In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has some (...) extra advantages. First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

In a recent article, Douven and Williamson offer both (i) a rebuttal of various recent suggested sufficient conditions for rational acceptability and (ii) an alleged ‘generalization’ of this rebuttal, which, they claim, tells against a much broader class of potential suggestions. However, not only is the result mentioned in (ii) not a generalization of the findings referred to in (i), but in contrast to the latter, it fails to have the probative force advertised. Their paper does however, if unwittingly, bring (...) us a step closer to a precise characterization of an important class of rationally unacceptable propositions—the class of lottery propositions for equiprobable lotteries. This helps pave the way to the construction of a genuinely lottery-paradox-proof alternative to the suggestions criticized in (i). (shrink)

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give (...) the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. (shrink)

This paper is concerned with formal solutions to the lottery paradox on which high probability defeasibly warrants acceptance. It considers some recently proposed solutions of this type and presents an argument showing that these solutions are trivial in that they boil down to the claim that perfect probability is sufficient for rational acceptability. The argument is then generalized, showing that a broad class of similar solutions faces the same problem. An argument against some formal solutions to the lottery (...) class='Hi'>paradox The argument generalized Some variations Adding modalities Anticipated objections. (shrink)

The lottery paradox can be solved if epistemic justification is assumed to be a species of permissibility. Given this assumption, the starting point of the paradox can be formulated as the claim that, for each lottery ticket, I am permitted to believe that it will lose. This claim is ambiguous between two readings, depending on the scope of ‘permitted’. On one reading, the claim is false; on another, it is true, but, owing to the general failure of permissibility (...) to agglomerate, does not generate the paradox. The solution generalizes to formulations of the paradox in terms of rational acceptability and doxastic rationality. (shrink)

This article considers the Gibbs paradox and its implications for three definitions of entropy in statistical mechanics: the “classical” Boltzmann entropy ; the modified Boltzmann entropy that is usually proposed in response to the paradox ; and a generalized version of the latter. It is argued that notwithstanding a recent suggestion to the contrary, the paradox does imply that SB1 is not a satisfactory definition of entropy; SB2 is undermined by “second-order” versions of the paradox; and (...) SB2G solves the paradox but is not a satisfactory definition of entropy. (shrink)

The Preface Paradox has led many philosophers to believe that, if it isassumed that high probability is necessary for rational acceptability, the principleaccording to which rational acceptability is closed under conjunction (CP)must be abandoned. In this paper we argue that the paradox is far less damaging to CP than is generally believed. We describe how, given certain plausibleassumptions, in a large class of cases in which CP seems to lead tocontradiction, it does not do so after all. A (...) restricted version of CP canthus be maintained. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic (...) framework of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox (...) synthesises elements of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

Most arguments against the possibility of time travel use the same old, familiar objection: If I could travel back in time, then I could kill my earlier (i.e. younger) self. Since I do exist such an action would result in a contradiction. Therefore time travel is impossible. This is a statement of the Principal Paradox of Time Travel. Some philosophers have argued that such actions as attempting to kill one’s earlier self would always fail and that there is nothing (...) especially strange about such failures. Despite these arguments, the problem generally is not viewed as being solved in favour of time travel. The above objection to time travel is also used to dismiss a particular class of cosmological models as being unphysical. This paper provides a solution to the Principal Paradox by exploring both the logical and causal implications of time travel. (shrink)

Whereas many others have scrutinized the Allais paradox from a theoretical angle, we study the paradox from an historical perspective and link our findings to a suggestion as to how decision theory could make use of it today. We emphasize that Allais proposed the paradox as a normative argument, concerned with ‘the rational man’ and not the ‘real man’, to use his words. Moreover, and more subtly, we argue that Allais had an unusual sense of the normative, (...) being concerned not so much with the rationality of choices as with the rationality of the agent as a person. These two claims are buttressed by a detailed investigation – the first of its kind – of the 1952 Paris conference on risk, which set the context for the invention of the paradox, and a detailed reconstruction – also the first of its kind – of Allais’s specific normative argument from his numerous but allusive writings. The paper contrasts these interpretations of what the paradox historically represented, with how it generally came to function within decision theory from the late 1970s onwards: that is, as an empirical refutation of the expected utility hypothesis, and more specifically of the condition of von Neumann–Morgenstern independence that underlies that hypothesis. While not denying that this use of the paradox was fruitful in many ways, we propose another use that turns out also to be compatible with an experimental perspective. Following Allais’s hints on ‘the experimental definition of rationality’, this new use consists in letting the experiment itself speak of the rationality or otherwise of the subjects. In the 1970s, a short sequence of papers inspired by Allais implemented original ways of eliciting the reasons guiding the subjects’ choices, and claimed to be able to draw relevant normative consequences from this information. We end by reviewing this forgotten experimental avenue not simply historically, but with a view to recommending it for possible use by decision theorists today. (shrink)

