Logic in Opposition

It is claimed hereby that, against a current view of logic as a theory of consequence, opposition is a basic logical concept that can be used to define consequence itself. This requires some substantial changes in the underlying framework, including: a non-Fregean semantics of questions and answers, instead of the usual truth-conditional semantics; an extension of opposition as a relation between any structured objects; a definition of oppositions in terms of basic negation. Objections to this claim will be reviewed

Negation in context

The present essay includes six thematically connected papers on negation in the areas of the philosophy of logic, philosophical logic and metaphysics. Each of the chapters besides the first, which puts each the chapters to follow into context, highlights a central problem negation poses to a certain area of philosophy. Chapter 2 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. I 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. Chapter 3 discusses 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. Chapter 4 highlights 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. Chapter 5 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. Chapter 6 investigates the definability of negation as "absolute" impossibility, i.e. where the notion of necessity or possibility in question corresponds to the global modality. The modality is not readily definable in the usual Kripkean languages and so neither is impossibility taken in the broadest sense. The languages considered here include one with counterfactual operators and propositional quantification and another bimodal language with a modality and its complementary. Among the definability results we give some preservation and translation results as well

Ancestor Worship in The Logic of Games. How foundational were Aristotle\u27s contributions?

Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it?\u27\u27 A recent suggestion is that at least part of the desired support might be found in the Greek dialectical writings. If so, perhaps we could say that those works possess a kind of foundational significance. The relation of being foundational for is interesting in its own right. In this paper, I explore its ancient applicability to relevant, paraconsistent and nonmonotonic logics, before returning to the question of its ancestral tie, or want of one, to the modern logics of games

A brief history of negation

AbstractThe history of scholarship on negation tracks and illuminates the major developments in the history of metaphysics, philosophy of language, and philosophy of mind, from Parmenides, Plato and Aristotle through Frege, Russell, and Wittgenstein to contemporary formal theorists. Our perspective focuses on the catalytic role played by the 20th century philosopher of language Paul Grice, whose views on negation serve as a fulcrum for his attempt to bridge the (neo-)Traditionalist and Formalist traditions in logical thought. Grice's remarks on negation and speaker meaning and the elaboration of his ideas by subsequent neo-Griceans are summarized and situated within a broader picture of the role of contradictory and contrary negation in the frameworks of Aristotelians, Medievals, early modern schoolmaster-logicians, 19th and early 20th century neo-Idealists and Formalists, Oxford ordinary-language analytics, practitioners of classical and non-classical logics, and a range of other philosophers and linguists. Particular attention is paid to the relations between negation and the other operators of propositional and predicate calculus. Implications for accounts of the semantics and pragmatics of natural language are also pursued and extensive references to related work are provided

On relationships between the logic of law, legal positivism and semiotics of law

The issue of reciprocal relationships between the logic of law, positivistic theory of the logic of law, and legal semiotics is among the most important questions of the modern theoretical jurisprudence. This paper has not attempted to provide any comprehensive account of the modern jurisprudence (and legal logic). Instead, the emphasis has been laid on those aspects of positivist legal theories, logical studies of law and legal semiotics that allow tracing the common points or the differences between these paradigms of legal research. One of the theses of the present work is that, at the comparative methodological level, the limits of legal semiotics and its object of inquiry could only be defined in relation to legal posi tivism and logical studies of law. This paper also argues for a proper position for legal semiotics in between legal positivism and legal logic. The differences between legal positivism, legal logic and legal semiotics are best captured in the issue of referent

A Preservationist Approach to Relevant Logic

The semantics I develop extend an approach to logic called preservationism. The preservationist approach to logic interprets non-classical consequence relations as preserving something other than truth. I specifically extend a preservationist approach, due to Bryson Brown, which interprets various paraconsistent consequence relations as preserving measures of ambiguity. Relevant logics are constructible by extending one of these logics with an implication connective. I develop a formal semantics which I show to be adequate for interesting relevant logics. I argue that the semantics I develop extend the preservationist approach to relevant logic by showing how the approach treats the implication connective. I conclude by arguing that some of the most pressing objections to the standard semantics for relevant logics do not apply to the ambiguity preservation account

Theistic Open Futurism: A Critical Philosophical Investigation

In this dissertation I critically evaluate and develop a model of God I dub “theistic open futurism”—the view that an omniscient, omnipotent, and omnibenevolent being exists but fails to know future contingent statements because such statements are not true. Contrary to what their free will critics have supposed, I argue that theistic open futurists do not subscribe to a metaphysical vision of the future that is logically or religiously incoherent. With respect to the latter, I suggest that while some open theists have overstated their case concerning the amount of providential control God could have given the reality of an open future, at least one rival model of divine providence that is often advertised as providing more control than the openness position may not have the clear advantage that some initially believed. In any case, I argue that if one holds to an incompatibilist account of free will and believes we occasionally act freely, then that person ought to think the future is open

To Be and Not to Be: Hamlet’s Identity. Lacan’s Errors and His Disappointing Interpretation of Shakespeare

Hamlet’s desire must be examined in relation to the desire to be, that is the desire for identity: this is the claim upheld in this study. Consequently, the article begins by making a distinction between the desire to be and the desire to have: this distinction was expressed in a new way by Freud, but was never adequately developed either by Freud himself or by Lacan. Therefore, the desire to be has remained prisoner of the Oedipus complex, even in Lacan’s reformulation in which it basically proves to be the desire to be the Phallus.Yet the desire to be must be understood starting from the “modal revolution” introduced by Heidegger, and this allows us to appreciate the more innovative thesis in Freud’s essay, “Group Psychology and the Analysis of the Ego” (1921). Identity is a relationship that may be considered to be a coincidence or a non-coincidence with oneself: in the latter case, we will refer to an “overcoming identity.” As a result, philosophy, the theory of the subject and the theory of literature are called upon to investigate the modes of identity.From the perspective of the modes of being, Hamlet is analyzed here starting from his refusal to subordinate his own identity to the role of avenger. His desire oversteps the borders of neurosis and melancholy, in which it had traditionally been imprisoned (also by Lacan). Hamlet is a hero of non-coincidence: he goes beyond the models that appear to him to be inadequate and attempts to construct a flexible identity. Adopting the mask of madness, he has the opportunity to display his linguistic creativity. This does not deny that Hamlet is a tormented hero: the shadow of his father and the lust of his mother are obstacles to the desire for identity.This interpretation is only delineated in the last pages of the article. It is first necessary to show that the limitations of Lacan’s interpretation derive from a narrow conception of the Symbolic and the desire to be for which Lacan never acknowledges creative possibilities. The Lacanian notion of “lack” is a logical and epistemological obstacle that prevents the development of the logic of flexibility and the nonof “non-coincidence.