Philosophical aspects of chaos : definitions in mathematics, unpredictability, and the observational equivalence of deterministic and indeterministic descriptions
This dissertation is about some of the most important philosophical aspects of chaos research, a famous recent mathematical area of research about deterministic yet unpredictable and irregular, or even random behaviour. It consists of three parts. First, as a basis for the dissertation, I examine notions of unpredictability in ergodic theory, and I ask what they tell us about the justification and formulation of mathematical definitions. The main account of the actual practice of justifying mathematical definitions is Lakatos's account on proof-generated definitions. By investigating notions of unpredictability in ergodic theory, I present two previously unidentified but common ways of justifying definitions. Furthermore, I criticise Lakatos's account as being limited: it does not acknowledge the interrelationships between the different kinds of justification, and it ignores the fact that various kinds of justification - not only proof-generation - are important. Second, unpredictability is a central theme in chaos research, and it is widely claimed that chaotic systems exhibit a kind of unpredictability which is specific to chaos. However, I argue that the existing answers to the question ~What is the unpredictability
Werndl, Charlotte
Mathematical definitions ; Lakatos ; Unpredictability ; Chaos ; Probability ; Determinism ; Indeterminism ; Statistical mechanics ; Ergodic theory ; Stochastic processes
Philosophical aspects of chaos : definitions in mathematics, unpredictability, and the observational equivalence of deterministic and indeterministic descriptions. This dissertation is about some of the most important philosophical aspects of chaos research, a famous recent mathematical area of research about deterministic yet unpredictable and irregular, or even random behaviour. It consists of three parts. First, as a basis for the dissertation, I examine notions of unpredictability in ergodic theory, and I ask what they tell us about the justification and formulation of mathematical definitions. The main account of the actual practice of justifying mathematical definitions is Lakatos's account on proof-generated definitions. By investigating notions of unpredictability in ergodic theory, I present two previously unidentified but common ways of justifying definitions. Furthermore, I criticise Lakatos's account as being limited: it does not acknowledge the interrelationships between the different kinds of justification, and it ignores the fact that various kinds of justification - not only proof-generation - are important. Second, unpredictability is a central theme in chaos research, and it is widely claimed that chaotic systems exhibit a kind of unpredictability which is specific to chaos. However, I argue that the existing answers to the question ~What is the unpredictability
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