A Model of Tolerance

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non-existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity of the consequence relation. A lattice-theoretical framework for a whole family of (zeroth-order) “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic.     

Suszko’s Thesis,Inferential Many-valuedness,and the Notion of a Logical System

According to Suszko’s Thesis, there are but two logical values, true and false. In this paper, R. Suszko’s, G. Malinowski’s, and M. Tsuji’s analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation.

[13, p. 281]

Presented by Jacek Malinowski     

Sharvy’s Lucy and Benjamin Puzzle

Sharvy’s puzzle concerns a situation in which common knowledge of two parties is obtained by repeated observation each of the other, no fixed point being reached in finite time. Can a fixed point be reached?     

Bayes factors: Prior sensitivity and model generalizability

Model selection is a central issue in mathematical psychology. One useful criterion for model selection is generalizability; that is, the chosen model should yield the best predictions for future data. Some researchers in psychology have proposed that the Bayes factor can be used for assessing model generalizability. An alternative method, known as the generalization criterion, has also been proposed for the same purpose. We argue that these two methods address different levels of model generalizability (local and global), and will often produce divergent conclusions. We illustrate this divergence by applying the Bayes factor and the generalization criterion to a comparison of retention functions. The application of alternative model selection criteria will also be demonstrated within the framework of model generalizability.     

PHYSICAL SCALE EFFECTS AND PHILOSOPHICAL THOUGHT EXPERIMENTS

Abstract: The scales across which physical properties exist are vast and subtle in their effects on particular systems placed locally on such scales. For example, human experiential access is restricted only to partial segments of the mass density, size, and temperature scales of the universe. I argue that philosophers must learn to appreciate better the effects of physical scales. Specifically, thought experiments in philosophy should be more sensitive to physical scale effects, because the conclusion of a thought experiment may be undermined by unintentionally ignored scale effects, and the changes required to obtain the foreground state of affairs in a thought experiment might require unacknowledged scale‐spanning changes to the contextual background. I discuss four philosophical thought experiments: Putnam's Twin Earth and Brain in a Vat, Searle's Chinese Room, and Chalmers's Zombies Without Qualia. I close by briefly defending the greater interest and importance of physical possibility over logical possibility.     

BEYOND BARBOUR OR BACK TO BASICS? THE FUTURE OF SCIENCE‐AND‐RELIGION AND THE QUEST FOR UNITY

Reflecting on the future of the field of science‐and‐religion, I focus on three aspects. First, I describe the history of the religion‐and‐science dialogue and argue that the emergence of the field was largely contingent on social‐cultural factors in Western theology, especially in the United States. Next, I focus on the enormous influence of science on Western society and on what I call cultural scientism, which influences discussions in science‐and‐religion, especially how theological notions are taken up. I illustrate by sketching the way divine action has been studied in science‐and‐religion. The divine‐action debates may seem irrelevant to theologians because the way divine action is dealt with in science‐and‐religion is theologically problematic. Finally, I analyze the quest for integration and unity of science and religion that underlies much of the contemporary field of science‐and‐religion and was stimulated particularly by the efforts of Ian Barbour. I argue that his quest echoes the logical positivist vision of unification and has a strong bias toward science as the sole source of rationality, which does not take theology fully seriously.     

Filtering Theories of Truth: Compositionality as a Criterion

The traditional way to filter out the implausible candidate solutions to the semantic paradoxes is to appeal to the so-called “cost/benefit analyses.” Yet it is often tedious and controversial to carry out such analyses in detail. Facing this, it would be helpful for us to rely upon some principles to filter out at least something, if not everything, from them. The proposal in this paper is thereby rather simple: We may use principles of compositionality as a “filter” for this purpose. The paper has four sections. In Section 2, the author uses the filter to examine Kripke’s fixed-point theory and to thereby show how it works. In Section 3, the author gives more examples from the classical theories of truth to demonstrate the power of the filter. In Section 4, the author addresses the skepticism concerning whether there is any consistent or non-trivial theory of truth that can survive this filtering procedure. A “nearly sufficient” condition for a theory of truth to survive this test is discussed in order to show that at least some consistent or non-trivial theories of truth do indeed survive the filtering procedure.     

Logical Positivism, Analytic Method, and Criticisms of Ethnophilosophy

Abstract: I argue that the analytic method has been circularly used to analyze the concept of “philosophy,” and that the result of this analysis has also been used to criticize African ethnophilosophy as nonphilosophical. I critically examine the criticism that ethnophilosophy implies cognitive relativism and the criticism that it implies authoritarianism. I defend ethnophilosophy against these criticisms, arguing that they are rooted in logical positivism, the view that philosophy essentially involves the use of the methods of science and logical analysis. I argue that such analysis and criticisms, given their pedigree, do not provide an adequate or accurate picture of the nature of philosophy.     

Strong Completeness Theorems for Weak Logics of Common Belief

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.