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.     

Frege's Puzzle for Perception

According to an influential variety of the representational view of perceptual experience—the singular content view—the contents of perceptual experiences include singular propositions partly composed of the particular physical object(s) a given experience is about or of. The singular content view faces well‐known difficulties accommodating hallucinations; I maintain that there is also an analogue of Frege's puzzle that poses a significant problem for this view. In fact, I believe that this puzzle presents difficulties for the theory that are unique to perception in that strategies that have been developed to respond to Frege's puzzle in the case of belief cannot be employed successfully in the case of perception. Ultimately, I maintain that this perceptual analogue of Frege's puzzle provides a compelling reason to reject the singular content view of perceptual experience.     

Anti-realism and Epistemic Accessibility

I argue that Fitch’s ‘paradox of knowability’ presents no special problem for the epistemic anti-realist who believes that reality is epistemically accessible to us. For the claim which is the target of the argument (If p then it is possible to know p) is not a commitment of anti-realism. The epistemic anti-realist’s commitment is (or should be) to the recognizability of the states of affairs which render true propositions true, not to the knowability of the propositions themselves. A formal apparatus for discussing the recognizability of states of affairs is offered, and other prima facie similar approaches to the paradox argument are reviewed.     

Plato's Theory of Punishment and Penal Code in the Laws

I argue that the degree to which a criminal should be punished is determined by three elements: a baseline amount that proportionally compensates the victim and an additional penalty that, first, reforms the criminal and, second, deters others from becoming unjust. My interpretation provides a solution to the interpretive puzzle that has most vexed commentators: the alleged tension between Plato's philosophical theory of punishment and the content of his penal code. I defend a two-step solution to the puzzle. First, on my interpretation, because of the broad role that deterrence must play, this alleged tension is—to a degree—merely apparent. Second, the actual tension can be explained by Plato's commitment to the rule of law, given the epistemic limitations of actual people.     

Comments on the paradox of analysis

A version of the so‐called paradox of analysis is enunciated which involves two principles of synonymy, referred to respectively as that of substitution and that of triviality. It is argued that for most “familiar” concepts of synonymy the former principle can be maintained whereas the latter one has to be rejected. I deal with some solutions to the paradox that have been proposed or discussed by Carnap, Lewy, Feyerabend and Hare, and adhere to Carnap's view that the puzzle arises from the use of unclarified and imprecise notions of synonymy.     

The Paradox of Wuwei? Yes (and No)

This essay considers P. J. Ivanhoe's critical challenge to Slingerland's analysis of wuwei(‘effortless action’). While I agree with Ivanhoe that we should do more work to embody and understand the concept of wuwei, I will defend Slingerland's notion that wuwei involves paradox—particularly in the cases of Zhuangi and Laozi. The present essay is not a defense of the specifics of Slingerland's analysis. Nonetheless, this essay focuses on defending the notion of paradox. Ivanhoe offers an alternative view of wuwei, one that sees the paradox as a riddle. I argue that this kind of formulation would frame the problem of wuwei in an unhelpful manner. I offer several novel ways of overcoming, or at least qualifying, the experience of paradox that seems to be at play in nondoing.     

An Illocutionary Logical Explanation of the Surprise Execution

This paper further develops the system of illocutionary logic presented in ‘Propositional logic of supposition and assertion’ (Notre Dame Journal of Formal Logic 1997, 38, 325-349) to accommodate an ‘I believe that’ operator and resolve Moore's Paradox. This resolution is accomplished by providing both a truth-conditional and a commitment-based semantics. An important feature of the logical system is that the correctness of some arguments depends on who it is that makes the argument. The paper then shows that the logical system can be expanded to resolve the surprise execution paradox puzzle. The prisoner's argument showing that he can't be executed by surprise is correct but his beliefs are incoherent. The judge's beliefs (and our beliefs) about this situation are not incoherent.     

The Paradox of Beginning: Hegel,Kierkegaard and Philosophical Inquiry

This paper reconsiders certain of Kierkegaard's criticisms of Hegel's theoretical philosophy in the light of recent interpretations of the latter. The paper seeks to show how these criticisms, far from being merely parochial or rhetorical, turn on central issues concerning the nature of thought and what it is to think. I begin by introducing Hegel's conception of “pure thought” as this is distinguished by his commitment to certain general requirements on a properly philosophical form of inquiry. I then outline Hegel's strategy for resolving a crucial problem he takes himself to face. For his account of the nature of thought depends upon the idea of a form of inquiry in which nothing whatsoever is presupposed; but this idea appears basically paradoxical inasmuch as the mere act of beginning to inquire in a certain way embodies an assumption about how it is appropriate to begin. Turning to Kierkegaard, I consider a key objection to the effect that Hegel's strategy for resolving this paradox depends on the incoherent idea of a purely reflexive act of thinking. Finally, I draw out some central features of the alternative account of “situated” thought and inquiry which Kierkegaard presents as distinctively Socratic.     

