WikiJournal Preprints/Semantics of an imperative logic

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Abstract

A number of problems have been raised in regards to the construction of an imperative logic, i.e. a formal system which can incorporate imperative statements as well as those normally utilized in logic. This paper applies a performative theory of truth to these problems, by placing imperative statements in a seperate system anterior to classical logic, by [stuff]. The latter half of this paper is a study of imperative statements as they occur in informal logic.

Introduction

Manuscript text goes here

Semantics of an imperative logic

The essential premise of this paper is that imperatives are anterior to propositions. Imperatives are necessarily social phenomena, the parallel between the performative act of truth in Strawson's theory should be clear. They are used to structure the space in which propositions inhabit, in fact their sole function is to establish propositions. Thus the imperative operator $!$ carries a meaning incredibly similar to the truth function in F. P. Ramsey's theory of truth, which is an important precursor. That is, within classical logic, $!P$ can only be

Imperative statements in informal logic and natural language

While classical logic does not normally concern itself with commands, other logics do regularly utilize imperatives. In mathematical logic, proof by contradiction is usually rendered in natural language with imperative statements:

Suppose $\neg p$.

While perhaps overly-simplistic, suppose (and assume) are imperatives. They do not have a logic value, but are rather artifacts of natural language. The above statement would simply be rendered as $\neg p$ in formal logic, a simple deceleration.

This highlights the actual function of the imperative as anterior to the logical content. Our formalization of imperatives

Problems with imperative logic

A major flaw in this conception of imperative logic is that it greatly simplifies imperative statements (which in natural language are incredibly complex and diverse) to a simple operator on a proposition.

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