The paradoxes of analysis and synonymy

The very idea of informative analysis gives rise to a well-known paradox. Yet a parallel puzzle, herein called the paradox of synonymy, arises for statements which do not express analyses. The paradox of synonymy has a straightforward metalinguistic solution: certain words are referring to themselves. Likewise, the paradox of analysis can be solved by recognizing that certain expressions in an analysis statement are referring to their own semantic structures.     

语境同义性逻辑(英文)

众所周知,基于可能世界语义的内涵逻辑由于对意义的刻画过于粗粝而导致了所谓的"超内涵问题"。为了解决超内涵问题,出现了各种超内涵逻辑,其中由Suszko提出的带等词的命题逻辑(SCI)是超内涵逻辑中最基本的一种。本文是对SCI的精炼,其动机是语境同义性论题(CST)。该论题认为,同义性标准具有语境依赖性。基于认知语境主义,我们给出了CST的一个论证。通过将SCI中的二元等词修改为一个三元结构,用来表示两个陈述相对某个语境表达同一命题,我们给出了CST的希尔伯特式公理系统。我们证明了该系统相对一个代数模型类是可靠的和完全的。该代数模型的论域由命题构成,同时附带一组命题上的全等关系,用以刻画相对于语境的命题同一性。我们运用该逻辑部分解决了分析悖论这一困扰逻辑学家多年的问题。与我们之前的基于相同动机的论文[17]相比,本文给出的形式语言更加丰富,从而能够表达不同语境之间以及不同语境的同义性之间的关系。     

Does the Quine/duhem Thesis Prevent Us from Defining Analyticity?

Quine claims that holism (i.e., the Quine-Duhem thesis) prevents us from defining synonymy and analyticity (section 2). In Word and Object, he dismisses a notion of synonymy which works well even if holism is true. The notion goes back to a proposal from Grice and Strawson and runs thus: R and S are synonymous iff for all sentences T we have that the logical conjunction of R and T is stimulus-synonymous to that of S and T. Whereas Grice and Strawson did not attempt to defend this definition, I try to show that it indeed gives us a satisfactory account of synonymy. Contrary to Quine, the notion is tighter than stimulus-synonymy – particularly when applied to sentences with less than critical semantic mass (section 3). Now according to Quine, analyticity could be defined in terms of synonymy, if synonymy were to make sense: A sentence is analytic iff synonymous to self-conditionals. This leads us to the following notion of analyticity: S is analytic iff, for all sentences T, the logical conjunction of S and T is stimulus-synonymous to T; an analytic sentence does not change the semantic mass of any theory to which it may be conjoined (section 4). This notion is tighter than Quine's stimulus-analyticity; unlike stimulus-analyticity, it does not apply to those sentences from the very center of our theories which can be assented to come what may, even though they are not synthetic in the intuitive sense (section 5).     

Moore's Paradox and the Structure of Conscious Belief

Propositions such as are paradoxical, in that even though they can be true, they cannot be truly asserted or believed. This is Moore's paradox. Sydney Shoemaker has recently argued that the paradox arises from a constitutive relation that holds between first- and second-order beliefs. This paper explores this approach to the paradox. Although Shoemaker's own account of the paradox is rejected, a different account along similar lines is endorsed. At the core of the endorsed account is the claim that conscious beliefs are always partly about themselves; it will be shown to follow from this that conscious beliefs in Moorean propositions are self-contradictory.     

The logic of Simpson’s paradox

There are three distinct questions associated with Simpson’s paradox. (i) Why or in what sense is Simpson’s paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal (and questionable) account of the first two questions. We argue that the “how to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.”     

Problems for Linguistic Solutions to the Paradox of Analysis

G. E. Moore opined that the paradox of analysis might be avoided if it could be shown that sentences expressing conceptual analyses convey information not only about concepts, but also about the expressions they use. If so, "to be a brother is to be a male sibling" and "to be a brother is to be a brother" might express the same proposition, and yet not be identical in information value as the paradox suggests. How sentences might do this, Moore could not see. Many philosophers have pointed out an obvious way in which sentences might be said to convey information about the expressions they use. Some have suggested this information might be used to develop Moore's intuition and resolve the paradox of analysis. I argue that this approach fails. I present a version of the paradox of analysis that resists this sort of solution.     

Is the paradox of fiction soluble in psychology?

