### Epistemology

**Epistemology**is a branch of philosophy that deals with the nature, origin and scope of knowledge.

The term 'epistemology' derives from the Greek words

**episteme**(knowledge) and

**logos**(word/speech).

**Epistemic**is an adjective that signifies being of or relating to epistemology.

**Epistemologists**are primarily interested in

**propositional**or theoretical knowledge rather than in skill sets.

A

**belief**is some proposition that the individual holds to be true. For a belief to count

**knowledge, no matter how strongly the individual feels the belief to be true, the belief must actually**

*as***be true**. That is, to count as knowledge, a belief must be

**justified**, and, according to Gettier, must be justified for the correct reasons (justified true belief that depends on

**false premises, also termed 'no false lemmas'). The term '**

*no***justification**' signifies that the person who believes something has an

*epistemic*reason to thinking that the belief is true. A belief that consists of accidentally stumbling upon the truth does

**not**constitute knowledge.

Relevant, empiric evidence can

*never*provide inductive proof for a principle, because inductive proof is logically

*impossible*. This means that failure to provide inductive proof is

**not**necessarily failure of a theory given the facts upon which the induction is based. This also does

**not**mean that there is

**not**an underlying principle (mechanism) that is in reality responsible for the observed phenomena. Thus, some inferred principles are much more

**likely**to reflect the actual underlying mechanism than are others, though a principle can

**never**be proved by induction from the observations.

Scientific method can lead only to disproof (falsification) or to experimental

**corroboration**that a scientific hypothesis or theory is the most

**probable**explanation for observed phenomena. Similarly,

**correlation**may result from

**causation**, but it may also reflect some other relationship other than cause and effect, so correlation alone cannot be taken to indicate causation.

**Epistemic probability**refers to degree of belief in judgement-requiring propositions, uncertain events, or problems.

**Bayes' theorem**(rule, law) derives from probability theory, a branch of mathematics that deals with the analysis of random phenomena.

**Bayes' theorem**relates the

**conditional**and

**marginal probability**distributions of random variables.

**Bayesianism**is the philosophical tenet that the mathematical theory of probability can be taken to apply to the degree of plausibility of a statement, or to the degree of believability contained within the rational agents of a truth statement. When a statement is employed within the Bayes' theorem, the statement becomes a Bayesian inference.

**Conditional probability**is the probability of some event A, given the occurrence of some other event B – P(A│B) – the conditional probability of A, given B. P(A│B) is also called the

**posterior probability**because it depends upon the specified value of B. P(B│A) is the conditional probability of B given A.

**Marginal probability**is the probability of one event, P(A),

*regardless*of the other event, P(B). P(A) is termed the prior probability or marginal probability of A. P(B) is the prior or marginal probability of B, and acts as a normalizing constant. The marginal probability is derived by integrating the joint probability over the unrequired event (marginalization).

The

**joint probability**is the probability of the two events in conjunction (both events together), where the joint probability of A and B is written P(A∩B) or P(A,B).

Bayes' Theorem: the conditional probability of

**event A**given event B

**=**the likelihood of event B given event A

**x**the prior likelihood of event A, divided by a normalizing constant (the prior probability of event B) .

................................... likelihood x prior

......... posterior =... _______________

................................. normalizing constant

......... posterior = standardized likelihood x prior

In some interpretations of probability, Bayes' theorem is taken as a guide of how to update or revise beliefs in light of new

*a posteriori*evidence. Here, Bayesian probability is an interpretation of Bayesian theory, which holds that the concept of probability can be defined as the degree to which a person believes a proposition.

Labels: a posteriori, Bayes' Theorem, conditional probability, epistemic, epistemic probability, Epistemology, Gettier problem, joint probability, marginal probability, no false lemmas, no false premises

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