Negation, Truth and Falsity

Abstract

The present article includes thematically connected questions on negation in the areas of the philosophy of logic, philosophical logic and metaphysics. It highlights a central problem negation poses to a certain area of philosophy. The purpose of the article is also to analyze negation in the areas of the philosophy of logic, philosophical logic and metaphysics. It highlights a central problem negation poses to a certain area of philosophy. It includes historical references, puts the problems discussed into context, and ties together a number of the main themes and problems. The investigation discusses the problem of logical revisionism and whether there is any room for genuine disagreement, and hence shared meaning, between the classicist and deviant’s respective uses of ‘not’. If there is not, revision is impossible. We argue that revision is indeed possible and provide an account of negation as contradictoriness according to which a number of alleged negations are declared genuine. Among them are the negations of FDE (First-Degree Entailment) and a wide family of other relevant logics, LP (Priest’s dialetheic “Logic of Paradox”), Kleene weak and strong 3-valued logics with either “exclusion” or “choice” negation, and intuitionistic logic. We also discuss the problem of furnishing intuitionistic logic with an empirical negation for adequately expressing claims of the form ‘A is undecided at present’ or ‘A may never be decided’ the latter of which has been argued to be intuitionistically inconsistent. We reveal the importance of various notions of consequence-as-s-preservation where s may be falsity (versus untruth), indeterminacy or some other semantic (or “algebraic”) value, in formulating rationality constraints on speech acts and propositional attitudes such as rejection, denial and dubitability. The article provides an account of the nature of truth values regarded as objects. It is argued that only truth exists as the maximal truthmaker. The consequences this has for semantics representationally construed are considered and it is argued that every logic, from classical to non-classical, is gappy. Moreover, a truthmaker theory is developed whereby only positive truths, an account of which is also developed therein, have truthmakers. We investigate the definability of negation as “absolute” impossibility, i.e. where the notion of necessity or possibility in question corresponds to the global modality.