deductions

Deductions are conclusions that logically follow from premises. The term spans disciplines such as logic, mathematics, philosophy, law, and everyday reasoning. In logic, a deduction aims to derive a conclusion that must be true if the premises are true. This contrasts with induction, which generalizes from cases, and with abductive reasoning, which seeks the best explanation for observed data.

In deductive reasoning, arguments are judged by validity and soundness. A valid argument has a structure such that if all premises are true, the conclusion must be true; a sound argument also has true premises. Common forms include modus ponens (if P, then Q; P; therefore Q) and syllogisms such as All A are B; All B are C; therefore All A are C.

In mathematics and formal logic, deductions are demonstrated in proofs where each step follows from axioms or previously proven theorems. They aim for certainty, given the chosen axioms and rules. The strength of a deduction rests on the reliability of its premises and the rigor of its inferential rules.

In law and finance, deductions have related but distinct meanings. Tax deductions reduce gross income or taxable income, lowering the amount of tax owed; they are different from tax credits. Examples include charitable donations, mortgage interest, and business expenses. In payroll, deductions are amounts withheld from earnings for taxes, retirement plans, or benefits. The rules governing these deductions vary by jurisdiction and purpose.

In everyday use, deduction refers to reasoning from evidence to a probable conclusion. People apply it to solve problems or interpret situations, but it requires careful attention to evidence and awareness of potential biases or fallacies.