Soundness, inductive strength and abductive reasoning

Program / Course 13: Foundations of Apologetics / Lesson 3.4

What you will learn

• Define a sound argument and explain how soundness differs from validity.
• Explain inductive reasoning and what it means for an inductive argument to be strong or cogent.
• Describe abductive reasoning, or inference to the best explanation, and the criteria used to judge explanations.
• Identify which kind of reasoning is at work in a given apologetic argument.

The big idea

A sound argument is a valid argument whose premises are all true. That is the highest standard for a deductive argument, and it guarantees a true conclusion. Most reasoning about the world, however, is not deductive. Inductive arguments move from observed cases to a probable general claim, and are called strong or weak, not valid or invalid. Abductive arguments choose the explanation that best accounts for the facts. Much apologetic reasoning, in history and philosophy, is of these two kinds, which is why it deals in degrees of support rather than proof.

Key terms

Sound

Describing a deductive argument that is valid and has all true premises. The conclusion of a sound argument must be true.

Unsound

Describing an argument that is invalid or has at least one false premise.

Inductive argument

An argument in which the premises are meant to make the conclusion probable, not certain.

Strong

Describing an inductive argument in which the premises, if true, would make the conclusion very likely.

Cogent

Describing a strong inductive argument whose premises are also true.

Abduction

Reasoning from a set of facts to the hypothesis that explains them best. It is also called inference to the best explanation.

Explanatory virtues

Qualities used to compare explanations, such as scope, simplicity, fit with what is already known and power to predict.

Background

The last lesson dealt with deduction, where the conclusion is guaranteed. Outside logic and mathematics, such guarantees are rare. A scientist, a historian and a judge usually reason from evidence that makes a conclusion more or less likely. Christian writers have used these forms from the start. Luke writes in Acts 1:3 of proofs given to the apostles after the resurrection, and in his Gospel he says he traced events carefully from the start (Luke 1:3).

The student of apologetics needs three questions. Is the argument meant to be deductive, inductive or abductive? How should each be judged? And what would count as a successful reply? The answers differ for each kind, and confusing them leads to frustration, as when a deductive standard is demanded of a historical argument.

Step-by-step explanation

Step 1: Soundness

A deductive argument can fail in two ways: it can be invalid, or it can have a false premise. A sound argument avoids both. All humans are mortal; Socrates is human; therefore Socrates is mortal. The form is valid and the premises are true, so the argument is sound and the conclusion must be true.

Soundness is the goal of deductive apologetics. To attack such an argument, a critic need only show that it is invalid or that one premise is false. To defend it, the apologist must show that the form is valid and that the premises deserve to be accepted. Most real disputes are about the premises, since the form is usually clear.

Step 2: Why soundness is hard to establish

The difficulty is that a premise is true only if it is in fact true, and people often disagree about what is true. The argument that whatever begins to exist has a cause, the universe began to exist, and so the universe has a cause, is valid. Whether it is sound depends on whether both premises are true. Defenders and critics offer reasons on each side.

For this reason, a sound argument is not by itself a persuasive one. A persuasive argument must also have premises that the listener has reason to accept. An argument built on premises that only the speaker believes will be sound at best in the speaker’s eyes.

Step 3: Inductive strength

An inductive argument reasons from some cases to a conclusion about more cases or about the next case. Every swan seen so far has been white; therefore the next swan will be white. The premises do not guarantee the conclusion. They make it more or less likely. The argument is called strong if the support is high and weak if it is low. A strong argument with true premises is cogent.

Strength depends on several things: how many cases were observed, how varied they were, whether anything is known against the conclusion, and how bold the conclusion is. The swan example shows the risk. Black swans were later found in Australia, and the generalization failed. Induction is useful and necessary, but it can be overturned by new evidence.

Step 4: Abduction

Abductive arguments start from puzzling facts and ask what would explain them. The lights are out and the room is cold; the likeliest explanation is a power failure. Doctors, detectives and historians constantly reason this way. The conclusion is not guaranteed, but it may be much better than any rival.

