A theory of properties

1987 ◽  
Vol 52 (2) ◽  
pp. 455-472 ◽  
Author(s):  
Ray Turner
Keyword(s):  
Recent Work ◽  
Set Theory ◽  
Semantic Theory ◽  
Truth Predicate ◽  
Minimal Logic ◽  
History Of ◽  
Concept Of Truth ◽  
Almost All ◽  
The Liar ◽  
Self Reference

Frege's attempts to formulate a theory of properties to serve as a foundation for logic, mathematics and semantics all dissolved under the weight of the logicial paradoxes. The language of Frege's theory permitted the representation of the property which holds of everything which does not hold of itself. Minimal logic, plus Frege's principle of abstraction, leads immediately to a contradiction. The subsequent history of foundational studies was dominated by attempts to formulate theories of properties and sets which would not succumb to the Russell argument. Among such are Russell's simple theory of types and the development of various iterative conceptions of set. All of these theories ban, in one way or another, the self-reference responsible for the paradoxes; in this sense they are all “typed” theories. The semantical paradoxes, involving the concept of truth, induced similar nightmares among philosophers and logicians involved in semantic theory. The early work of Tarski demonstrated that no language that contained enough formal machinery to respresent the various versions of the Liar could contain a truth-predicate satisfying all the Tarski biconditionals. However, recent work in both disciplines has led to a re-evaluation of the limitations imposed by the paradoxes.In the foundations of set theory, the work of Gilmore [1974], Feferman [1975], [1979], [1984], and Aczel [1980] has clearly demonstrated that elegant and useful type-free theories of classes are feasible. Work on the semantic paradoxes was given new life by Kripke's contribution (Kripke [1975]). This inspired the recent work of Gupta [1982] and Herzberger [1982]. These papers demonstrate that much room is available for the development of theories of truth which meet almost all of Tarski's desiderata.

scholarly journals On the supposed first stage larva of Leptohylemyia coarctata, Fall.

1917 ◽  
Vol 8 (2) ◽  
pp. 121-123 ◽  
Author(s):  
D. Keilin
Keyword(s):  
Life History ◽  
Recent Work ◽  
European Countries ◽  
Stage Larva ◽  
History Of ◽  
Almost All

It has been well known since the studies of Taschenberg (1864–1872) that the larvae of Leptohylemyia coarctata, Fall., attack wheat and rye. The damage due to this fly has been observed many times in almost all European countries, and many papers have been devoted to its life-history. Of these papers the most important are those of E. Ormerod (1882–1895), S. Rostrup (1905–1911), T. Hedlund (1906- 1907), P. Marchal (1909) and finally the recent work of Kurdjumov (1914).

Construction of Truth Predicates: Approximation Versus Revision

1998 ◽  
Vol 4 (4) ◽  
pp. 399-417 ◽  
Author(s):  
Juan Barba
Keyword(s):  
Liar Paradox ◽  
Predicate Symbol ◽  
Main Idea ◽  
Truth Predicate ◽  
Order Language ◽  
Fixed Model ◽  
Contextual Dependence ◽  
The Subject ◽  
Concept Of Truth ◽  
The Liar

§1. Introduction. The problem raised by the liar paradox has long been an intriguing challenge for all those interested in the concept of truth. Many “solutions” have been proposed to solve or avoid the paradox, either prescribing some linguistical restriction, or giving up the classical true-false bivalence or assuming some kind of contextual dependence of truth, among other possibilities. We shall not discuss these different approaches to the subject in this paper, but we shall concentrate on a kind of formal construction which was originated by Kripke's paper “Outline of a theory of truth” [11] and which, in different forms, reappears in later papers by various authors.The main idea can be presented as follows: assume a first order language ℒ containing, among other unspecified symbols, a predicate symbol T intended to represent the truth predicate for ℒ. Assume, also, a fixed model M = 〈D, I〉 (the base model)where D contains all sentences of ℒ and I interprets all non-logical symbols of ℒ except T in the usual way. In general, D might contain many objects other than sentences of ℒ but as that would raise the problem of the meaning of sentences in which T is applied to one of these objects, we shall assume that this is not the case.

SUPER LIARS

2010 ◽  
Vol 3 (3) ◽  
pp. 374-414 ◽  
Author(s):  
PHILIPPE SCHLENKER
Keyword(s):  
Fixed Points ◽  
Detailed Analysis ◽  
Expressive Power ◽  
Truth Predicate ◽  
Truth Values ◽  
Kripke’S Theory Of Truth ◽  
Domain Restrictions ◽  
The Liar ◽  
Self Reference ◽  
Linguistic Means

Kripke’s theory of truth offered a trivalent semantics for a language which, like English, contains a truth predicate and means of self-reference; but it did so by severely restricting the expressive power of the logic. In Kripke’s analysis, the Liar (e.g., This very sentence is not true) receives the indeterminate truth value, but this fact cannot be expressed in the language; by contrast, it is straightforward to say in English that the Liar is something other than true. Kripke’s theory also fails to handle the Strengthened Liar, which can be expressed in English as: This very sentence is something other than true. We develop a theory which seeks to overcome these difficulties, and is based on a detailed analysis of some of the linguistic means by which the Strengthened Liar can be expressed in English. In particular, we propose to take literally the quantificational form of the negative expression something other than true. Like other quantifiers, it may have different implicit domain restrictions, which give rise to a variety of negations of different strengths (e.g., something other than true among the values {0, 1}, or among {0, 1, 2}, etc). This analysis naturally leads to a logic with as many truth values as there are ordinals—a conclusion reached independently by Cook (2008a). We develop the theory within a generalization of the Strong Kleene Logic, augmented with negations that each have a nonmonotonic semantics. We show that fixed points can be constructed for our logic, and that it enjoys a limited form of ‘expressive completeness’. Finally, we discuss the relation between our theory and various alternatives, including one in which the word true (rather than negation) is semantically ambiguous, and gives rise to a hierarchy of truth predicates of increasing strength.

