Interpreting GĂ¶del : historical and philosophical perspectives
The main project of the thesis is to provide a comprehensive examination of GĂ¶delâs philosophy of mathematics and logic, in defence of his Platonism and the idea of mathematical intuition. The whole work is considered to be partly historical, explaining GĂ¶del's ideas and arguments in comparison with his contemporaries such as Carnap, Russell, Turing and Hilbert; partly mathematical, relying especially on his incompleteness theorem to refute certain philosophical positions; and partly philosophical, shedding light on debates in current discussions of philosophy of mathematics and logic such as the nature of paradoxes, the indispensability argument, the feasibility of formalism, etc. After the introduction, chapter one deals with GĂ¶delâs critique and refutation of Carnapâs syntactical view of mathematics, which interprets mathematics purely in terms of linguistic rules of symbols, and thus void of content. Chapter two discusses GĂ¶delâs criticism of Russellâs constructivistic view towards logic, especially his no-class theory and the vicious circle principle. Chapter three turns attention to GĂ¶delâs role in the development of computability theory, using it as a case study for conceptual analysis
Chen, Long
Interpreting GĂ¶del : historical and philosophical perspectives. The main project of the thesis is to provide a comprehensive examination of GĂ¶delâs philosophy of mathematics and logic, in defence of his Platonism and the idea of mathematical intuition. The whole work is considered to be partly historical, explaining GĂ¶del's ideas and arguments in comparison with his contemporaries such as Carnap, Russell, Turing and Hilbert; partly mathematical, relying especially on his incompleteness theorem to refute certain philosophical positions; and partly philosophical, shedding light on debates in current discussions of philosophy of mathematics and logic such as the nature of paradoxes, the indispensability argument, the feasibility of formalism, etc. After the introduction, chapter one deals with GĂ¶delâs critique and refutation of Carnapâs syntactical view of mathematics, which interprets mathematics purely in terms of linguistic rules of symbols, and thus void of content. Chapter two discusses GĂ¶delâs criticism of Russellâs constructivistic view towards logic, especially his no-class theory and the vicious circle principle. Chapter three turns attention to GĂ¶delâs role in the development of computability theory, using it as a case study for conceptual analysis
interpreting historical philosophical perspective main project_provide comprehensive_examination philosophy_mathematics logic defence platonism idea mathematical intuition whole work consider partly historical explain idea argument comparison contemporary carnap russell partly mathematical rely especially theorem refute certain philosophical position partly philosophical shed_light debate current discussion philosophy_mathematics logic nature paradox argument feasibility formalism etc introduction one_deal critique refutation carnap syntactical view mathematics interprets mathematics purely term linguistic_rule symbol thus void content two_discus criticism russell view towards logic especially class theory circle principle turn_attention role development theory use case_study conceptual analysis