To deduce is to reach a conclusion by reasoning from evidence — Holmes deduces the answer. To deduct is to subtract an amount — deduct tax from a salary. Both come from the same Latin root meaning to lead away, and English split them for reasoning and arithmetic.
The core difference
One reasons; the other subtracts.
- deduce — conclude by reasoning: deduce the cause from the evidence.
- deduct — subtract: deduct expenses.
The nouns are the trap
Both give deduction, which does double duty: a logical deduction is a conclusion, and a tax deduction is a subtraction. Context always separates them, but it is why the verbs get confused — the noun offers no clue.
Deduction versus induction
In logic, deduction reasons from general premises to a specific conclusion; induction generalises from specific observations. Holmes, famously, mostly does the second while calling it the first.