Hans Christian Andersen is a cultural icon, and his fairy tales are famous around the world. But despite the positive ring to this description, his status as a canonized author poses a challenge when he is passed on to new generations of readers. In this article, we show examples of how this challenge reveals itself in Danish primary school teaching where Andersen is an obligatory figure in the subject Danish where he is frequently framed as a national romantic author of (...) morally unambiguous texts. Taking the current use of “The Ugly Duckling” (1844) in primary school teaching materials as a point of departure, we aim to show Andersen’s potential to be presented as an element in primary school teaching that draws on dialogic inquiries rooted in Philosophy with Children. Philosophical inquiries are characterized by an open mindset that incite teachers as well as school children to engage with the rich ethical themes and literary qualities of Andersen’s fairy tales. We conclude the article with our own inquiry manual to “The Ugly Duckling” to illustrate a way to overcome the current hegemonic framing of Andersen and reopen his fairy tale for future discussions and interpretations. (shrink)

Jaakko Hintikka (1998) has argued that clarifying the notion of abduction is the fundamental problem of contemporary epistemology. One traditional interpretation of Peirce on abduction sees it as a recipe for generating new theoretical discoveries . A second standard view sees abduction as a mode of reasoning that justifies beliefs about the probable truth of theories. While each reading has some grounding in Peirce's writings, each leaves out features that are crucial to Peirce's distinctive understanding of abduction. I develop and (...) defend a third interpretation, according to which Peirce takes abductive reasoning to lead to judgments about the relative pursuitworthiness of theories; conclusions that can be thoroughly disconnected from assessments of truth-value. Even if Peirce's use of "abduction" slides around among each of these three importantly different though potentially compatible senses, this neglected third understanding makes sense of a large number of Peirce's remarks and directs our attention to the cognitive structure of judgments that scientists face after the initial proposal of explanatory hypotheses but prior to their experimental testing; a topic which should be of interest to contemporary philosophers of science. (shrink)

Two studies compared the development of beliefs about the stability and origins of physical and psychological traits in Japan and the United States in three age groups: 5–6-year-olds, 8–10-year-olds, and college students. The youngest children in both cultures were the most optimistic about negative traits changing in a positive direction over development and being maintained over the aging period. The belief that individual differences in traits are inborn increased with age, and in all age groups, this belief was related to (...) predictions of greater trait stability. In both cultures, all ages believed positive traits would be maintained over development. In addition to developmental similarities across cultures, cultural variations, consistent with the hypothesis that interdependent cultures have a more incremental view of traits, were present. Japanese participants were more optimistic than American participants about negative traits changing towards the positive and were more likely to attribute differences in trait expression to effort. © 2007 Elsevier Inc. All rights reserved. (shrink)

Using a densely constructed ethnographic subject, Josephine, the “ugly duckling,” I use Foucault’s complex notion of an Apparatus to examine how Josephine’s decision to have weight-loss surgery is understandable even though it permanently destroys her normally functioning digestive system. I try to illuminate how the decision is deeply embedded in extraordinarily complex neoliberal biopolitical structures and dynamics of fat hatred camouflaged by liberatory discourses that promise “empowerment,” becoming “normal,” and discovery of her “real self.” I argue that in (...) contemporary America, Fat Hatred must be understood as a powerful systemic structure of racialized gendered oppression, that one tactic to normalize weight-loss surgery involves assimilating it to “normal” cosmetic surgery, and that Josephine must be seen, simultaneously, as legitimizing dominant obesity discourses and practices, enacting genuinely liberating personal choices, demonstrating her status as a “good American bio-citizen,” and contributing to the collective physical health and mental health of the nation since “obesity” is soon to be included in the fifth edition of the canonical Diagnostic and Statistical Manual of Mental Disorders as a mental disorder. (shrink)