To compare explanations, thinkers use standards often called explanatory virtues. A good explanation covers all the relevant facts, is not more complicated than necessary, fits what is already well established, makes testable predictions and does not need to be adjusted for each new fact. These standards cannot be applied mechanically. People weigh them differently, and that is part of why abductive arguments in religion are disputed.

Step 5: Which kind of argument is it?

Apologetic arguments vary. The classical argument for God from the beginning of the universe is offered as deductive. The argument for the resurrection from the early reports is usually presented as abductive. The argument from the success of Christian communities in changing lives is inductive. The argument from the reliability of ancient manuscripts mixes induction and historical judgment.

Knowing the type tells you how to reply. A deductive argument is answered by finding a false premise or an invalid step. An inductive argument is answered by showing that the sample is biased or too small, or that there is counter-evidence. An abductive argument is answered by proposing a better explanation or showing that the proposed one has hidden costs. Replying with the wrong kind of objection wastes effort.

1. What two conditions make a deductive argument sound?
2. Why is a sound argument not always a persuasive one?
3. What makes an inductive argument strong, and what makes it cogent?
4. What are the explanatory virtues, and why do people weigh them differently?
5. Which kind of reasoning is at work in an argument that claims the resurrection best explains the early belief of the disciples?
6. How should a critic reply to an abductive argument?

Examples

Different perspectives

Catholic tradition

Catholic teaching has long held that reasons of several kinds, including signs of credibility such as miracles, prophecies and the holiness of the Church, make faith reasonable. The vocabulary of probability is modern, but the idea that evidence can make belief credible without compelling it is long established.

Evangelical Protestant

Many evangelical writers speak of evidence in terms of strong cumulative support and best explanation. Some stress that sound deductive arguments are possible for the existence of God, while others prefer the language of probability.

Presuppositional critics

These writers argue that probabilistic arguments cannot yield the confidence Scripture demands and that the Christian worldview should be defended as a unit. They question whether a probable God is the God of the Bible.

Philosophy of science

Philosophers of science, among them Peter Lipton, have studied inference to the best explanation as a central pattern of scientific reasoning, while debating whether the best explanation is likely to be true. Their work shows that abduction is respectable but not simple.

Skeptical critics

Skeptics note that the standards for the best explanation can be shaped by prior worldview, so that those who exclude miracles in advance will never find a miracle the best explanation. A fair apologist should say what evidence would count against the view proposed.

Why it matters

Confusion about these three kinds of reasoning causes many useless arguments. One person demands proof and the other offers probability; they talk past each other. Someone who understands soundness, strength and best explanation can ask the right question: not, is this proved, but, how strong is this support, compared with the rivals, and which premises are open to challenge? This also encourages honesty about what an argument can claim.

Common misunderstandings

Knowledge check

Think it through

1. Which of your own firmly held beliefs rest on inductive or abductive reasoning, not proof?
2. How much probability is enough for you to act on a belief?
3. Is there anything that, if found, would change your mind about your best explanation of some important fact?
4. Why might people with different background beliefs judge the same explanation differently?

Independent assignment

Classify and grade

In your own notebook, write 500 to 700 words. Select four arguments from this module or from your reading, two for Christianity and two against it or neutral. Classify each as deductive, inductive or abductive. For each, say what would make it sound, strong or best, and name the weakest point. Do not state which side is right. Keep this for yourself.

Further study

• Stanford Encyclopedia of Philosophy, Fallacies Review the sections on formal and informal fallacies.
• Richard Swinburne, The Existence of God See how arguments are graded as raising or lowering probability.
• Stanford Encyclopedia of Philosophy, Teleological Arguments for God’s Existence An example of an argument that may be read as inductive or abductive.
• N. T. Wright, The Resurrection of the Son of God An extended abductive argument in historical form.
• Acts 1:3 Read the verse about many proofs and compare it to a reasoned appeal to evidence.