# Confirmation Theory

As I’ve continued reading about methodology (the philosophy of science), I’ve dipped into the topic of confirmation theory, which deals with the question of how to measure the extent to which a piece of evidence confirms a scientific theory. Here’s an overview of some key terms and concepts in this subject.

The concept of probability plays a key role in confirmation theory. There are four “axioms of the probability calculus” that any measurement of probability must follow:

- The probability of proposition
*P* = a number between zero and one. (For example, .55, or 55% probability.)
- The probability of proposition
*P* = one, if *P* is a necessary truth. (a.k.a. 100%)
- The probability of proposition
*P* = zero, if *P* is impossible. (a.k.a. 0%)
- The probability of proposition
*P* or proposition *Q* = the probability of *P* + the probability of *Q*, if *P* and *Q* are mutually exclusive. (Example: There is a 20% chance I will wear a red shirt today, and a 30% chance I will wear a blue shirt. So there is a 50% chance I will wear a red or blue shirt today.)

There are two types of “interpretations” of these axioms (ways of assigning numbers to probabilities): subjective and objective.

1. Subjective interpretations consider probability to be a measure of belief in a proposition. Numbers are assigned to degrees of belief, typically based on how much someone would bet on a proposition’s likelihood.

One particular subjective interpretation is the Bayesian Confirmation Theory, which relies on Bayes’s Theorem. In essence, Bayes’s Theorem says that a piece of evidence confirms a given theory if and only if the theory increases the probability of the evidence.

(Special thanks to my friend Jacques for first informing me about Bayes’s Theorem and about some of the contexts in which it is often discussed. I recommend Jacques’s blog on ontology and quantum mechanics.)

2. Objective interpretations apply probability only to propositions that can be tested repeatedly. Numbers are assigned to the frequencies or tendencies of the proposition’s outcome in repeated trials.

To sum up: confirmation theory is a subject within the philosophy of science. It aims to measure how much a given piece of evidence confirms a given theory. Two ways of creating such measurements are 1) by measuring someone’s belief in the likelihood of an evidence and/or theory (subjective) and 2) by measuring the outcomes of repeated trials of the evidence and/or theory (objective).

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