Proceedings of the Canadian Society for History and Philosophy of Mathematics.

This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. -/- A series of chapters all set in the eighteenth century consider topics such as John Marsh’s (...) techniques for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. -/- After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. -/- Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics. (shrink)

This volume contains ten papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics from the seventeenth century to the modern era. -/- The volume begins with an exposition of the life and work of Professor Bolesław Sobociński. It then moves on to cover a collection of topics about twentieth-century philosophy (...) of mathematics, including Fred Sommers’s creation of Traditional Formal Logic and Alexander Grothendieck’s work as a starting point for discussing analogies between commutative algebra and algebraic geometry. Continuing the focus on the philosophy of mathematics, the next selections discuss the mathematization of biology and address the study of numerical cognition. The volume then moves to discussing various aspects of mathematics education, including Charles Davies’s early book on the teaching of mathematics and the use of Gaussian Lemniscates in the classroom. A collection of papers on the history of mathematics in the nineteenth century closes out the volume, presenting a discussion of Gauss’s “Allgemeine Theorie des Erdmagnetismus” and a comparison of the geometric works of Desargues and La Hire. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics. (shrink)

J. S. Silverberg, The Most Obscure and Inconvenient Tables ever Constructed.- D. J. Melville, Commercializing Arithmetic: The Case of Edward Hatton.- C. Baltus, Leading to Poncelet: A Story of Collinear Points.- R. Godard, Cauchy, Le Verrier et Jacobi sur le problème algébrique des valeurs propres et les inégalités séculaires des mouvements des planètes.- A. Ackerberg-Hastings, Mathematics in Astronomy at Harvard College Before 1839 as a Case Study for Teaching Historical Writing in Mathematics Courses.- J. J. Tattersall, S. L. McMurran, "Lectures (...) for Women" and the Founding of Newnham College, Cambridge.- D. Waszek, Are Euclid's Diagrams "Representations"? On an Argument by Ken Manders.- B. Buldt, Abstraction by Embedding and Constraint-Based Design.- W. Meyer, The Birth of Undergraduate Modern Algebra in the United States.- P. Liu, History as a Source of Mathematical Narrative in Developing Students' Interpretations of Mathematics.- F. Kamareddine, J. P. Seldin, Thoughts on Using the History of Mathematics to Teach the Foundations of Mathematical Analysis. (shrink)

First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

Author note: Naomi Zack is Assistant Professor in the Department of Philosophy at the State University of New York at Albany. She herself is of mixed race: Jewish, African American, and Native American.

ABSTRACT:Determining the biological function of phenomenal consciousness appears necessary to explain its origin: evolution by natural selection operates on organisms’ traits based on the biological functions they fulfill. But identifying the function of phenomenal consciousness has proven difficult. Some have proposed that the function of phenomenal consciousness is to facilitate mental processes such as reasoning or learning. But mental processes such as reasoning and learning seem to be possible in the absence of phenomenal consciousness. It is difficult to pinpoint in (...) what way phenomenal consciousness enhances these processes or others like them. In this paper, we explore a possibility that has been neglected to date. Perhaps phenomenal consciousness has no function of its own because it is either a by-product of other traits or a (functionless) accident. If so, then phenomenal consciousness has an evolutionary explanation even though it fulfills no biological function. (shrink)

Much of our behavior is guided by our understanding of events. We perceive events when we observe the world unfolding around us, participate in events when we act on the world, simulate events that we hear or read about, and use our knowledge of events to solve problems. In this book, Gabriel A. Radvansky and Jeffrey M. Zacks provide the first integrated framework for event cognition and attempt to synthesize the available psychological and neuroscience data surrounding it. This synthesis leads (...) to new proposals about several traditional areas in psychology and neuroscience including perception, attention, language understanding, memory, and problem solving.Radvansky and Zacks have written this book with a diverse readership in mind. It is intended for a range of researchers working within cognitive science including psychology, neuroscience, computer science, philosophy, anthropology, and education. Readers curious about events more generally such as those working in literature, film theory, and history will also find it of interest. (shrink)

Testimonio que recoge algunas experiencias y reflexiones de la artista visual costarricense María Rapela en Alemania y de cómo se involucró en la gestión cultural, coordinando el Fieber Festival, una plataforma colaborativa y auto-gestionada de mujeres artistas migrantes iberoamericanas en Berlín entre el 2011 y el 2017.