For more than fifty years, taxonomists have proposed numerous alternative definitions of species while they searched for a unique, comprehensive, and persuasive definition. This monograph shows that these efforts have been unnecessary, and indeed have provably been a pursuit of a will o’ the wisp because they have failed to recognize the theoretical impossibility of what they seek to accomplish. A clear and rigorous understanding of the logic underlying species definition leads both to a recognition of the inescapable ambiguity that (...) affects the definition of species, and to a framework-relative approach to species definition that is logically compelling, i.e., cannot not be accepted without inconsistency. An appendix reflects upon the conclusions reached, applying them in an intellectually whimsical taxonomic thought experiment that conjectures the possibility of an emerging new human species. (shrink)

Once upon a time, an ugly duckling became famous in the history of European fairy tales. It was said of him that "… the poor duckling, who had come last out of his eggshell, and was so ugly, was bitten, pecked, and teased by both ducks and hens.… The poor thing scarcely knew what to do; he was quite distressed because he was so ugly."Today, in America—the mecca of MakeOver culture—that ugly duckling would (...) know exactly what to do: tell his pitiful tale and be accepted for an "Extreme Makeover" that would be televised around the world. This paper uses Foucault's rich and complex notion of an Apparatus to examine how weight-loss surgery is migrating into the repertoire of "normalized procedures" listed under .. (shrink)

One quality of remarriage comedies is that, for all their ingratiating manners, and for all the ways in which they are among the most beloved of Hollywood films, a moral cloud remains at the end of each of them. And that moral cloud has to do with what is best about them. What is best are the conversations that go on in them, where conversation means of course talk, but means also an entire life of intimate exchange between the principal (...) pair. We are bound to remember from these films, even years after viewing them, something of their sound: of conversation between Cary Grant and Irene Dunne in The Awful Truth, or between Grant and Rosalind Russell in His Girl Friday, or Grant and Katharine in Bringing up Baby, or those two together with James Stewart in The Philadelphia Story, or between Hepburn and Spencer Tracy in Adam’s Rib. We feel that these people know one another, and they know how to play together in a way to make one happy and hope for the best. But the moral cloud has to do with what that conversation is meant to do, and what I say about those films is that the conversation is in service of the woman’s sense of herself as in need of an education. Importantly for that reason, I call her a descendent of Nora in Henrik Ibsen’s A Doll’s House, who in one of the most celebrated moments in modern theater, ends a play by closing a door behind her. She leaves the dollhouse saying to her husband that she requires an education and that he is not the man who can provide it for her. The implication is that since he is not this man, he cannot be her husband. And implying the contrary as well: if he were, then he would be, and their relationship would accordingly—“miracle of miracles”—constitute a marriage. Stanley Cavell is the Walter M. Cabot Professor of Aesthetics and the General Theory of Value at Harvard University. His most recent works include In Quest of the Ordinary: Lines of Skepticism and Romanticism , This New Yet Unapproachable America , and Conditions Handsome and Unhandsome. (shrink)

The elimination of ambiguity and redundancy are unquestioned goals in the exact sciences, and yet, as this paper shows, there are inescapable lower bounds that constrain our wish to eliminate them. The author discusses contributions by Richard Hamming (inventor of the Hamming code) and Satosi Watanabe (originator of the Theorems of the Ugly Duckling). Utilizing certain of their results, the author leads readers to recognize the unavoidable, central roles in effective communication, of redundancy, and of ambiguity of meaning, (...) reference, and identification. (shrink)

According to Satosi Watanabe's "theorem of the ugly duckling", the number of predicates satisfied by any two different particulars is a constant, which does not depend on the choice of the two particulars. If the number of predicates satisfied by two particulars is their number of properties in common, and the degree of resemblance between two particulars is a function of their number of properties in common, then it follows that the degree of resemblance between any two (...) different particulars is also constant, which is absurd. Avoiding this absurd conclusion requires questioning assumptions about infinity in the proof or interpretation of the theorem, adopting a sparse conception of properties, or denying degree of resemblance is a function of number of properties in common. After arguing against both the first two options, this paper argues for a version of the third which analyses degree of resemblance as a function of properties in common, but weighted by their degree of naturalness or importance. (shrink)

