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the mental activity that makes a connection between disparate thoughts, linking them in a set of premises and conclusions. It is by inference that the norms and categories of such connections, which are inherently present in the social or individual consciousness, are expressed on the level of “inner speech.” Indeed, these norms and categories themselves—in any given instance—constitute the psychological basis of inference; when they coincide with the rules and laws of logic, the inference is judged by its result to be equivalent to logical deduction, although generally speaking there is a qualitative difference between logical deduction and inference.
Logical deduction, as distinct from inference, rests on “external means”; it operates through the verbal (symbolic) recording of thoughts or through their formalization—that is, the codification of thoughts and representation of their connections by one or another formal language or system, such as calculus—with the goal of reducing to a minimum the subconscious, enthymematic, and elliptical elements of deduction and translating abstract or “convoluted” thought processes into the language of “images.” Furthermore, the “legitimacy” of inference need not necessarily be determined by logical norms. For example, an incomplete induction is precisely an inference and not a logical deduction, inasmuch as the connection between premises and conclusions in induction has a factual and psychological basis (as expressed in the well-known norms of generalization) but lacks a logical basis—that is, lacks those formal rules by which thinking proceeds from the particular to the general.
A further distinction is drawn between inference and reasoning: the latter is always a consciously willed mental activity, while an inference, in principle at least, can be both involuntary and an act of the subconscious.
M. M. NOVOSELOV