If feeling a genuine emotion requires believing that its object actually exists, and if this is a belief we are unlikely to have about fictional entities, then how could we feel genuine emotions towards these entities? This question lies at the core of the paradox of fiction. Since its original formulation, this paradox has generated a substantial literature. Until recently, the dominant strategy had consisted in trying to solve it. Yet, it is more and more common for scholars to try to dismiss it using data and theories from psychology. In opposition to this trend, the present paper argues that the paradox of fiction cannot be dissolved in the ways recommended by the recent literature. We start by showing how contemporary attempts at dissolving the paradox assume that it emerges from theoretical commitments regarding the nature of emotions. Next, we argue that the paradox of fiction rather emerges from everyday observations, the validity of which is independent of any such commitment. This is why we then go on to claim that a mere appeal to psychology in order to discredit these theoretical commitments cannot dissolve the paradox. We bring our discussion to a close on a more positive note by exploring how the paradox could in fact be solved by an adequate theory of the emotions.     

On Kripke’s Dogmatism Paradox: A Logical Dynamical Analysis

As a byproduct of solving the surprise-exam paradox, Saul Kripke formulates a “dogmatism paradox” which seems to show that knowledge entails dogmatism. In this paper, the author analyzes the nature of the dogmatism paradox from a logical dynamical perspective. The author suggests that the dogmatism paradox is better understood as a paradox of knowledge attribution rather than of knowledge. Therefore, the dogmatism paradox could be solved without sacrificing the principle of epistemic closure. Based on a famous version of relevant alternatives theory, the author formalizes a logic of knowledge attribution in the style of logical dynamics, namely, public retraction logic, and analyzes how knowledge attributions are retracted with the expansion of relevant alternatives.     

Explaining the Paradox of Hedonism

The paradox of hedonism is the idea that making pleasure the only thing that we desire for its own sake can be self-defeating. Why would this be true? In this paper, I survey two prominent explanations, then develop a third possible explanation, inspired by Joseph Butler's classic discussion of the paradox. The existing accounts claim that the paradox arises because we are systematically incompetent at predicting what will make us happy, or because the greatest pleasures for human beings are found in certain special goods which hedonists cannot enjoy. On the account that I develop, the paradox is a consequence of a theory about the nature of pleasure, together with a view about the requirements of rational belief. Which of these explanations is correct, I argue, bears on central questions about how to understand the nature and extent of the paradox.     

Paradox and process

A paradox must be accepted on its own terms, without resolution, and, at the same time, valued as a pointer to a new level of comprehension. Many of the phenomena we encounter in our psychoanalytic work have simultaneously a quality of remarkable similarity and radical, even contradictory, dissimilarity. The apparent paradox is ultimately resolvable by an understanding of the process that underlies and therefore relates the phenomena. The twin dangers that inhere in dealing with paradox and process are, first, the inability to accept the paradox, that is, a premature resolution of it, and, second, a clinging to the paradox so as to avoid articulating the process that would allow one to climb into a new grasp of reality. Among the questions touched on in this paper are: How can there both be and not be a baby inside? How can there be both need and no need at the same time? How can there be both destruction and transcendence in the same moment?     

Semantic Knowledge,Semantic Guidance,and Kripke's Wittgenstein

Saul Kripke's influential ‘sceptical paradox’ of semantic rule‐following alleges that speakers cannot have any justification for using a word one way rather than another. If it is correct, there can be no such thing as meaning anything by a word. I argue that the paradox fails to undermine meaning. Kripke never adequately motivates its excessively strict standard for the justified use of words. The paradox lacks the resources to show that its standard is truly mandatory or that speakers do not frequently satisfy the well‐motivated competitor I offer. So the paradox fails.     

What is wrong with Allais' Certainty Effect?

Several choice situations are constructed to explore whether the violation of expected utility theory in an Allais paradox choice situation can be attributed to what Tversky and Kahneman (1986) describe as the Allais certainty effect. Problems are developed where the Allais certainty effect would be expected to occur but results show it does not. Other problems demonstrate that the Allais ‘paradox’ is observed in the absence of the Allais certainty effect. The study concludes that, although expected utility theory is known to be wrong through the Allais paradox, the Allais certainty effect does not appear to be able to rescue it.     

How Braess’ paradox solves Newcomb's problem*

Newcomb's problem is regularly described as a problem arising from equally defensible yet contradictory models of rationality. Braess’ paradox is regularly described as nothing more than the existence of non‐intuitive (but ultimately non‐contradictory) equilibrium points within physical networks of various kinds. Yet it can be shown that Newcomb's problem is structurally identical to Braess’ paradox. Both are instances of a well‐known result in game theory, namely that equilibria of non‐cooperative games are generally Pareto‐inefficient. Newcomb's problem is simply a limiting case in which the number of players equals one. Braess’ paradox is another limiting case in which the ‘players’ need not be assumed to be discrete individuals. The result is that Newcomb's problem is no more difficult to solve than (the easy to solve) Braess’ paradox.     

An axiomatic version of Fitch’s paradox

A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the paradox.     