Philosophers have little to lose in making practical proposals. If the proposals are enacted, the power of ideas to change the world is affirmed. If the proposals are rejected, there is new material for theoretical reflection. During the 1990s, I believed that broad public recognition of mixed race, particularly black and white mixed race, would contribute to an undoing of rigid and racist, socially constructed racial categories. I argued for such recognition in my first book, Race and Mixed Race (Zack (...) 1993), a follow-through anthology, American Mixed Race (Zack 1995), and numerous articles, especially the essay, ''Mixed Black and White Race and Public Policy," which appeared first in Hypatia in 1995. I aho delivered scores of public and academic lectures and presentations on this subject, all of which expressed the following in varied forms and formats: Race is an idea that lacks the biological foundation it is commonly assumed to have. There is need for broad education about this absence of foundation; mixed-race identities should be recognized, especially black-white identities. (shrink)

Batteries are a fundamental storage component due to its various applications in mobility, renewable energies and consumer electronics among others. Regardless of the battery typology, one key variable from a user’s perspective is the remaining energy in the battery. It is usually presented as the percentage of remaining energy compared to the total energy that can be stored and is labeled State Of Charge (SOC). This work addresses the development of a hybrid model based on a Lithium Iron Phosphate (LiFePO4) (...) power cell, due to its broad implementation. The proposed model calculates the SOC, by means of voltage and electric current as inputs and the latter as the output. Therefore, four models based on k-Means, Agglomerative Clustering, Gaussian Mixture and Spectral Clustering techniques have been tested in order to obtain an optimal solution. (shrink)

National early childhood education and care (ECEC) systems have been shaped by external influences and have taken different forms in developed countries than in post-colonial countries. This study systematically compares and examines the autonomous elements in national ECEC systems and the countervailing homogenisation process in Slovakia and Indonesia -two countries located in a different hemisphere with different historical, cultural, and political backgrounds. The study shows new rhetoric triggering different tendencies. In Slovakia, the “competency” and “standards” turn led to steps to (...) increase ECEC institutions’ autonomy and give them greater power to create tailor-made education programmes. While in Indonesia, the turn went in the opposite direction, reinforcing curriculum centralisation and increasing its regulatory functions regarding ECEC. This shift towards the same discourse, terminology and concepts does not automatically trigger processes that lead to a significant similarity and the convergence between ECEC systems due to their specific historical, cultural, and political contexts. (shrink)

There has been a push in recent years to provide better explanations for how AIs make their decisions. Most of this push has come from the ethical concerns that go hand in hand with AIs making decisions that affect humans. Outside of the strictly ethical concerns that have prompted the study of explainable AIs (XAIs), there has been research interest in the mere possibility of creating XAIs in various domains. In general, the more accurate we make our models the harder (...) they are to explain. Go playing AIs like AlphaGo and KataGo provide fantastic examples of this phenomenon. In this paper, I discuss a non-exhaustive list of the leading theories of explanation and what each of these theories would say about the explainability of AI-played moves of Go. Finally, I consider the possibility of ever explaining AI-played Go moves in a way that meets the four principles of XAI. I conclude, somewhat pessimistically, that Go is not as imminently explainable as other domains. As such, the probability of having an XAI for Go that meets the four principles is low. (shrink)

People tend to perceive ongoing continuous activity as series of discrete events. This partitioning of continuous activity may occur, in part, because events correspond to dynamic patterns that have recurred across different contexts. Recurring patterns may lead to reliable sequential dependencies in observers' experiences, which then can be used to guide perception. The current set of simulations investigated whether this statistical structure within events can be used 1) to develop stable internal representations that facilitate perception and 2) to learn when (...) to update such representations in a self-organizing manner. These simulations demonstrate that experience with recurring patterns enables a system to accurately predict upcoming stimuli within an event, to identify boundaries between such events based on transient increases in prediction error, and to use such boundaries to improve prediction about subsequent activities. (shrink)

The philosophical literature on the standing to forgive is divided. The majority view holds that only victims have the standing to forgive (Murphy and Hampton 1988, Owens 2012, Zaragoza 2012, Walker 2013), while recent contributions challenge the majority view and argue that third parties also have the standing to forgive (MacLachlan 2008, Norlock 2009, Pettigrove 2009, Chaplin 2019). This chapter defends the victim’s unique standing to forgive by way of a specific account of the nature of forgiveness. The standard account (...) of forgiveness says that forgiveness is the overcoming of resentment for the right reasons. The standard account can explain how forgiveness differs from similar responses, like excusing and condoning, but falls short of explaining how forgiveness can be a voluntary action. A satisfactory account of forgiveness should be able to explain how forgiveness can be separate from excusing and condoning, as well as how forgiveness can be voluntary. To account for all the desiderata, this chapter suggests an account of forgiveness that depends on the wrongdoer’s repentance and the victim’s decision to absorb the cost of the wrongdoing. On this account, forgiveness is necessarily the prerogative of the victim. (shrink)

Eric Scerri and other authors have acknowledged that the reality of chemical orbitals is not compatible with quantum mechanics. Recently, however, Scerri and Sharon Crasnow have argued that if chemists cannot consider orbitals as real entities, then chemistry is in danger of being reduced to physics. I argue that the question of the existence of orbitals is best viewed as an issue of explanation, not metaphysics: In many chemically important cases orbitals do not make sufficiently accurate predictions, and must be (...) replaced. Chemists and physicists can acknowledge this fact while maintaining the utility of orbitals and the autonomy of chemistry. (shrink)

Razón, poesía, historia.--La cuestión del estoicismo español.--El querer.

Logical form is thought to be discovered by keeping fixed the logical constants and allowing the non-logical content in the sentence to vary. The problem of logical constants is the problem of defining what counts as a logical constant. In this paper, I will argue that the concept ’logical constant’ is vague. I demonstrate the vagueness of logical constancy by providing a sorites argument, thereby showing the sorites-susceptibility of the concept. Many prior papers in the literature on logical constants hint (...) at this vagueness, but do not explore how theories of vagueness apply to logical constants. In the second half of this paper, I do just this. I consider approaches to logical constants that resemble nihilism about vagueness and more recent theories that relativize truth to precisifications. Finally, I argue that approaches that accept the potential indeterminate status of putative logical constants are preferable to nihilism or relativism about logical constancy. (shrink)

Was Iris Murdoch a virtue ethicist? At first sight, it would appear that she was not. She does not offer an explicit definition of account of the term ‘virtue’, and there are significant differences between her views and those of standard Aristotelian virtue ethicists. There is no reason, however, to think that the standard Aristotelian view represents the only legitimate form of virtue ethics. In this chapter, I begin by recalling (in section 1) the main commonalities between Murdoch’s criticisms of (...) the prevailing moral theories of her time and those of other first-wave virtue-ethicists. I then highlight (in section 2) some cornerstones of Murdoch’s peculiar approach to morality, which represent the background against which her account of virtue is developed, and I propose to trace these cornerstones back to a more diverse range of influences than the standard version of Aristotelianism. In section 3, I sketch the basics of Murdoch’s account of virtue, and I argue that there are at least three routes to vindicate it as a genuine virtue-ethical approach: the Buddhist, the Kantian and the Socratic-Aristotelian. I explore each of these routes in turn in sections 4, 5, and 6. In conclusion, I argue that the virtue-ethical field would benefit a great deal from the kind of pluralistic account of virtue that Murdoch offers. (shrink)

