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.

Proposed Improvement of the Iowa State Capitol Grounds, An Address before the Iowa Chapter American Institute of Architects at the State Historical Buiding, Des Moines, Iowa, October 22, 1913.

Concerning improvements to the State Capitol Grounds including placement of the Allison memorial and Soldiers and Sailor's momuments; removal of heating plant and relieving the state of coal, ashes, gas and smoke; provision of office space to the Adjutant General; an eventual executive mansion; provision of office buildings; and for a Supreme Court building where together with its library auxiliaries will have perpetual growth and constant accessbility; and propose restoration of natural scenic value of the capitol site.

Historical Map

Note the land allocated for Brock University shaded in gray between Thorold and Grantham townships.

The Midnight express phenomenon : a historical materialist approach to the reception of the film Midnight express /

This thesis examines the Midnight Express phenomenon focusing on the film's reception by audiences in Europe, North America, and Turkey between 1978-2003. Using and enhancing the "historical materialist approach" to film reception developed by Janet Staiger, the thesis considers the historical determinants of the film's nationally and culturally differential readings in different periods and of the transformations in those readings. The thesis argues that while Midnight Express was most likely read in the late 1970s as an attempt to reaffirm American social identity by projecting Turks as an instance of the negative Other, there has been an important shift in the reception of the film in the West during the 1990s due to the changes in the discursive contexts in which the film has been circulating. One does not observe any specific reference to Turkish prisons as a part of the issue of human rights violations in Turkey in the initial reception of the film by European and American critics, whereas these issues appear to be important constituents of a particular reception of the film in the West in the present. The thesis explains this shift by pointing to the constitution of a particular discourse on human rights violations in Turkey after 1980, and especially throughout the 1990s, which has become a part of the discursive repertoires of the Western audience. Therefore, the thesis argues that today, Midnight Express functions as a more legitimate political statement about Turkey in the eyes of some Western audiences than it had been in the 1970s. On the other hand, parallel to the increasing desire of Turkey to connect itself to the West, particularly to become a member of the European Union, one observes an immense increase in the belief in and defense against the negative effects of Midnight Express on Turkey's international representation since the 1990s. The historical and current discourses that audiences, both in Turkey and abroad, bring into play suggest that these audiences engage with Midnight Express by assuming or denying not only the subject positions constructed by the film text but also certain history-specific extra-filmic subject positions produced by other social and discursive formations.

Multinational drug corporations, intellectual property rights and the Canadian state : a historical and critical analysis

This study critically analyzes the historical role and influence of multinational drug cotpOrations and multinational corporations in general; the u.s. government and the Canadian state in negotiating the global recognition ofIntellectual Property Rights (IPR) under GATT/NAFTA. This process began in 1969 when the Liberal government, in response to high prices for brand-name drugs amended the Patent Act to introduce compulsory licensing by reducing monopoly protection from 20 to seven years. Although the financial position ofthe multinational drug industry was not affected, it campaigned vigorously to change the 1969 legislation. In 1987, the Patent Act was amended to extend protection to 10 years as a condition for free trade talks with the u.s. Nonetheless, the drug industry was not satisfied and accused Canada of providing a bad example to other nations. Therefore, it continued to campaign for global recognition ofIPR laws under GATT. Following the conclusion of the GATTI Trade-Related aspects of Intellectual Property Rights agreement (TRIPS) in 1991, the multinational drug industry and the American government, to the surprise of many, were still not satisfied and sought to implement harsher conditions under NAFTA. The Progressive Conservative government readily agreed without any objections or consideration for the social consequences. As a result, Bill C-91 was introduced. It abandoned compulsory licenses and was made retroactive from December 21, 1991. It is the contention of this thesis that the economic survival of multinational corporations on a global scale depends on the role and functions of the modem state. Similarly, the existence of the state depends on the ideological-political and socioeconomic assistance it gives to multinational corporations on a national and international scale. This dialectical relation of the state and multinational corporations is explored in our theoretical and historical analysis of their role in public policy.

The utility of sedimentary diatoms as a measure of historical lake ph

As a result of increased acid precipitation, the pH of a large number of Canadian Shield lakes has been falling. Prior to this study there was no documentation available to explain the history of lake acidification for the Algoma area lakes. In order to obtain this information the diatom inferred pH technique was developed in this study. During two field seasons, July 1981 and July 1982, short sediment cores (circa 25-30 cm) were collected from 28 study lakes located north of Lake Superior, District Algoma, Ontario. The surface sediment diatoms (0-1 cm) from each of these lakes were carefully identified, enumerated, and classified in terms of their pH indicator status. The surface sediment diatom analysis indicated that lake pH is one of the most important factors affecting the species composition and relative abundance of diatom populations. Thus diatom assemblages can be sensitive indicators of lake acidification. When Nygaard's index alpha was plotted against observed lake pH, a statistically significant relationship resulted (r=-0.89; p=

The red book of Niagara : a comprehensive guide to the scientific, historical and scenic aspects of Niagara for the use of travellers /

Includes bibliographical references and index.

Fifth series of historical documents : [All relating to the War of 1812].

Published under the auspices of "The Literary and Historical Society of Quebec".

The wars of the gulls; : an historical romance in three chapters; chap. I, Shewing how and why and with whom the gulls went to war: chap. II, Shewing how the gulls make the deep to boil like a pot: chap. III, Shewing how a certain doughty general of the gulls goes forth to play the game of hull-gull in Upper Canada.

Transcribed on front paste-down: W.G. Phelps Oct. 29 1890.

Niagara Historical Society and Museum papers, 1898, 1914, 1969, n.d.

The Niagara Historical Society and Museum papers include a revision of a publication originally prepared by Janet Carnochan, a poem by Janet Carnochan written to commemorate the battle of Lundy’s Lane, one item of correspondence and a scrapbook of historical documents on microfilm.

Niagara Regional Historical Council fonds, 1960-1989

The Lincoln County Historical Council began meeting December 17,1960 under the advisement of the Publicity, Planning and Development Committee of Lincoln County. The group was composed of three members appointed from each of the four existing historical societies: one member appointed from the executive of the Women’s Institute, one member from Lincoln County Council, the Deputy-Clerk and Treasurer of the County and a member from the Niagara Editorial Bureau. The Welland County Historical Council was soon formed after this along the same lines. In the early 1960’s the Lincoln and Welland County historical councils began work on an inventory of historic buildings with the intent to emphasize the historical significance of this area. The information gathered by volunteers and a professional photographer and an architect was used to present a “brief” to the federal government in 1962 and the provincial government in 1963. This brief, An Area of Historical Interest in the Counties of Lincoln and Welland, Ontario was published in 1962 and revised and distributed to schools and libraries in the area in 1965. The Ontario Buildings Inventory Project became a provincial initiative spearheaded by the Department of Public Records and Archives, a branch of the Department of Tourism and Information, ca. 1966. Volunteers collected and photographed buildings of historical interest in Lincoln and Welland counties. This information was recorded on standardized survey forms for every township in the Niagara region. Niagara Regional Historical Council was created with the merger of Lincoln County Historical Council and Welland County Historical Council, at the time of the formation of Niagara Regional Government in 1970. The first meeting of the new council was held January 1970.