00388 - Philosophy of Science

Course contents

Logic and the Knowledge of Nature  
From Kant to Hilbert  
 
• Davos 1929  
• Kant and the problem of philosophy: Heidegger vs Cassirer    
• Existence, truth, proof 
• Logic and ontology 
• Being and 'nothing': Carnap vs Heidegger
• Logical empiricism and its 'dogmas'
• Between logic and experience: Hilbert's vision of mathematics
• Axiomatic method and 'ideal elements' 
• Symbolic forms 
• Kant and the new mathematics: Cassirer vs Hilbert?
• Königsberg 1930

Readings/Bibliography

• Friedman M. (2000), A Parting of the Ways, Open Court, Chicago  
 
Cassirer-Heidegger Debate at Davos (1929). In: M. Heidegger, Kant and the Problem of Metaphysics, Indiana Univ. Press, Bloomington and Indianapolis 1997
Heidegger M. (1929), "What is Metaphysics?". In: D. Krell (ed.), Basic Writings, Harper & Row, New York 1977            
 

• Carnap R. (1932), " The Elimination of Metaphysics Through Logical Analysis of Language", Erkenntnis (60-81)
• Carnap R. (1950), "Empiricism, Semantics, and Ontology", Revue Internationale de Philosophie (4 : 20–40)
• Cassirer E. (1907), "Kant und die moderne Mathematik", Kantstudien (12: 1-49)
  
• Cassirer E. (1910), Substance and Function, Open Court, Chicago 1923 (Chap. 3) 
  
• Cassirer e. (1921), Einstein's Theory of Relativity, Open Court, Chicago 1923 (Chap. 7) 
• Cassirer E. (1923-29), The Philosophy of Symbolic Forms – vol. III.2, Yale Univ. Press, New Haven 1957 (§I.1, chap. IV, §V.1, §V.3) 
  
• Dedekind R. (1872), "Continuity and Irrational Numbers", (Ewald (1996: 765-779)
• Ewald W. (eds) (1996), From Kant to Hilbert: A source book in the foundations of mathematics – vol. II, OUP, Oxford (765-779, 1096-1124, 1149-1165)
  
• Hilbert D. (1900), "Mathematical Problems", (Ewald 1996: 1096-1105)
• Hilbert D. (1918), "Axiomatic Thought", (Ewald 1996: 1105-1115)
  
• Hilbert D. (1922), "The New Grounding of Mathematics, (Ewald 1996: 1117-1124)
• Hilbert D. (1926), "On the Infinite", in J. van Heijenoort (ed.), From Frege to Gödel. Harvard Univ. Press, Cambridge Mass. (1967: 367-384)
  
• Hilbert D. (1930), "Logic and the Knowledge of Nature", (Ewald 1996: 1157-1165)   
• Hilbert D. (1931), "The Grounding of Elementary Number Theory", (Ewald 1996: 1149-1157)   

Quine W. V. (1948), " On What There Is", in From a Logical Point of View, Harvard Univ. Press, Cambridge US 1961   
Quine W. V. (1951), "Two Dogmas of Empiricism", in From a Logical Point of View, Harvard Univ. Press, Cambridge US 1961 [to be downloaded from teaching material]   
Quine W. V. (1950), Methods of Logic, Holt, Rinehart and Winston, New York (§§ 1–10; 12–17, 22, 33–37)  
Stillwell J. (2010), "Logic", in Road to Infinity, A.K. Peters Ltd, Natick Mass. 2010 (Chap. 4) [to be downloaded from teaching material]  

 
Further reading

Bernays P. (1922), "Hilbert's Significance for the Philosophy of Mathematics", in P. Mancosu (ed.), From Brouwer to Hilbert, Oxford Univ. Press, Oxford 1998
Carnap R. (1928), The Logical Structure of the World, Univ. of California Press, Berkeley 1967  
Coffa A. (1991), The Semantic Tradition from Kant to Carnap: to the Vienna Station, Cambridge Univ. Press, Cambridge 
Dedekind R. (1888), "Was sind und was sollen die Zahen?", (Ewald 1996: 787-833) 
Heis J. (2011), " Ernst Cassirer's Neo-Kantian Philosophy of Geometry", British Journal for the History of Philosophy, 19(4) 
Stillwell J. (2013),  Road to Infinity, A.K. Peters Ltd, Natick Mass.   
Weyl H. (1949), Philosophy of Mathematics and Natural Sciences, Princeton U.P., Princeton

[Kant I. (1787), Critique of Pure Reason – "Transcendental Analytic"]

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