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This volume contains thirteen papers that were presented at the
2014 Annual Meeting of the Canadian Society for History and
Philosophy of Mathematics/La Societe Canadienne d'Histoire et de
Philosophie des Mathematiques, held on the campus of Brock
University in St. Catharines, Ontario, Canada. It contains
rigorously reviewed modern scholarship on general topics in the
history and philosophy of mathematics, as well as on the meeting's
special topic, Early Scientific Computation. These papers cover
subjects such as *Physical tools used by mathematicians in the
seventeenth century *The first historical appearance of the
game-theoretical concept of mixed-strategy equilibrium *George
Washington's mathematical cyphering books *The development of the
Venn diagram *The role of Euler and other mathematicians in the
development of algebraic analysis *Arthur Cayley and Alfred Kempe's
influence on Charles Peirce's diagrammatic logic *The influence
publishers had on the development of mathematical pedagogy in the
nineteenth century *A description of the 1924 International
Mathematical Congress held in Toronto, told in the form of a
"narrated slide show" Written by leading scholars in the field,
these papers will be accessible to not only mathematicians and
students of the history and philosophy of mathematics, but also
anyone with a general interest in mathematics.
Structural realism has rapidly gained in popularity in recent
years, but it has splintered into many distinct denominations,
often underpinned by diverse motivations. There is, no monolithic
position known as 'structural realism,' but there is a general
convergence on the idea that a central role is to be played by
relational aspects over object-based aspects of ontology. What
becomes of causality in a world without fundamental objects? In
this book, the foremost authorities on structural realism attempt
to answer this and related questions: 'what is structure?' and
'what is an object?' Also featured are the most recent advances in
structural realism, including the intersection of mathematical
structuralism and structural realism, and the latest treatments of
laws and modality in the context of structural realism. The book
will be of interest to philosophers of science, philosophers of
physics, metaphysicians, and those interested in foundational
aspects of science.
This volume contains seventeen papers that were presented at the
2015 Annual Meeting of the Canadian Society for History and
Philosophy of Mathematics/La Societe Canadienne d'Histoire et de
Philosophie des Mathematiques, held in Washington, D.C. In addition
to showcasing rigorously reviewed modern scholarship on an
interesting variety of general topics in the history and philosophy
of mathematics, this meeting also honored the memories of
Jacqueline (Jackie) Stedall and Ivor Grattan-Guinness; celebrated
the Centennial of the Mathematical Association of America; and
considered the importance of mathematical communities in a special
session. These themes and many others are explored in these
collected papers, which cover subjects such as New evidence that
the Latin translation of Euclid's Elements was based on the Arabic
version attributed to al-Hajjaj Work done on the arc rampant in the
seventeenth century The history of numerical methods for finding
roots of nonlinear equations An original play featuring a dialogue
between George Boole and Augustus De Morgan that explores the
relationship between them Key issues in the digital preservation of
mathematical material for future generations A look at the first
twenty-five years of The American Mathematical Monthly in the
context of the evolving American mathematical community The growth
of Math Circles and the unique ways they are being implemented in
the United States Written by leading scholars in the field, these
papers will be accessible to not only mathematicians and students
of the history and philosophy of mathematics, but also anyone with
a general interest in mathematics.
Structural realism has rapidly gained in popularity in recent
years, but it has splintered into many distinct denominations,
often underpinned by diverse motivations. There is, no monolithic
position known as 'structural realism, ' but there is a general
convergence on the idea that a central role is to be played by
relational aspects over object-based aspects of ontology. What
becomes of causality in a world without fundamental objects? In
this book, the foremost authorities on structural realism attempt
to answer this and related questions: 'what is structure?' and
'what is an object?' Also featured are the most recent advances in
structural realism, including the intersection of mathematical
structuralism and structural realism, and the latest treatments of
laws and modality in the context of structural realism. The book
will be of interest to philosophers of science, philosophers of
physics, metaphysicians, and those interested in foundational
aspects of science.
This Element shows that Plato keeps a clear distinction between
mathematical and metaphysical realism and the knife he uses to
slice the difference is method. The philosopher's dialectical
method requires that we tether the truth of hypotheses to existing
metaphysical objects. The mathematician's hypothetical method, by
contrast, takes hypotheses as if they were first principles, so no
metaphysical account of their truth is needed. Thus, we come to
Plato's methodological as-if realism: in mathematics, we treat our
hypotheses as if they were first principles, and, consequently, our
objects as if they existed, and we do this for the purpose of
solving problems. Taking the road suggested by Plato's Republic,
this Element shows that methodological commitments to mathematical
objects are made in light of mathematical practice; foundational
considerations; and, mathematical applicability. This title is also
available as Open Access on Cambridge Core.
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