Most discussions frame the Liar Paradox as a formal logical-linguistic puzzle. Attempts to resolve the paradox have focused very little so far on aspects of cognitive psychology and processing, because semantic and cognitive-psychological issues are generally assumed to be disjunct. I provide a motivation and carry out a cognitive-computational treatment of the liar paradox based on a cognitive-computational model of language and conceptual knowledge within the Predictive Processing framework. I suggest that the paradox arises as a (...) failure of synchronization between two ways of generating the liar situation in two different PP sub-models, one corresponding to language processing and the other to the processing of meaning and world-knowledge. In this way, I put forward the claim that the liar sentence is meaningless but has an air of meaningfulness. I address the possible objection that the proposal violates the Principle of Unrestricted Compositionality, which purportedly regulates the conceptual competence of thinkers. (shrink)

Jim buys a ticket in a million-ticket lottery. He knows it is a fair lottery, but, given the odds, he believes he will lose. When the winning ticket is chosen, it is not his. Did he know his ticket would lose? It seems that he did not. After all, if he knew his ticket would lose, why would he have bought it? Further, if he knew his ticket would lose, then, given that his ticket is no different in its chances (...) of winning from any other ticket, it seems that by parity of reasoning he should also know that every other ticket would lose. But of course he doesn’t know that; in fact, he knows that not every ticket will lose. (shrink)

Most discussions frame the Liar Paradox as a formal logical-linguistic puzzle. Attempts to resolve the paradox have focused very little so far on aspects of cognitive psychology and processing, because semantic and cognitive-psychological issues are generally assumed to be disjunct. I provide a motivation and carry out a cognitive-computational treatment of the liar paradox based on a model of language and conceptual knowledge within thePredictive Processing(PP) framework. I suggest that the paradox arises as a failure of (...) synchronization between two ways of generating the liar situation in two different (idealized) PP sub-models, one corresponding to language processing and the other to the processing of meaning and world-knowledge. In this way, I put forward the claim that the liar sentence is meaningless but has an air of meaningfulness. I address the possible objection that the proposal violates thePrinciple of Unrestricted Compositionality, which purportedly regulates the conceptual competence of thinkers. (shrink)

Most discussions frame the Liar Paradox as a formal logical-linguistic puzzle. Attempts to resolve the paradox have focused very little so far on aspects of cognitive psychology and processing, because semantic and cognitive-psychological issues are generally assumed to be disjunct. I provide a motivation and carry out a cognitive-computational treatment of the liar paradox based on a model of language and conceptual knowledge within the Predictive Processing framework. I suggest that the paradox arises as a failure (...) of synchronization between two ways of generating the liar situation in two different PP sub-models, one corresponding to language processing and the other to the processing of meaning and world-knowledge. In this way, I put forward the claim that the liar sentence is meaningless but has an air of meaningfulness. I address the possible objection that the proposal violates the Principle of Unrestricted Compositionality, which purportedly regulates the conceptual competence of thinkers. (shrink)

I argue that the standard Bayesian solution to the ravens paradox— generally accepted as the most successful solution to the paradox—is insufficiently general. I give an instance of the paradox which is not solved by the standard Bayesian solution. I defend a new, more general solution, which is compatible with the Bayesian account of confirmation. As a solution to the paradox, I argue that the ravens hypothesis ought not to be held equivalent to its contrapositive; more (...) interestingly, I argue that how we formally represent hypotheses ought to vary with the context of inquiry. This explains why the paradox is compelling, while dealing with standard objections to holding hypotheses inequivalent to their contrapositives. (shrink)

