The Relationship Between Evidence and Probability

Understanding the relationship between evidence and probability is crucial for making sound logical arguments and drawing valid conclusions. The correlation between two events, for example, does not necessarily indicate causation or provide irrefutable proof. This article explores how probabilities and evidence work together and the logical implications of different scenarios.

Evidence vs. Proof

Both evidence and proof have multiple definitions, but generally, they can be distinguished as follows:

Evidence: Observations used to support or refute a hypothesis or theory. Proof: A logical argument based on evidence that demonstrates the validity of a statement with a high degree of certainty.

For instance, if a daughter exists, it may make it probable that her parents had sex. However, it does not prove it conclusively, as there are alternative explanations.

The Fallacy of Post Hoc Ergo Propter Hoc

Correlation does not establish causation. This is often referred to as the logical fallacy of post hoc ergo propter hoc (after this, therefore because of this). Simply because two events occur together does not mean one causes the other. Establishing causation requires a 1:1 correlation or strong empirical evidence that one event directly leads to another.

Probability and Evidence in Practice

The statement "if something exists that makes it probable something else happened, is the first thing evidence of the second happening" must be interpreted carefully. Saying that the existence of A makes B probable does not mean A equals B.

For example:

Having cards in a person's pocket makes it probable they were playing poker, but it is not proof, as there are many other possibilities. In another scenario, if a person is addicted to poker and cards are found in their pocket, it might suggest doubt about their claim of giving up. However, for a normal person, the presence of cards is not strong evidence of poker.

Formalism in Reasoning

Reasoning about logic without formalism can be challenging, but this formalism is essential for understanding logical relationships. A statement like "If something exists that makes it sure something else happened, the first thing is evidence of the second happening" holds when the first event guarantees the second. However, "probable" is less certain and requires a different discussion.

While "sure" is usually defined as a probability of 1, defining "probable" can be subjective. Therefore, definitively stating that the existence of A as evidence for B is "no" is straightforward given the context.

Understanding the nuances between evidence and probability helps in formulating logical arguments and avoiding common fallacies that can mislead reasoning.