Search Results

Boolean Negation

Graham Priest

in Doubt Truth to be a Liar

This chapter argues that in the context of an account of meaning appropriate for dialetheism, Boolean (classical) negation is a meaningless notion.

Chapter 6: Contradictory Pairs

C. W. A. Whitaker

in Aristotle's De Interpretatione: Contradiction and Dialectic

This chapter, which concludes the introductory section of the work, narrows the focus to simple assertions. Aristotle demonstrates with brilliant neatness that all such assertions either affirm or ... More

This chapter, which concludes the introductory section of the work, narrows the focus to simple assertions. Aristotle demonstrates with brilliant neatness that all such assertions either affirm or deny, and that moreover they may be ordered into pairs, one representing a pair of simple elements as combined, the other as separated. His approach reflects his ’internal’ theory of negation: very different from the Stoic ’external’ view more familiar to later logicians. His definition of negation does not presuppose anything about the truth or falsehood of the two members of a contradictory pair.Less

Do Paracomplete Solutions Depend on Expressive Limitations?

Hartry Field

in Saving Truth From Paradox

The chapter considers various versions of the charge that paradox has been avoided only by limiting the expressive power of the language. The charge that the language has no ‘exclusion negation’ but ... More

The chapter considers various versions of the charge that paradox has been avoided only by limiting the expressive power of the language. The charge that the language has no ‘exclusion negation’ but only ‘choice negation’ is rejected as incorrect. It is true that the language contains no negation or conditional that obeys all the classical or intuitionist laws, but it is argued that no language can coherently contain such operators. Two ingenious arguments by Wright and Restall, according to which we ought to be able to define intuitionist operators from fairly uncontroversial resources, are considered at length and rejected. In the case of the Restall argument, this involves some considerations about how to understand infinite conjunctions and disjunctions.Less

The Influence of Political Institutions on the Effectiveness of Western Democracies

Edeltraud Roller

in The Performance of Democracies: Political Institutions and Public Policy

This chapter examines the hypotheses about the impact of formal and informal institutions on the level, stability, and the structure of political effectiveness of western democracies. It presents a ... More

This chapter examines the hypotheses about the impact of formal and informal institutions on the level, stability, and the structure of political effectiveness of western democracies. It presents a re-analysis of Arend Lijphart's Pattern of Democracy (1999) and investigates the validity of various veto player indices. It is shown that political institutions do matter, but formal and informal institutions cause different effects; both matter only sometimes and only to a limited degree.Less

Contradiction

Graham Priest

in Doubt Truth to be a Liar

This chapter provides an account of the nature of negation which not only endorses the traditional idea of negation as a contradictory-forming operator, but also allows for the possibility of ... More

This chapter provides an account of the nature of negation which not only endorses the traditional idea of negation as a contradictory-forming operator, but also allows for the possibility of dialetheism.Less

Denial and Rejection

Graham Priest

in Doubt Truth to be a Liar

This chapter discusses the connection between negation, denial, and untruth. There are close connections between these notions, but not the simplistic ones that are standardly supposed to obtain.

Introduction

Henny Fiskå Hägg

in Clement of Alexandria and the Beginnings of Christian Apophaticism

This chapter provides an overview of the book. It begins by describing apophatic theology (approaching the divine through negation) in relation to kataphatic theology (based on affirmation) or ... More

This chapter provides an overview of the book. It begins by describing apophatic theology (approaching the divine through negation) in relation to kataphatic theology (based on affirmation) or mystical theology (based on an inner relationship to God). Works that have influenced the approach of this book are surveyed and the remaining chapters outlined.Less

Connectives, Quantifiers, Logic

Stewart Shapiro

in Vagueness in Context

This chapter defines various connectives and quantifiers, and settles on a local notion of validity. The ultimate goal is to delimit a plausible notion of logical consequence and to explore what ... More

This chapter defines various connectives and quantifiers, and settles on a local notion of validity. The ultimate goal is to delimit a plausible notion of logical consequence and to explore what happens with the sorites paradox. It might be noted that the notion of ‘context’ does not appear, as such, in the formal development. Several features of the deployment of vague terms can go under that name, and there is no need to call one of them the context of utterance. This might attenuate any misunderstandings of the philosophical term ‘contextualist’.Less

Negative Concord

Doris Penka

in Negative Indefinites

This chapter is concerned with the phenomenon of negative concord, where multiple instances of morph-syntactically negative elements contribute a single negation to the semantics. It discusses ... More

This chapter is concerned with the phenomenon of negative concord, where multiple instances of morph-syntactically negative elements contribute a single negation to the semantics. It discusses different approaches which treat negative indefinites in languages exhibiting negative concord as either negative polarity items, negative quantifiers, or as ambiguous between both. It shows that none of these can fully account for the behaviour of negative indefinites. The approach of Zeijlstra (2004), which analyses negative concord as form of syntactic agreement and assumes that negative indefinites are semantically non-negative indefinites that have to be licensed by negation, is shown to be able to account for a wide range of data. This approach is elaborated and revised to accommodate the behaviour of negative indefinites in a wider range of negative concord languages.Less

The General Form of the Proposition

Denis McManus

in The Enchantment of Words: Wittgenstein's “Tractatus Logico-Philosophicus”

This chapter explores Wittgenstein’s remarks on ‘the general form of the proposition’ and argues that these too are informed by his desire to show that the impression that there are substantial ... More