The Knower Paradox has had a brief but eventful history, and principles of epistemic closure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can tell, however, no (...) one working in either area has emphasized the result I emphasize in this paper: the Knower Paradox just falsifies even the most widely accepted general principles of epistemic closure. After establishing that result, I discuss five of its more important consequences. (shrink)

Classical particles of the same kind are distinguishable: they can be labeled by their positions and follow different trajectories. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and via S=k ln W this leads to a non-extensive expression for the entropy. This result is generally considered wrong because of its inconsistency with thermodynamics. It is sometimes concluded from this inconsistency, notoriously illustrated by the Gibbs paradox, that identical particles must be treated (...) as indistinguishable after all; and even that quantum mechanics is indispensable for making sense of this. In this article we argue, by contrast, that the classical statistics of distinguishable particles and the resulting non-extensive entropy function are perfectly all-right both from a theoretical and an experimental perspective. We remove the inconsistency with thermodynamics by pointing out that the entropy concept in statistical mechanics is not completely identical to the thermodynamical one. Finally, we observe that even identical quantum particles are in some cases distinguishable; and conclude that quantum mechanics is irrelevant to the Gibbs paradox. (shrink)

The ancient sorites paradox has important implications for metaphysics, for logic, and for semantics. Metaphysically, the paradox can be harnessed to produce a powerful argument for the claim that there cannot be vague objects or vague properties. With respect to logic, the paradox forces a choice between the highly counterintuitive ‘epistemic’ account of vagueness and the rejection of classical two-valued logic. Regarding semantics, nonclassical approaches to the logic of vagueness lead naturally to the idea that truth, for (...) vague discourse, is not direct language-world correspondence grounded in referential connections linking a statement’s basic subsentential constituents (names, predicates, the apparatus of quantification) to real objects and real properties; rather, truth is a matter of indirect correspondence between vague language and nonvague reality. (shrink)

In defense of the minimalist conception of truth, Paul Horwich(2001) has recently argued that our acceptance of the instances of the schema,`the proposition that p is true if and only if p', suffices to explain our acceptanceof truth generalizations, that is, of general claims formulated using the truth predicate.In this paper, I consider the strategy Horwich develops for explaining our acceptance of truth generalizations. As I show, while perhaps workable on its own, the strategy is in conflictwith his response to (...) the liar paradox. Something must give. I consider and reject variousalternatives and emendations to the strategy. In order to resolve the conflict,I propose an alternative approach to the liar, one that supports Horwich's strategywhile leaving minimalism maximally uncompromised. (shrink)

The preface paradox is a problem for everyone; you don’t need to be committed to any special epistemological theory to face the problem it raises. The problem of easy knowledge is supposed to be different in this respect. It is generally thought to arise only for those who believe there is such a thing as basic knowledge, i.e. knowledge acquired through a source that one does not know to be reliable or trustworthy. Because it is thought to arise only (...) for those who believe in basic knowledge, the problem of easy knowledge is generally regarded as a problem for, or objection to, the possibility of basic knowledge. (shrink)

Disregarding trends of secularization, the Virgin Mary still plays an important role in religious devotions all over the world, even in the West. This does not diminish the controversies, debates and theo-political struggles that surround Mary and a Marian theology, as will be shown in this article. Western feminist theologies mostly choose, in general accordance with the Second Vatican Council, for a liberating, biblical, human Mary contra a more cosmological Mary, object of devotional piety. This contribution gives a critical sketch (...) of the background of these developments in Mariology and argues for a closer look at Marian devotional practices in order to find some inspiring elements for rethinking divine presence, Mary and perhaps a new Mariology. Can feminists find inspiration in this approach without forfeiting critical power and without denying the paradoxical and dangerous dimensions of Mary? (shrink)

