Negative Introspection Is Mysterious

The paper provides a short argument that negative introspection cannot be algorithmic. This result with respect to a principle of belief fits to what we know about provability principles. Autoepistemic reasoning is reasoning the inferences of which depend on representing one’s own state of belief. A cognitive agent engaged in autoepistemic reasoning draws conclusion from introspective beliefs. Such epistemic beliefs express that the cognitive agent has this and that non-epistemic beliefs. If agent a has the belief “The cat is on the mat” the introspective belief is “I believe that the cat is on the mat” or – without self-representation – “It is believed that the cat is on the mat”. Formally this can be expressed using epistemic modal operators like “B” (for belief). One question may be now, how much access and how reliable access some cognitive agent a has to its non-epistemic beliefs (typically called ‘first order beliefs’ as they do not involve epistemic operators). Let B be the set of the agent’s beliefs. An agent with ideal self-access or ideal introspective capacities may fulfil both of i) positive introspection: α∈B ⇒ Bα∈B ii) negative introspection: α∉B ⇒ yBα∈B Further on, the ideal agent may also fulfil some version of logical omniscience or deductive closure with respect to its first order and autoepistemic beliefs: