An Aristotelian Realist Philosophy of Mathematics [electronic resource] : Mathematics as the Science of Quantity and Structure /
Franklin, J.author.
Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Description based upon print version of record.
""Cover ""; ""Half-Title""; ""Title ""; ""Copyright ""; ""Contents""; ""List of Figures""; ""List of Tables""; ""Introduction                   ""; ""Part I The Science of Quantity and Structure                                                   ""; ""1  The Aristotelian Realist Point of View""; ""The reality of universals                                ""; ""Platonism and nominalism                               ""; ""The reality of relations and structure                                             ""; ""â€?Unit-makingâ€? properties and sets                                        ""
""Causality                """"Aristotelian epistemology                                ""; ""2  Uninstantiated Universals and â€?Semi-Platonistâ€? Aristotelianism""; ""Determinables and determinates                                     ""; ""Uninstantiated shades of blue and huge numbers                                                     ""; ""Possibles by recombination?                                  ""; ""Semi-Platonist Aristotelianism                                     ""; ""3  Elementary Mathematics: The Science of Quantity""
""Two realist theories of mathematics: quantity versus structure                                                                     """"Continuous quantity and ratios                                     ""; ""Discrete quantity and numbers                                    ""; ""Discrete quantity and sets                                 ""; ""Discrete and continuous quantity compared                                                ""; ""Defining â€?quantityâ€?                          ""; ""4  Higher Mathematics: Science of the Purely Structural""
""The rise of structure in mathematics                                           """"Structuralism in recent philosophy of mathematics                                                        ""; ""Abstract algebra, groups, and modern pure mathematics                                                            ""; ""Structural commonality in applied mathematics                                                    ""; ""Defining â€?structureâ€?                           ""; ""The sufficiency of mereology and logic                                             ""
""Is quantity a kind of structure?                                       """" 5  Necessary Truths about Reality""; ""Examples of necessity                            ""; ""Objections and replies                             ""; ""6  The Formal Sciences Discover the Philosophersâ€? Stone""; ""A brief survey of the formal or mathematical sciences                                                            ""; ""The formal sciences search for a place in the sun                                                        ""
""Real certainty: program verification                                           ""
Includes bibliographical references and index.
Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Aristotle.
Aristoteles.
Aristotle.
Mathematics-Philosophy.
Logic.
Mathematics.
History.
Philosophy of Mathematics.
Logic.
History of Mathematical Sciences.