Other forms: deduced, deduces, deducing
To deduce is to work out an answer by reasoning from what you already know. From the mud on his boots she deduced he had come across the field.
In logic it has a strict meaning: deduction reasons from a general rule to a particular case, and the conclusion is guaranteed if the premises are true. Induction goes the other way and guarantees nothing. Ordinary speech blurs the two and uses deduce for any reasoning from clues, which is what Sherlock Holmes is usually doing when he says deduce. Note that deduce and deduct are different verbs from the same Latin root: you deduce a conclusion and deduct a sum.
1verbdeduceTo reach a conclusion by reasoning from what is known.
“From the dust on the sill she deduced nobody had opened it in months.”
2verblogicIn logic, to derive a conclusion that must follow from the premises.
“The theorem can be deduced from the first two axioms.”
deduce is a way of reasoning.
Also accepted in games: infer
Latin deducere meant to lead down or lead away — de- plus ducere, to lead, the same verb behind conduct, produce and duke. Deducing is being led from one thing to another, which is exactly what an argument does to you.
Proto-Indo-European
*dewk- — to lead; to draw, pull
Latin
dēdūcere
Middle English
deducen — to demonstrate, prove, show; to argue, infer; to bring, lead; to turn (something) to a use; to deduct
English, today
deduce
Built from
From Late Middle English deducen (“to demonstrate, prove, show; to argue, infer; to bring, lead; to turn (something) to a use; to deduct”), borrowed from Latin dēdūcere, the present active infinitive of dēdūcō (“to lead or bring out or away; to accompany, conduct, escort; (figuratively) to derive, discover, deduce”); from dē- + dūcere (the present active infinitive of dūcō (“to conduct, guide, lead; to draw, pull; to consider, regard, think”), ultimately from Proto-Indo-European dewk- (“to lead; to draw, pull”)).
Etymology from Wiktionary, CC BY-SA