What is the difference between inference and deduction?

This question contains my question, but tries to accomplish too much at once; I would like a clear answer to the distinction between inference and deduction. What is the difference between coming to a conclusion via inference and coming to a conclusion via deduction? The way I understand it, we deduce conclusions by using inferences. Inferences are statements in the form "if X then Y" and when it turns out previous statements which we assume or have otherwise proven to be true match the "X" part, we call it deduction. Since we used that inference, we say that we obtained our conclusion via inference. (This seems to suggest that while they are different terms, whenever you obtain a conclusion via deduction, you also obtain that conclusion via inference, and vice versa.) However, other sources claim that deduction must come from originally observed or assumed facts, and that after you deduce one conclusion, you can no longer use that conclusion to "deduce" more; it then becomes "inference". Is there any widely agreed upon difference between "deduction" and "inference"? If so, what is it? If not, in what ways might the terms differ?

See Inference : "Inferences are steps in reasoning, moving from premises to logical consequences. Charles Sanders Peirce divided inference into three kinds: deduction, induction, and abduction. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular premises to a universal conclusion. Abduction is inference to the best explanation."

Deduction : "Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion."

4 Answers 4

The term 'deduction' is often used rather loosely in ordinary English. Conan Doyle infamously used it to describe Sherlock Holmes' reasoning, whereas today we would say that what Holmes did was abductive reasoning, which is generally taken to mean reasoning to the best explanation. In logic, we only use 'deduction' to refer to reasoning where there is no possibility of the conclusion being false if the premises are true. It is frequently used, even more narrowly, only in cases where the reasoning relies on formal rules of implication, rather than semantic or model theoretic considerations.

'Inference' is a more general term and refers to any reasoning by which a conclusion is reached from premises. As such, it encompasses both deductive and non-deductive kinds of reasoning. If I see a friend who has been absent for two weeks and notice he has a suntan, I might well infer that he has just returned from holiday. This is not a certain inference, since there are other possible explanations, but it is the most likely. This would be an example of abductive reasoning. If I notice that every morning the sun rises, I might infer that it is likely to do so again tomorrow. Again, this is not certain, but it might be characterised as a plausible inductive inference.

To make matters slightly more confusing, 'inference' is sometimes used for the individual steps within an argument, and logicians traditionally use the term 'rules of inference' for the formal rules, such as modus ponens, that characterise deductive logic. Gilbert Harman, among others, has long argued that this usage is misleading and we should be careful to distinguish between logic and reasoning. He advocates using the term 'rules of implication' for these formal rules.

In any case, deduction and inference have nothing to do with whether your premises are direct observations, assumptions, reported facts, or were themselves inferred from other things. It does not matter where your premises come from.