inferences

An inference is a conclusion drawn from evidence and reasoning rather than direct observation. In logic, an inference is the process of deriving a conclusion from premises using rules of valid argument. In everyday use, inferences fill the gaps between what is observed and what is assumed.

There are several types of inference. Deductive inferences move from general premises to specific conclusions and are truth-preserving: if the premises are true, the conclusion must be true. Inductive inferences generalize from specific observations to broader generalizations and are probabilistic: true premises make the conclusion likely but not guaranteed. Abductive inferences seek the best explanation for a set of observations, often under uncertainty and with incomplete information.

Examples help distinguish them. A deductive inference: all mammals have lungs; whales are mammals; therefore whales have lungs. An inductive inference: the sun has risen every day so far; therefore it will rise tomorrow. An abductive inference: seeing wet streets and cloudy skies, you infer that it probably rained recently.

Statistical inference concerns drawing conclusions about populations from samples, quantifying uncertainty. Bayesian inference updates prior beliefs with new data, while frequentist methods rely on long-run frequencies. In machine learning, inferences are predictions or classifications made about unseen data based on trained models.

In practice, inferences are central to science, law, and everyday reasoning. They depend on credible evidence and sound reasoning but are vulnerable to bias and error, such as confusing correlation with causation or ignoring base rates. Clear articulation of premises and uncertainty helps distinguish strong inferences from weak ones.