Structuralism in the philosophy of mathematics

• Authors: MENŠÍK Josef
• Year of publication: 2016
• Description: This bachelor's thesis enquires into the approach of mathematical structuralism, the differentiation within this approach and the nature and the relevance of its criticisms. Particular attention is given to the still unresolved issue of the relation between category theory and mathematical structuralism. It turned out that there exists a general agreement in the philosophy of mathematics that mathematical thinking is structural. Opposition is almost nonexistent and the few concerned voices only amount to adding that mathematics is done by actual people capable of applying the structural thinking in varying contexts. There are five principal approaches to mathematical structuralism endorsed at the most general level - implicit structuralism, formalist structuralism, model structuralism, universals structuralism and modal structuralism. Category structuralism, while representing special case of all the previous, provides structuralists with a valuable tool of strictly structural external descriptions.