Public and private communication are different: results on relative expressivity

Dynamic Epistemic Logic (DEL) is the study of how to reason about knowledge, belief, and communication. This paper studies the relative expressivity of certain fragments of the DEL language for public and private communication. It is shown that the language of public communication with common knowledge and the language of private communication with common knowledge are expressively incomparable for the class of all pointed Kripke models, which provides a formal proof that public and private communication are fundamentally different in the presence of common knowledge. It is also shown that single-recipient private communication does not add expressive power to the language of modal logic with common knowledge for any class of transitive pointed Kripke models. The latter result provides a sense in which positive introspection—believing our own beliefs—induces a kind of self-dialog.     

Koopmans’ constant discounting for intertemporal choice: A simplification and a generalization

Koopmans provided a well-known preference axiomatization for discounted utility, the most widely used model for maximizing intertemporal choice. There were, however, some technical problems in his analysis. For example, there was an unforeseen implication of bounded utility. Some partial solutions have been advanced in various fields in the literature. The technical problems in Koopmans’ analysis obscure the appeal of his intuitive axioms. This paper completely resolves Koopmans’ technical problems. In particular, it obtains complete flexibility concerning the utility functions that can be used. This paper, thus, provides a clean and complete preference axiomatization of discounted utility, clarifying the appeal of Koopmans’ intuitive axioms.     

Kant and the problem of existential judgment: critical comments on Wayne Martin’s Theories of Judgment

The paper assesses Martin’s recent logico-phenomenological account of judgment that is cast in the form of an eclectic history of judging, from Hume and Kant through the 19th century to Frege and Heidegger as well as current neuroscience. After a preliminary discussion of the complex unity and temporal modalities of judgment that draws on a reading of Titian’s “Allegory of Prudence” (National Gallery, London), the remainder of the paper focuses on Martin’s views on Kant’s logic in general and his theory of singular existential judgment in particular. The paper argues against Martin’s key claims of the primacy of formal logic over transcendental logic and of the synthetic nature of judgment in Kant. It also takes issue with each of the four interpretations of singular existential judgment in Kant offered by Martin: existence as logical predicate, as copula, as thesis and as logical subject.     

Soames on Russell’s logic: a reply

In “What is History For?,” Scott Soames responds to criticisms of his treatment of Russell’s logic in volume 1 of his Philosophical Analysis in the Twentieth Century. This note rebuts two of Soames’s replies, showing that a first-order presentation of Russell’s logic does not fit the argument of the Introduction to Mathematical Philosophy, and that Soames’s contextual definition of classes does not match Russell’s contextual definition of classes. In consequence, Soames’s presentation of Russell’s logic misrepresents what Russell took to be its technical achievement and its philosophical significance.     

Arguments by Parallels in the Epistemological Works of Phya pa Chos kyi seng ge

The works of the Tibetan logician Phya pa Chos kyi seng ge (1109–1169) make abundant use of a particular type of argument that I term ‘argument by parallels’. Their main characteristic is that the instigator of the argument, addressing a thesis in a domain A, introduces a parallel thesis in an unrelated domain B. And in the ensuing dialogue, each of the instigator’s statements consists in replicating his interlocutor’s previous assertion, mutatis mutandis, in the other domain (A or B). I show that such a dialogue involves two parallel arguments that develop in an intersecting zigzag pattern, and discuss the principles involved in the establishment of the conclusion from the perspective of parity of reasoning and analogical argument. I examine the overall rhetorical strategy directing the use of arguments by parallels and the pedagogical and explanatory functions they can serve. I also evaluate the plausibility of their use in Phya pa Chos kyi seng ge’s works mirroring a contemporary practice of oral debate, and reflect on the status of such arguments in the framework of Indo-Tibetan logic.

儒家智者的逻辑——析荀子正名论

荀子适应当时社会需要 ,从儒家智者的视角 ,创发孔子正名的逻辑内涵 ,建构以概念论为中心的逻辑体系 ,继墨辩之后把中国古代逻辑推向又一高峰。荀子对概念论和语言论、本体论、认识论、判断论、推理论、诡辩论、语言规范化、华夏大一统的相关论述 ,是当前仍有积极价值的学术精华。以现代方法揭示荀子正名论的逻辑意义 ,是中国逻辑元研究的课题。     

Action negation and alternative reductions for dynamic deontic logics

Dynamic deontic logics reduce normative assertions about explicit complex actions to standard dynamic logic assertions about the relation between complex actions and violation conditions. We address two general, but related problems in this field. The first is to find a formalization of the notion of ‘action negation’ that (1) has an intuitive interpretation as an action forming combinator and (2) does not impose restrictions on the use of other relevant action combinators such as sequence and iteration, and (3) has a meaningful interpretation in the normative context. The second problem we address concerns the reduction from deontic assertions to dynamic logic assertions. Our first point is that we want this reduction to obey the free-choice semantics for norms. For ought-to-be deontic logics it is generally accepted that the free-choice semantics is counter-intuitive. But for dynamic deontic logics we actually consider it a viable, if not, the better alternative. Our second concern with the reduction is that we want it to be more liberal than the ones that were proposed before in the literature. For instance, Meyer's reduction does not leave room for action whose normative status is neither permitted nor forbidden. We test the logics we define in this paper against a set of minimal logic requirements.     

Logic programs, iterated function systems, and recurrent radial basis function networks

Graphs of the single-step operator for first-order logic programs—displayed in the real plane—exhibit self-similar structures known from topological dynamics, i.e., they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which approximate logic programs in the presence of function symbols.     

Conflicting imperatives and dyadic deontic logic

Often a set of imperatives or norms seems satisfiable from the outset, but conflicts arise when ways to fulfill all are ruled out by unfortunate circumstances. Semantic methods to handle normative conflicts were devised by B. van Fraassen and J.F. Horty, but these are not sensitive to circumstances. The present paper extends these resolution mechanisms to circumstantial inputs, defines dyadic deontic operators accordingly, and provides a sound and (weakly) complete axiomatic system for such deontic semantics.     

Logic,Rules and Intention: The Principal Aim Argument

Stephen Mumford develops his view of sport spectatorship partly through a rejection of an argument he attributes to Best, which distinguishes between two categories of sports, the ‘purposive’ and the ‘aesthetic’, on the basis of the claim that they have different principal aims. This paper considers the principal aim argument and one feature of Mumford’s rejection of that argument, namely, Best’s observation that the distinctions to which he draws attention are based on logical differences. The paper argues that Mumford misconstrues Best’s argument by taking it to be about the intentions of players and athletes, while it is actually about a specific feature of the rules of each sport.