On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Nieuwe paskaart voor een gedeelte van de Oost-Zee = Nouvelle carte hydrographique d'une partie de la Mer Baltique = Nya pass cort öfwer yen dehl af Oster-Siöön = The new sea map of the second of the East-Sea

Sisältää myös kartakkeet: Pastkaartje van de Noord Bodem, Suomenlahden itäosa ja Laatokka

Nieuwe paskaart voor een gedeelte van de Oost-Zee = Nouvelle carte hydrographique d'une partie de la Mer Baltique = Nya pass cort öfwer yen dehl af Oster-Siöön = The new sea map of the second of the East-Sea

Sisältää myös kartakkeet: Pastkaartje van de Noord Bodem, Suomenlahden itäosa ja Laatokka

An exploration of the experience of implementing the second step violence prevention curriculum in one primary general learning disabilities class /

Violence has always been a part of the human experience, and therefore, a popular topic for research. It is a controversial issue, mostly because the possible sources of violent behaviour are so varied, encompassing both biological and environmental factors. However, very little disagreement is found regarding the severity of this societal problem. Most researchers agree that the number and intensity of aggressive acts among adults and children is growing. Not surprisingly, many educational policies, programs, and curricula have been developed to address this concern. The research favours programs which address the root causes of violence and seek to prevent rather than provide consequences for the undesirable behaviour. But what makes a violence prevention program effective? How should educators choose among the many curricula on the market? After reviewing the literature surrounding violence prevention programs and their effectiveness, The Second Step Violence Prevention Curriculum surfaced as unique in many ways. It was designed to address the root causes of violence in an active, student-centred way. Empathy training, anger management, interpersonal cognitive problem solving, and behavioural social skills form the basis of this program. Published in 1992, the program has been the topic of limited research, almost entirely carried out using quantitative methodologies.The purpose of this study was to understand what happens when the Second Step Violence Prevention Curriculum is implemented with a group of students and teachers. I was not seeking a statistical correlation between the frequency of violence and program delivery, as in most prior research. Rather, I wished to gain a deeper understanding of the impact ofthe program through the eyes of the participants. The Second Step Program was taught to a small, primary level, general learning disabilities class by a teacher and student teacher. Data were gathered using interviews with the teachers, personal observations, staff reports, and my own journal. Common themes across the four types of data collection emerged during the study, and these themes were isolated and explored for meaning. Findings indicate that the program does not offer a "quick fix" to this serious problem. However, several important discoveries were made. The teachers feU that the program was effective despite a lack of concrete evidence to support this claim. They used the Second Step strategies outside their actual instructional time and felt it made them better educators and disciplinarians. The students did not display a marked change in their behaviour during or after the program implementation, but they were better able to speak about their actions, the source of their aggression, and the alternatives which were available. Although they were not yet transferring their knowledge into positive action,a heightened awareness was evident. Finally, staff reports and my own journal led me to a deeper understanding ofhow perception frames reality. The perception that the program was working led everyone to feel more empowered when a violent incident occurred, and efforts were made to address the cause rather than merely to offer consequences. A general feeling that we were addressing the problem in a productive way was prevalent among the staff and students involved. The findings from this investigation have many implications for research and practice. Further study into the realm of violence prevention is greatly needed, using a balance of quantitative and qualitative methodologies. Such a serious problem can only be effectively addressed with a greater understanding of its complexities. This study also demonstrates the overall positive impact of the Second Step Violence Prevention Curriculum and, therefore, supports its continued use in our schools.

The law of the sea: the United States, Canada and the deep seabed

The Falkland Islands War of 1982 was fought over competing claims to sovereignty over a group of islands off the east coast of South America. The dispute was between Argentina and the United Kingdom. Argentina claims the islands under rights to Spanish succession, the fact that they lie off the Argentine coast line and that in 1833 Great Britain took the islands illegally and by force. The United Kingdom claims the islands primarily through prescription--the fact that they have governed the islands in a peaceful, continuous and public manner since 1833. The British also hold that the population living on the islands, roughly eighteen hundred British descendants, should be able to decide their own future. The United Kingdom also lays claim to the islands through rights of discovery and settlement, although this claim has always been challenged by Spain who until 1811 governed the islands. Both claims have legal support, and the final decision if there will ever be one is difficult to predict. Sadly today the ultimate test of sovereignty does not come through international law but remains in the idea that "He is sovereign who can defend his sovereignty." The years preceding the Argentine invasion of 1982 witnessed many diplomatic exchanges between The United Kingdom and Argentina over the future of the islands. During this time the British sent signals to Argentina that ii implied a decline in British resolve to hold the islands and demonstrated that military action did more to further the talks along than did actual negotiations. The Argentine military junta read these signals and decided that they could take the islands in a quick military invasion and that the United Kingdom would consider the act as a fait accompli and would not protest the invasion. The British in response to this claimed that they never signaled to Argentina that a military solution was acceptable to them and launched a Royal Navy task force to liberate the islands. Both governments responded to an international crisis with means that were designed both to resolve the international crisis and increase the domestic popularity of the government. British Prime Minister Margaret Thatcher was facing an all-time low in popularity for post-War Prime Ministers while Argentine President General Galtieri needed to gain mass popular support so he could remain a viable President after he was scheduled to lose command of the army and a seat on the military junta that ran the country. The military war for the Falklands is indicative of the nature of modern warfare between Third World countries. It shows that the gap in military capabilities between Third and First World countries is narrowing significantly. Modern warfare between a First and Third World country is no longer a 'walk over' for the First World country.

Letter from the Secretary of War, transmitting a return of the arms and military stores furnished to the respective states, under the provisions of the law of one thousand eight hundred and twelve.

At head of title: [107].

A sermon, delivered at the meeting house of the second parish in Portland, August 20, 1812 : on the occasion of the national fast /

Published at the particular request of the congregation.

Letter from the Secretary of War, transmitting a return of the arms and military stores furnished to the respective states, under the provisions of the law of one thousand eight hundred and twelve

At head of title: [107]. 15th Congress, 1st session, 1817-1818. House. February 20, 1818. Read, and ordered to lie upon the table.

A sermon, delivered at the meeting house of the second parish in Portland, August 20, 1812 : on the occasion of the national fast

Published at the particular request of the congregation.

Two discourses, delivered to the Second Presbyterian Society in Newburyport, August 20, 1812, the day recommended by the President of the United States, for national humiliation and prayer

Printed by W.R. and H. G. Allen

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page (3 pages, handwritten), n.d.

Commentaries on the law of municipal corporations

UANL

The law of psychic phenomena : working hypothesis for the systematic study of hypnotism. spiritism, mental therapeutic, etc.

UANL