1,720,978 research outputs found
Cantor's Abstractionism and Hume's Principle
No full textRichard Kimberly Heck and Paolo Mancosu have claimed that the possibility of non-Cantorian assignments of cardinalities to infinite concepts shows that Hume's Principle (HP) is not implicit in the concept of cardinal number. Neologicism would therefore be threatened by the 'good company' HP is kept by such alternative assignments. In his review of Mancosu's book, Bob Hale argues, however, that 'getting different numerosities for different countable infinite collections depends on taking the groups in a certain order - but it is of the essence of cardinal numbers that the cardinal size of a collection does not depend upon how its members are ordered'. This paper's goal is to implement Hale's response to the Good Company problem by producing a Cantorian argument for HP. In Section 2, we present the Heck-Mancosu argument against neologicism. In Section 3, we discuss Hale's defence of Hume's Principle. In Section 4, we discuss Cantor's abstractionist definitions of number. In Section 5, we argue that good abstraction must comply with what we call 'Godel's Minimal Account of Abstraction' (GMAA). We finally show (Sections 5 and 6) that non-Cantorian theories of cardinality fail to satisfy GMAA
Peano's Conception of a Single Infinite Cardinality
Full text linkWhile Peano's negative attitude towards infinitesimals, in particular,
geometric infinitesimals, is widely documented, his conception of a single
infinite cardinality and, more generally, his views on the infinite, are a lot
less known. The paper reconstructs the evolution of Peano's ideas on these
questions, and formulates several hypotheses about their underlying
motivations
Ipotesi del Continuo
Full text linkL’Ipotesi del Continuo, formulata da Cantor nel 1878, è una delle congetture più note della teoria degli insiemi. Il Problema del Continuo, che ad essa è collegato, fu collocato da Hilbert, nel 1900, fra i principali problemi insoluti della matematica. A seguito della dimostrazione di indipendenza dell’Ipotesi del Continuo dagli assiomi della teoria degli insiemi, lo status attuale del problema è controverso. In anni più recenti, la ricerca di una soluzione del Problema del Continuo è stata anche una delle ragioni fondamentali per la ricerca di nuovi assiomi in matematica. L’articolo fornisce un quadro generale dei risultati matematici fondamentali, e un’analisi di alcune delle questioni filosofiche connesse al Problema del Continuo
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Gödel’s Cantorianism
Full text linkGödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no
conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully
reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to
describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics
Mathematical platonism and set-theoretic indeterminacy
No full textIn this work, I will be looking at the issues raised by set-theoretic indeterminacy for a Gődelian platonist, who holds that there is a universe of independently existing math- ematical objects and that there are objective unique truth-values for any set-theoretic statement. After careful consideration of the philosophical and mathematical issues involved, I claim that Gődelian platonism is untenable. In Chapter 1, I examine dif- ferent forms of mathematical platonism and I elucidate their features. In particular, I distinguish between a substantive form (Gődel's platonism) and an operational form (anti-constructivism). I also make it clear that I will be concerned with set-theoretic Gődelian platonism. In Chapter 2, I examine the indeterminacy phenomenon in set theory through a detailed analysis of the most famous open conjecture, the Continuum Hypothesis (CH). In Chapter 3, I move on to describe the main philosophical orien- tations with regard to the indeterminacy phenomenon and I show how model-theoretic relativity is the main source of trouble for platonism. In Chapter 4, I examine the the- oretical ancestry of Gődel's conceptions (which may date back to Cantor's philosophy of the infinite) and Gődel's philosophy of indeterminacy. In Chapter 5 and Chapter 6, I deal with, respectively, Maddy's set-theoretic naturalism and plenitudinous platonism (in the form presented by Balaguer, FEP), and I raise some objections against these conceptual frameworks. In Chapter 7, I propose abandoning ontological platonism and I defend a mild form of conceptual realism resting upon the notion of non-arbitrary expansions. Finally, in Chapter 8, I tackle the problem of insolubility in contempo- rary set theory and I advise that operational platonism, qua anti-constructivism, as described in Chapter 1, is the only bit of platonism which could be upheld.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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