A rewrite of an earlier article “two kinds of certainty”.
A quick explanation of two types of certainty that people tend to confuse.
The first is the one we typically mean in normal language. It’s called psychological certainty. It’s a feeling of certainty; A confidence in something. This is the one we’re talking about when we say things like “Are you 100% sure?”. It is possible that someone is 100% psychologically certain that something is true and that the something is actually false. Psychological certainty comes in degrees. Good examples of psychological certainty and false beliefs are found in religious people and various sport fans.
The second is epistemic certainty. This is the one that philosophers usually talk about. It’s the inability to be wrong type of certainty. If one is epistemically certain, then one cannot be wrong in some sense. This type of certainty is also called cartesian (after Descartes) certainty, infallible certainty and absolute certainty. This type of certainty does not come in degrees; Either one is epistemically certain or one is not. It is not entirely clear how to explicate this kind of certainty. Here are two proposals:
For all agents and for all propositions, (that an agent believes a proposition and that proposition is necessarily the case) logically implies that that agent is epistemically certain of that proposition.
For all agents and for all propositions, that an agent believes a proposition logically implies that proposition.
Domains. x is agents. P is propositions.
Bx(P) means x believes that P.
Cx(P) means x is epistemically certain that P.
⇒ is logical implication.
For convenience, it smart to type p-certain and e-certain to distinguish between them.
http://philofreligion.homestead.com/files/CertaintyandIrrevisability.htm (About psychological and epistemic certainty.)