Kant’s theory of taste, as expounded in the Critique of Judgment, deals exhaustively with judgments of beauty. Rarely does Kant mention ugliness. This omission has led to a debate among commentators about how judgments of ugliness should be explained in a Kantian framework. I argue that the judgment of ugliness originates in the disharmonious play between the faculties of imagination and understanding. Such disharmony occurs when the understanding finds that it cannot in principle form any concept suitable to a representation (...) as it is presented by the imagination. (shrink)

In the Lambek calculus of order 2 we allow only sequents in which the depth of nesting of implications is limited to 2. We prove that the decision problem of provability in the calculus can be solved in time polynomial in the length of the sequent. A normal form for proofs of second order sequents is defined. It is shown that for every proof there is a normal form proof with the same axioms. With this normal form we can give (...) an algorithm that decides provability of sequents in polynomial time. (shrink)

'Ugly as sin', 'ugly duckling', 'rear its ugly head'. The word 'ugly' is used freely, yet it is a loaded term: from the simply plain and unsightly to the repulsive and even offensive, definitions slide all over the place. Hovering around 'feared and dreaded', ugliness both repels and fascinates. But the concept of ugliness has a lineage that has long haunted our cultural imagination. Gretchen E. Henderson explores perceptions of ugliness through history, from ancient Roman (...) feasts to medieval grotesque gargoyles, from Mary Shelley's monster cobbled from corpses to the Nazi Exhibition of Degenerate Art. Covering literature, art, music and even Uglydolls, Henderson reveals how ugliness has long posed a challenge to aesthetics and taste. Henderson digs into the muck of ugliness, moving beyond the traditional philosophic argument or mere opposition to beauty, and emerges with more than a selection of fascinating tidbits. Following ugly bodies and dismantling ugly senses across periods and continents, [this book] draws on a wealth of fields to cross cultures and times, delineating the changing map of ugliness as it charges the public imagination. Illustrated with a range of artefacts, this book offers a refreshing perspective that moves beyond the surface to ask what 'ugly' truly is, even as its meaning continues to shift. (shrink)

The theorem that the arithmetic mean is greater than or equal to the geometric mean is investigated for cardinal and ordinal numbers. It is shown that whereas the theorem of the means can be proved for n pairwise comparable cardinal numbers without the axiom of choice, the inequality a2 + b2 ≥ 2ab is equivalent to the axiom of choice. For ordinal numbers, the inequality α2 + β2 ≥ 2αβ is established and the conditions for equality are derived; (...) stronger inequalities are obtained for finite and infinite sequences of ordinals under suitable monotonicity hypotheses. MSC: 03E10, 04A10, 03E25, 04A25. (shrink)

x1. This paper is a contribution to matrix semantics for sentential logics as presented in Los and Suszko [1] and Wojcicki [3], [4]. A generalization of Lindenbaum completeness lemma says that for each sentential logic there is a class K of matrices of the form such that the class is adequate for the logic, i.e., C = CnK.

A substantial portion of produce harvested around the world is wasted because it does not meet consumers’ shape expectations. Only recently has research begun investigating the causes underlying misshapen produce rejection by consumers. Generally, this limited research has concluded that misshapen produce is subject to an ugly penalty, leading consumers to form biased expectations regarding product attributes (e.g., healthiness, tastiness, or naturalness). In this research, we propose that this ugly penalty extends to the moral valuation of misshapen produce (...) and that this moral penalty is rooted in the feelings of disgust evoked by the visual appearance of such produce. Across five studies and two pilot studies, we show that misshapen fruits and vegetables are disgust elicitors, and that felt disgust causes consumers to make negative moral associations with produce which, in turn, leads to decreased preference. We also show that pairing misshapen produce with a positive unconditioned stimulus (i.e., an image of attractive individuals) is an efficient solution to counteract the effect of this stereotype. This research contributes to the growing body of work demonstrating the link between consumption behaviors, consumer preferences, and morality. (shrink)

A new formulation of what may be called the “fundamental theorem of the theory of relativity” is presented and proved in -space-time, based on the full classification of special transformations and the corresponding velocity addition laws. A system of axioms is introduced and discussed leading to the result, and a study is made of several variants of that system. In particular the status of the group axiom is investigated with respect to the condition of the two-way isotropy of light. (...) Several issues which are ignored or misunderstood in the literature are emphasized. (shrink)

