The Tractatus and the Riddles of Philosophy*

The notion of the riddle plays a pivotal role in Wittgenstein’s Tractatus. By examining the comparisons he draws between philosophical problems and riddles, this paper offers a reassessment of the aims and methods of the book. Solving an ordinary riddle does not consist in learning a new fact; what it requires is that we transform the way we use words. Similarly, Wittgenstein proposes to transform the way philosophers understand the nature of their problems. But since he holds that these problems are ultimately unsolvable, rather than attempting to solve the riddles of philosophy, he aims to dissolve them.     

Assertoric Semantics and the Computational Power of Self-Referential Truth

There is no consensus as to whether a Liar sentence is meaningful or not. Still, a widespread conviction with respect to Liar sentences (and other ungrounded sentences) is that, whether or not they are meaningful, they are useless. The philosophical contribution of this paper is to put this conviction into question. Using the framework of assertoric semantics, which is a semantic valuation method for languages of self-referential truth that has been developed by the author, we show that certain computational problems, called query structures, can be solved more efficiently by an agent who has self-referential resources (amongst which are Liar sentences) than by an agent who has only classical resources; we establish the computational power of self-referential truth. The paper concludes with some thoughts on the implications of the established result for deflationary accounts of truth.     

Testability and Ockham’s Razor: How Formal and Statistical Learning Theory Converge in the New Riddle of Induction

Nelson Goodman’s new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper’s notion of degrees of testability is linked to minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham’s razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered, of which Goodman’s riddle is just one example.     

Editorial Introduction

I survey some important semantical and axiomatic theories of self-referential truth. Kripke's fixed-point theory, the revision theory of truth and appraoches involving fuzzy logic are the main examples of semantical theories. I look at axiomatic theories devised by Cantini, Feferman, Freidman and Sheard. Finally some applications of the theory of self-referential truth are considered.     

谜语问题解决中线索的作用

汉语谜语在性质上属于顿悟问题,当谜语的谜底为汉语成语时,这样的谜语问题称为成语谜语问题。本研究探讨线索在成语谜语问题解决中的作用特点与方式。三个实验以汉语成语谜语问题为实验材料,采用了语义线索与规则线索,操纵了线索的有效性（有效线索占75％,无效线索占25％）,以及线索呈现的时间长短（长时间即阈限上呈现线索（实验1）,短时间（20ms）即阈限下呈现线索（实验2与实验3））两个因素。实验1与实验2的任务是要求被试写出成语谜语问题的答案（谜底）,实验3则要求被试从6个备择答案中选择出正确的答案。被试为武汉某大学的206名低年级本科生。实验结果表明,（1）无论是阈限上还是阈限下呈现规则线索,有效规则线索对成语谜语问题的解决具有促进作用;（2）有效语义线索对谜语问题的解决具有促进作用,而且,阈限上有效语义线索对谜语问题解决的促进作用更大;（3）阈限上呈现两类无效线索时,它们对成语谜语问题的解决都具有干扰作用;但是,阈限下呈现两类无效线索时,它们对成语谜语问题的解决没有干扰作用。     

A one-person doxastic characterization of Nash strategies

Within a formal epistemic model for simultaneous-move games, we present the following conditions: (1) belief in the opponents’ rationality (BOR), stating that a player believes that every opponent chooses an optimal strategy, (2) self-referential beliefs (SRB), stating that a player believes that his opponents hold correct beliefs about his own beliefs, (3) projective beliefs (PB), stating that i believes that j’s belief about k’s choice is the same as i’s belief about k’s choice, and (4) conditionally independent beliefs (CIB), stating that a player believes that opponents’ types choose their strategies independently. We show that, if a player satisfies BOR, SRB and CIB, and believes that every opponent satisfies BOR, SRB, PB and CIB, then he will choose a Nash strategy (that is, a strategy that is optimal in some Nash equilibrium). We thus provide a sufficient collection of one-person conditions for Nash strategy choice. We also show that none of these seven conditions can be dropped.     

The Development of Strategic Processing of Ambiguous Words: Riddles Versus Neutral Context

Children in Grades 4 and 6 read isolated target words following the auditory presentation of an ambiguous word (e.g., deck). The ambiguous word occurred as the last word in either a neutral sentence (e.g., “There is the deck”) or as the last word in a riddle (“Why couldn't anybody play poker on the ark? Because Noah sat on the deck). Related target words were consistent with either the dominant meaning (e.g., porch) or the subordinate meaning (cards) of the ambiguous word. In the neutral context, Grade 4 children showed equivalent facilitation for dominant and subordinate targets relative to unrelated target words; Grade 6 children showed facilitation only for the dominant targets. In the riddle context, both groups of children showed equivalent facilitation for the two types of related targets. The neutral context results supported the hypothesis that the two bases of context effects—automatic lexical access and selective access—develop at different rates (Simpson &; Foster, 1986). The results obtained from the riddles suggest that the selective process is strategic (Ceci, 1989).     

Developmental changes in the structural complexity of children’s riddles

Riddles were collected from 156 boys and girls from Years 1 to 6 (six- to twelve-year-olds) of a large, middle-class school. The riddles were scored on nine measures of structural complexity based on the presence of incongruity or linguistic devices in the question and answer of the riddle. The number of riddles increased from Year 1 to Year 5 and then declined slightly in Year 6. Grade differences were found for five of the nine complexity measures, and girls tended to tell riddles with greater total complexity than boys. Production data are compared with the preference data from other studies, and grade changes in riddle structure and content are discussed in terms of a search for novelty which finally leads to the more flexible structure of the joke.     