The lesson of Newcomb’s paradox

In Newcomb’s paradox you can choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to accurately deduce your choice, and uses that deduction to fill the two boxes. The way they do this guarantees that you made the wrong choice. Newcomb’s paradox is that game theory’s expected utility and dominance principles appear to provide conflicting recommendations for what you should choose. Here we show that the conflicting recommendations assume different probabilistic structures relating your choice and the algorithm’s prediction. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the probabilistic structure relating the problem’s random variables is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcomb’s paradox, the focus of much previous work, is irrelevant. We end by showing that Newcomb’s paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its ‘prediction’ after you make your choice rather than before.     

PARADOXICAL PROPOSITIONS

This paper concerns two paradoxes involving propositions. The first is Russell's paradox from Appendix B of The Principles of Mathematics, a version of which was later given by Myhill. The second is a paradox in the framework of possible worlds, given by Kaplan. This paper shows a number of things about these paradoxes. First, we will see that, though the Russell/Myhill paradox and the Kaplan paradox might appear somewhat different, they are really just variants of the same phenomenon. Though they do this in different ways, the core of each paradox is to use the notion of a proposition to construct a function, f, from the power set of some set into the set itself. Next we will see how this paradox fits into the Inclosure Schema. Finally, I will provide a model of the paradox in question, showing its results to be non‐trivial, though inconsistent.     

Ambiguity and synonymy effects in lexical decision,naming, and semantic categorization tasks: interactions between orthography,phonology, and semantics

In this article, ambiguity and synonymy effects were examined in lexical decision, naming, and semantic categorization tasks. Whereas the typical ambiguity advantage was observed in lexical decision and naming, an ambiguity disadvantage was observed in semantic categorization. In addition, a synonymy effect (slower latencies for words with many synonyms than for words with few synonyms) was observed in lexical decision and naming but not in semantic categorization. These results suggest that (a) an ambiguity disadvantage arises only when a task requires semantic processing, (b) the ambiguity advantage and the synonymy disadvantage in lexical decision and naming are due to semantic feedback, and (c) these effects are determined by the nature of the feedback relationships from semantics to orthography and phonology.     

Rose's Prevention Paradox

Geoffrey Rose's ‘prevention paradox’ occurs when a population‐based preventative health measure that brings large benefits to the community – such as compulsory seatbelts, a ‘fat tax’, or mass immunisation – offers little to each participating individual. Although the prevention paradox is not obviously a paradox in the sense in which philosophers understand the term, it does raise important normative questions. In particular, should we implement population‐based preventative health measures when the typical individual is not expected to gain from them? After canvassing other attempts to address the paradox, I argue that what is significant about the prevention paradox is that it involves intra‐personal trade‐offs; the costs and benefits of the choice to implement or not implement a preventative health measure fall on the same individuals. The intra‐personal nature of these trade‐offs has two implications. First, the solutions to the paradox proposed by other authors are deficient. Second, the policy choice to not implement some preventative health measures can be normatively justified.     

Who cares about winning?

Why do we so often care about the outcomes of games when nothing is at stake? There is a paradox here, much like the paradox of fiction, which concerns why we care about the fates and threats of merely fictional beings. I argue that the paradox threatens to overturn a great deal of what philosophers have thought about caring, severing its connection to value and undermining its moral weight. I defend a solution to the paradox that draws on Kendall Walton's solution to the paradox of fiction, developing his idea that it be extended to games. The solution takes games to involve make-believe: in particular, players and spectators make-believe that the outcome of the game matters. I also explore how the phenomenon extends beyond games. And I explore some moral implications: in particular, my view preserves the idea that we have reason not to impede others in their pursuit of what they care about.     

How Braess’ paradox solves Newcomb's problem: Not!

In an engaging and ingenious paper, Irvine (1993) purports to show how the resolution of Braess’ paradox can be applied to Newcomb's problem. To accomplish this end, Irvine forges three links. First, he couples Braess’ paradox to the Cohen‐Kelly queuing paradox. Second, he couples the Cohen‐Kelly queuing paradox to the Prisoner's Dilemma (PD). Third, in accord with received literature, he couples the PD to Newcomb's problem itself. Claiming that the linked models are “structurally identical”, he argues that Braess solves Newcomb's problem. This paper shows that Irvine's linkage depends on structural similarities—rather than identities—between and among the models. The elucidation of functional disanalogies illuminates structural dissimilarities which sever that linkage. I claim that the Cohen‐Kelly queuing paradox cloaks a fine structure that decouples it from both Braess’ paradox and the PD (Marinoff, 1996a). I further assert that the putative reduction of the PD to a Newcomb problem (e.g. Brams, 1975; Lewis, 1979) is seriously flawed. It follows that Braess’ paradox does not solve Newcomb's problem via the foregoing and herein sundered chain. I conclude by substantiating a stronger claim, namely that Braess'paradox cannot solve Newcomb's problem at all.