Recently, there has been an upsurge of attention focused on bias and its impact on specialized artificial intelligence applications. Allegations of racism and sexism have permeated the conversation as stories surface about search engines delivering job postings for well-paying technical jobs to men and not women, or providing arrest mugshots when keywords such as “black teenagers” are entered. Learning algorithms are evolving; they are often created from parsing through large datasets of online information while having truth labels bestowed on them (...) by crowd-sourced masses. These specialized AI algorithms have been liberated from the minds of researchers and startups, and released onto the public. Yet intelligent though they may be, these algorithms maintain some of the same biases that permeate society. They find patterns within datasets that reflect implicit biases and, in so doing, emphasize and reinforce these biases as global truth. This paper describes specific examples of how bias has infused itself into current AI and robotic systems, and how it may affect the future design of such systems. More specifically, we draw attention to how bias may affect the functioning of a robot peacekeeper, a self-driving car, and a medical robot. We conclude with an overview of measures that could be taken to mitigate or halt bias from permeating robotic technology. (shrink)

Ernest Gellner's final book, first published in 1998, is a synoptic interpretation of the thought of Wittgenstein and Malinowski.

We are accustomed to thinking that a primrose is "concrete" and a prime number is "abstract," that "roundness" is more abstract than "round," and that "property" is more abstract than "roundness." In reality, the relation between "abstract" and "concrete" is more like the (non)relation between "abstract" and "concave," "concrete" being a sensory term [about what something feels like] and "abstract" being a functional term (about what the sensorimotor system is doing with its input in order to produce its output): Feelings (...) and things are correlated, but otherwise incommensurable. Everything that any sensorimotor system such as ourselves manages to categorize successfully is based on abstracting sensorimotor "affordances" (invariant features). The rest is merely a question of what inputs we can and do categorize, and what we must abstract from the particulars of each sensorimotor interaction in order to be able to categorize them correctly. To categorize, in other words, is to abstract. And not to categorize is merely to experience. Borges's Funes the Memorious, with his infinite, infallible rote memory, is a fictional hint at what it would be like not to be able to categorize, not to be able to selectively forget and ignore most of our input by abstracting only its reliably recurrent invariants. But a sensorimotor system like Funes would not really be viable, for if something along those lines did exist, it could not categorize recurrent objects, events or states, hence it could have no language, private or public, and could at most only feel, not function adaptively (hence survive). Luria's "S" in "The Mind of a Mnemonist" is a real-life approximation whose difficulties in conceptualizing were directly proportional to his difficulties in selectively forgetting and ignoring. Watanabe's "Ugly Duckling Theorem" shows how, if we did not selectively weight some properties more heavily than others, everything would be equally (and infinitely and indifferently) similar to everything else. Miller's "Magical Number Seven Plus or Minus Two" shows that there are (and must be) limitations on our capacity to process and remember information, both in our capacity to discriminate relatively (detect sameness/difference, degree-of-similarity) and in our capacity to discriminate absolutely (identify, categorize, name), The phenomenon of categorical perception shows how selective feature-detection puts a Whorfian "warp" on our feelings of similarity in the service of categorization, compressing within-category similarities and expanding between-category differences by abstracting and selectively filtering inputs through their invariant features, thereby allowing us to sort and name things reliably. Language does allow us to acquire categories indirectly through symbolic description.... (shrink)

This article explores the distinctive artistic form of caricature and the philosophical treatment it receives in the work of Karl Rosenkranz (1805–1879), who gives it a central role in the context of his remarkable book The Aesthetics of Ugliness (Die Ästhetik des Hässlichen). Rosenkranz’ legacy on this score is not much discussed (certainly in Anglo-American philosophical circles), but its importance for the development of post-eighteenth-century aesthetics—in particular, for an aesthetics that stretches beyond the conventional concerns with the beautiful and the (...) sublime—can hardly be overstated. After a presentation of Rosenkranz’ project on the aesthetics of ugliness, this article examines his take on caricature and its relation to philosophy (as well as philosophy’s relation to caricature), and then takes up some pressing contemporary questions that arise for caricature’s use of stereotypes. (shrink)

