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This book offers a plurality of perspectives on the historical
origins of logicism and on contemporary developments of logicist
insights in philosophy of mathematics. It uniquely provides
up-to-date research and novel interpretations on a variety of
intertwined themes and historical figures related to different
versions of logicism. The essays, written by prominent scholars,
are divided into three thematic sections. Part I focuses on major
authors like Frege, Dedekind, and Russell, providing a historical
and theoretical exploration of such figures in the philosophical
and mathematical milieu in which logicist views were first
expounded. Part II sheds new light on the interconnections between
these founding figures and a number of influential other
traditions, represented by authors like Hilbert, Husserl, and
Peano, as well as on the reconsideration of logicism by Carnap and
the logical empiricists. Finally, Part III assesses the legacy of
such authors and of logicist themes for contemporary philosophy of
mathematics, offering new perspectives on highly debated
topics-neo-logicism and its extension to accounts of ordinal
numbers and set-theory, the comparison between neo-Fregean and
neo-Dedekindian varieties of logicism, and the relation between
logicist foundational issues and empirical research on numerical
cognition-which define the prospects of logicism in the years to
come. This book offers a comprehensive account of the development
of logicism and its contemporary relevance for the
logico-philosophical foundations of mathematics. It will be of
interest to graduate students and researchers working in philosophy
of mathematics, philosophy of logic, and the history of analytic
philosophy.
This volume covers a wide range of topics in the most recent
debates in the philosophy of mathematics, and is dedicated to how
semantic, epistemological, ontological and logical issues interact
in the attempt to give a satisfactory picture of mathematical
knowledge. The essays collected here explore the semantic and
epistemic problems raised by different kinds of mathematical
objects, by their characterization in terms of axiomatic theories,
and by the objectivity of both pure and applied mathematics. They
investigate controversial aspects of contemporary theories such as
neo-logicist abstractionism, structuralism, or multiversism about
sets, by discussing different conceptions of mathematical realism
and rival relativistic views on the mathematical universe. They
consider fundamental philosophical notions such as set, cardinal
number, truth, ground, finiteness and infinity, examining how their
informal conceptions can best be captured in formal theories. The
philosophy of mathematics is an extremely lively field of inquiry,
with extensive reaches in disciplines such as logic and philosophy
of logic, semantics, ontology, epistemology, cognitive sciences, as
well as history and philosophy of mathematics and science. By
bringing together well-known scholars and younger researchers, the
essays in this collection - prompted by the meetings of the Italian
Network for the Philosophy of Mathematics (FilMat) - show how much
valuable research is currently being pursued in this area, and how
many roads ahead are still open for promising solutions to
long-standing philosophical concerns. Promoted by the Italian
Network for the Philosophy of Mathematics - FilMat
This volume covers a wide range of topics in the most recent
debates in the philosophy of mathematics, and is dedicated to how
semantic, epistemological, ontological and logical issues interact
in the attempt to give a satisfactory picture of mathematical
knowledge. The essays collected here explore the semantic and
epistemic problems raised by different kinds of mathematical
objects, by their characterization in terms of axiomatic theories,
and by the objectivity of both pure and applied mathematics. They
investigate controversial aspects of contemporary theories such as
neo-logicist abstractionism, structuralism, or multiversism about
sets, by discussing different conceptions of mathematical realism
and rival relativistic views on the mathematical universe. They
consider fundamental philosophical notions such as set, cardinal
number, truth, ground, finiteness and infinity, examining how their
informal conceptions can best be captured in formal theories. The
philosophy of mathematics is an extremely lively field of inquiry,
with extensive reaches in disciplines such as logic and philosophy
of logic, semantics, ontology, epistemology, cognitive sciences, as
well as history and philosophy of mathematics and science. By
bringing together well-known scholars and younger researchers, the
essays in this collection - prompted by the meetings of the Italian
Network for the Philosophy of Mathematics (FilMat) - show how much
valuable research is currently being pursued in this area, and how
many roads ahead are still open for promising solutions to
long-standing philosophical concerns. Promoted by the Italian
Network for the Philosophy of Mathematics - FilMat
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