Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or (...) ‘how’ questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)

It is argued that mathematics is unreasonably effective in fundamental physics, that this is genuinely mysterious, and that it is best explained by a version of Pythagorean metaphysics. It is shown how this can be reconciled with the fact that mathematics is not always effective in real world applications. The thesis is that physical structure approaches isomorphism with a highly symmetric mathematical structure at very high energy levels, such as would have existed in the early universe. As the universe cooled, (...) its underlying symmetry was broken in a sequence of stages. At each stage, more forces and particles were differentiated, leading to the complexity of the observed world. Remnant structure makes mathematics effective in some real world applications, but not all. (shrink)

I argue that a recent version of the doctrine of mathematical naturalism faces difficulties arising in connection with Wigner's old puzzle about the applicability of mathematics to natural science. I discuss the strategies to solve the puzzle and I show that they may not be available to the naturalist.

Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or (...) ‘how’ questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)

Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or (...) ‘how’ questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)

In his influential 1960 paper ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’, Eugene P. Wigner raises the question of why something that was developed without concern for empirical facts—mathematics—should turn out to be so powerful in explaining facts about the natural world. Recent philosophy of science has developed ‘Wigner’s puzzle’ in two different directions: First, in relation to the supposed indispensability of mathematical facts to particular scientific explanations and, secondly, in connection with the idea that aesthetic criteria (...) track theoretical desiderata such as empirical success. An important aspect of Wigner’s article has, however, been overlooked in these debates: his worries about the underdetermination of physical theories by mathematical frameworks. The present paper argues that, by restoring this aspect of Wigner’s argument to its proper place, Wigner’s puzzle may become an instructive case study for the teaching of core issues in the philosophy of science and its history. (shrink)

According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner’s conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner’s original thought experiment was central to the development of QBist thinking. The (...) focus of this paper concerns two very instructive modifications to Wigner’s puzzle: One, a recent no-go theorem by Frauchiger and Renner, and the other a thought experiment by Baumann and Brukner. We show that the paradoxical features emphasized in these works disappear once both friend and Wigner are understood as agents on an equal footing with regard to their individual uses of quantum theory. Wigner’s action on his friend then becomes, from the friend’s perspective, an action the friend takes on Wigner. Our analysis rests on a kind of quantum Copernican principle: When two agents take actions on each other, each agent has a dual role as a physical system for the other agent. No user of quantum theory is more privileged than any other. In contrast to the sentiment of Wigner’s original paper, neither agent should be considered as in “suspended animation.” In this light, QBism brings an entirely new perspective to understanding Wigner’s friend thought experiments. (shrink)

Bub's criticism of Bell's locality postulate is discussed. The locality postulate is explained, and it is shown that Bub is in fact arguing against a class of theories which are subject to stronger restrictions than this postulate, and therefore his “refutation” of the latter is misleading.

We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator (...) of this sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for physical equivalence. (shrink)

The Wigner--Eckart theorem is central to the application of symmetry principles throughout atomic, molecular, and nuclear physics. Nevertheless, the theorem has a puzzling feature: it is dispensable for solving problems within these domains, since elementary methods suffice. To account for the significance of the theorem, I first contrast it with an elementary approach to calculating matrix elements. Next, I consider three broad strategies for interpreting the theorem: conventionalism, fundamentalism, and conceptualism. I argue that the conventionalist framework is unnecessarily pragmatic, while (...) the fundamentalist framework requires more ontological commitments than necessary. Conceptualism avoids both defects, accounting for the theorem's significance in terms of how it epistemically restructures the calculation of matrix elements. Specifically, the Wigner--Eckart theorem modularizes and unifies matrix element problems, thereby changing what we need to know to solve them. (shrink)

In a paper titled, “The Unreasonable Effectiveness of Mathematics”, published 20 years after Wigner’s seminal paper, the mathematician Richard W. Hamming discussed what he took to be Wigner’s problem of Unreasonable Effectiveness and offered some partial explanations for this phenomenon. Whether Hamming succeeds in his explanations as answers to Wigner’s puzzle is addressed by other scholars in recent years I, on the other hand, raise a more fundamental question: does Hamming succeed in raising the same question as Wigner? The (...) answer is no. My goal is to show that Hamming’s reading misses Wigner’s highly original formulation of the problem.Through a close and contextual reading of Wigner’s work, as I will show, we are led in new directions in addressing and solving the applicability problem. (shrink)

