We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...) KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀. (shrink)

consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non-trivial fashion. The extended methods of formal proof must capture the essentials of the so-called ‘semantical argument’ for the truth of the Gödel sentence. We are concerned to show that the (...) deflationist has at his disposal such extended methods—methods which make no use or mention of a truth-predicate. This consideration leads us to reassess arguments recently advanced—one by Shapiro and another by Ketland—against the deflationist's account of truth. Their main point of agreement is this: they both adduce the Gödel phenomena as motivating a ‘thick’ notion of truth, rather than the deflationist's ‘thin’ notion. But the so-called ‘semantical argument’, which appears to involve a ‘thick’ notion of truth, does not really have to be semantical at all. It is, rather, a reflective argument. And the reflections upon a system that are contained therein are deflationarily licit, expressible without explicit use or mention of a truth-predicate. Thus it would appear that this anti-deflationist objection fails to establish that there has to be more to truth than mere conformity to the disquotational T-schema. (shrink)

I am not a deflationist. I believe that truth and falsity are substantial. The truth of a proposition consists in its having a constructive proof, or truthmaker. The falsity of a proposition consists in its having a constructive disproof, or falsitymaker. Such proofs and disproofs will need to be given modulo acceptable premisses. The choice of these premisses will depend on the discourse in question.

Any consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non-trivial fashion. The extended methods of formal proof must capture the essentials of the so-called 'semantical argument' for the truth of the Gödel sentence. We are concerned to show that (...) the deflationist has at his disposal such extended methods-methods which make no use or mention of a truth-predicate. This consideration leads us to reassess arguments recently advanced-one by Shapiro and another by Ketland-against the deflationist's account of truth. Their main point of agreement is this: they both adduce the Gödel phenomena as motivating a 'thick' notion of truth, rather than the deflationist's 'thin' notion. But the so-called 'semantical argument', which appears to involve a 'thick' notion of truth, does not really have to be semantical at all. It is, rather, a reflective argument. And the reflections upon a system that are contained therein are deflationarily licit, expressible without explicit use or mention of a truth-predicate. Thus it would appear that this anti-deflationist objection fails to establish that there has to be more to truth than mere conformity to the disquotational T-schema. (shrink)

This discussion of pride, shame, and guilt centers on the beliefs involved in the experience of any of these emotions. Through a detailed study, the author demonstrates how these beliefs are alike--in that they are all directed towards the self--and how they differ. The experience of these three emotions are illustrated by examples taken from English literature. These concrete cases supply a context for study and indicate the complexity of the situations in which these emotions usually occur.

Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called (...) conservativeness. I present some technical results, some of which may be found in Tarski (1936), concerning the logical properties of truth theories; in particular, concerning the conservativeness of adding a truth theory for an object level language to any theory expressed in it. It transpires that various deflationary truth theories behave somewhat differently from the standard Tarskian truth theory. These results suggest that Tarskian theories of truth are not redundant or dispensable. Finally, I hint at an analogy between the behaviour of mathematical theories and of standard (Tarskian) theories of truth with respect to their indispensability to, as Quine would put, our 'scientific world-view'. (shrink)

Any (1-)consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a nontrivial fashion. The extended methods of formal proof must capture the essentials of the so-called 'semantical argument' for the truth of the Gödel sentence. We are concerned to show that (...) the deflationist has at his disposal such extended methods--methods which make no use or mention of a truth-predicate. (edited). (shrink)