In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there (...) was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (shrink)

The paper deals with an analysis of the controversial novel Truismes by Marie Darrieussecq. In this work, the author sensitively maintains an oscillation between the plausibility of truth, hidden behind metaphors and symbols, and the implausibility of the whole story in its individual components. The occurrence of ugliness as a decisive aesthetic dimension is continual, graded into almost all its shapes and forms, until it finally fills in the entire space and time of the fictional story. The astonishing horror of (...) the author’s aesthetic world does not lie in the brutality of the language she uses, but rather in the similarity of the real and the imaginary, in the way she makes cruelty appear visible though the fictional narrative. The paper thus shows that classical aesthetic views fail when used as tools for understanding the nature of the aesthetic world modelled by Darrieussecq. (shrink)

Wilkie 5 397) proved a “theorem of the complement” which implies that in order to establish the o-minimality of an expansion of with C∞ functions it suffices to obtain uniform bounds on the number of connected components of quantifier free definable sets. He deduced that any expansion of with a family of Pfaffian functions is o-minimal. We prove an effective version of Wilkie's theorem of the complement, so in particular given an expansion of the ordered field with finitely (...) many C∞ functions, if there are uniform and computable upper bounds on the number of connected components of quantifier free definable sets, then there are uniform and computable bounds for all definable sets. In such a case the theory of the structure is effectively o-minimal: there is a recursively axiomatized subtheory such that each of its models is o-minimal. This implies the effective o-minimality of any expansion of with Pfaffian functions. We apply our results to the open problem of the decidability of the theory of the real field with the exponential function. We show that the decidability is implied by a positive answer to the following problem ): given a language L expanding the language of ordered rings, if an L-sentence is true in every L-structure expanding the ordered field of real numbers, then it is true in every o-minimal L-structure expanding any real closed field. (shrink)

The alt-right claims it responsibly advocates for its positions while the Ku Klux Klan was “ad-hoc.” This allows them to accept the philosophy of white nationalism while rejecting comparisons with prior white nationalist organizations. I confront this by comparing the methodologies of alt-right trolls and the KKK. After studying each movement’s genesis in pranks done for amusement, I demonstrate that each uses threats to police behavior, encourages comradery around ethnic heritage, and manipulates politics to exclude voices from public deliberation. Differences (...) between alt-right trolls and the KKK originate in the technologies they use, not out of a concern for responsible advocacy. (shrink)

This article presents a weak system of intuitionistic second-order arithmetic, WKV, a subsystem of the one in S.C. Kleene, R.E. Vesley [The Foundations of Intuitionistic Mathematics: Especially in Relation to Recursive Functions, North-Holland Publishing Company, Amsterdam, 1965]. It is then shown that some statements of real analysis, like a version of the Heine–Borel Theorem, and some statements of logic, e.g. compactness of classical proposition calculus, are equivalent to the Fan Theorem in this system.

The theorem of convergence of opinions is an important theorem in the subjective theory of probability.It demonstrates that the subjectivity of a prior probability will be substituted with the objectivity of a posterior probability as evidences increase.The theorem of convergence of opinions is regarded as the dynamic principle of rationality concerning the subjective probability,and therefore is used to resolve Hume's problem,i.e.,the problem of inductive rationality.However,Hacking convincingly argues that the theorem of convergence of opinions is not about (...) the convergence of a posterior probability Pre(h),but about the convergence of a conditional probability Pr(h/e).The subjective theory of probability implies a tacit acceptance of an equation that is Pre(h)=Pr(h/e),usually called "the rule of conditionalisation".Thus,the problem of rationality of induction is converted into one concerning the rule of conditionalisation.In this paper a new principle of rationality(the principle of minimum number of initial probabilities)is put forward,which,in combination with the concept of "local rationality",offers a justification for the rule of conditionalisation. (shrink)

I prove several natural preservation theorems for the countable support iteration. This solves a question of Rosłanowski regarding the preservation of localization properties and greatly simplifies the proofs in the area.

