Axiom D (Epistemic and Doxastic Logic)

A description of the version of Axiom D that is included in Epistemic and Doxastic Logic.

Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!

Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!

[Alkis]

The point of doxastic logic is not necessarily to describe or represent how real people think. It is to examine if a set of believes that a real person holds would be acceptable by someone trying to hold only self consistent system of believes. That is why it is not a problem to demand that believes should not be contradictory in this case.

[Elgeneralsimo]

It seems that Axiom D deals with a strong operator implying a weaker version of that operator.

So we have "necessity implies possibility", "Obligation implies permissiveness", and "Always implies sometimes".

None of these are negations of the other yet this version is.

Would not "Knowledge implies Belief", K(s) > B(s) be more in line, be more isomorphic, with the other versions of Axiom D?

[Ansatz]

"Someone who believes in a nonclassical logic could break this principle even though their beliefs are completely rational."

Nonclassical beliefs cannot break a principle that's defined using classical logic. You would first need to provide a definition of Axiom D for the nonclassical logic of the belief. The definitions supplied in this video are for classical negation; they say nothing about whatever form of negation might be used in some nonclassical logic.

A logic is a formal system, not a worldview. It doesn't make sense to say that someone "believes in a nonclassical logic." Logics don't make any synthetic claims that a person could trust or doubt.