This article focuses on a set of problems involving a controversial portion of the HHA that describes the performance of the Delian chorus in a rare instance of early performance criticism. First, the two variants for a key noun in line 162, bambaliastus and krembaliastus, are discussed. Skepticism is expressed about the applicability to this scene of the first variant. On the contrary, krembaliastus——the suitability of which has not been discussed in detail, even by scholars who seem to have favored (...) it——can make good sense. Literary and iconographic evidence makes it plausible that krembaliastus denotes the act of generating through percussion devices called krembala rhythmic patterns meant to govern stylized movement, what the Greeks called schêêmata. The marked term krembaliastus was probably employed to evoke a characteristic trait of the highly skilled Deliades. Furthermore, as vocal and kinetic activities were inextricably linked in choral practices, they are ultimately conceptualized as part of the same unified expressive mechanism. The author also questions the conventional interpretation of mimeisthai as ““mimicking,”” instead reading it as ““representation,”” involving the evocation of the essence of an entity but not necessarily exact reproduction of its formal details. Finally the essay argues that the Delian chorus' art of ““knowing how to represent the voices and the rhythmic patterns of all people”” designates the perfection of choral performance, as an all-inclusive enactment that forms a powerful trans-local bond. (shrink)

The article shows that in the Archaic period the Greeks did not possess a term equivalent to Classical ποιητής “poet-composer.” The principal meaning of the word άοιδός, often claimed to correspond to ποιητής and modern English poet, was “tuneful” or “singer” . The secondary meaning “poet working in the hexameter medium” is limited to the post-Iliadic hexameter corpus. It is furthermore possible to show that the simplex άοιδός was backderived from a compound. More specifically, following Hermann Koller, I propose that (...) the secondary meaning, being an epic innovation, developed from the compound *θεσπιαοιδός “singer of things divine,” whereas the primary meaning “singer” may go back to έπαοιδός, which later acquired the specialized meaning “singer of incantations.”. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s (...) system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

In a fluent, clear, and lively style this translation by two of Maslov's junior colleagues brings the work of the late Soviet scientist S. Yu. Maslov to a wider audience. Maslov was considered by his peers to be a man of genius who was making fundamental contributions in the fields of automatic theorem proving and computational logic. He published little, and those few papers were regarded as notoriously difficult. This book, however, was written for a broad audience (...) of readers and describes elegant examples of applications in such fields as computer science, artificial intelligence, operations research, economic modeling, and biological modeling, among others. The book also brings to light the work by the American mathematician E. L. Post, which inspired Maslov's own work in the development of a general theory and which has been long neglected by mathematicial logicians and systems theorists in the United States. The book's first chapter introduces the Rules of the Game. Part I, Mathematics of Calculi, covers E. L. Post's canonical systems, deductive systems and algorithms, and probabilistic calculi and deductive information. Part II, Horizonal Modeling, takes up a "toy" economy, the calculi of technological possibilities, and the development of rules. Part III, Vertical Modeling, deals with the topics of "to fight and to search" and the consequences of the asymmetry of cognitive mechanisms. Vladimir Lifschitz is affiliated with the Department of Computer Science at Stanford University, and Michael Gelfond with the Department of Electrical Engineering and Computer Science at the University of Texas, El Paso. Theory of Deductive Systems and Its Applicationsis included in the Foundation of Computing Series, edited by Michael Garey. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

We further investigate a divisibility relation on the set of BN ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...) truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it. (shrink)

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

We continue the research of an extension of the divisibility relation to the Stone‐Čech compactification. First we prove that ultrafilters we call prime actually possess the algebraic property of primality. Several questions concerning the connection between divisibilities in and nonstandard extensions of are answered, providing a few more equivalent conditions for divisibility in. Results on uncountable chains in are proved and used in a construction of a well‐ordered chain of maximal cardinality. Probably the most interesting result is the existence of (...) a chain of type in. Finally, we consider ultrafilters without divisors in and among them find the greatest class. (shrink)

We construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation for the corresponding class of structures and prove that the class has a unique model in every uncountable cardinality. This gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation.

In this paper we develop a general theory of algorithmic fairness. Drawing on Johnson King and Babic’s work on moral encroachment, on Gary Becker’s work on labor market discrimination, and on Strawson’s idea of resentment and indignation as responses to violations of the demand for goodwill toward oneself and others, we locate attitudes to fairness in an agent’s utility function. In particular, we first argue that fairness is a matter of a decision-maker’s relative concern for the plight of people from (...) different groups, rather than of the outcomes produced for different groups. We then show how an agent’s preferences, including in particular their attitudes to error, give rise to their decision thresholds. Tying these points together, we argue that the agent’s relative degrees of concern for different groups manifest in a difference in decision thresholds applied to these groups. (shrink)

We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations \ and \. The set of its minimal elements proves to be very rich, and the \-hierarchy is used to get a better intuition of this richness. We find the place of the set of \-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of subsets (...) of \, and compare it to other such notions, important for infinite combinatorics and topological dynamics. (shrink)

The essential role of language in rational cognition is analysed. The approach is functional: only the results of the connection between language, reality, and thinking are considered. Scientific language is analysed as an extension and improvement of everyday language. The analysis gives a uniform view of language and rational cognition. The consequences for the nature of ontology, truth, logic, thinking, scientific theories, and mathematics are derived.

