The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this (...) article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics. (shrink)

Publication date: 30 November 2016 Source: Author: Mahshid Mirmasoomi King Lear is one of the political tragedies of Shakespeare in which the playwright censures Lear's hamartia wrecking havoc not only upon people's lives but bringing devastation on his own kindred. Shakespeare castigates Lear's wrath, sense of superiority, and misjudgments which lead to catastrophic consequences. In Death of Yazdgerd, an anti-authoritarian play, Bahram Beyzayie, the well-known Persiaian tragedian, also depicts the hamartia of King Yazdgerd III whose pride and unjust treatment (...) of people end in devastation. By demonstrating such defective and reprehensible tragic heroes, both playwrights set at providing audience with an anti-heroic representation of the kings and also shattering the common god-like heroism attributed to hero kings. Bearing in mind the political instability of England after the succession of James I, Shakespeare avails himself of such anti-heroic representation to forewarn those monarchs incapable of maintaining a balance between their judgments and the society's need for a genuine authority. In a similar fashion, Beyzayie narrates the true historical event of a Persian king whose improper exercise of authority, withdrawal from battle, and an ultimate escape leave people helpless against the invasion of Arabs. The article initially aims to discuss the concept of hamartia within the tragedies based on Aristotle's definition of hamartia and golden mean; by defining the nature of the kings' unforgivable errors and their extremely imbalanced temperament, the paper demonstrates how such ignoble failure relegates the hero kings to anti-heroes whose punishment equals their mistakes. Contrary to Aristotle’s idea, the article also elucidates how Shakespeare and Beyzaie have caused the audiences’ catharsis of emotion not through fear and pity but through the creation of a sense of justice by portraying characters who deserve their ultimate downfall. (shrink)

The philosophical problem of pictorial conversational implicatures can be summarized as follows: We have three propositions that are independently plausible and jointly inconsistent. -/- (Non-P) Anti-propositionalism: pictures do not have context-independent, conventionally encoded propositional content (propositional function). -/- (C) Only those representations can be used to convey conversational implicatures which have associated with them a context-independent, conventionally encoded propositional content (function). -/- (I) Pictures can be used to convey conversational implicatures. -/- There are three ways of responding to the problem: (...) affirm (Non-P) and (C) while denying (I); affirm (C) and (I) while denying (Non-P); or affirm (Non-P) and (I) while denying (C). (shrink)

Expectations play a distinctive role in shaping emerging technologies and producing hype cycles when a technology is adopted or fails on the market. To harness expectations, facilitate and provoke forward-looking discussions, and identify policy alternatives, futures studies are required. Here, expert anticipation of possible or probable future developments becomes extremely arbitrary beyond short-term prediction, and the results of futures studies are often controversial, divergent, or even contradictory; thus they are contested. Nevertheless, such socio-technical imaginaries may prescribe a future that seems (...) attainable to those involved in the visioneering process, and other futures may thus become less likely and shaping them could become more difficult. This implies a need to broaden the debate on socio-technological development, creating spaces where policy, science, and society can become mutually responsive to each other. Laypeople’s experiential and value-based knowledge is highly relevant for complementing expertise to inform socially robust decision-making in science and technology. This paper presents the evolution of a transdisciplinary, forward-looking co-creation process—a demand-side approach developed to strengthen needs-driven research and innovation governance by cross-linking knowledge of laypeople, experts, and stakeholders. Three case studies serve as examples. We argue that this approach can be considered a method for adding social robustness to visioneering and to responsible socio-technical change. (shrink)

We investigate the extension of monadic second-order logic of order with cardinality quantifiers "there exists uncountably many sets such that... " and "there exists continuum many sets such that... ". We prove that over the class of countable linear orders the two quantifiers are equivalent and can be effectively and uniformly eliminated. Weaker or partial elimination results are obtained for certain wider classes of chains. In particular, we show that over the class of ordinals the uncountability quantifier can be effectively (...) and uniformly eliminated. Our argument makes use of Shelah's composition method and Ramsey-like theorem for dense linear orders. (shrink)

