Academic journal article Linguistic and Philosophical Investigations

Definition of Necessity with Entailment

Academic journal article Linguistic and Philosophical Investigations

Definition of Necessity with Entailment

Article excerpt

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) ? 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.

Keywords: necessity, possibility, entailment, truth, possible worlds, counterfactuals, implication, fiction

The concept of necessity has been examined for many years but still we do not have a good theory of it. There is some variety of accounts but after all they do not seem to be convincing. Perhaps the reason is that we need a new approach. In this article I make a step towards a new direction.

After five introductory paragraphs I present my theory in the next twelve ones (6-16). The concept of necessity is defined with the concepts of truth, law and entailment, so my attempt is reductive. Paragraph 16 is a short recap, and the following paragraphs (17-23) present some further discussion. I raise such questions like kinds of necessity (logical, physical, practical etc.), unavoidability, real and fictional necessity, possible worlds, epistemic necessity, necessity de re, conceivability and implication.

1. Various Kinds of Necessity

What is striking when you analyze the concept of necessity (and possibility as well) is that there are many kinds of necessity. You have logical, conceptual, physical, psychological and many other types of necessity. Many authors concentrate only on some chosen cases or examine them separately. Some kinds of necessity are still omitted as it is with practical necessity, usually expressed with the word "must".

My idea is that a good theory of necessity is not to be a theory of a kind of necessity or a set of theories, each for a detailed case, but a theory that explains what is to be necessity in general, and only then elucidate what the reason is for the variety of necessities and how to deal with them. The idea is based on the belief that the various kinds are the kinds of one common concept, and that it is not a case of essential polysemy.

Thus from my point of view numerous authors which have worked on detailed kinds of necessity missed the general point, though their works may be valuable as case studies. For example, in The Critique of Pure Reason Kant worked on a priori and analytic (kind of logical) necessity. Carnap (1956) also worked on analytic necessity as did Quine in his famous essay on dogmas (1951), also Bealer (2006) worked on logical necessity. Many authors like Horgan (1993) or Chalmers (1996) dealt with both logical and physical necessity.

On the other hand every necessity is of a kind. So the authors, who worked on the concept of necessity without any specification, also called "metaphysical necessity", as C. I. Lewis (1932) or Kripke (1959), (1963), 1970), (1980) and their numerous followers (even of the counterfactuals approach like Stalnaker (1968), Lewis (1973a), Hill (2006), Kment (2006) and Williamson (2007)), and as it is usually in theology or similar domains, also have missed the general point. …

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