Bertrand Russell - On Induction

Principle of the Uniformity of Nature: The assumption that the laws of nature operating in the past will continue to hold in the future, meaning every event is an instance of a general law without exceptions.
Principle of Induction: The broader principle asserting that the future will resemble the past.
Fundamental Question: Whether any number of past cases where a law has been fulfilled provide evidence or proof that it will be fulfilled in the future.

The "Past Future" Fallacy: Justifying expectations by claiming that past futures always resembled past pasts is question-begging, as it assumes that "future futures" will behave like past futures.
Scope Beyond the Future: The problem of induction is not strictly forward-looking; it applies equally to unobserved past events, such as geological occurrences from millions of years ago or theories regarding the origin of the Solar System and cosmogonies.
Instinct vs. Epistemic Justification:
- Frequent repetition of a uniform succession creates an instinctive cause for expecting the same result on the next occasion in both humans and animals.
- Crude expectations of uniformity can be misleading, as illustrated when a chicken's neck is wrung by the person who previously fed it.
- Scientific and everyday expectations—including the laws of motion, the movement of the sun, and the nourishing value of bread—remain merely probable rather than certain.

Limits of Probability: While a greater number of repeated cases increases the probability that two co-occurring phenomena will be found together in the next instance, the probability can never reach absolute certainty.
Uncertainty of Formulated Laws: Even if a law with no exceptions exists, it cannot be known with certainty whether the law formulated by observation is that true law or one to which exceptions exist.
Foundation of Belief: The overarching belief in the "reign of law" across unexamined past and future cases rests entirely on the Principle of Induction itself.