The Gibbs' Paradox is commonly explained by invoking some type of "principle of indistinguishability," which asserts that the interchange of identical particles is not a real physical event, i.e., is operationally meaningless. However, if this principle is to provide a satisfactory resolution of the Paradox, it must be operationally possible to determine whether, in fact, two given systems are identical or not. That is, the assertion that the Gibbs' Paradox is resolvable by an indistinguishability principle actually is (...) an assertion that we can in principle possess a complete set of effective procedures for determining the identity or non-identity of arbitrary physical systems. We show that, in rather general situations, an assertion of this type is not well founded. It is further pointed out that a failure to recognize an incomplete set of "sameness criteria" can lead to serious blunders in physics and in biology. (shrink)

Summary With the help of psychological and biological concepts it is possible todescribe adequately a fundamental class of inductive inferences that are intuitively correct. Moreover, by relying on evolutionary theories it is possible tojustify them, because they reflect innate, hence useful, capacities. These inferences, however, refer to the past, i.e. the inferred generalization is of the form All Awere B . The reason is that evolutionary theories only claim that innate capacitieshad survival value. With respect to inductive inferences about the (...) future the situation is different. In particular, they are affected by the Goodman paradox. In the article, a method is proposed which enables us to describe adequately a basic class of inductive inferences about the future which are intuitively correct. These inferences can also be justified, but their justification requires a very specific assumption. The conclusions arrived at in the article can be viewed as a satisfactory solution to the Goodman paradox. (shrink)

Evidentiary propositions E 1 and E 2, each p-positively relevant to some hypothesis H, are mutually corroborating if p > p, i = 1, 2. Failures of such mutual corroboration are instances of what may be called the corroboration paradox. This paper assesses two rather different analyses of the corroboration paradox due, respectively, to John Pollock and Jonathan Cohen. Pollock invokes a particular embodiment of the principle of insufficient reason to argue that instances of the corroboration paradox (...) are of negligible probability, and that it is therefore defeasibly reasonable to assume that items of evidence positively relevant to some hypothesis are mutually corroborating. Taking a different approach, Cohen seeks to identify supplementary conditions that are sufficient to ensure that such items of evidence will be mutually corroborating, and claims to have identified conditions which account for most cases of mutual corroboration. Combining a proposed common framework for the general study of paradoxes of positive relevance with a simulation experiment, we conclude that neither Pollock’s nor Cohen’s claims stand up to detailed scrutiny. I am quite prepared to be told…”oh, that is an extreme case: it could never really happen!” Now I have observed that this answer is always given instantly, with perfect confidence, and without any examination of the proposed case. It must therefore rest on some general principle: the mental process being something like this—“I have formed a theory. This case contradicts my theory. Therefore, this is an extreme case, and would never occur in practice.”Rev. Charles L. Dodgson. (shrink)

ABSTRACTMany discussions of the ‘preface paradox’ assume that it is more troubling for deductive closure constraints on rational belief if outright belief is reducible to credence. I show that this is an error: we can generate the problem without assuming such reducibility. All that we need are some very weak normative assumptions about rational relationships between belief and credence. The only view that escapes my way of formulating the problem for the deductive closure constraint is in fact itself a (...) reductive view: namely, the view that outright belief is credence 1. However, I argue that this view is unsustainable. Moreover, my version of the problem turns on no particular theory of evidence or evidential probability, and so cannot be avoided by adopting some revisionary such theory. In sum, deductive closure is in more serious, and more general, trouble than some have thought. (shrink)

The liar paradox in its simplest form is the following argument. Consider the sentence 'this sentence is false'; call that the "liar sentence". Suppose the liar sentence is true. Then, since it says it is false, the liar sentence is false. So our supposition that it is true was mistaken, and the liar sentence must be false. But that's precisely what the liar sentence says, so it is true after all. The liar sentence is, therefore, both true and false---an (...) absurd result. ;Hans Herzberger has argued that several solutions to the Grelling paradox exhibit a common pattern: the very devices we introduce in order to avoid one version of the paradox are integral components of new versions of the paradox. Herzberger suggests that this is typical of semantic paradox in general. Chapters 1, 2, and 3 of this dissertation examine several possible solutions to the liar---especially appeals to language levels and to contexts---and attempt to locate these possible solutions in Herzberger's pattern. ;There is some reason to think that this pattern is inescapable---that is, that the liar paradox is ultimately unsolvable---so the remaining two chapters of this dissertation explore what follows from the claim that it is unsolvable. Chapter 4 develops an argument from the claim that the liar is unsolvable to the claim that we cannot understand ourselves. Chapter 5, then, attempts to make sense of this circumstance by invoking a Nietzschean view of thinking and truth---perspectivalism, which holds that all thinking concerns interpretation and that there are no uninterpreted facts. Given some perspectivalist assumptions, we can see how it is inevitable that we will be unable to understand ourselves---and how we can nevetherless attain a certain limited kind of understanding. Perspectivalism also recommends a certain intellectual humility: if everything is interpretation, then no view of mine can be a comprehensive and accurate view of the way the world really is. This by itself is not a surprising claim; the surprising claim is that the liar paradox is the basis of it. (shrink)