As these opening quotes acknowledge, the Prisoner’s Dilemma (PD) represents a core puzzle within the formal mathematics of game theory.3 Its rise in conspicuity is evident figure 2.1 above demonstrating a relatively steady rise in incidences of the phrase’s usage between 1960 to 1995, with a stable presence persisting into the twenty first century. This famous two-person “game,” with a stock narrative cast in terms of two prisoners who each independently must choose whether to remain silent or speak, each (...) advancing self-interest at the expense of the other and thereby achieving a mutually suboptimal outcome, mires any social interaction it is applied to into perplexity. The logic of this game proves the inverse of Adam Smith’s invisible hand: individuals acting on self interest will achieve a mutually suboptimal outcome. However, as this chapter illuminates, the assumptions underlying game theory drive this conclusion. (shrink)

Aristotle's claim in Metaphysics Z.6 that "each substance is the same as its essence" has long puzzled commentators. For it seems to conflict with two other Aristotelian theses: (1) primary substances are individuals (e.g., Socrates and Callias), and (2) essences are universals (e.g., Man and Horse). Three traditional solutions to this difficulty are considered and rejected. Instead, to make the Z.6 equation consistent with (1) and (2), I propose that it be interpreted to be making something other than a straightforward (...) identity claim. Callias is the same as his essence in the sense that to be identical to Callias is to be the same man as Callias (where Man is the essence of Callias). In general, x is identical to y if, and only if, x and y are the same E (where E specifies the "what it is to be" for x, i.e., the essence of x). So each of Socrates and Callias is the same as his essence, and Man is that essence, but Socrates and Callias are not identical, for they are not the same man. (shrink)

Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented (...) a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.A Structural Account of Mathematics will be required reading for anyone working in this field. (shrink)

In the first chapter of his Knowledge and Lotteries, John Hawthorne argues that thinkers do not ordinarily know lottery propositions. His arguments depend on claims about the intimate connections between knowledge and assertion, epistemic possibility, practical reasoning, and theoretical reasoning. In this paper, we cast doubt on the proposed connections. We also put forward an alternative picture of belief and reasoning. In particular, we argue that assertion is governed by a Gricean constraint that makes no reference to knowledge, and that (...) practical reasoning has more to do with rational degrees of belief than with states of knowledge. (shrink)

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of universal or (...) conditional claims in everyday life. (shrink)

Polanyi’s philosophy of “man in thought,” by all appearances, chronologically and structurally, seems to be founded on his epistemology. Polanyi’s epistemology of tacit knowing as integration is teleological. By his “ontological equation,” he patterned comprehensive (and complex) entities as emergence on his epistemology. This forces him to make puzzling formulaic statements which land him in trouble with fellow scientists. The equation also lends itself to unwarranted problematic interpretations. The exploration leads me to suggest that Polanyi may be understood as a (...) “rational realist” who insisted on a tacit knowledge version of interactionist mode of mind-body relation. (shrink)

Incompletely understood medical texts, like other kinds of technical writing, pose problems that require a multi-disciplinary approach. In addition, the etymological writings of ancient commentators hint at their own cultures priorities and limitations. Progress today, therefore, also depends partly upon how well we can harmonize our own thinking with the beliefs and practices of an alien culture, whose medicine may overlap with culinary and other social uses. A puzzling word may have been reshaped to reflect the supposed properties of the (...) entity denoted or the use made of it. Plant names, which figure strongly in such texts, are particularly liable to be passed from language to language as ‘culture borrowings’ and are thus especially vulnerable to this false rationalization process, commonly known as ‘folk etymology’. In a personal exploration I analyse some modern vocabulary and identify several varieties of the process and then illustrate its effects by means of toponyms and medicinal plant names from mediaeval Italy and ancient Mesopotamia, Anatolia, Greece and Italy. Since no known language seems immune from etymologizing, the generic points that emerge are offered as a contribution to the decipherers craft. (shrink)

