Chance, determinism and the classical theory of probability

Area of Science:

• Philosophy of Science
• History of Mathematics
• Probability Theory

Background:

• The metaphysical antinomy between chance and determinism is a long-standing philosophical problem.
• Classical probability theorists have been accused of equivocating between subjective (epistemic) and objective (statistical) interpretations of probability.
• This interpretation, popularized by Hacking, suggests a duality in early probability theory.

Purpose of the Study:

• To re-evaluate the historical context of the chance-determinism antinomy within early mathematical probability.
• To challenge the prevailing view that the core tension in classical probability lies solely in the subjective-objective interpretation duality.
• To propose a deeper understanding of the paradox rooted in the commensurability of causal and probabilistic reasoning.

Main Methods:

• Historical analysis of early developments in the mathematical theory of probability.
• Critical examination of existing scholarship on classical probability theorists.
• Philosophical interpretation of the tension between chance and determinism in this historical context.

Main Results:

• The tension in classical probability theory is not adequately explained by the subjective-objective interpretation dichotomy.
• Classical probabilists exhibited a more profound ambivalence regarding the compatibility of causal and probabilistic reasoning.
• The paradox of chance and determinism is better understood through this deeper ambivalence.

Conclusions:

• The historical development of probability theory reveals a complex relationship between chance, determinism, and reasoning.
• A nuanced understanding of classical probabilists' views on causal and probabilistic reasoning is crucial.
• This reinterpretation offers a deeper insight into the metaphysical antinomy of chance and determinism.