déduction

Déduction refers to the process of deriving conclusions from premises according to accepted rules of inference. In general use, it denotes moving from general statements to specific conclusions and, in accounting, to amounts subtracted from income for tax purposes. The term is Latin in origin and is widely used in many disciplines under the same basic idea: to obtain a result by applying logical steps to given data.

In logic and philosophy, deduction is the form of reasoning where the conclusion necessarily follows from the premises if the reasoning is valid. For example, all humans are mortal; Socrates is human; therefore Socrates is mortal. Deductive reasoning aims for necessity, assuming true premises and correct inference.

In mathematics and formal sciences, deduction denotes deriving theorems and results from axioms via formal rules. Proofs are sequences of deductions that establish propositions beyond reasonable doubt within a given system. The discipline emphasizes validity of inference over empirical confirmation.

In finance and law, déduction (tax deduction) refers to amounts or expenses subtracted from gross income to reduce taxable income, thereby lowering tax liability. Common deductions include charitable donations, business expenses, and certain personal allowances. Deductions differ from tax credits, which reduce tax liability directly, and from exemptions.

Overall, deduction is a foundational concept across disciplines, linked to the legitimacy of conclusions reached through specified rules of inference or subtraction from a larger total.