Mathematics as a Science of Non-abstract Reality: Aristotelian Realist Philosophies of Mathematics

  title={Mathematics as a Science of Non-abstract Reality: Aristotelian Realist Philosophies of Mathematics},
  author={James Franklin},
  journal={Foundations of Science},
  • J. Franklin
  • Published 20 March 2021
  • Philosophy
  • Foundations of Science
There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity… 



Aristotelianism in the Philosophy of Mathematics

Aristotelianism in the Philosophy of Mathematics Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism

Philosophy of mathematics : structure and ontology

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively

Mathematics as a science of patterns

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling

Proof and Other Dilemmas: Mathematics and Philosophy

Acknowledgments Introduction Part I. Proof and How it is Changing: 1. Proof: its nature and significance Michael Detlefsen 2. Implications of experimental mathematics for the philosophy of

The Indispensability of Mathematics

Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical

Pythagorean powers or a challenge to platonism

The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend.

Proof and other Dilemmas: Extreme Science: Mathematics as the Science of Relations as Such

The question of what mathematics is has never received a satisfactory answer, we feel, although “mathematics is the science of patterns” may come close. Devlin’s chapter (which takes that as its de fi

Philosophy of Mathematics: An Introduction

Introduction. Part I: Plato versus Aristotle: . A. Plato . 1. The Socratic Background. 2. The Theory of Recollection. 3. Platonism in Mathematics. 4. Retractions: the Divided Line in Republic VI

The Architecture of Mathematics

1. Mathematic or mathematics? To present a view of the entire field of mathematical science as it exists,-this is an enterprise which presents, at first sight, almost insurmountable difficulties, on

An Aristotelian approach to mathematical ontology

The paper begins with an exposition of Aristotle’s own philosophy of mathematics. It is claimed that this is based on two postulates. The first is the embodiment postulate, which states that