DEFINITION OF NECESSITY WITH ENTAILMENT
DEFINITION OF NECESSITY WITH ENTAILMENT

Summary/Abstract: The main idea of the article is to give a reductive explanation of the concept of necessity. It is done with the concepts of truth, law and entailment. I claim that the sentence “It is necessary that P” means that (1) There is a set of truths and (2) There is a set of laws such that (3) P is implied by the set of truths and the set of laws. Because of some implicature phenomenon the sentence “It is possible that P” means that (1) There is such a set of truths that (2) There is no such a set of laws that (3) It is implied by the set of truths and the set of laws that not P. Kinds of necessity (like logical or physical) rely on the kinds of laws which are used. After the theory is presented some detailed questions are discussed. I raise such questions like kinds of practical necessity, unavoidability, real and fictional necessity, possible worlds, epistemic necessity, necessity de re, conceivability and implication. The main author I refer to is Kripke, though in the main I criticize him. Also I indicate a mistake in Quine’s “number 9” reasoning, and I present how to introduce the natural implication to the propositional calculus without use of any modal operators.

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