DISCIPLINING RELATIVISM AND TRUTH

Abstract. Imre Lakatos's philosophy of science can provide helpful leads for theological methodology, but only when mediated by the disciplines that lie between the natural sciences and theology. The questions of relativism and truth are used as indices for comparing disciplines, and Lakatos's theory of natural science is taken as the starting point. Major modifications of Lakatos's work are demanded as one moves from the natural sciences, through economics, the interpretive social sciences, literary theory, and into theology. Although theology may consist of Lakatosian research programs, it also includes programs of interpretation and programs for living. This conclusion must influence our definition of theological truth and our assessment of theological relativism.     

TRUTH, RELATIVISM, AND CROSSWORD PUZZLES

Abstract. Neither the correspondence nor the coherence theory of truth does justice to the truth claims made in science and theology. I propose a new definition that relates truth to solving puzzles. I claim that this definition is more adequate than either of the traditional theories and that it offers two additional benefits: first, it provides grounds for a theory regarding the relations between theology and science that may stand up better to philosophical scrutiny than does critical realism; and second, it blocks the move to relativism based on recognition of the plurality of perspectives and the historical and social conditioning of knowledge.     

On Vagueness,Truth Values and Fuzzy Logics

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus. Presented by Daniele Mundici     

TRUTH AS AN EPISTEMIC IDEAL

Several philosophers—including C. S. Peirce, William James, Hilary Putnam and Crispin Wright—have proposed various versions of the notion that truth is an epistemic ideal. More specifically, they have held that a proposition is true if and only if it can be fixedly warranted by human inquirers, given certain ideal epistemic conditions. This paper offers a general critique of that idea, modeling conceptions of ideality and fixed warrant within the semantics that Kripke developed for intuitionistic logic. It is shown that each of the two plausible notions of fixed warrant faces difficulties and that, moreover, “truth” defined in terms of either of them is distressingly dependent upon one’s conception of idealized inquiry and perhaps also upon one’s standards of warrant.     

Henkin Quantifiers and the Definability of Truth

Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension L _* ¹(H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close L _* ¹(H) with respect to Boolean operations, and obtain the language L ¹(H). At the next level, we consider an extension L _* ²(H) of L ¹(H) in which every sentence is an L ¹(H)-sentence prefixed with a Henkin quantifier. We repeat this construction to infinity. Using the (un)-definability of truth – in – N for these languages, we show that this hierarchy does not collapse. In addition, we compare some of the present results to the ones obtained by Kripke (1975), McGee (1991), and Hintikka (1996).     

RELIGION VERSUS SCIENCE: THE CONFLICT IN REFERENCE TO TRUTH VALUE,NOT CASH VALUE

Abstract. The rift between science and religion needs to be assessed not merely on pragmatic grounds, on the basis of the effect of scientific versus religious beliefs on people's behavior, as John Caiazza's essay does, but also and above all in regard to the cogency of the respective beliefs in reference to what we can reasonably assume is the true face of reality. About such truth value, the conflict is not irremediable; there are elements of belief regarding the nature of reality that are strikingly similar regardless of whether one arrived at them on the basis of faith in revealed knowledge or on the basis of knowledge acquired by reasoning from or in reference to experience. Two such items are selected here by way of example: belief that in certain states of mind and consciousness individuals can experience union with something larger or deeper than themselves, and belief that the universe we inhabit is the result of an original creative act.     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt     

Why Combine Logics?

Combining logics has become a rapidly expanding entreprise that is inspired mainly by concerns about modularity and the wish to join together tailor made logical tools into more powerful but still manageable ones. A natural question is whether it offers anything new over and above existing standard languages.By analysing a number of applications where combined logics arise, we argue that combined logics are a potentially valuable tool in applied logic, and that endorsements of standard languages often miss the point. Using the history of quantified modal logic as our main example, we also show that the use of combined structures and logics is a recurring theme in the analysis of existing logical systems.     

Taking Degrees of Truth Seriously

This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the particular cases of Łukasiewicz’s many-valued logics and of logics associated with varieties of residuated lattices are also presented. Finally the extension of this paradigm to other, more general situations is discussed, highlighting the need for philosophical or applied motivations in the selection of the truth degrees, due both to the interpretation of the idea of truth degree and to some mathematical difficulties.     

Truth as Translation – Part B

This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate – this is possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to first-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted language with a high degree of expressiveness leads to changes in the ontology of the language.     

Theories of Truth Which Have No Standard Models

This papers deals with the class of axiomatic theories of truth for semantically closed languages, where the theories do not allow for standard models; i.e., those theories cannot be interpreted as referring to the natural number codes of sentences only (for an overview of axiomatic theories of truth in general, see Halbach[6]). We are going to give new proofs for two well-known results in this area, and we also prove a new theorem on the nonstandardness of a certain theory of truth. The results indicate that the proof strategies for all the theorems on the nonstandardness of such theories are "essentially" of the same kind of structure.     

Note on Some Fixed Point Constructions in Provability Logic

We present a quite simple proof of the fixed point theorem for GL. We also use this proof to show that Sambin's algorithm yields a fixed point.     

Truth as Translation – Part A

According to Tarski's Convention T, the adequacy of a truth definition is (implicitly) defined relatively to a translation mapping from the object language to the metalanguage; the translation mapping itself is left unspecified. This paper restates Convention T in a form in which the relativity to translation is made explicit. The notion of an interpreted language is introduced, and a corresponding notion of a translation between interpreted languages is defined. The latter definition is stated both in an algebraic version, and in an equivalent possible worlds version. It is a consequence of our definition that translation is indeterminate in certain cases. Finally, we give an application of our revised version of Convention T and show that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate. This is possible if only truth is based on a nonstandard translation mapping by which, e.g., the Liar sentence is translated to its own negation. In this part of the paper this existence result is proved only for languages without quantifiers; in Part B the result will be extended to first-order languages.     

ON THE EVOLUTION OF MORALITY AND RELIGION: A RESPONSE TO LEE CRONK

Abstract. Issue is taken with Dawkins and Krebs's (1978) conception of communication as being by nature manipulative and with Cronk's proposals concerning the evolution of morality, both of which are grounded in evolutionary biology. An alternative view, which recognizes that which humanity has in common with other species but which emphasizes humanity's distinctiveness, is offered to account for religion and morality.     

A COMPARISON OF THE EFFECTS OF FIXED AND VARIABLE RATIO SCHEDULES OF REINFORCEMENT ON THE BEHAVIOR OF DEAF CHILDREN

The performance of all five students in an adjustment class for deaf children was compared under fixed and variable ratio schedules of reinforcement. During the fixed ratio (FR) condition, students earned checks if they were attentive and did not engage in disruptive behavior. These checks could be exchanged for the opportunity to draw a prize from a grab bag. During the variable ratio (VR) condition, they earned a draw from the grab bag according to a variable ratio schedule with a mean ratio equal to the value of the preceding FR schedule. During the VR condition, students visually attended more and engaged in disruptive behavior less often than during the FR condition. The number of math problems completed per minute was also higher during the VR condition although no specific consequences were applied to math performance.