This chapter explores Wittgenstein’s remarks on ‘the general form of the proposition’ and argues that these too are informed by his desire to show that the impression that there are substantial ‘logical truths’ is an illusion. It explores Wittgenstein’s understanding of logical inference as ‘unpacking’, his analysis of truth-functional connectives using truth-tables, his account of logical propositions as tautologies and contradictions, and the philosophical significance for Wittgenstein of providing a ‘topic-neutral’ account of logical inference and the logical connectives. Drawing on retrospective remarks of Wittgenstein’s, an explanation is offered on how he could have failed to recognize that his notion of the general form of the proposition is laden with problematic metaphysical commitments.Less

Periphrasis in Tundra Nenets1

Irina Nikolaeva

in Periphrasis: The Role of Syntax and Morphology in Paradigms

A detailed picture of periphrasis in Nenets (Uralic) presents a typologically rare instance of periphrasis in a nominal paradigm (as opposed to more familiar verbal periphrasis). Previous accounts ... More

A detailed picture of periphrasis in Nenets (Uralic) presents a typologically rare instance of periphrasis in a nominal paradigm (as opposed to more familiar verbal periphrasis). Previous accounts treated Nenets nouns as an uncontroversial example of periphrasis, but this chapter demonstrates that a closer look reveals a more complicated picture. It argues that the choice between the usage of the periphrastic dual form and the numeral ‘two’ (which takes the singular) correlates with definiteness and/or discourse givenness. In addition, analysis of this rare instance of periphrasis in a noun system reveals interesting aspects of the way the number system works in the language. The chapter also investigates the periphrastic realization of verbal negation, where the auxiliary carries the information of the verb type. For intransitive verbs, the type is either ‘subjective’ or ‘reflexive’ and there are, surprisingly, arguments in favour of treating these as purely morphological classes.Less

Sentence Negation and Periphrasis

Andrew Spencer

in Periphrasis: The Role of Syntax and Morphology in Paradigms

In order to establish a typological picture of periphrastic negation, this chapter begins from the criteria for periphrasis established by Ackerman and Stump. These are feature intersection, ... More

In order to establish a typological picture of periphrastic negation, this chapter begins from the criteria for periphrasis established by Ackerman and Stump. These are feature intersection, non-compositionality, and distributed exponence. It is argued that while the first two work well for defining periphrasis, the third criterion is not sufficiently robust, and should therefore be substituted by the criterion of multiple exponence. Multiple exponence is a recurrent feature of morphology and therefore, when found in a syntactic construction, it signals its morphology-like status. The chapter analyses the applicability of the criteria by testing them on data from genetically and typologically diverse languages (such as Japanese, and languages within Oto-Manguean, Nilotic, Tungusic, Uralic, Nakh-Daghestanian, and Semitic languages). It shows the extent to which the existing criteria can be applied to languages of different types, and justifies the new criterion (multiple exponence) for identifying periphrasis.Less

Illusion, Irony, and Tragedy

James Davison Hunter

in To Change the World: The Irony, Tragedy, and Possibility of Christianity Today

Politics has become a “social imaginary” that defines the horizon of understanding and the parameters for action. What is never challenged is the proclivity to think of the Christian faith and its ... More

Politics has become a “social imaginary” that defines the horizon of understanding and the parameters for action. What is never challenged is the proclivity to think of the Christian faith and its engagements with culture in political terms. For all, the public has been conflated with the political. But the ressentiment that marks the way they operate makes it clear that a crucial part of what motivates politics is a will to dominate. However, for politics to be about more than power, it depends upon a realm that is independent of the political process. The deepest irony is that the Christian faith has the possibility of autonomous institutions and practices that could be a source of ideals and values that could elevate politics to more than a quest for power. Instead, by nurturing its resentments, they become functional Nietzcheans, participating in the very cultural breakdown they so ardently strive to resist.Less

Indeterminacy and Truth Value Gaps

Mark Richard

in Cuts and Clouds: Vagueness, its Nature, & its Logic

This chapter argues for the following theses. There are perfectly possible meanings (ones of a sort one would think are possessed by many vague predicates) which would necessitate a predicate's being ... More

This chapter argues for the following theses. There are perfectly possible meanings (ones of a sort one would think are possessed by many vague predicates) which would necessitate a predicate's being gappy. Many arguments against the coherence of truth value gaps depend on a very narrow picture of saying, which ignores the possibility of such things as sui generis denial. Frege/Geach objections to things like sui generis denial dissolve once we observe that ‘not’ and other sentence compounding devices lead a double life, sometimes contributing to sense, sometimes to force. There is a simple compositional story about how (for instance) embedding a denial operator within a ‘force conditional’ makes if not A, then B fit to perform a sort of speech act which, when combined with B's denial, commits one to the aptness of asserting A. The trisection thesis — predicates trisect their domains into three groups, those they are true of, those they are false of, and the rest — is correct. The objection to the trisection thesis —that it is inconsistent with the idea that there are no sharp boundaries in a Sorites series — is not compelling: there is no conception of a ‘sharp boundary’ on which it's plausible, both that there are no sharp boundaries in a Sorites series, and that trisection involves the creation of sharp boundaries. Once we recognize that talk of indeterminacy is contrastive, we also recognize that higher order vagueness is not inconsistent with trisection. We also, once we think of indeterminacy as contrastive, come to see that indeterminacy itself is indeterminate: if it is indeterminate whether p, that indeterminacy itself is not something that is settled, but is itself indeterminate.Less

Introduction

Doris Penka

in Negative Indefinites

This chapter lays the ground for the following discussion by introducing central concepts such as negative indefinites, sentential negation, and constituent negation. It also provides background on ... More

This chapter lays the ground for the following discussion by introducing central concepts such as negative indefinites, sentential negation, and constituent negation. It also provides background on the syntactic and semantic framework in which the book is couched, and gives an outline of the following chapters.Less