Identical Twins,Deduction Theorems,and Pattern Functions: Exploring the Implicative BCSK Fragment of S5

We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we show that for the pure logic of one of these implicational connectives two – in general distinct – consequence relations (global and local) definable in the Kripke semantics for modal logic turn out to coincide, though this is not so for the pure logic of the other connective, and that there is an intimate relation between formulas constructed by means of the former connective and the local consequence relation. (Corollary 5.8. This, as we show in an Appendix, is connected to the fact that the ‘propositional operations’ associated with both of our implicational connectives are close to being what R. Quackenbush has called pattern functions.) Between these discussions Section 4 examines some of the replacement-of-equivalents properties of the two connectives, relative to these consequence relations, and Section 6 closes with some observations about the metaphor of identical twins as applied to such pairs of connectives.     

Fibring Argumentation Frames

This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see how to bring logic and networks closer together. Section 3 develops the formal properties of the new kind of network and Section 4 offers general discussion and comparison with the literature.     

Resource-origins of Nonmonotonicity

Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles. Edited by Hannes Leitgeb     

传统中国历史思想中的"时间"与"超时间"概念

在中国文化中,“时间”铭记刻画了人所身处之境况、时势的脉动以及历史中的个人的种种表现,绝非只是对自然事件的机械式载录而已。在传统中国历史思维之中,以永恒典律(如“道”、“理”)或不朽范型(如尧、舜、三代)为标竿,而尝试去存留、体现的实践过程,构成了中国历史上各个时代的具体内容。在中国传统文化中,生命的意义与价值在于领悟历史上存在过的典范,并将这些典范接引、召唤至人们所生存的时代,也因此中国文化中的“时间”概念寓涵了某种的“超时间”特质：中国人对过往历史的学习,其实只是掌握“超时间”的基点,其究极目的在于将典律范型落实于当代时空之中。中国人所认知的“时间”概念与人文关怀紧密相系;历史上的“时代”就是“时间”的会串、整合与界分;所谓“超时间”乃是从各时代中提炼出的典律范型;而经由人们的描摹叙述,“时间”会经由口语及交书而被转化成“历史”。抽象的“超时间”概念实取自“时间”,俯瞰着“时间”的流转,并且贯穿了整部“历史”的发展。本文先论述中国人文主义具有强烈的“天人合一”特质,表现出明显的社会政治取向,一切思想都落实到当下即是的人生与现实。人与自然、超自然的关系在传统中国仍被统纳入“人事”的范畴。本文第一节论证中国史学体现：中国历史意识中,“时间”与“超时间”有其错综复杂的关系：“时间”将确切发生的一桩桩事件织结成全幅的网络,而“超时间”是从网络中凝塑出来的中心意义。第二节论证“时间”如何汇淬成“超时间”,而第三节分析“超时间”必须以“时间”为基础始可形成,最后一节则对中国历史思维的特质作进一步的探讨。     

From Bayesian epistemology to inductive logic

Inductive logic admits a variety of semantics (Haenni et al. (2011) [7, Part 1]). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010 [16, Chapter 7]). Section 1 introduces the semantics and then, in Section 2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008) [2]. Section 3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising.     

Logical operations and iterated infinitely deep languages

We discuss an abstract notion of a logical operation and corresponding logics. It is shown that if all the logical operations considered are implicitely definable in a logic ?*, then the same holds also for the logic obtained from these operations. As an application we show that certain iterated forms of infinitely deep languages are implicitely definable in game quantifier languages. We consider also relations between structures and show that Karttunen's characterization of elementary equivalence for the ordinary infinitely deep languages can be generalized to hold for the iterated infinitely deep languages. An early version of this work was presented in the Abstracts Section of ICM '78.     

Applications of weak Kripke semantics to intermediate consequences

Section 1 contains a Kripke-style completeness theorem for arbitrary intermediate consequences. In Section 2 we apply weak Kripke semantics to splittings in order to obtain generalized axiomatization criteria of the Jankov-type. Section 3 presents new and short proofs of recent results on implicationless intermediate consequences. In Section 4 we prove that these consequences admit no deduction theorem. In Section 5 all maximal logics in the 3 ^rd counterslice are determined. On these results we reported at the 1980 meeting on Mathematical Logic at Oberwolfach. This paper concerns propositional logic only.     