Frege's Puzzle is About Identity After All

Many philosophers have argued or taken for granted that Frege's puzzle has little or nothing to do with identity statements. I show that this is wrong, arguing that the puzzle can only be motivated relative to a thinker's beliefs about the identity or distinctness of the relevant object. The result is important, as it suggests that the puzzle can be solved, not by a semantic theory of names or referring expressions as such, but simply by a theory of identity statements. To show this, I sketch a framework for developing solutions of this sort. I also consider how this result could be implemented by two influential solutions to Frege's puzzle, Perry's referential‐reflexivism and Fine's semantic relationism.     

THE PARADOX OF INQUIRY IN AUGUSTINE'S CONFESSIONS

Abstract: The Confessions recounts Augustine's successful search for God. But Augustine worries that one cannot search for God if one does not already know God. That version of the paradox of inquiry dominates and structures Confessions 1–10. I draw connections between the dramatic opening lines of book 1 and the climactic discussion in book 10.26–38 and argue that the latter discussion contains Augustine's resolution of the paradox of inquiry as it applies to the special case of searching for God. I claim that he develops a model, relying on the universal human experience of joy and truth, that identifies a starting point that (1) is common to all human beings, (2) is sufficient for guiding a successful search for God, and (3) avoids commitment to recollection of experiences prior to birth. The model is crucial to Augustine's rejection of traditional Platonist views about recollection.     

With and Without End

Ways and words about infinity have frequently hidden a continuing paradox inspired by Zeno. The basic puzzle is the tortoise's – Mr T's – Extension Challenge, the challenge being how any extension, be it in time or space or both, moving or still, can yet be of an endless number of extensions. We identify a similarity with Mr T's Deduction Challenge, reported by Lewis Carroll, to the claim that a conclusion can be validly reached in finite steps. Rejecting common solutions to both challenges, we use a Wittgensteinian approach for dissolution, noting also that other paradoxes, such as the Surprise Examination and Yablo's, trap us inconsistently into similar endlessnesses. In so doing, we encounter a hopping flea, generate a proportionality paradox and consider the knight's move in chess.     

Conceptual Analysis and Epistemic Progress

This essay concerns the question of how we make genuine epistemic progress through conceptual analysis. Our way into this issue will be through consideration of the paradox of analysis. The paradox challenges us to explain how a given statement can make a substantive contribution to our knowledge, even while it purports merely to make explicit what one’s grasp of the concept under scrutiny consists in. The paradox is often treated primarily as a semantic puzzle. However, in “Sect. 1” I argue that the paradox raises a more fundamental epistemic problem, and in “Sects.1 and 2” I argue that semantic proposals—even ones designed to capture the Fregean link between meaning and epistemic significance—fail to resolve that problem. Seeing our way towards a real solution to the paradox requires more than semantics; we also need to understand how the process of analysis can yield justification for accepting a candidate conceptual analysis. I present an account of this process, and explain how it resolves the paradox, in “Sect. 3”. I conclude in “Sect. 4” by considering the implications for the present account concerning the goal of conceptual analysis, and by arguing that the apparent scarcity of short and finite illuminating analyses in philosophically interesting cases provides no grounds for pessimism concerning the possibility of philosophical progress through conceptual analysis.     

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.     

Evil and God's Toxin Puzzle

I show that Kavka's toxin puzzle raises a problem for the “Responsibility Theodicy,” which holds that the reason God typically does not intervene to stop the evil effects of our actions is that such intervention would undermine the possibility of our being significantly responsible for overcoming and averting evil. This prominent theodicy seems to require that God be able to do what the agent in Kavka's toxin story cannot do: stick by a plan to do some action at a future time even though when that time comes, there will be no good reason for performing that action (and very good reason not to). I assess various approaches to solving this problem. Along the way, I develop an iterated variant of Kavka's toxin case and argue that the case is not adequately handled by standard causal decision theory.     