This is an investigation of Aristotle's conception of accidental compounds (or "kooky objects," as Gareth Matthews has called them)—entities such as the pale man and the musical man. I begin with Matthews's pioneering work into kooky objects, and argue that they are not so far removed from our ordinary thinking as is commonly supposed. I go on to assess their utility in solving some familiar puzzles involving substitutivity in epistemic contexts, and compare the kooky object approach to more modern approaches (...) involving the notion of referential opacity. I conclude by proposing that Aristotle provides an implicit role for kooky objects in such metaphysical contexts as the Categories and Metaphysics. (shrink)

Much of our know-how is acquired through practice: we learn how to cook by cooking, how to write by writing, and how to dance by dancing. As Aristotle argues, however, this kind of learning is puzzling, since engaging in it seems to require possession of the very knowledge one seeks to obtain. After showing how a version of the puzzle arises from a set of attractive principles, I argue that the best solution is to hold that knowledge-how comes in (...) degrees, and through practice a person gradually learns how to do something. However, the two standard accounts of know-how in the literature, intellectualism and anti-intellectualism, cannot properly account for the distinctive way in which know-how is gradually acquired by practice, a process in which conceptual representations and practical abilities are intimately interwoven. Drawing on Gareth Evans's work, I outline an account that may do so, and use this account to distinguish between two forms of learning to explain why skill generally cannot be learnt through testimony, and requires practice. (shrink)

When I first began to study philosophy I was introduced to the discipline in that magically traditional way by being assured that what lay before me was the love of wisdom. Why this had any adolescent appeal still puzzles me, but, like many others, I joined in as spectator to and occasionally as a removed participant in all the rough and tumble of a Socratic sparring match in the Athenian marketplace. There was some talk of wisdom, to be sure, which (...) seemed to link it with a humble admission of ignorance or a pitch against yielding to temptation, but neither was ever deeply revealing. I waited for more. My next encounter a few years later turned up little more than the surname of an English disciple of Wittgenstein. Somehow the trail had gone to brush, despite the apparent health and energy of philosophy. (shrink)

Next SectionThis article argues against two dominant accounts of the nature of nostalgia. These views assume that nostalgia depends, in some way, on comparing a present situation with a past one. However, neither does justice to the full range of recognizably nostalgic experiences available to us – in particular, ‘Proustian’ nostalgia directed at involuntary autobiographical memories. Therefore, the accounts in question fail. I conclude by considering an evaluative puzzle raised by Proustian nostalgia when it is directed at memories that (...) the nostalgist herself regards as non-veridical. (shrink)

Polanyi’s philosophy of “man in thought,” by all appearances, chronologically and structurally, seems to be founded on his epistemology. Polanyi’s epistemology of tacit knowing as integration is teleological. By his “ontological equation,” he patterned comprehensive (and complex) entities as emergence on his epistemology. This forces him to make puzzling formulaic statements which land him in trouble with fellow scientists. The equation also lends itself to unwarranted problematic interpretations. The exploration leads me to suggest that Polanyi may be understood as a (...) “rational realist” who insisted on a tacit knowledge version of interactionist mode of mind-body relation. (shrink)

Polanyi’s philosophy of “man in thought,” by all appearances, chronologically and structurally, seems to be founded on his epistemology. Polanyi’s epistemology of tacit knowing as integration is teleological. By his “ontological equation,” he patterned comprehensive (and complex) entities as emergence on his epistemology. This forces him to make puzzling formulaic statements which land him in trouble with fellow scientists. The equation also lends itself to unwarranted problematic interpretations. The exploration leads me to suggest that Polanyi may be understood as a (...) “rational realist” who insisted on a tacit knowledge version of interactionist mode of mind-body relation. (shrink)