To propose a revisionist ontology of art one has to hold that our everyday intuitions about the identity and persistence conditions of various kinds of artworks can be massively mistaken. In my presentation I defend this view: our everyday intuitions about the nature of art can be (and sometimes are) mistaken. First I reconstruct an influential argument of Amie L. Thomasson (2004; 2005; 2006; 2007a; 2007b) against the fallibility of our intuitive judgments about the identity and persistence conditions of various (...) kinds of artworks. Second, I present three objections to this account: two of them concern the semantic and pragmatic rules regulating the use of art-kind terms, while the third one is based on the assumption that the history of art partly comprises a series of successful attempts of transgression of artistic conventions and expectations, therefore our artistic intuitions are dynamic. Taking this point I finally argue that in philosophy of art we need a “reverse” methodology: first we have to provide a general definition, containing all the sufficient and necessary conditions of artworks (“being an artwork”) in any period within the history of art. Only after completing this task are we ready to answer the metaphysical question about the ontological status of works of art. (shrink)

Beginning at the end of the nineteenth century, systematic scientific abstracting played a crucial role in reconfiguring the sciences on an international scale. For mathematicians, the 1931 launch of the Zentralblatt für Mathematik and 1940 launch of Mathematical Reviews marked and intensified a fundamental transformation, not just to the geographic scale of professional mathematics but to the very nature of mathematicians’ research and theories. It was not an accident that mathematical abstracting in this period coincided with an embrace across mathematical (...) research fields of a distinctive form of symbolic and conceptual abstraction. This essay examines the historical, institutional, embodied, and conceptual bases of mathematical abstracting and abstraction in the mid-twentieth century, placing them in historical context within the first half of the twentieth century and then examining their consequences and legacies for the second half of the twentieth century and beyond. Focused on scale, media, and the relationship between mathematical knowledge and its forms of articulation, my analysis connects the changing social structure of modern mathematical research communities to their changing domains of investigation and resources for representation and collective understanding. (shrink)

This paper identifies ‘savage numbers’ – number-like or number-replacing concepts and practices attributed to peoples viewed as civilizationally inferior – as a crucial and hitherto unrecognized body of evidence in the first two decades of the Victorian science of prehistory. It traces the changing and often ambivalent status of savage numbers in the period after the 1858–1859 ‘time revolution’ in the human sciences by following successive reappropriations of an iconic 1853 story from Francis Galton's African travels. In response to a (...) fundamental lack of physical evidence concerning prehistoric men, savage numbers offered a readily available body of data that helped scholars envisage great extremes of civilizational lowliness in a way that was at once analysable and comparable, and anecdotes like Galton's made those data vivid and compelling. Moreover, they provided a simple and direct means of conceiving of the progressive scale of civilizational development, uniting societies and races past and present, at the heart of Victorian scientific racism. (shrink)

In this paper we analyze and discuss Jennifer Saul’s account of the famous Gricean notions of ‘what is said’ and ‘what is implicated’ and the alleged conflict between them and the so- called Speaker- Meaning Exhaustiveness Thesis (SMET), which is standardly attributed to Grice in the literature. SMET declares that speaker- meaning divides exhaustively into what is said and what is (conventionally or nonconventionally) implicated by the speaker. After a detailed interpretation of Saul’s position, we argue that her analysis partly (...) misconstrues the relation between Grice’s theory of speaker- meaning and his normative account of conversational implicature. First of all, because SMET is not a genuine part of the Gricean theory of language and meaning – Grice was never committed to it. Secondly, Saul’s interpretation of the Gricean account of conversational implicature does not reflect accurately his original ideas. Although we agree with Saul that conversational implicature has an essential normative aspect, her account cannot capture well the real nature of this normativity, since it does not identify its source and does not delineate its scope. Finally, we present an alternative, speaker- oriented normative interpretation of Grice’s account of conversational implicatures, and argue that it fits better with the Gricean picture of communication and handles better the various problematic cases of conversational implicature than Saul’s mainly audience- oriented interpretation. (shrink)