Attemts to explain causal paradoxes of Quantum Mechanics (QM) have tried to solve the problems within the framework of Quantum Electrodynamics (QED). We will show, that this is impossible. The original theory of QED by Dirac (Proc Roy Soc A117:610, 1928) formulated in its preamble four preliminary requirements that the new theory should meet. The first of these requirements was that the theory must be causal. Causality is not to be derived as a consequence of the theory since it was (...) a precondition for the formulation of the theory; it has been constructed so that it be causal. Therefore, causal paradoxes logically cannot be explained within the framework of QED. To transcend this problem we should consider the following points: Dirac himself stated in his original paper (1928) that his theory was only an approximation. When he returned to improve the theory later (Proc Roy Soc A209, 1951), he noted that the new theory “involves only the ratio e / m , not e and m separately”. This is a sign that although the electromagnetic effects (whose source is e ) are magnitudes stronger than the gravitational effects (whose source is m ), the two are coupled. Already in 1919, Einstein noted that “the elementary formations which go to make up the atom” are influenced by gravitational forces. Although in that form the statement proved not to be exactly correct, the effects of gravitation on QM phenomena have been established. The conclusion is that we should seek a resolution for the causal paradoxes in the framework of the General Theory of Relativity (GTR)—in contrast to QED, which involves only the Special Theory of Relativity (STR). We show that causality is necessarily violated in GTR. This follows from the curvature of the space-time. Although those effects are very small, one cannot ignore their influence in the case of the so-called “paradox phenomena”. (shrink)

The idea that nature is importantly frame-less is an entrenched dogma in much of environmental aesthetics. Although there are powerful arguments that support this position, there are also powerful arguments supporting the view that observers often - or even inevitably - frame, bound, or otherwise confine natural objects in the course of aesthetic regard. Facing these opposing arguments off against each other produces the 'framing paradox': On the one hand, frames seem to be an indispensable condition for the aesthetic (...) experience of anything whatsoever, and on the other hand the aesthetic appreciation of natural environments seems to require the dissolving or penetrating of boundaries of all sorts. To resolve this paradox, we must abandon an overly narrow conception of 'frame' that has generally been assumed throughout the debate and pay closer attention to what various framing devices (in both natural and artifactual settings) do to focus, rather than confine, aesthetic attention. Doing this enables us to make better sense of the way intelligence and imagination cooperate in carrying attention beyond perceptual phenomena. From the perspective that results, rival claims about the framability of nature can be seen as variable markers on an endless scale of aesthetic selectivity. (shrink)

It is now more than 50 years that the Goodman paradox has been discussed, and many different solutions have been proposed. But so far no agreement has been reached about which is the correct solution to the paradox. In this paper, I present the naturalistic solutions to the paradox that were proposed in Quine (1969, 1974), Quine and Ullian (1970/1978), and Stemmer (1971). At the same time, I introduce a number of modifications and improvements that are needed (...) for overcoming shortcomings of the solutions. The discussion of this improved version suggests that the Goodman paradox actually embodies three different problems; yet, one of them is not Goodman’s but Hume’s problem. The discussion also suggests that the naturalistic approach is probably the best for basing on it a theory of confirmation. Finally, I analyze one of Hume’s insights that seems to have been largely ignored. This insight shows a surprising similarity to a central feature of the naturalistic solutions. (shrink)