Contemporary Complex Cinema. Complex conditions: the resurgence of narrative complexity ; Complex cinema as brain-candy for the empowered viewer ; Narrative taxonomies: simple, complex, puzzle plots -- Cognitive Approach to Contemporary Complex Cinema. Why an (embodied-)cognitive approach? ; Various forms of complexity and their effects on sense making ; Problematizing narrative linearity ; Complicating narrative structures and ontologies ; Under-stimulation and cognitive overload ; Contradictions and unreliabilities ; A cognitive approach to classifying complexity ; Deceptive unreliability and the twist (...) film ; Disorienting but solvable puzzle films ; Impossible puzzle films -- Narrative Complexity and Dissonant Cognitions. The concept of cognitive dissonance ; Cognitions in dissonance: from social psychology to narrative engagement ; Types of dissonance in narrative comprehension ; Narrative incongruities ; Narrative impossibilities ; Cognitive access to impossible storyworlds: immersed and reflected operations ; 'Impossibilities' and embodied cognition ; Disrupting viewers' reliance on image schemas by perceptual impossibility ; Disrupting viewers' reliance on image schemas by formal impossibility -- Taming Dissonance: Cognitive Operations and Interpretive Strategies. Cognitive dissonance versus narrative coherence ; Reducing dissonance: interpretation and naturalization ; Foregrounding ; Narrating agency and authorship ; Artefact emotions and metareflexive appreciation ; Interpretation as dissonance reduction ; Coping with dissonance: frame-switches and poetic and aesthetic readings ; Frame-switching as hermeneutic play in impossible puzzle films ; Switching between narrative and symbolical readings: Enemy and Mulholland Drive ; Cognitive hesitation and the fantastic -- Impossible Puzzle Films: Between Art-Cinema and (Post-) Classical Narration. From art-cinema to puzzle films ; Art-cinema as a narrative mode ; Dissonance in modernist art-cinema ; Art-cinema as a cognitive reception frame ; Narrative complexity and meaning-making in art-cinema ; Impossible puzzle films and (post-)classical narration ; High degree of tellability ; Identification with goal-oriented characters ; Strong reliance on classical genre elements ; Adherence to classical narrative cohesion devices ; Inclusion of quasi-rational frames of naturalization -- Wallowing in Dissonance: The Attractiveness of Impossible Puzzles. Hermeneutic play and interpretive multiplicity ; Orientation, navigation, mapping ; Game logic and the fascination in failure ; Effort justification ; Diegetization of decoupling ; Fascination in infinity ; Destabilized ontological certainty ; Eudaimonic motivations and intrinsic needs. (shrink)

Many people feel the pull of both creationism and evolution as explanations for the origin of species, despite the direct contradiction. Some respond by endorsing theistic evolution, integrating the scientific and religious explanations by positing that God initiated or guided the process of evolution. Others, however, simultaneously endorse both evolution and creationism despite the contradiction. Here, we illustrate this puzzling phenomenon with interviews with a diverse sample. This qualitative data reveals several approaches to coping with simultaneous inconsistent explanations. For example, (...) some people seem to manage this contradiction by separating out ideological claims, which prioritize identity expression, from fact claims, which prioritize truth. Fitting with this interpretation, ambivalent individuals tended to call explanations “beliefs”, avoid mention of truth or falsity, and ground one or both beliefs in identity and personal history. We conclude with a brief discussion of the affordances of this distinction. (shrink)

In this paper we examine a puzzle recently posed by Aaron Preston for the traditional realist assay of property (quality) instances. Consider Socrates (a red round spot) and red1—Socrates’ redness. For the traditional realist, both of these entities are concrete particulars. Further, both involve redness being `tied to’ the same bare individuator. But then it appears that red1 is duplicated in its ‘thicker’ particular (Socrates), so that it can’t be predicated of Socrates without redundancy. According to Preston, this suggests (...) that a concrete particular and its property instances aren’t genuinely related. We argue that Preston’s proffered solution here—to treat property instances as “mental constructs”—is fraught with difficulty. We then go on to show how, by fine-tuning the nature of bare particulars, treating them as abstract modes of things rather than concrete particulars, the traditional realist can neatly evade Preston’s puzzle. (shrink)

In recent years, many non-consequentialists such as Frances Kamm and Thomas Scanlon have been puzzling over what has come to be known as the Number Problem, which is how to show that the greater number in a rescue situation should be saved without aggregating the claims of the many, a typical kind of consequentialist move that seems to violate the separateness of persons. In this article, I argue that these non-consequentialists may be making the task more difficult than necessary, because (...) allowing aggregation does not prevent one from being a non-consequentialist. I shall explain how a non-consequentialist can still respect the separateness of persons while allowing for aggregation. (shrink)

