- #1

- 1,866

- 34

This is the introductory definitions of two different types of probability:

I am only familiar with the first concept, probability based on the empirical evidence (for example a statiscial survey may help approximate the probability of a person holding a certain opinion), or determined with knowledge of all factors which can affect the outcome (for example a thought experiment by flipping a perfect coin, e.g. the unit disc thrown on a plane).

Bayesian probability states that there is a certain probability to every statement. I find this hard to justify, given that many statements is either true or false. For example, how can one determine the probability that there is 4 apples in a given basket? The statement becomes: "A: The basket

The above may be hair-splitting (in a practical sense), but my problem comes when bayesian probability is expanded to statements regarding the truth of undeterminable events, such as the existence of ghosts, angles, etc. When one places a probability value to a statement that is by definition undeterminable, how can this be justified by the degree of one's belief?

Frequentiststalk about probabilities only when dealing with experiments that are random and well-defined. The probability of a random event denotes the relative frequency of occurrence of an experiment's outcome, when repeating the experiment. Frequentists consider probability to be the relative frequency "in the long run" of outcomes.[1]

Bayesians, however, assign probabilities to any statement whatsoever, even when no random process is involved. Probability, for a Bayesian, is a way to represent an individual's degree of belief in a statement, given the evidence.

I am only familiar with the first concept, probability based on the empirical evidence (for example a statiscial survey may help approximate the probability of a person holding a certain opinion), or determined with knowledge of all factors which can affect the outcome (for example a thought experiment by flipping a perfect coin, e.g. the unit disc thrown on a plane).

Bayesian probability states that there is a certain probability to every statement. I find this hard to justify, given that many statements is either true or false. For example, how can one determine the probability that there is 4 apples in a given basket? The statement becomes: "A: The basket

**b**contains 4 apples". Do bayesian probability state that this true or non-true statement has a probability value attached to it, so that [tex]0 < P(A) < 1[/tex] based on a*degree of belief*? [tex]P(A)[/tex] should in my opinion be equal to either 1 or 0, determined by the truth of the statement. The probability that a basket chosen arbitrarily contains 4 apples is another thing. The statement becomes: "B: An arbitrarily chosen basket contains 4 apples". This, however does have a probability value [tex]0 \leq P(B) \leq 1[/tex] attached to it. I can agree that bayesian probability makes sense accompanied with extensive statistical data, but to point to a certain case which is either true or false - isn't it formally wrong to assign a probability value to it?The above may be hair-splitting (in a practical sense), but my problem comes when bayesian probability is expanded to statements regarding the truth of undeterminable events, such as the existence of ghosts, angles, etc. When one places a probability value to a statement that is by definition undeterminable, how can this be justified by the degree of one's belief?

Last edited: