What historical probability means

Program / Course 16: Historical Defense / Lesson 1.3

What you will learn

• Explain why historical conclusions are expressed as degrees of confidence and not as proofs.
• Describe the difference between certainty, high probability and bare possibility.
• Explain in plain terms how prior assumptions and new evidence combine.
• Recognize two common mistakes: demanding certainty and treating any possibility as a likelihood.

The big idea

History cannot be repeated in a laboratory, so historical conclusions are matters of degree. A claim may be nearly certain, probable, doubtful or unlikely, depending on how well it explains the evidence compared with the alternatives. This is not a weakness peculiar to religion. The same reasoning is used to decide whether Julius Caesar was assassinated or where an ancient battle took place. Two errors need to be avoided: demanding proof beyond all doubt, and treating every conceivable doubt as a reason to suspend judgment.

Key terms

Probability

A measure of how likely a claim is to be true given the evidence and background knowledge. In history it is usually a rough judgment, not a calculated number.

Prior probability

How likely a claim seemed before the new evidence was considered, based on background knowledge.

Inference to the best explanation

Reasoning that accepts the hypothesis which explains the evidence best, judged by how well it accounts for the data, fits what is already known, and avoids needless assumptions.

Burden of proof

The responsibility to give reasons for a claim. In history both sides of a dispute usually owe reasons.

Argument from silence

Reasoning that something did not happen because a source does not mention it. It is strong only when the source would have been expected to mention it.

Bayes’ theorem

A mathematical rule showing how to update a probability when new evidence arrives. Some historians use it as a model for reasoning, though most do not assign actual numbers.

Background

Students often assume that either something has been proved or it has not. In everyday life, and in the courts, decisions are made on less. A jury convicts when a case is strong enough that doubt is no longer reasonable. It does not need to remove every conceivable doubt. Historians work in a similar way, though without verdicts or sentences.

The point matters for a course about the resurrection. A historical argument for or against it will never reach mathematical certainty. The honest question is how strong the case is and what would change that judgment. Seen this way, an argument that claims to prove everything and an argument that dismisses everything because nothing is certain are both mistaken.

Step-by-step explanation

Step 1: Degrees of confidence

Historians speak of claims that are virtually certain, such as the existence of the emperor Augustus; claims that are probable, such as particular details of a battle; claims that are possible but not supported; and claims that are improbable. Most ancient history lies between certainty and ignorance.

Words like probably and likely are not evasions. They tell the reader where the evidence stands. A historian who writes certainly about everything is either claiming too much or is not paying attention to the evidence.

Step 2: Best explanation

Historians usually compare hypotheses. Given the surviving evidence, which story explains it best? A good explanation accounts for the known facts, needs few unsupported assumptions, fits what is known about the world, and is not contradicted by other data. Scholars use different words for these virtues, but the idea is the same.

The method works by comparison. It is not enough to show that a hypothesis is possible or that it has some difficulties. All hypotheses have difficulties. The question is which has fewer and less serious ones. The later modules apply this comparison to the resurrection and its rivals.

Step 3: Prior assumptions and new evidence

Before looking at the evidence for any claim, every person carries background beliefs about what is likely. A report that a coin was found in a field is easy to accept. A report that a man walked on water meets much stronger resistance, because it conflicts with ordinary experience. Probability reasoning makes this explicit: the evidence must be strong enough to overcome the initial improbability.

The difficulty is that people disagree about the starting point. Someone who believes God exists and sometimes acts may begin with a higher prior for a miracle than someone who holds that nature is a closed system. That disagreement will return in Module 8. For now it is enough to see that part of the dispute about the resurrection is a dispute about background beliefs, not only about the sources.

Step 4: Arguments from silence and cumulative cases

A source that does not mention an event is not proof that it did not happen. It is evidence only if the source would likely have mentioned it. If a Roman writer says nothing about an obscure teacher in a distant province, little can be concluded. If a writer who covers that province in detail says nothing, the silence counts for more.

Many historical cases are cumulative. No single piece of evidence settles the matter, but several pieces together may make a conclusion strong. The risk is that a cumulative case may hide weak links. Each link should be examined, and the overall strength cannot exceed the strength of the weakest steps that are essential.

Step 5: Two mistakes

The first mistake is demanding certainty. If nothing counts unless it is beyond all doubt, then almost nothing in ancient history can be known. The second mistake is the reverse. It treats a bare possibility as if it were a probability: that something could have happened is not evidence that it did. Someone who suggests a theft of the body or a mass hallucination needs reasons for thinking it fits the evidence, just as the defender of the resurrection does.

A careful student states the claim, gives the evidence, names the competing explanations, says how strong the conclusion is, and says what could change it.

1. How strong is this claim: nearly certain, probable, doubtful or unlikely?
2. What are the competing explanations of the same evidence?
3. What background assumptions am I bringing to the evidence?
4. Am I treating a possibility as if it were a probability?
5. Would I demand this level of proof for an ordinary historical claim?
6. What evidence would make me change my mind?

Examples

Different perspectives

Secular historians

Most academic historians accept that history works with probabilities. Many hold that an event of an extremely unusual kind needs a correspondingly strong case, and that historical method is better suited to ordinary events than to miracles.

Christian philosophers and historians who defend the resurrection

Many argue that the evidence for the resurrection is strong enough to make it the best explanation, and that refusing to consider miracles in advance is a philosophical decision, not a historical finding. They accept that the case is probabilistic and not a mathematical proof.

Catholic and Orthodox Christians

Both traditions teach that faith is a gift and a response to God, not only the conclusion of an argument. Catholic teaching holds that reason can know certain truths about God and can show that faith is not unreasonable, while the act of faith itself goes beyond historical inference.

Protestant Christians

Some Protestants, especially in evidential traditions, value historical argument highly. Others, following the emphasis on the inner witness of the Holy Spirit, say that faith does not stand or fall with probabilities. Both views appear within the same churches.

Philosophers of history

Discussions of method debate whether Bayesian reasoning clarifies historical judgment or gives a misleading sense of precision, since the inputs are usually guesses. Most agree that the underlying idea of weighing alternatives is sound.

Why it matters

Most arguments about Jesus and the resurrection run into the same confusion: one side demands proof and the other side offers it. Understanding probability gives a student a fairer way to read both. It allows a person to say, honestly, that a case is strong, or weak, or mixed, and to explain why.

Common misunderstandings

Knowledge check

Think it through

1. Which claims do you accept as nearly certain, and what is the evidence?
2. Have you ever treated a bare possibility as if it were evidence?
3. What are your background beliefs about miracles, and where did they come from?
4. How would you explain the difference between a strong argument and a proof to a friend?

Independent assignment

Grading three claims

In your own notebook, write 300 to 500 words. Choose three historical claims, one very well established, one disputed and one doubtful. For each, state the evidence, name the main alternative and give your degree of confidence in words. Explain why you placed each where you did. Do not send this to anyone.

Further study

• Stanford Encyclopedia of Philosophy, Philosophy of History Read for the problem of explanation in history.
• Stanford Encyclopedia of Philosophy, Fallacies Read the entries on arguments from ignorance and from silence.
• Stanford Encyclopedia of Philosophy, Hume on Religion Read the section on miracles to see how probability and testimony are linked.
• N. T. Wright, The Resurrection of the Son of God Read the early methodological chapters for one scholar’s approach to historical argument.
• Luke 1:3 Luke describes careful investigation as his method.
• Acts 1:3 Luke claims many proofs after the suffering.