00388 - Philosophy of Science

Course contents

Misunderstandings about Nothing   
From metaphysics to information 

Introduction to Logic  
1. Syllogismus 
2. Arguments, validity, contradictions  
3. Syntax and semantics of propositional logic 
4. Formalization in propositional logic 
5. Syntax of predicate logic
   
• What is metaphysics 
• The universal characteristic   
• Geometric vision and calculus ratiocinator  
• The irrational
• Kant and 'modern' mathematics   
• Kant and the problem of philosophy: Heidegger vs Cassirer        
• The problem of metaphysics: Heidegger vs Carnap
• Intuitive knowledge and symbolic knowledge: Leibniz vs Hilbert?
• From continuous to discrete
• The universal computer  
• What is information?

Readings/Bibliography

• 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)

Cassirer E. (1907), "Kant und die moderne Mathematik", Kantstudien (12: 1-49)  
Cassirer E. (1923), Philosophy of Symbolic Forms, Yale Univ. Press, New Haven 1957 (vol. I - Introduction; vol. III.2 - §§IV.1, IV.3)
• Cassirer-Heidegger Debate at Davos (1929). In: M. Heidegger, Kant and the Problem of Metaphysics, Indiana Univ. Press, Bloomington and Indianapolis 1997 

Hilbert D. (1930), "Logic and the Knowledge of Nature", From Kant to Hilbert: A source book in the foundations of mathematics (vol. II), edited by W. Ewald, OUP, Oxford (1996:: 1157-1165)
Hilbert D. (1931), "The Grounding of Elementary Number Theory", (Ewald 1996: 1149-1157)    

• Kant I. (1787), Critique of Pure Reason – "Preface"

Leibniz G. W. (1684),
Leibniz G. W. (1686),  

Davis M. (2000), The Universal Computer, W. W. Norton & Company, New York (Chaps. 1-5, 7)
Friedman M. (2000), A Parting of the Ways, Open Court, Chicago 
Stillwell J. (2006), Yearning for the Impossible, A K Peters Ltd, Natick Mass. (Chap. 1)

Further reading

Cassirer E. (1910), Substance and Function, Open Court, Chicago-London 1923 (chap. II) 
Dedekind R. (1872), "Continuity and Irrational Numbers", (Ewald 1996: 765-779)
Dedekind R. (1888), "Was sind und was sollen die Zahen?", (Ewald 1996: 787-833)  
Sieg W. (2006), " On mind & Turing's machines", Natural Computing 6 (187-205) 
Skidelsky E. (2008), Ernst Cassirer: the last philosopher of culture, Princeton Univ. Press, Princeton
Stillwell J. (2013),  The Real Numbers, Springer
Wang H. (1974), From Mehematics to Philosophy, Routledge & Kegan Paul, London

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

Office hours

See the website of Rossella Lupacchini