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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.

Philosophy. --- Epistemology. --- Logic. --- Philosophy and science. --- Mathematical logic. --- Philosophy of Science. --- Mathematical Logic and Foundations. --- Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Science --- Genetic epistemology. --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Developmental psychology --- Knowledge, Theory of --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Reasoning --- Thought and thinking --- Normal science --- Philosophy of science --- Methodology --- Epistemology --- Theory of knowledge --- Science and philosophy

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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 established and up-and-coming scholars, are divided into three thematic sections. The first section focuses on major authors like Frege, Russell, and Carnap, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Section II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Bolzano, Dedekind, Husserl, Peano, Hilbert, Goedel, and Wittgenstein. Finally, the third section assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics-neo-Logicism, set-theory, abstractionism, the relation between cardinal and ordinal conceptions of numbers, and mathematical cognition-which define the prospects of logicism in the years to come. This book represents a comprehensive account of the development of logicism and its contemporary relevance. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy"--

Arithmetic. --- Arithmétique --- Philosophie.