"When it happens that a new belief comes to one as consciously generated from a previous belief, - an event which can only occur in consequence of some third belief (stored away in some dark closet of the mind, as a habit of thought) being in a suitable relation to that second one, - I call the event and inference, or a reasoning." ('An Essay toward Improving Our Reasoning in Security and in Uberty', EP 2:463, 1913)

"Reasoning is the process by which we attain a belief which we regard as the result of previous knowledge. [---]
     Again, a given belief may be regarded as the effect of another given belief, without our seeming to see clearly why or how. Such a process is usually called an inference; but it ought not to be called a rational inference, or reasoning. A blind force constrains us. [---]
     The word illation signifies a process of inference. Reasoning, in general, is sometimes called ratiocination. Argumentation is the expression of a reasoning." ('Short Logic', EP 2: 11-12, 1895)

"Inference is any act of deliberate assent, in any degree, however slight, which a man accords to a proposition because he thinks that assent warranted by his already accorded assent to another proposition or propositions, called the premisses." (' Hume's Argument against Miracles, and the Idea of Natural Law (Hume)', MS 873: (Variant) 3, n.d.)