Epistemological accounts that make use of a safety condition on knowledge, historically, face serious problems regarding beliefs that are necessarily true. This is because necessary truths are true in all possible worlds, so such beliefs can be safe even when the bases for the beliefs are epistemically problematic. The existence of such problematically safe beliefs would undermine a major motivation for the condition itself: the ability to evaluate how well a belief tracks the truth. In this paper, we’ll argue that (...) incorporating impossible worlds into the evaluation of beliefs solves this problem, but only if the relevant account of impossible worlds entails that many impossible worlds are incredibly similar to the actual world. Further, we’ll argue that, as a result of including impossible worlds, some philosophical beliefs are unsafe, and many more are potentially unsafe. But, we argue, even if this is the case, we can still make philosophical progress. (shrink)

In Western society bicycling is commonly perceived as either a sport, a form of leisure, an activity for children, or at best, a utilitarian transportation technology. In this paper, I contest these assumptions by discussing ways in which both bicycling and bicycle technologies are politicized as a response to the cultural, social and political norms of Western society. Through historical examples that include 19th century Socialists, 'first wave' feminists, and 1960's Dutch Anarchists, I provide a theoretical context in which one (...) can understand how present day activists appropriate the bicycle through a dialectic of action and communication. In short, I demonstrate how a seemingly neutral technology (the bicycle) and an everyday activity (bicycling can be utilized as tools for dissent, protest, and cultural critique. (shrink)

This chapter contains sections titled: We're Not Blocking Traffic… Background and (Dis)organization Interpretations Influences and Impacts …We (Still) Are Traffic Notes.

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)

Analyzes popular music's aesthetics, production, marketing, and consumption toward articulating a clearer understanding of how intimacy is constructed, mediated, and perceived in and through music.

Picture a young infant sitting in a room staring at two objects occluded by a screen. For the first few trials, the researcher manipulating the objects performs the same action: both sticks move in...

Did you know we used to have tails that helped us connect to each other and the world around us? But then of course we lost our tails — or so the story goes — and now we need new ways to connect. In From Tails to Tales, best friends Huk and Tuk find a way to compensate for this loss. They discover that by discussing stories — or tales, if you like — they can recreate that deeper understanding of (...) themselves, each other and the world, essential for feeling connected. Although the tales they discuss may seem simple, the complex questions they raise make them rewarding for adults and children to ponder together. -/- Doing philosophy with people of all ages inspires Maria daVenza Tillmanns to explore profound ideas through playful stories that help us who have lost our tails to reconnect through meaningful communication and endless curiosity. (shrink)

Dibujar el pensamiento de Seneca es dibujar su figura viva, trazar el esquema de su persona. Seneca es un mediador que para alzarse sobre nosotros necesita de nuestra necesidad, pues solo apoyado en nuestra indigencia tiene sentido. Maria Zambrano lleva a cabo un lucido estudio de la figura y significacion del pensador cordobes y presenta una seleccion de sus escritos.

Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293–305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. https://doi.org/10.1103/PhysRevD.104.025012 ) establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin [ 1 ] labels (...) such scenarios ‘impossible measurements’. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the ‘impossible measurements’ problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez et al. (Phys Rev D, 2022. https://doi.org/10.1103/physrevd.105.065003 ) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851–889, 2020). Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating ‘impossible measurements’, the abandonment of the operational interpretation of local algebras \({\mathcal {A}}(O)\) as representing possible operations carried out in region _O_, and the interpretation of state update rules. Finally, we examine the form that the ‘impossible measurements’ problem takes in histories-based approaches and we discuss the remaining challenges. (shrink)

Low levels of media literacy in Bulgaria have provided fertile soil for anti-vaxxers and spawned disinformation campaigns as a major means of influencing the public opinion. Bulgaria has gained a reputation as the poorest and most corrupt country in the European Union (EU) and the fastest-shrinking nation in the world. The COVID-19 pandemic exacerbated some of the well-known, long-standing problems in the healthcare system in Bulgaria – rising morbidity, an insufficient number of hospital beds, a low rate of COVID-19 vaccination, (...) and, above all, a high mortality rate. (shrink)