A striking paradox underlies corporate governance reform during the past fifteen years: center-left political parties have pushed for pro-shareholder corporate governance reforms, while the historically pro-business right has generally resisted them to protect established forms of organized capitalism, concentrated corporate stock ownership, and managerialism. Case studies of Germany, France, Italy, and the United States reveal that center-left parties used corporate governance reform to attack the legitimacy of existing political economic elites, present themselves as pro-growth and pro-modernization, strike political alliances (...) with segments of the financial sector, and appeal to middle-class voters. Conservative parties’ established alliances with managers constrained them from endorsing corporate governance reform. (shrink)

Despite the burgeoning research in recent years on what is called analogical reasoning and transfer, the problem of how similarity or invariant relations are fundamentally accessed is typically either unrecognized, or ignored in componential and computational analyses. The access problematic is not a new one, being outlined by the paradox found in Plato’s Meno. In order to understand the analogical-access problematic, it is suggested that the concepts of analogical relations including the lexical concept metaphor, isomorphic relation in mathematics, homology (...) in biology, stimulus generalization in psychology, transfer of learning in education, and transposition phenomena in perception, be reconceptualized as subsets of a higher-order domain as all share the problem of how invariance relations are generated and accessed. A solution is suggested based on two specific evolutionary and neurological models, coupled with findings regarding the cognitive importance of knowledge-base. The paper constitutes a reciprocal complementarity analysis of a previous paper on metaphor. A higher-order form of analogical reasoning called analogical progression is introduced. Implications for research are discussed that indicate the need for a paradigm shift. The paper concludes with a four-stage model of analogical access. (shrink)

Two ideal standard clocks, effectively isolated from interaction with other physical systems, and in a region of the universe free of gravitational fields, are assumed to move in any arbitrary manner so that they coincide on at least two occasions. In general, the reading of one of them will become retarded relative to the other in the interval between successive coincidences. This relative retardation is predicted by the restricted theory of relativity, taken together with the assumption that the 'rate' of (...) a clock depends only on its velocity and not on its acceleration. The recognized procedure for calculating the retardation in terms of clock 'rates' is set out, and is illustrated by its application to a simple hypothetical experiment in which one clock remains at rest and the other travels away from and back to it with constant speed in a straight line. There is nothing paradoxical in the predicted retardation as such. The so-called 'clock paradox' arises because an alternative, and apparently valid, calculation procedure, also based on clock 'rates', leads to a contradictory result. The term 'paradox' is something of a euphemism since the two predictions are contradictories. It is shown that the paradox does not arise when direct use is made of the Lorentz transformation without introducing the additional, and non-essential, step in reasoning involved in utilizing the clock 'rates'. It is then shown that the paradox arises only through using these clock 'rates' without due regard to the exact significance of the quantities so described; once this is recognized the paradox is resolved completely within the framework of the restricted theory, which then provides a unique and unambiguous prediction of the relative retardation. Once the paradox is thus resolved, the general theory of relativity can add nothing significant to the analysis. It is shown that the application of the principle of equivalence is essentially trivial; in effect, Einstein and Tolman evaded the real logical issue raised by the contradictory predictions by denying the applicability of the restricted theory and then utilizing, by means of the principle of equivalence, results obtained from it. This tortuous procedure succeeded in evading the paradox rather than in resolving it; it would obviously be quite invalid were the restricted theory indeed inapplicable to the problem. (shrink)

This dissertation is a study of some recent theories of truth. The theories fall into three groups: The Revision Theories, the context-sensitive theories, and the "Chrysippian theories". ;The "Chrysippian theories" are based on the intuition that pathologicalities arising from the concept of truth can be recognized and acknowledged with the concept of truth itself. Thus, from the pathologicality of the Liar, for example, we can conclude that the Liar is not true. This leads to immediate difficulties since the Liar claims (...) just that--that it is not true--and it would thus seem to be true. The Chrysippian theories are designed to avoid these difficulties while preserving the motivating intuition. Haim Gaifman's Pointer Semantics, and Brian Skyrms' Intensional Fixed-Point Theory of Truth are examples of such theories. They are exposited and criticized. ;The context-sensitive theories dealt with are Tyler Burge's Indexical Theory of Truth and the theory of Jon Barwise and John Etchemendy. These theories claim that an ambiguity due to a contextual parameter is the reason for the difficulties we encounter. Burge offers a theory of Tarskian levels coupled with a pragmatic theory that explains the assignment of levels to occurrences of 'true'. Barwise and Etchemendy make explicit a situational parameter in their account of propositions. They consider the ambiguity with respect to the situation a propositions is about a main source of the paradoxes. ;Finally, the Revision Theories of Truth of Anil Gupta and Nuel Belnap and two variations of this theory are considered. One is due to Aladdin Yaqub, the other, the "fully-varied theory", is due to Gupta and Belnap but remains largely unexplored. Revision theories are put forward as the most promising account of the difficulties. They are based on a definitional reading of all Tarski biconditionals. The circularity implied by such a reading is handled by Gupta's and Belnap's general theory of definitions. ;Yaqub's objections raised against the standard theory are examined, and his proposed solution is shown to be inadequate. The fully-varied Revision Theory is shown to provide a better solution. (shrink)

