In what sense is the no-no paradox a paradox?

Philosophical Studies - Cook regards Sorenson’s so-called ‘the no-no paradox’ as only a kind of ‘meta-paradox’ or ‘quasi-paradox’ because the symmetry...     

The liar: What paradox?

Most philosophers believe that the Liar Paradox is semantical in character, and arises from difficulties in the predicate true. The author argues that the paradox is pragmatic, not semantic, and arises from violations of essential conditions that define statement-making speech acts. The author shows that his solution to the paradox will not only handle the classical Liar sentences that are necessarily or intrinsically paradoxical, but also sets of Kripke-sentences that are contingently paradoxical.     

Meno’s paradox and medicine

The measurement of diagnostic accuracy is an important aspect of the evaluation of diagnostic tests. Sometimes, medical researchers try to discover the set of observations that are most accurate of all by directly inspecting diseased and not-diseased patients. This method is perhaps intuitively appealing, as it seems a straightforward empirical way of discovering how to identify diseased patients, which amounts to trying to correlate the results of diagnostic tests with disease status. I present three examples of researchers who try to produce definitive diagnostic criteria by directly inspecting diseased and not diseased patients. Despite this method’s intuitive appeal, I will argue that it is impossible to carry out. Before researchers can inspect these patients to discover definitive diagnostic criteria, they must be able to distinguish diseased and not-diseased patients; and they do not know how to do this, because this is what they are trying to discover. I suspect the intuitive appeal of directly inspecting patients makes this difficult to appreciate. To counter this difficulty, I present this problem as a manifestation of ‘Meno’s paradox’, which was described in classical antiquity, and of ‘the problem of nomic measurement’, described more recently. Considering these philosophical problems may help researchers address the methodological issues they face when evaluating diagnostic tests.

     

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.     

Morinaga’s paradox and figure-ground organization

Morinaga’s paradox of displacement is constructed by setting several copies of the two Mueller-Lyer figures one above the other. The Mueller-Lyer illusion is that the wings pointing out seem farther apart than wings pointing in, and Morinaga’s paradox is that when one looks down a column of wings pointing alternately one way and the other, they appear misaligned but in the opposite direction from the Mueller-Lyer illusion. The hypothesis of this paper is that the subject, under instructions to align the vertical array of wings, sets up a vertical figure-ground organization different from that used in judging the horizontal distance between wings, and that the two illusions are contingent upon the two organizations. The experiment showed that Morinaga’s paradox occurs when only one column of wings is shown, in agreement with the figure-ground hypothesis, and also shows that Morinaga’s paradox disappears when short line segments are introduced which disrupt the vertical figure-ground organization.     

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.”     

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.     

Brightnesses,luminances, and Fechner’s paradox

Monocular brightnesses were varied, without varying monocular luminances, both by means of simultaneous contrast and by means of changes in the level of adaptation. Binocular brightness was shown to change in accord with monocular brightness, independent of monocular luminances.     

Beyond Reasonable Doubt – a paradox of ideological immunity

Abstract

Ideology criticism, like scepticism, calls into question the objective or justified status of beliefs. However, where scepticism only refutes, and never puts forward, a substantive claim about anything, the ideology critic must maintain some criterion for distinguishing ideas which support relations of domination from those that do not, in virtue of her criticism of a particular set of ideas as “ideological”. The trouble for the ideology critic is that the sceptical methods she deploys undermine any critical thesis, including her own. Thus, the theory of ideology tends to undercut ideology criticism with a fundamental problem of self-implication.

This paper draws on the epistemological problem of the criterion to explain and define a basic problem of justification for the theory of ideology. A problem of self-implication is introduced in part one. I argue that the basis for ideology criticism inevitably succumbs to the very doubt it puts forward. I draw on various criticisms of ideology criticism to formulate a specific account of the basic, fundamental problem for the theory of ideology. I show how norms for ideology criticism are vulnerable to an Ancient sceptical problem for epistemic criteria, which brings the ideology critic to a dilemma: either (i) find independent grounds for criticism, immune to ideology, or (ii) show how ideology is self-undermining. Each horn of the dilemma is ideological.     

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.     

Kripke’s paradox and the Church–Turing thesis

Kripke (1982, Wittgenstein on rules and private language. Cambridge, MA: MIT Press) presents a rule-following paradox in terms of what we meant by our past use of “plus”, but the same paradox can be applied to any other term in natural language. Many responses to the paradox concentrate on fixing determinate meaning for “plus”, or for a small class of other natural language terms. This raises a problem: how can these particular responses be generalised to the whole of natural language? In this paper, I propose a solution. I argue that if natural language is computable in a sense defined below, and the Church–Turing thesis is accepted, then this auxiliary problem can be solved.     

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.     

Moore’s paradox and the priority of belief thesis

Moore’s paradox is the fact that assertions or beliefs such as Bangkok is the capital of Thailand but I do not believe that Bangkok is the capital of Thailand or Bangkok is the capital of Thailand but I believe that Bangkok is not the capital of Thailand are ‘absurd’ yet possibly true. The current orthodoxy is that an explanation of the absurdity should first start with belief, on the assumption that once the absurdity in belief has been explained then this will translate into an explanation of the absurdity in assertion. This assumption gives explanatory priority to belief over assertion. I show that the translation involved is much trickier than might at first appear. It is simplistic to think that Moorean absurdity in assertion is always a subsidiary product of the absurdity in belief, even when the absurdity is conceived as irrationality. Instead we should aim for explanations of Moorean absurdity in assertion and in belief that are independent even if related, while bearing in mind that some forms of irrationality may be forms of absurdity even if not conversely.     

The IQ paradox: resolved? Still an open question

A generalized Dickens-Flynn (2001) model is presented and various simulations undertaken with it to give readers a better sense of the properties of such models. In particular, the inclusion of moderate degrees of persistence of intelligence and intelligence-relevant environment did not have much impact on the overall behavior of the models, although more extreme degrees of persistence did. Even moderate degrees, however, affected the internal relationships in the models. The importance of specifying the time scale and of addressing developmental aspects of the models is emphasized. It is noted that the translation of individual changes to population changes is not a simple matter in resolving the "IQ paradox" of large population gains over time in intelligence test scores.     

The psychological side of Hempel’s paradox of confirmation

People often test hypotheses about two variables (X andY), each with two levels (e.g.,X1 andX2). When testing “IfX1, thenY1,” observing the conjunction ofX1 andY1 is overwhelmingly perceived as more supportive than observing the conjunction ofX2 andY2, although both observations support the hypothesis. Normatively, theX2&Y2 observation provides stronger support than theX1&Y1 observation if the former is rarer. Because participants in laboratory settings typically test hypotheses they are unfamiliar with, previous research has not examined whether participants are sensitive to the rarity of observations. The experiment reported here showed that participants were sensitive to rarity, even judging a rareX2&Y2 observation more supportive than a commonX1&Y1 observation under certain conditions. Furthermore, participants’ default strategy of judgingX1&Y1 observations more informative might be generally adaptive because hypotheses usually regard rare events.     

So truth is safe from paradox: now what?

The article is part of a symposium on Hartry Field’s “Saving truth from paradox”. The book is one of the most significant intellectual achievements of the past decades, but it is not clear what, exactly, it accomplishes. I explore some alternatives, relating the developed view to the intuitive, pre-theoretic notion of truth.