S. 39: "My project in this paper is to develop the initial distinction which I have drawn between recognition and appraisal respect into a more detailed and specific account of each. These accounts will not merely be of intrinsic interest. Ultimately I will use them to illuminate the puzzles with which this paper began and to understand the idea of self-respect." 42 " Thus, insofar as respect within such a pursuit will depend on an appraisal of the participant from the (...) perspective of whatever standards are held to be appropriate to the pursuit, such respect will depend on a judgement to which excellences of character are thought relevant. Note that exactly what aspect of the person's character is thought to be relevant in this instance is his recognition respect (or lack of it) for the standards of the pursuit." 44 "This attitude fails of being appraisal respect in that my having it toward the person is conditional on those traits being such as to make him server a particular purpose that I happen to have" 44 - 45 "To sum up: Appraisal respect is an attitude of positibe appraisal of a person either judged as a person or as engaged in some more specific pursuit. In the first case, the appropriate grounds are features of the person's character: dispositions to act for particular reasons or a higher-level disposition to act for the best reasons. In the second case, though features of character do not exhaust the appropriate grounds for appraisal respect, some such character traits will be relevant (recognition respect for the standards of a particular pursuit). Also, the other features which constitute the appoprate excellences of the pursuit must be related to traits of character in the way specified. In both cases, the positive appraisal of the person, and of his traits, must be categorical. It cannot depend on the fact that the person, because of his traits, serves an interest or purpose of one's own." 45 "To have recognition respect for someone as a person is to give appropriate weight to the fact that he or she is a person by being willing to constrain one's behaviour in ways required by that fact." 45 "This is rather different from having an attitude of appraisal respect for someone as a person. The latter is a positive appraisal oif an individual made with regard ti those features which are excellences of persons. As such, it is not owed to everone, for it may or may not be merited. When it is, what is merited is just the positive appraisal itself." 47 "Second, the only beings who are approriate objects of appraisal respect are those who are capable of acting for reasons and hence capable of conceiving of various facts as meriting more or less consideration in deliberation.". (shrink)

There is a cognitive, an affective, a conative, and an attitudinal component to a genuine apology. In discussing these components, I address the following questions. Might apologies be due for non-culpable actions? Might apologies be due for choices in moral dilemmas? What is the link between sympathy, remorse and making amends? Is it meaningful for resilient akratics to apologize? How much moral renewal is required when one apologizes? Why should apologies be offered in a humble manner? And is there some (...) truth to P. G. Wodehouse's dictum that 'the right sort of people do not want apologies'? (shrink)

This book focuses on the degree to which certain moral and legal doctrines are rooted in specific passions that are then institutionalised in the form of criminal law. A philosophical analysis is developed of the following questions: when, if ever, should hatred be overcome by sympathy or compassion? What are forgiveness and mercy and to what degree do they require - both conceptually and morally - the overcoming of certain passions and the motivation by other passions? If forgiveness and mercy (...) indeed are moral virtues, what role, if any, should they play in the law? (shrink)

Nearly everyone has wronged another. Who among us has not longed to be forgiven? Who has not struggled to forgive? Charles Griswold has written the first comprehensive philosophical book on forgiveness in both its interpersonal and political contexts, as well as its relation to reconciliation. Having examined the place of forgiveness in ancient philosophy and in modern thought, he discusses what forgiveness is, what conditions the parties to it must meet, its relation to revenge and hatred, when it is permissible (...) and whether it is obligatory, and why it is a virtue. Griswold argues that forgiveness is inappropriate in politics, and analyzes the nature and limits of political apology with reference to historical examples. The book concludes with an examination of the relation between memory, narrative, and truth. (shrink)

According to how we treat others, we acquire merit or guilt, deserve praise or blame, and receive reward or punishment, looking in the end for atonement. In this study distinguished theological philosopher Richard Swinburne examines how these moral concepts apply to humans in their dealings with each other, and analyzes these findings, determining which versions of traditional Christian doctrines--sin and original sin, redemption, sanctification, and heaven and hell--are considered morally acceptable.

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the (...) Second Theorem, and exploring a family of related results. The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic. (shrink)

This book focuses on the degree to which certain moral and legal doctrines are rooted in specific passions that are then institutionalised in the form of criminal law. A philosophical analysis is developed of the following questions: when, if ever, should hatred be overcome by sympathy or compassion? What are forgiveness and mercy and to what degree do they require - both conceptually and morally - the overcoming of certain passions and the motivation by other passions? If forgiveness and mercy (...) indeed are moral virtues, what role, if any, should they play in the law? (shrink)