Pseudonymous mathematician Nicolas Bourbaki and his lesser-known counterpart E.S. Pondiczery, devised respectively in France and in Princeton in the mid-1930s, together index a pivotal moment in the history of modern mathematics, marked by international infrastructures and institutions that depended on mathematicians’ willingness to play along with mediated personifications. By pushing these norms and practices of personification to their farcical limits, Bourbaki’s and Pondiczery’s impersonators underscored the consensual social foundations of legitimate participation in a scientific community and the symmetric fictional character (...) of both fraud and integrity in scientific authorship. To understand authorial identity and legitimacy, individual authors’ conduct and practices matter less than the collective interpersonal relations of authorial assertion and authentication that take place within disciplinary institutions. (shrink)

It is conventionally understood that computers play a rather limited role in theoretical mathematics. While computation is indispensable in applied mathematics and the theory of computing and algorithms is rich and thriving, one does not, even today, expect to find computers in theoretical mathematics settings beyond the theory of computing. Where computers are used, by those studying combinatorics , algebra, number theory, or dynamical systems, the computer most often assumes the role of an automated and speedy theoretician, performing manipulations and (...) checking cases in a way assumed to be possible for human theoreticians, if only they had the time, the memory, and the precision. Automated proofs have become standard tools in mathematical logic, and it is often expected that proofs be published in a computer-checkable format. It is not surprising, then, that most philosophical work on computers in theoretical mathematics has been on computers' roles as supplementary mathematicians. Donald MacKenzie's 2001 book Mechanizing Proof demonstrates the rich potential for social and historical studies to complement the substantial analytic debate in this area of philosophy. But what of computers in theoretical mathematics behaving as computers, and not as mere mechanized mathematicians? Very little role is commonly assumed for computers working as supplements to mathematicians, rather than as supplementary mathematicians themselves. Accordingly, very little philosophy has attempted to grapple with theoretical mathematics in which computers play an essential but essentially non-theoretical role. My presentation will draw on work I conducted as a researcher in harmonic analysis on fractals at Cornell University. I will analyze the explicit and implicit conceptual apparatus employed in my and my fellow researchers' use of computers in the theoretical study of second order differential equations, such as those for sound and heat flow, on various fractal analogues of the Sierpinski gasket. Such gaskets are easy to visualize in very crude approximation in a low number of dimensions. As one increases the complexity of the gasket or the refinement of one's analysis, visualization and precise computation become impossible, and soon computers are unable to produce even approximate data to model differential equations in these situations. We thus had to carefully choose analytic approaches and methods to make our theoretical mathematics amenable to computer simulation. In my case, studying the transformation of the gaskets as they are expanded into increasingly high dimensions, computer simulation eventually required that the problem be reimagined entirely in terms of interlinked systems of parameters. This computer-approximation-driven theoretical orientation shaped my mathematical intuitions toward the problem and guided my fellow researchers and me in both theoretical and computational directions. We discovered both that computer approximation could be incredibly powerful as an aid to intuition, and that it can be incredibly difficult to transfer computer-oriented mathematics back into the purely theoretical standards of our area of specialty. I will address the philosophical implications of computer-driven theoretical mathematics, asking how computer experiments can shape both the content and standards of theoretical sciences. (shrink)

Among the ideas implicitly present and generally accepted in legal theory we can find claims, such as: 1. Justice concerns distribution of goods and burdens. 2. It is connected with the relationship between law and morality. 3. Justice has an existential dimension and is rooted partially in irrational attitudes and intuitions. The first two prepositions make it possible to characterize justice as the conformity with that part of morality which concerns the distribution and exchange of goods and burdens. Justice connects (...) law as an intentionally rational phenomenon with irrationality and particular existential experience. Thus the proposed understanding of justice connects the law or other social phenomena with a specific part of morality, irrationality and particular existential experience. (shrink)