scholarly journals Gestalt Shifts in the Liar orWhy KT4M Is the Logic of Semantic Modalities

2017 ◽  
Author(s):  
Susanne Bobzien ◽  
Bradley Armour-Garb ◽  
Bradley Armour-Garb
Keyword(s):  
Modal Logic ◽  
Classical Logic ◽  
Liar Paradox ◽  
Truth Predicate ◽  
Free Solution ◽  
Formal Representation ◽  
Concept Of Truth ◽  
The Liar ◽  
The Liar Paradox ◽  
Truth Operator

This chapter offers a revenge-free solution to the liar paradox and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why (and how) truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M. Drawing on the structure of KT4M, the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable.

Some Recent Work on Early Benedictine History

1964 ◽  
Vol 1 ◽  
pp. 35-46
Author(s):  
David Knowles
Keyword(s):  
Recent Work ◽  
New Testament ◽  
Critical Edition ◽  
Historical Scholarship ◽  
The Past ◽  
History And Literature ◽  
History Of ◽  
Almost All ◽  
Monastic History ◽  
Benedictine Monasticism

Thirty years ago a phase of monastic historical scholarship was drawing towards its close. For some forty years previously a group of scholars, who may fitly be considered the founders of critical monastic history of our century, had been actively at work. Almost all belonged to, or were connected with, three Benedictine abbeys: Maredsous in Belgium, Farnborough and Downside in England, belonging respectively to the Congregations of Beuron, France and England. Among them stood out Ursmer Berlière of Maredsous, creator and for long editor of the Revue Bénédictine and historian of medieval monasticism; his colleague Germain Morin, equally distinguished in the patristic and monastic fields; André Wilmart of Farnborough, unrivalled in our age in his knowledge of monastic literature and spirituality, and his colleagues Ferdinand Cabrol and Henri Leclercq; and at Downside Edmund Bishop and Cuthbert Butler. To these may be added John Chapman, originally of Maredsous and later of Downside who, though primarily a patristic and New Testament scholar, turned in his last years to the age of St Benedict; and Abbot Delatte of Solesmes who, though not an historian, distilled and presented to modern monks the wisdom of innumerable commentators of the past on the Rule of St Benedict. Taken as a group, these men had surveyed the history and literature of the Benedictine order between 540 and 1350, while Butler had produced a sound critical edition of the Rule and, together with others, had analysed the legislation and spiritual doctrine of Benedictine monasticism with a fulness that had not been achieved for any other medieval order, save perhaps that of St Francis.

From the Tower of London to the Thomas More Society of Buenos Aires: “Give me thy grace, good Lord, to set the world at nought”

Moreana ◽  
2005 ◽  
Vol 42 (Number 164) (4) ◽  
pp. 187-206
Author(s):  
Clare M. Murphy
Keyword(s):  
Buenos Aires ◽  
Short History ◽  
Thomas More ◽  
Tower Of London ◽  
Hebrew Poetry ◽  
Prayer Book ◽  
The World ◽  
History Of ◽  
Book Of Hours ◽  
Almost All

The Thomas More Society of Buenos Aires begins or ends almost all its events by reciting in both English and Spanish a prayer written by More in the margins of his Book of Hours probably while he was a prisoner in the Tower of London. After a short history of what is called Thomas More’s Prayer Book, the author studies the prayer as a poem written in the form of a psalm according to the structure of Hebrew poetry, and looks at the poem’s content as a psalm of lament.

Conversation with a Truth Seeker

2006 ◽  
Vol 8 (1) ◽  
pp. 161-170 ◽  
Author(s):  
Jaap Bos
Keyword(s):  
History Of Psychoanalysis ◽  
History Of ◽  
Concept Of Truth ◽  
Forms Of Knowledge

This paper is an invited response to Peter Rudnytsky's ‘Guardians of truth’ article. Taking issue with what are presented as fundamental theoretical and methodological caveats, this article discusses the question of when and how differing discourses on the history of psychoanalysis may or may not be compatible. In particular the author questions the validity of a concept of truth as defined from within a field of knowledge, to arrive at definitions of discourse and dialogue that can be useful to acquire new forms of knowledge.

Microlanguages, Vagueness, and Paradox

2017 ◽  
Author(s):  
Peter Ludlow ◽  
Bradley Armour-Garb
Keyword(s):  
Recent Work ◽  
Dynamic Theory ◽  
Liar Paradox ◽  
Context Sensitivity ◽  
Static Picture ◽  
The Liar ◽  
The Liar Paradox

This chapter follows recent work in philosophy, linguistics, and psychology, which rejects the standard, static picture of languages and highlights its context sensitivity—a dynamic theory of the nature of language. On the view advocated, human languages are things that we build on a conversation-by-conversation basis. The author calls such languages microlanguages. The chapter argues that thinking of languages in terms of microlanguages yields interesting consequences for how we should think about the liar paradox. In particular, we will see that microlanguages have admissible conditions that preclude liar-like sentences. On the view presented in the chapter, liar sentences are not even sentences of any microlanguage that we might construct (or assertorically utter). Accordingly, the proper approach to such a paradoxical sentence is to withhold the sentence—not permitting it to be admitted into our microlanguage unless, or until, certain sharpening occurs.

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