What is a proof for? What is the characteristic use of a proof as a computation, as opposed to its use as an experiment? What is the relationship between mathematical procedures and natural processes? The essays collected in this volume address such questions from different points of view and will interest students and scholars in several branches of scientific knowledge. Some essays deal with the logical skeleton of deduction, others examine the interplay between natural systems and models of computation, yet others use significant results from the natural sciences to illustrate the character of procedures in applied mathematics. Focusing on relevant conceptual and logical issues underlying the overall quest for proving, the volume seeks to cast light on what the effectiveness of proof rests on.
Author(s): Rossella Lupacchini, Giovanna Corsi
Edition: 1
Publisher: Springer
Year: 2008
Language: English
Pages: 285
Contents......Page 8
Why Proof? What is a Proof?......Page 12
On Formal Proofs......Page 39
Toy Models in Physics and the Reasonable Effectiveness of Mathematics......Page 59
Experimental Methods in Proofs......Page 75
Proofs Verifying Programs and Programs Producing Proofs: A Conceptual Analysis......Page 90
The Logic of the Weak Excluded Middle: A Case Study of Proof-Search......Page 104
Automated Search for Gödel's Proofs......Page 126
Proofs as Efficient Programs......Page 150
Quantum Combing......Page 167
Proofs instead of Meaning Explanations: Understanding Classical vs Intuitionistic Mathematics from the Outside......Page 183
Proof as a Path of Light......Page 203
Computability and Incomputability of Differential Equations......Page 230
Phenomenology of Incompleteness: From Formal Deductions to Mathematics and Physics......Page 250
B......Page 279
F......Page 280
J......Page 281
M......Page 282
S......Page 283
Z......Page 284