Reading the writings of Nietzsche is somewhat like putting together a large and complex jigsaw puzzle. In this paper I aim to show how two pieces of Nietzsche’s puzzle fit together: the first piece being the Doctrine of Eternal Recurrence; and the second piece being On the Genealogy of Morals. In order to see how these two pieces lock in to one another we must understand that Nietzsche’s great love of fate – his ‘Amor Fati’ – is what (...) he calls the “formula for greatness in a human being” (BGE 1:6).2 In this paper I will address the question of how we are to reconcile Nietzsche’s amor fati, understood as a brand of determinism, with Nietzsche’s own understanding of the Doctrine of the Eternal Recurrence as the ultimate test for the highest affirmation of life. Through an investigation of how Nietzsche thinks we should react to the thought of the application of the doctrine of Eternal Recurrence to our own lives – namely, the psychological implications of the doctrine – I aim to show that by proposing the Doctrine as the ultimate test for the highest affirmation of life, Nietzsche also provides part of what he takes to be the solution to the threat of both the impending nihilism and the inhibiting current morality of his age as he discusses them in the Genealogy. (shrink)

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.

The phrase “the end of art” has a long association with Arthur C. Danto.1 Indeed, Danto popularized the idea and offered an explanation of this puzzling notion. How could there have been an end of art when it has robustly continued? For this question to make sense, the meaning of “end” is not in the sense of termination, finality, or death in a literal, physical sense. So in 1912 when Marius de Zayas pronounced “art is dead,” he must have thought (...) the historical circumstances warranted it and found the metaphor illuminating: “[Art’s] present movements are not at all indications of vitality; they are not even the convulsions of agony prior to death; they are the mechanical reflex actions of a corpse.”2 In less .. (shrink)

One of the ironies of literary history is that the survival of Aristophanic comedy and indeed of all Greek drama is due to the more or less faithful transmission of a written text. Reading a play and watching one, after all, are very different sorts of activities. Unlike a book, in which the reader can leaf backward for reminders of what has already happened or forward for information about what is to come, a play onstage can be experienced in one (...) direction only, from ‘beginning’ to ‘end’. Nor can a play be put down and picked up again at one's leisure or interrupted while the audience puzzles over a difficult or intriguing passage. Live theatre is an ephemeral and essentially independent thing, which must be experienced in its own time and on its own terms or not at all, and as a result we modern readers, dependent on the written page, are at a marked disadvantage in understanding ancient drama. Taplin's study of staging in Aeschylus has shed considerable light on the dramatic technique of Athenian tragedy. Stage-practice in Aristophanic comedy, and in particular the ways in which names and naming are used there, has received much less attention. (shrink)

My objective in this project is to explore the concept of moral luck as it relates to sports. I am especially interested in constitutive luck. As a foundation I draw from both Bernard Williams and Thomas Nagel’s classic handling of moral luck, generally. Within the philosophy of sport are similar explorations of this nexus by Robert Simon and David Carr that also factor into the present work. My intent is to put a new lens in front of a puzzle (...) drawn from Torbjörn Tännsjö’s well-known article ‘Is Our Admiration of Sports Heroes Facistoid?’ Specifically, the idea that we might admire an athlete who excels without having worked hard for it. If we may call this puzzle ‘the talent problem,’ the questions driving the present work are as follows: what is the relationship between moral luck and the talent problem, and can this relationship provide a prescription for morally assessing the talent problem? The thesis that this exploratory work suggests that more complex games (and... (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large type-2 problems. they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of (...) recoding biases so as to reduce specific type-2 problems to (tractable) type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general (not task-specific) strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy representational redescription language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

"The Hardest Logic Puzzle Ever" was first described by the late George Boolos in the Spring 1996 issue of the Harvard Review of Philosophy. Although not dissimilar in appearance from many other simpler puzzles involving gods (or tribesmen) who always tell the truth or always lie, this puzzle has several features that make the solution far from trivial. This paper examines the puzzle and describes a simpler solution than that originally proposed by Boolos.