Oedipus the king: Quest for self‐knowledge – denial of reality. Sophocles’ vision of man and psychoanalytic concept formation

In the Oedipus myth we find a dramatic representation of the child’s passionate ties to its parents. In the play Oedipus the King, Sophocles relates the theme of the myth to the question of self‐knowledge. This was the predominant reading in German 19th century thinking, and even as a student Freud was fascinated by Oedipus’ character – not primarily as the protagonist of an oedipal drama, but as the solver of divine riddles and as an individual striving for self‐knowledge. Inspired by Vellacott, Steiner has proposed an alternative reading of Oedipus the King as a play about a cover‐up of the truth. The text supports both these arguments. The pivotal theme of the tragedy is Oedipus’ conflict between his desire to know himself and his opposing wish to cover up the truth that will bring disaster. It is this complex character of Oedipus and the intensity of his conflict‐ridden struggle for self‐knowledge that has made the tragedy to a rich source of inspiration for psychoanalytic concept formation and understanding both of emotional and cognitive development up to our own time.     

Tolerant, Classical, Strict

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.     

A Contextual-Hierarchical Approach to Truth and the Liar Paradox

This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad hoc nor unnatural.     

Dialectic and argument in philosophy: A case study of Hegel's phenomenological preface

This article examines two problems: the role of argument in philosophy, vis-àÏs other philosophical activities; and the nature of argument in philosophy, vis-à-vis argument in other fields. The examination proceeds by reference to the notion of dialectic, which is regarded by some as offering an alternative to argument, and by reference to Hegel's Preface to the Phenomenology of Spirit, which explicitly discusses these very issues. The latter is reconstructed as the argument that philosophy is dialectical in part because it is pluralistic, conceptual, concrete, self-reflective, spiritual, systematic, negative, and self-referential, and in part because it sublimates the opposition between truth and falsity, method and result, change and permanence, form and content, and subject and predicate.     

Now is the time

The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only ‘real’ time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the other. I shew that this translation is preserved at the metalinguistic level, so that equivalent truth conditions can be defined in a tensed metalanguage or an indexical metalanguage. I then make some remarks about the connection between proofs of relative consistency and metaphysical truth; and some historical remarks about Arthur Prior's use of formal logic in expressing his presentist views.     

Deflationism beyond arithmetic

The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over subject matters ‘richer’ than arithmetic, such as set theory. The move to this new formal setting provides deflationists with better defence and brings a broader perspective to the debate.

     

How to eliminate self-reference: a précis

We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h ₀(F), h ₁(F), ..., stated in a quantificational language L ^*. Under certain conditions, we show that none of the translations is self-referential, but that any one of them perfectly mirrors the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, Analysis, 53, 251–252; 2004, Self-reference, CSLI) and Cook (2004, Journal of Symbolic Logic, 69(3), 767–774), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language.     

Prospects for Peircean Truth

Peircean Truth (PT) is the view that truth is in some sense epistemically constrained, constrained that is by what we would, if we inquired long enough and well enough, eventually come to believe. Contemporary Peirceans offer various different formulations of the view, which can make it difficult, particularly for critics, to see exactly how PT differs from popular alternatives such as correspondence theories or deflationism. This article, therefore, considers four possible formulations of PT, and sets out the different objections and challenges they each face and their relationships with one another. I focus upon the question of what, if anything, PT has to say about the property of truth.     

On the Dynamics of Conversation

There is a longstanding debate in the literature about static versus dynamic approaches to meaning and conversation. A formal result due to van Benthem ( 1986 , 1996 ) is often thought to be important for understanding what, conceptually speaking, is at issue in the debate. We introduce the concept of a conversation system, and we use it to clarify the import of van Benthem's result. We then distinguish two classes of conversation systems, corresponding to two concepts of staticness. The first class corresponds to a generalization of the class of systems that van Benthem's result concerns. These are the strongly static conversation systems. The second class is broader, and allows for a certain commonly recognized form of context sensitivity. These are the weakly static conversation systems. In the vein of van Benthem's result, we supply representation theorems which independently characterize these two varieties of conversation system. We observe that some canonically dynamic semantic systems correspond to weakly static conversation systems. We close by discussing some hazards that arise in trying to bring our formal results to bear on natural language phenomena, and on the debate about whether the compositional semantics for natural language should take a dynamic shape.     

Predication and cognitive context: Between minimalism and contextualism

In this paper, we suggest a strategy for modelling cognitive context within a truth‐conditional semantics, using Asher's model of predication. This allows us to introduce the notion of type presupposition intended as a lexical constraint to the composition of the truth‐conditional content. More specifically, we suggest that this model of predication produces a notion of truth‐conditional meaning where the cognitive context fixes a set of lexical restrictions and forced modifications. We conclude that this model might offer an intermediate position between Minimalism and Contextualism: an account that provides intuitive truth conditions within a formal semantic theory.     

Equality: Putting the Theory into Action

We outline our central reasons for pursuing the project of equality studies and some of the thinking we have done within an equality studies framework. We try to show that a multi-dimensional conceptual framework, applied to a set of key social contexts and articulating the concerns of subordinate social groups, can be a fruitful way of putting the idea of equality into practice. Finally, we address some central questions about how to bring about egalitarian social change. Editors’ note. John Baker et al’s article below condenses the key themes and arguments of their book, Equality: From Theory to Action. In the next issue of Res Publica, four writers will respond to these arguments, and there will be a reply from the book’s authors. We are grateful to Jurgen De Wispelaere for organising the original workshop on which the article and replies are based, and for his work in putting together this symposium.