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 as knowledge, no matter how strongly the individual feels the belief to be true, the belief must actually 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 no false premises, also termed 'no false lemmas'). The term '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.

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