In this paper, we reflect on the connection between the notions of organism and organisation, with a specific interest in how this bears upon the issue of the reality of the organism. We do this by presenting the case of Buffon, who developed complex views about the relation between the notions of “organised” and “organic” matter. We argue that, contrary to what some interpreters have suggested, these notions are not orthogonal in his thought. Also, we argue that Buffon has a (...) view in which organisation is not just ubiquitous, but basic and fundamental in nature, and hence also fully natural. We suggest that he can hold this view because of his anti-mathematicism. Buffon’s case is interesting, in our view, because he can regard organisation, and organisms, as perfectly natural, and can admit their reality without invoking problematic supernaturalist views, and because he allows organisation and the organismal to come in kinds and degrees. Thus, his view tries to do justice to two cautionary notes for the debate on the reality of the organism: the need for a commitment to a broadly naturalist perspective, and the need to acknowledge the interesting features of organisms through which we make sense of them. (shrink)

We continue the research of the relation $\hspace {1mm}\widetilde {\mid }\hspace {1mm}$ on the set $\beta \mathbb {N}$ of ultrafilters on $\mathbb {N}$, defined as an extension of the divisibility relation. It is a quasiorder, so we see it as an order on the set of $=_{\sim }$ -equivalence classes, where $\mathcal {F}=_{\sim }\mathcal {G}$ means that $\mathcal {F}$ and $\mathcal {G}$ are mutually $\hspace {1mm}\widetilde {\mid }$ -divisible. Here we introduce a new tool: a relation of congruence modulo an (...) ultrafilter. We first recall the congruence of ultrafilters modulo an integer and show that $=_{\sim }$ -equivalent ultrafilters do not necessarily have the same residue modulo $m\in \mathbb {N}$. Then we generalize this relation to congruence modulo an ultrafilter in a natural way. After that, using iterated nonstandard extensions, we introduce a stronger relation, which has nicer properties with respect to addition and multiplication of ultrafilters. Finally, we introduce a strengthening of $\hspace {1mm}\widetilde {\mid }\hspace {1mm}$ and show that it also behaves well with respect to the congruence relation. (shrink)

If definitive evidence concerning treatment effectiveness becomes available from an ongoing randomized clinical trial, then the trial could be stopped early, with the public release of results benefiting current and future patients. However, stopping an ongoing trial based on accruing outcome data requires methodological rigor to preserve validity of the trial conclusions. This has led to the use of formal interim monitoring procedures, which include inefficacy monitoring that will stop a trial early when the experimental treatment appears not to be (...) working. For participants, inefficacy monitoring is especially important as it ensures that they are not being treated worse than if they had not enrolled on the trial. We discuss the importance of reporting with trial results the formal interim inefficacy monitoring guidelines that were utilized, and, if none were used, the reasons for their absence. A survey of two leading medical journals suggests that this is not current practice. (shrink)

In this paper, I argue that Kant adopted, throughout his career, a position that is much more akin to classical accounts of epigenesis, although he does reject the more radical forms of epigenesis proposed in his own time, and does make use of preformationist sounding terms. I argue that this is because Kant thinks of what is pre-formed as a species, not an individual or a part of an individual; has no qualm with the idea of a specific, teleological principle (...) or force underlying generation, and conceives of germs and predispositions as specific constraints on such a principle or force. Neither of these conceptions of what is “preformed”, I argue, is in strict opposition to classical epigenesis. I further suggest that Kant’s lingering use of preformationist terminology is due to his belief that this is required to account for the specificity of the specific generative force; his resistance towards the unrestricted plasticity of the generative force in radical epigenesis, which violates species-fixism; and his insistence on the internal, organic basis of developmental plasticity and variation within species. I conclude by suggesting that this terminological and interpretative peculiarity is partly due to a larger shift in the natural philosophical concerns surrounding the debate on epigenesis and preformation. Specifically, it is a sign that the original reasons for resisting epigenesis, namely its use of specific, teleological principles and its commitment to the natural production of biological structure, became less of a concern, whereas unrestricted plasticity and its undermining of fixism became a real issue, thereby also becoming the focal point of the debate. (shrink)

Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that match actuality in (...) the facts causally unaffected by your decision (the “unaffected facts”). Moreover, you should evaluate A on the assumption that A is compossible with the unaffected facts. This view entails that you should use EDT when evaluating A on the assumption that the unaffected facts determine your action, but use CDT when assessing A on the opposite assumption. A's choiceworthiness equals a weighted average of these conditional assessments. The weights are determined by your beliefs about whether the unaffected fact determine your action. This account gets both Newcomb and Ahmed cases right. According to an influential view, whether you take the unaffected facts to determine your action can make a difference to whether you can regard yourself as free and the action as being under your control. While my account is neutral on this issue, it entails that whether you take the unaffected facts to determine your action is important in a different way: it matters to whether you should follow EDT or CDT. (shrink)

We investigate two questions, the relevance of memory for evaluative conditioning effects based on smell-taste pairings, and the potential preparedness of smell-taste combinations for...

