generalisations

Generalisation, or generalisation in British spelling, is the process of extending observations or known facts from specific cases to broader statements, principles, or theories. It involves moving from particular instances to more universal claims, and is a common mode of reasoning in everyday thought as well as in scientific inquiry.

In science and philosophy, generalisation helps researchers form hypotheses and laws that apply across a range of phenomena. In mathematics, generalisation refers to extending concepts to more general settings or structures, such as moving from real numbers to complex numbers, or from arithmetic to abstract algebra. In linguistics and cognitive science, generalisation describes how learned rules or patterns apply to new inputs or situations beyond those originally encountered.

In statistics and social sciences, generalisability (external validity) concerns how well findings from a study apply to a broader population or different contexts. In machine learning and artificial intelligence, generalisation denotes a model’s ability to perform well on unseen data, not only on the training set.

Common problems include hasty generalisation, where broad conclusions are drawn from too few or unrepresentative examples, and overgeneralisation, where rules become too widely applied. Such errors are mitigated through additional data, critical testing, cross-validation, and careful justification of assumptions.

Examples illustrate the idea and its limits. From observing many white swans, one might generalise that all swans are white, yet the existence of black swans falsifies this generalisation. Generalisation remains central to science, mathematics, and empirical reasoning, balancing the search for broad explanatory power with the need for evidence and falsifiability.