According to Hume’s classical definition of causal relations, a cause must fulfill two distinct conditions: a) be a sufficient condition for the occurrence of its effect; b) be temporally prior to it. However, a careful logical analysis shows that the combination of sufficiency and temporality is impossible. This is because if a complete cause is a sufficient condition for its effect to occur-then the effect is a necessary condition for the occurrence of its own complete cause! Thus, there can be (...) no complete cause for anything to occur, which means that causal determination is logically impossible.The paper goes on to examine some possible responses to this argument, and then concludes with a nontemporal version of the paradox that shows that even the first of Hume’s above conditions cannot be fulfilled on its own. This is because if something (e.g., the cause) is a sufficient condition of something else (e.g., the effect), then it cannot be a sufficient condition of itself. (shrink)

According to Hume’s classical definition of causal relations, a cause must fulfill two distinct conditions: a) be a sufficient condition for the occurrence of its effect; b) be temporally prior to it. However, a careful logical analysis shows that the combination of sufficiency and temporality is impossible. This is because if a complete cause is a sufficient condition for its effect to occur-then the effect is a necessary condition for the occurrence of its own complete cause! Thus, there can be (...) no complete cause for anything to occur, which means that causal determination is logically impossible. The paper goes on to examine some possible responses to this argument, and then concludes with a nontemporal version of the paradox that shows that even the first of Hume’s above conditions cannot be fulfilled on its own. This is because if something is a sufficient condition of something else, then it cannot be a sufficient condition of itself. (shrink)

As part of an exceptionally lucid analysis of the Lottery Paradox, Dana Nelkin castigates the solutions to that paradox put forward by Laurence Bonjour and Sharon Ryan. According to her, these are “so finely tailored to lottery-like cases that they are limited in their ability to explain [what seem the intuitively right responses to such cases]”. She then offers a solution to the Lottery Paradox that allegedly has the virtue of being independently motivated by our intuitions regarding (...) certain non-lottery-like cases. This note argues that Nelkin fails to show that her solution applies to other than lottery-like cases or in any event that it is more general than Bonjour’s and Ryan’s solutions. (shrink)

A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that (...) is intrinsically vague. We propose application of the language of relative analysis—a type of non-standard analysis—to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’ and satisfies a moderately weakened form of the Conjunction Principle. We also propose an adaptation of the model that is able to deal with beliefs that are less firm than ‘almost certainty’. The adapted version is also of interest for the epistemicist account of vagueness. (shrink)

Simple random sampling resolutions of the raven paradox relevantly diverge from scientific practice. We develop a stratified random sampling model, yielding a better fit and apparently rehabilitating simple random sampling as a legitimate idealization. However, neither accommodates a second concern, the objection from potential bias. We develop a third model that crucially invokes causal considerations, yielding a novel resolution that handles both concerns. This approach resembles Inference to the Best Explanation (IBE) and relates the generalization’s confirmation to confirmation of (...) an associated law. We give it an objective Bayesian formalization and discuss the compatibility of Bayesianism and IBE. (shrink)

In a number of earlier writings, I have outlined what may perhaps be called a game-theoretical semantics. This semantics can be applied both to formal first-order languages, with or without modalities, and to certain fragments of English. The basic idea of this semantics is to associate with each sentence S under consideration a two-person game G. The players are called Myself and Nature.