In this article, logical concepts are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language.

Autorova je namjera da u ovom članku tematizira Augustinovu kritiku rimskih vrlina slijedeći uvide iz njegovog voluminoznog teksta O državi Božjoj. Augustinove uvide i zaključke o praksama Imperija povezat ću s kritikom Hardtovog i Negrijevog tumačenja globalnog neo-republikanskog Imperija. U oba slučaja vrline Imperija kulminiraju u različitim oblicima terora kojima je jedini cilj povećanje kapitala. Promišljajući o kapitalu i teroru kao o imperijalnim, autor će ponuditi teološku kritiku ta dva teksta. Pri kraju članka, autor će pokušati konstruirati stanovitu teo-političku sintezu (...) koja bi ponudila modele otpora vrlinama Imperija. Takav model otpora Imperijalnim praksama nužno mora sadržavati militantne oblike askeze.Author’s intention in this article is to reflect about St. Augustine critics of Roman virtues in fifth book of his voluminous text City of God. Augustine’s insights and conclusions on Imperial practice author will connect with specific critics of Hardt’s and Negri’s interpretations of global neo-republican Empire. In both cases virtues of Empire culminate in different form of terror with one intention to produce and expend more capital. Once again author will reflect on imperial virtues and offer theological critique of these two texts. At the end of the article author will construct specific theopolitical synthesis and model of resistance to Empire. This resistance to imperial practices necessarily must content militant forms of ascetics. (shrink)

The discovery of a small collection of Darwin manuscripts at the Whipple Museum of the History of Science has allowed a reconsideration of Darwin’s interest in and knowledge of microscopy. Concentrating on the years between his return from the Beagle voyage and the publication of the major taxonomic work on barnacles, this paper recovers a number of important aspects of Darwin’s intellectual and practical development: on returning from the Beagle voyage he acquainted himself with the work of C. G. Ehrenberg, (...) and this informed both his private and public work; then through the 1840s Darwin transformed himself from a fascinated observer and consumer of others’ work into an expert on microscopy. I characterise this move as a piece of clever manoeuvring, and discuss more generally the kind of scientist—gentlemanly and expert—that Darwin was attempting to become.Keywords: Charles Darwin; Microscopy; Beagle voyage; Classification; Accuracy. (shrink)

Este ensayo intenta mostrar las posibilidades analíticas del concepto de pausa sugerido por Estanislao Zuleta, a partir de su lectura del capítulo 1 de El Capital de Marx. Enlazándolo con desarrollos recientes de Kojin Karatani y Slavoj Zizek, muestra que el concepto de pausa –equivalente al de brecha o salto mortal de los dos últimos– introduce la emergencia de muchos mundos posibles en la metamorfosis de las mercancías en dinero, estableciendo la posibilidad permanente de la crisis. En consecuencia, ni las (...) crisis conducen a la revolución política, ni ésta puede detener la reproducción del capital: la revolución es una tarea de todos los días. (shrink)

Merleau-Ponty's «Phenomenology of Perception» suggests perception to be the primary level of the giveness of the world. Perception appears as always an incomplete synthesis of the plural, bringing together bodily and material aspects. Such the simplest interpretation of perception as rendering a contact within the dyad «body-world» is a preliminary axiom for explaining the rest of the process of noematic sense formation. At the same time, Merleau-Ponty’s theoretical intuitions clearly presuppose more, and perception is also thought of as the final (...) point where sense is already given by some way. Thus, in Phenomenology, the second interpretation of perception presumes it to be sense-giving accompanied by the tacit cogito. Merleau-Ponty suggests that these interpretations are compatible with each other, but the transition between them seems really problematic. In the research author shos that the limit of the initial synthesis of perception - some sense of the perceived (exemplyfing meanings as «this horse», «the green density that rushed towards me») - is unattainable from within perception itself and by its means. Perception is itself mediated by other faculties, such as memory, reflection, and imagination. Argumentation for this thesis is carried out in several ways; the relations in the perception/imagination pair show us the most characteristic case, where Merleau-Ponty, judging by later works, himself comes close to recognizing the limitations of the hypothesis of «the world of perception», to the need for a phenomenological development of the topic of faculties. Based on the application of the phenomenological method and the analysis of the conceptual constructions of Merleau-Ponty, we can conclude the following: «the world of perception» does not exist, but the phenomenology of faculties is demanded. (shrink)