Fiction,Pleasurable Tragedy,and the HOT Theory of Consciousness

Abstract

The ‘feeling fiction problem’ asks: is it rational to be moved by what happens to fictional characters? The so-called ‘paradox of tragedy’ is embodied in the question: Why or how is it that we take pleasure in artworks which are clearly designed to cause in us such feelings as sadness and fear? My focus in this paper is to examine these problems from the point of view of the so-called ‘higher-order thought theory of consciousness’ (HOT theory) which says that the best explanation for what makes a mental state conscious is that it is accompanied by a thought that one is in that state. I examine the feeling fiction problem in light of the HOT theory and through a critique of Colin Radford's view. For example, I argue that Radford equivocates in his use of the term ‘aware’ in his response to some of the proposed solutions to the feeling fiction problem. Finally, I show how Susan Feagin's approach to the paradox of tragedy can be analysed and supported by the HOT theory.     

Rights

Liberals claim that some perceptual experiences give us immediate justification for certain perceptual beliefs. Conservatives claim that the justification that perceptual experiences give us for those perceptual beliefs is mediated by our background beliefs. In his recent paper ‘Basic Justification and the Moorean Response to the Skeptic’, Nico Silins successfully argues for a non-Moorean version of Liberalism. But Silins's defence of non-Moorean Liberalism leaves us with a puzzle: why is it that a necessary condition for our perceptual experiences to justify us in holding certain perceptual beliefs is that we have some independent justification for disbelieving various sceptical hypotheses? I argue that the best answer to this question involves commitment to Crispin Wright's version of Conservatism. In short, Wright's Conservatism is consistent with Silins's Liberalism, and the latter helps to give us grounds for accepting the former.     

On Russell's vulnerability to Russell's paradox

Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ‘the most important event’ in ‘the most important year in my intellectual life’. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell was thus vulnerable to (at least one version of) Russell's paradox and hence that the paradox exposes a pre-existing difficulty in Russell's Moorean philosophy. Contrary to Hylton, I argue that the Moorean Russell adhered to views which insulated him against the paradox. Further, I argue that Russell became vulnerable to his paradox as a result of changes in his Moorean position occasioned, first, by his acceptance of Cantor's theory of the transfinite, and, second, by his correspondence with Frege. I conclude with some general comments regarding Russell's acceptance of naïve set theory.     

Moore’s Paradox is not just another pragmatic paradox

One version of Moore’s Paradox is the challenge to account for the absurdity of beliefs purportedly expressed by someone who asserts sentences of the form ‘p & I do not believe that p’ (‘Moorean sentences’). The absurdity of these beliefs is philosophically puzzling, given that Moorean sentences (i) are contingent and often true; and (ii) express contents that are unproblematic when presented in the third-person. In this paper I critically examine the most popular proposed solution to these two puzzles, according to which Moorean beliefs are absurd because Moorean sentences are instances of pragmatic paradox; that is to say, the propositions they express are necessarily false-when-believed. My conclusion is that while a Moorean belief is a pragmatic paradox, it is not just another pragmatic paradox, because this diagnosis does not explain all the puzzling features of Moorean beliefs. In particularly, while this analysis is plausible in relation to the puzzle posed by characteristic (i) of Moorean sentences, I argue that it fails to account for (ii). I do so in the course of an attempt to formulate the definition of a pragmatic paradox in more precise formal terms, in order to see whether the definition is satisfied by Moorean sentences, but not by their third-person transpositions. For only an account which can do so could address (ii) adequately. After rejecting a number of attempted formalizations, I arrive at a definition which delivers the right results. The problem with this definition, however, is that it has to be couched in first-person terms, making an essential use of ‘I’. Thus the problem of accounting for first-/third-person asymmetry recurs at a higher order, which shows that the Pragmatic Paradox Resolution fails to identify the source of such asymmetry highlighted by Moore’s Paradox.     

Why Four-Dimensionalism Explains Coincidence

In ‘Does Four-Dimensionalism Explain Coincidence?’ Mark Moyer argues that there is no reason to prefer the four-dimensionalist (or perdurantist) explanation of coincidence to the three-dimensionalist (or endurantist) explanation. I argue that Moyer's formulations of perdurantism and endurantism lead him to overlook the perdurantist's advantage. A more satisfactory formulation of these views reveals a puzzle of coincidence that Moyer does not consider, and the perdurantist's treatment of this puzzle is clearly preferable.     

Being of Two Minds (or of One in Two Ways): A New Puzzle for Constitution Views of Personal Identity

According to constitution views of persons, we are constituted by spatially coinciding human animals. Constitution views face an ‘overpopulation' puzzle: if the animal has my brain, there is another thinker where I am. An influential solution to this problem distinguishes between derivative and non-derivative property possession: persons non-derivatively have their personal properties, while inheriting others from their constituters. I will show that this solution raises a new problem, by constructing a puzzle with the absurd result that we instantiate certain properties incompatibly. In setting up the puzzle, I demonstrate the relevance of the bodily awareness and self-awareness literatures to overpopulation puzzles.