Existence,presupposition and anaphoric space

The following paper deals with the notion of existence, especially as concerns natural languages. In Section 1, starting from some quite obvious examples drawn from logic, I sketch the problem of the existential presupposition usually ascribed to noun phrases. My opinion is that the point of view frequently adopted in this case is unduly restrictive, for the existence which is believed to be presupposed here is actual existence. Accordingly, I emphasize the need for having a weaker notion of existential presupposition, such that the existence (if this word can still be used) here referred to is relevant only to linguistic goals. Section 2 sketches this notion, by assimilating existence (in the weak sense) to identification in a linguistic space. (I deal here only with intuitive considerations: a more formal account will be given, I hope, in another paper.) Finally, in Section 3, the notion of actual existence is examined by contrast with the linguistic (or weak) notion of existence: and this is a question which of course can't be tackled in terms of a purely linguistic analysis, for it needs a general, epistemo-logical approach.     

Noise,uncertainty, and interest: Predictive coding and cognitive penetration

This paper concerns how extant theorists of predictive coding conceptualize and explain possible instances of cognitive penetration. Section 1 offers brief clarification of the predictive coding framework and of cognitive penetration. Section 2 develops more precise ways that the predictive coding framework can explain genuine top-down causal effects on perceptual experience. Section 3 develops these insights further with an eye towards tracking one extant criterion for cognitive penetration, namely, that the relevant cognitive effects on perception must be sufficiently direct. In Section 4, we analyze and criticize a claim made by some theorists of predictive coding, namely, that (interesting) instances of cognitive penetration tend to occur in perceptual circumstances involving substantial noise or uncertainty. We argue that, when applied, the claim fails to explain (or perhaps even be consistent with) a large range of important and uncontroversially interesting possible cases of cognitive penetration. We conclude with a general speculation about how the recent work on the predictive mind may influence the current dialectic concerning top-down effects on perception.     

Reasoning about visibility

We consider properties of sequences of spatial regions, as seen from a viewpoint. In particular, we concentrate on two types of regions: (1) general domains in which a region is any subset of the space, and (2) axis-parallel domains, where the regions are boxes in an N-dimensional space. We introduce binary relations allowing to express properties of these sequences and present two approaches to process them. First, we show that constraints on these relations can be solved in polynomial time for general domain and that the same problem is NP-complete in the axis-parallel case. Second, we introduce a modal logic on these relations, called Visibility Logic, and show that model-checking on a finite sequence of regions can be done in polynomial time (both in the general and axis-parallel cases). Finally, we present applications to image processing and firewall filtering.     

A Note on Bisimulation and Modal Equivalence in Provability Logic and Interpretability Logic

Provability logic is a modal logic for studying properties of provability predicates, and Interpretability logic for studying interpretability between logical theories. Their natural models are GL-models and Veltman models, for which the accessibility relation is well-founded. That’s why the usual counterexample showing the necessity of finite image property in Hennessy-Milner theorem (see [1]) doesn’t exist for them. However, we show that the analogous condition must still hold, by constructing two GL-models with worlds in them that are modally equivalent but not bisimilar, and showing how these GL-models can be converted to Veltman models with the same properties. In the process we develop some useful constructions: games on Veltman models, chains, and general method of transformation from GL-models/frames to Veltman ones.     

Synonymy and Intra-Theoretical Pluralism

The starting point of this paper is a version of intra-theoretical (logical) pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second move, I explain how a natural generalisation of the notion of synonymy (adapted to the 3-sided sequent-calculus used by Hjortland) can be used to counter this objection, but I also show how the solution can be turned into an equally devastating ‘one logic after all’ type of objection. Finally, I propose the general diagnosis that these problems could only arise in the presence of conceptual distinctions that are too coarse to accommodate coherent pluralist theses. The latter leads to the general methodological recommendation that the conceptual resources used to think and talk about logic should be kept in line with the formal resources that are used to define and describe a logical theory.     

Dretske on knowledge and content

In this paper I discuss Fred Dretske's account of knowledge critically, and try to bring out how his account of informational content leads to cases of extreme epistemic good luck in his treatment of knowledge. My main interest, however, is to establish that the cases of epistemic luck arise because Dretske's account of knowledge in a fundamental way fails to take into account the role our actual recognitional capacities and powers of discrimination play in perceptually based knowledge. This result is, I believe, new. The paper has three sections. In Section 1 I give a short exposition of Dretske's theory, and make some necessary qualifications about how it is to be understood. In Section 2 I discuss in greater detail how the theory actually works, and provide some examples I think are very troublesome for Dretske. In Section 3 I argue that these cases establish my main claim. I also show that there are cases of epistemic bad luck due to Dretske's account of how information causes belief.     