In this study, the author compares several proofs of the compactness theorem for propositional logic with countably many atomic sentences. He thereby takes some steps towards a systematic philosophical study of the compactness theorem. He also presents some data and morals for the theory of mathematical explanation. [The author is not responsible for the horrific mathematical typo in the second sentence.].

A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes’ Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making (...) inferences. Scientists, philosophers, and theologians accumulate knowledge when analyzing different aspects of reality and search for particular hypotheses or models to fit their respective subject matters. Of course, a main goal is then to integrate all kinds of knowledge into an all-encompassing worldview that would describe the whole of reality. A generous description of the whole of reality would span, in the order of complexity, from the purely physical to the supernatural. These two extreme aspects of reality are bridged by a nonphysical realm, which would include elements of life, man, consciousness, rationality, mental and mathematical abstractions, etc. An urgent problem in the theory of knowledge is what science is and what it is not. Albert Einstein’s notion of science in terms of sense perception is refined by defining operationally the data that makes up the subject matter of science. It is shown, for instance, that theological considerations included in the prior information assumed by Isaac Newton is irrelevant in relating the data logically to the model or hypothesis. In addition, the concepts of naturalism, intelligent design, and evolutionary theory are critically analyzed. Finally, Eugene P. Wigner’s suggestions concerning the nature of human consciousness, life, and the success of mathematics in the natural sciences is considered in the context of the creative power endowed in humans by God. (shrink)

The prime number theorem, established by Hadamard and de la Vallée Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1/ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erdos in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

In this paper, we present two proofs of the reciprocal butterfly theorem. The statement of the butterfly theorem is: Let us consider a chord PQ of midpoint M in the circle Ω(O). Through M, two other chords AB and CD are drawn, such that A and C are on the same side of PQ. We denote by X and U the intersection of AD respectively CB with PQ. Consequently, XM = YM. For the proof of this theorem, (...) see [1]. The reciprocal of the butterfly theorem has the following statement: In the circle Ω(O), let us consider the chords PQ, AB and CD which are concurrent in the point M≠O, such as the points A and C are on the same side of the line PQ. Let X and Y respectively be the intersections of the chord PQ with AD and BC respectively. If XM = YM, then M is the middle of the chord PQ. (shrink)

In this paper we bring together results from a series of previous papers to prove the constructive version of the Gelfand duality theorem in any Grothendieck topos , obtaining a dual equivalence between the category of commutative C*-algebras and the category of compact, completely regular locales in the topos.

Greenberger. Horne. Shimony, and Zeilinger gave a new version of the Bell theorem without using inequalities (probabilities). Mermin summarized it concisely; but Bohm and Hiley criticized Mermin's proof from contextualists' point of view. Using the branching space-time language, in this paper a proof will be given that is free of these difficulties. At the same time we will also clarify the limits of the validity of the theorem when it is taken as a proof that quantum mechanics is (...) not compatible with a deterministic world nor with a world that permits correlated space-related events without a common cause. (shrink)

We show that the respective oversights in the von Neumann's general theorem against all hidden variable theories and Bell's theorem against their local-realistic counterparts are homologous. When latter oversight is rectified, the bounds on the CHSH correlator work out to be ±2√2 instead of ±2.

In autumn 2009, BBC television ran a natural history series, ‘Last Chance to See’, with Stephen Fry and wildlife writer and photographer, Mark Carwardine, searching out endangered species. In one episode they retraced the steps Carwardine had taken in the 1980s with Douglas Adams, when they visited Madagascar in search of the aye-aye, a nocturnal lemur. Fry and Carwardine visited an aye-aye in captivity, and upon first setting eyes on the creature they found it rather ugly. After spending an (...) hour or so in its company, Fry said he was completely ‘under its spell’. A subsequent encounter with an aye-aye in the wild supported Fry's judgment of ugliness and fascination for the creature: ‘The aye-aye is beguiling, certainly bizarre, for some even a little revolting. And I say, long may it continue being so.’. (shrink)

In this study, several proofs of the compactness theorem for propositional logic with countably many atomic sentences are compared. Thereby some steps are taken towards a systematic philosophical study of the compactness theorem. In addition, some related data and morals for the theory of mathematical explanation are presented.

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)