Examining how, and to what effect, the phrase “truly international” became central to the rhetoric and organization of the American-hosted 1950 International Congress of Mathematicians, this essay traces the negotiation of a “truly international” discipline from mathematicians’ first international congresses around the turn of the century across two world wars and their divisive interlude. Two failed attempts to host international congresses of mathematicians in the United States, for 1924 and 1940, defined the stakes for those who became the principal organizers (...) for 1950. Combining American organizational records with contexts and sources that extend across and beyond traditional mathematical centers in Europe and North America, the essay shows how a small cohort of American mathematicians marshaled an emphatic but ambiguous “international” rhetoric to guide policies and command cooperation and support while responding to persistent challenges. Their adaptations and compromises left a lasting mark on the terms and achievements of international inclusion, cooperation, and hegemony in mathematics. (shrink)

Astronomer Charles Piazzi Smyth’s 1864–65 expedition to measure the Great Pyramid of Giza was planned around a system of linear measures designed to guarantee the validity of his measurements and settle ongoing uncertainties as to the Pyramid’s true size. When the intended system failed to come together, Piazzi Smyth was forced to improvise a replacement that presented a fundamental challenge to the metrological enterprise upon which his system had been based. The astronomer’s new system centered around a small lump of (...) basalt, now held at Cambridge’s Whipple Museum of the History of Science, which nucleated a wide array of material and scientific considerations. Through a bipartite analysis of the physical and narrative dimensions of Piazzi Smyth’s basalt Standard, I develop the implications of its use and construction for understanding the material constitution of scientific instruments. In particular, I illustrate how instruments are locally constituted through co-accountable systems and how their material features become integrally implicated in both their uses and meanings. (shrink)

Sociology originated in the mid-nineteenth century from a new confidence in the power of science to explain the world on a mathematical foundation. Both mathematics and sociology transformed over the ensuing century, inverting the hierarchical relationship from sociology as a mathematics-based science of complex human configurations to mathematics as a complex science based on social institutions. That is, where sociology began as the hard case for mathematics, it became possible to see mathematics as the hard case for sociology. In this (...) light, we examine a number of motivations and provocations for the sociology of mathematics, from language and social cognition to Marxist and materialist skepticism of ideology, and sample the evidence and arguments brought to bear on the sociology of mathematics at a range of scales. (shrink)

Comparing my historical account of the early years of Laurent Schwartz’s theory of distributions with number theorist Michael Harris’s narrative of the early years of Peter Scholze’s perfectoid theory, I develop a perspective on change and temporality in mathematics that emphasizes the relationships between concepts, expectations, and communities of practice. Contemporary mathematics, understood as mathematics imbued with temporality, reflects the dynamic relationship between the people, ideas, pasts, and prospects of mathematical knowledge. Studying these historically may offer critical perspectives on the (...) social and political conditions and implications of mathematical research and the communities that practice it. (shrink)

This paper probes the foundations and limits of visual representation in the sciences through a close reading of the diagrams that accompanied definitions of the geometric point in the first century of printed editions of Euclid’s Elements. I begin with the modal form for such diagrams of Euclid’s “small and unsensible shape,” showing how it incorporates a broad spectrum of conventions and practices related to the point’s philosophical and practical roles in the surrounding Euclidean geometry. I then explore the form’s (...) several variations in order to consider the role of “mere representation” in geometric exegesis, and conclude by characterizing the curious relationship between things and their images and that relationship’s implications for understanding scientific knowledge and practice. (shrink)

The thesis of this paper is that even some of the most fundamental concepts of Marxism have been used and abused to fit their advocates' purposes. More specifically, the interpretation of the concept of the "dictatorship of the proletariat" has been subject to a dual development. First, the dictatorship of the proletariat has come to denote an increasingly violent regime. Second, the term has been used to refer to a rule exercised by an ever smaller segment of society. This paper (...) seeks to analyze and elucidate this much disputed and frequently misunderstood Marxist concept. In the first part Marx's use of the term is examined. The second section explores how the same concept was explicated in the writings of some of the most important first generation Marxist thinkers and "practitioners" like Engels, Lenin, Kautsky, Bukharin, and Stalin. Following the summary of my findings I attempt to formulate some meaningful generalizations about the usage of the concept by Marxist thinkers. (shrink)

