Limitedness, Quasiobservability, and Two Types of Logical Necessity

The article substantiates that not all accessible possible worlds are conceivable, and not all conceivable worlds are accessible. The first part shows that the conceivable should (ideally, without taking into account the agent’s limits) be accessible, and the second that the inaccessible (due to the agent’s limits) possible worlds may be quasiobservable. A comparison is made between the ideas of logical omniscience and the idea of the intellectual limits of the knower. The idea of logical omniscience is associated with the idea of pure logic. The idea of a limited agent is associated with the idea of the possible world’s counterfactuality to the real world. The opposition of these ideas is interpreted in the context of an instrumentalist interpretation of logic and mathematics. It is argued that logic and mathematics are only tools of limited agents. The opposition of the purely logical (omniscience) and the logical within the framework of the semantics of possible worlds (agent relativization) also relates the opposition of the purely logical a priori and the conceptual (or informative) a priori. Thus, two interpretations of logical accessibility appear. The idea is expressed that both the formally contradictory and the conceptually contradictory may be beyond the framework of logical accessibility in a limited sense. The accessibility is determined by the semantics of possible worlds linked to a separate distinguished (“real”) world and has a metaphysical character. The ontology is determined by the limits and language of the cognizing agent. Finally, it is argued that the idea of a posteriori necessity is not correct due to the fact that empirical sciences do not have strict limitations on the field of the possible. There is neither a “physical necessity” nor a “biological necessity”, etc. There is only a logical necessity of the two types mentioned earlier. Therefore, the term “a posteriori necessity” should always be replaced by the term “metaphysically necessary”. The connection of the semantics of possible worlds with metaphysics is considered. The reasons why the “epistemically possible” is broader than the “logically possible” in the narrow sense, that is, within the semantics of possible worlds, are explained.

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