Towards a Semantics Based on the Notion of Justification

Suppose we want to take seriously the neoverificationist idea that an intuitionistic theory of meaning can be generalized in such a way as to be applicable not only to mathematical but also to empirical sentences. The paper explores some consequences of this attitude and takes some steps towards the realization of this program. The general idea is to develop a meaning theory, and consequently a formal semantics, based on the idea that knowing the meaning of a sentence is tantamount to having a criterion for establishing what is a justification for it. Section 1 motivates a requirement of epistemic transparency imposed onto justifications conceived as mental states. In Section 2, the formal notion of justification for an atomic formula is defined, in terms of the notion of cognitive state. In Section 3, the definition is extended to logically complex formulas. In Section 4, the notion of truth-ground is introduced and is used to give a definition of logical validity.     

A Logical Analysis of Monty Hall and Sleeping Beauty

Hintikka and Sandu’s independence-friendly (IF) logic is a conservative extension of first-order logic that allows one to consider semantic games with imperfect information. In the present article, we first show how several variants of the Monty Hall problem can be modeled as semantic games for IF sentences. In the process, we extend IF logic to include semantic games with chance moves and dub this extension stochastic IF logic. Finally, we use stochastic IF logic to analyze the Sleeping Beauty problem, leading to the conclusion that the thirders are correct while identifying the main error in the halfers’ argument.     

Kant and Hegel on purposive action

This essay discusses Kant and Hegel’s philosophies of action and the place of action within the general structure of their practical philosophy. We begin by briefly noting a few things that both unite and distinguish the two philosophers. In the sections that follow, we consider these and their corollaries in more detail. In so doing, we map their differences against those suggested by more standard readings that treat their accounts of action as less central to their practical philosophy. Section 2 discusses some central Kantian concepts (Freedom, Willkür, Wille, and Moral Law). In Section 3, we take a closer look at the distinction between internal and external action, as found in Kant’s philosophy of morality and legality. In Section 4, we turn to Hegel and his distinctions between abstract right (legality), morality, and ethical life, as well as the location of his account of action within his overall theory of morality. We discuss the distinction between Handlung and Tat, and non-imputable consequences. The overall aims of our essay are to shed light on some puzzles in Kant and Hegel’s conceptions and to examine where their exact disputes lie without taking a stand on which philosophy is ultimately the most satisfactory.     

SUPERVALUATION FIXED-POINT LOGICS OF TRUTH

Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a consequence relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived.     

Excess in Art: The Case of Oversinging

“Oversinging” is singing that is excessive in one or more dimensions: too loud, too ornamented, too melismatic, too expressive, or employing too much vibrato. I begin with a characterization of oversinging and establish a context for discussion (Section I). Next I consider performances by Christina Aguilera and Michael Bolton as examples (Section II). In light of these examples, I consider how oversinging might be both aesthetically and morally problematic (Section III). Along the way I raise concerns about authenticity and sincerity (Section IV). Finally (Section V), I consider a “paradox” of oversinging involving the role of skill in artistic performance. My discussion touches on the aesthetics of performance, aesthetic judgment, virtuosity, and taste.     

What is it to be aware of your awareness of red? A review essay of Michelle Montague’s The Given

In this review essay of Michelle Montague’s The Given we focus on the central thesis in the book: the awareness of awareness thesis. On that thesis, a state of awareness constitutively involves an awareness of itself. In Section 2, we discuss what the awareness of awareness thesis amounts to, how it contrasts with the transparency of experience, and how it might be motivated. In Section 3, we discuss one of Montague’s two theoretical arguments for the awareness of awareness thesis. A view that accepts the awareness of awareness thesis, Montague argues, is to be preferred over competing views because it outperforms them in accounting for the property attributions one makes in perceptual experience. We suggest that it is not clear that this argument for the awareness of awareness thesis is successful. Finally, in Section 4 we consider the relation between Montague’s view of color experience and what she calls Strawson’s datum, arguing that Montague may not be able to explain this datum as straightforwardly as she supposes. This, we suggest, threatens Montague’s second theoretical argument for the awareness of awareness thesis.