Looking back on the many prophets who tried to predict the future as if it were predetermined, at first sight any forward-looking activity is reminiscent of making predictions with a crystal ball. In contrast to fortune tellers, today’s exercises do not predict, but try to show different paths that an open future could take. A key motivation to undertake forward-looking activities is broadening the information basis for decision-makers to help them actively shape the future in a desired way. Experts, laypeople, (...) or stakeholders may have different sets of values and priorities with regard to pending decisions on any issue related to the future. Therefore, considering and incorporating their views can, in the best case scenario, lead to more robust decisions and strategies. However, transferring this plurality into a form that decision-makers can consider is a challenge in terms of both design and facilitation of participatory processes. In this paper, we will introduce and critically assess a new qualitative method for forward-looking activities, namely CIVISTI (Citizen Visions on Science, Technology and Innovation; www.civisti.org), which was developed during an EU project of the same name. Focussing strongly on participation, with clear roles for citizens and experts, the method combines expert, stakeholder and lay knowledge to elaborate recommendations for decision-making in issues related to today’s and tomorrow’s science, technology and innovation. Consisting of three steps, the process starts with citizens’ visions of a future 30–40 years from now. Experts then translate these visions into practical recommendations which the same citizens then validate and prioritise to produce a final product. The following paper will highlight the added value as well as limits of the CIVISTI method and will illustrate potential for the improvement of future processes. (shrink)

Looking back on the many prophets who tried to predict the future as if it were predetermined, at first sight any forward-looking activity is reminiscent of making predictions with a crystal ball. In contrast to fortune tellers, today’s exercises do not predict, but try to show different paths that an open future could take. A key motivation to undertake forward-looking activities is broadening the information basis for decision-makers to help them actively shape the future in a desired way. Experts, laypeople, (...) or stakeholders may have different sets of values and priorities with regard to pending decisions on any issue related to the future. Therefore, considering and incorporating their views can, in the best case scenario, lead to more robust decisions and strategies. However, transferring this plurality into a form that decision-makers can consider is a challenge in terms of both design and facilitation of participatory processes. In this paper, we will introduce and critically assess a new qualitative method for forward-looking activities, namely CIVISTI (Citizen Visions on Science, Technology and Innovation; www.civisti.org ), which was developed during an EU project of the same name. Focussing strongly on participation, with clear roles for citizens and experts, the method combines expert, stakeholder and lay knowledge to elaborate recommendations for decision-making in issues related to today’s and tomorrow’s science, technology and innovation. Consisting of three steps, the process starts with citizens’ visions of a future 30–40 years from now. Experts then translate these visions into practical recommendations which the same citizens then validate and prioritise to produce a final product. The following paper will highlight the added value as well as limits of the CIVISTI method and will illustrate potential for the improvement of future processes. (shrink)

Recent developments in Europe and the United States (US) attest to an increasing fascination with and nostalgia for the strong leaders of the past – especially those that emerged in the aftermath of the creation of nation states and during the period between the First World War and the end of the Cold War era. Considerations of the “strongman syndrome” have a long lineage in premodern European and Islamic political thought. The famous Italian humanist Leonardo Bruni (ca. 1370–1444), for example, (...) provides in his History of the Florentine People a narrative of the events that led to the ascension, ten-month rule and downfall of Walter VI of Brienne in 1342 in Florence. Writing one hundred years earlier, the historian and political writer Żiyā' al-Dīn Baranī (ca. 1285–1357) in his History of Fīrūz Shāh analyzes the failed leadership of the sultan of Delhi, Muḥammad b. Tughluq (r. 1324–1351). This article presents an exploration of specific variants of autocratic leadership in Renaissance Florence and the Delhi Sultanate – as recorded in Bruni’s and Baranī’s writings, respectively – which demonstrates that both authors seek to offer reflections on the emergence and gradual degeneration of strongman rule that are embedded in a broader discussion of the didactic value of the study of history and its relevance to good government. Both Bruni and Baranī highlight the transience of political authority and the dangers that can arise when a leader is out of touch with the overall social climate, alienates his constituency and operates without popular consent. A detailed examination of premodern modes of envisioning strongman rule can yield fresh insights into the circumstances that incubate the strongman syndrome and the ascent of strong leaders that are still timely today. (shrink)