ABOUT IT:

Can you think of an alternative explanation for Aristotle’s observation? For example, What if the earth were shaped like an upside-down bowl? What if the sky was shaped like a bowed or wavy sheet? What if…? Would these alternative hypotheses explain Aristotle’s data equally well? If Aristotle’s argument is weak, how could he have found additional support for his “round earth” hypothesis that would make it stronger?

Word Watch:

Inductive argument

Abductive argument

Universal law

Sample bias

Surprise principle

Only game in town fallacy

Most scientific arguments are nondeductive: statistical studies involve inductive inferences, while the articulation and confirmation of natural laws (or putative natural laws) involves abduction.

Philosophical arguments are of many different kinds, and there may be “good arguments” that do not fit any of the three types described here. In reading philosophical works, you should try to identify the type of argument that is being presented. This will be very helpful as you try to critically evaluate it.