One of the ironies of literary history is that the survival of Aristophanic comedy and indeed of all Greek drama is due to the more or less faithful transmission of a written text. Reading a play and watching one, after all, are very different sorts of activities. Unlike a book, in which the reader can leaf backward for reminders of what has already happened or forward for information about what is to come, a play onstage can be experienced in one (...) direction only, from ‘beginning’ to ‘end’. Nor can a play be put down and picked up again at one's leisure or interrupted while the audience puzzles over a difficult or intriguing passage. Live theatre is an ephemeral and essentially independent thing, which must be experienced in its own time and on its own terms or not at all, and as a result we modern readers, dependent on the written page, are at a marked disadvantage in understanding ancient drama. Taplin's study of staging in Aeschylus has shed considerable light on the dramatic technique of Athenian tragedy. Stage-practice in Aristophanic comedy, and in particular the ways in which names and naming are used there, has received much less attention. (shrink)

ABSTRACTIn ‘Universals’, Ramsey declares that we do not, and cannot, know the forms of atomic propositions. A year later, in a symposium with Braithwaite and Joseph, he announces a change of mind: atomic propositions may, after all, be discoverable by analysis. It is clear from the 1926 paper that Ramsey intends this to be a revision of the 1925 claim. Puzzlingly, however, Ramsey does not mention analysis in 1925. My task in this article is to provide a justification for that (...) change of mind. My argument consists of two parts. I first show what relation holds between the negative 1925 assertion and the more positive 1926 assertion which allows us to read the latter claim as a retraction of the former, as Ramsey appears to have intended it. Then I shall argue that the retraction of the 1925 claim is forced upon Ramsey by reflection on the fact that three theses, all of which he held in or around the relevant period, are, rather surprisingly, revealed to be inconsistent. (shrink)

This paper is concerned with the notion of ambiguity—or what I shall refer to more generally as homonymy—and its bearing upon various familiar puzzles about intensional contexts. It would hardly of course be a novel claim that the unravelling of such puzzles may well involve recourse to something like ambiguity. After all, Frege, who bequeathed to us one of the most enduring of the puzzles, proposed as part of his solution an analysis of intensional contexts according to which all expressions (...) change their sense when embedded in such contexts. And many contemporary philosophers who have discussed the puzzles, while not perhaps endorsing Frege's own somewhat extreme view, nevertheless take ambiguities in the contained sentences to be the key to the puzzles. In this paper, however, I wish to follow those who take the crucial source of homonymy, at least in the most difficult of the puzzles, to lie primarily not in the embedded sentences, but rather in the intensional verbs that embed them. I begin with a brief examination of certain aspects of ambiguity and homonymy. (shrink)

This paper is concerned with the notion of ambiguity—or what I shall refer to more generally as homonymy—and its bearing upon various familiar puzzles about intensional contexts. It would hardly of course be a novel claim that the unravelling of such puzzles may well involve recourse to something like ambiguity. After all, Frege, who bequeathed to us one of the most enduring of the puzzles, proposed as part of his solution an analysis of intensional contexts according to which all expressions (...) change their sense when embedded in such contexts. And many contemporary philosophers who have discussed the puzzles, while not perhaps endorsing Frege's own somewhat extreme view, nevertheless take ambiguities in the contained sentences to be the key to the puzzles. In this paper, however, I wish to follow those who take the crucial source of homonymy, at least in the most difficult of the puzzles, to lie primarily not in the embedded sentences, but rather in the intensional verbs that embed them. I begin with a brief examination of certain aspects of ambiguity and homonymy. (shrink)

In "Futurc Generations: Further Problems,"‘ and Part Four of Reasons and Persons} Derek Pariit raises many perplexing questions. Although some think his ingenious arguments little more than delightful puzzles, I believe they challenge some of our deepest beliefs. In this article, I examine some of Pariit’s arguments, focusing mainly on "The Mere Addition Paradox." If my analysis is correct, Parfit’s arguments have extremely interesting and important implications that not even Pariit rcalized. In Part I, I present ParHt’s argument for the (...) Merc Addition Paradox, and show that given Pa.rHt’s assumptions, a radical conclusion seems t0 follow; the notion of "bctter th2m"—indced, even the notion of "aH things.. (shrink)