While there is always a proposition inferred in inference, there is generally, if not always a second proposition (or set of propositions) involved in inferring. Inference seems to be essentially a three-place relation between the individual doing the inferring and two propositions (or a proposition and set thereof): a proposition inferred (the conclusion); and the proposition or propositions (the premises) from which the conclusion is inferred. Logicians here distinguish inductive from deductive inference. Deductive inferences establish or purport to establish the certainty of the conclusion given the premises. Inductive inferences establish (or purport to establish) the probability of the conclusion given the premises. If the truth of the conclusion really is certain given the truth of the premises, the premises are said to "imply" or "entail" the conclusion, and the corresponding inference (the actual drawing of the conclusion) is deemed "deductively valid". If the conclusion really is probable on the evidence cited (i.e., given the truth of the premises stating it) the corresponding inference is said to be "inductively strong".
The intentionality of inference, as pretheoretically understood,
poses a special bootstrapping challenge for so called "inferential role
semantics". Inferential role semantics hold that the meaning or semantic
content of a term (or concept) is determined by its role in the various
inferences it enters into. But if inferential processes are themselves
intentional -- as they are on our everyday understanding -- whence do these
inferences derive their content? More generally, any sort of CONCEPTUAL
ROLE SEMANTICS -- inferential or otherwise -- faces a similar challenge.
Conceptual roles, pretheoretically understood, being roles that CONCEPTS
enter into; and concepts, pretheoretically understood, being already
imbued with semantic content; this content already has to exist
before there can even be conceptual roles as pretheoretically understood.
Consequently, conceptual role theories must give "concept" and "conceptual
role" technical senses that do not already presuppose SEMANTIC
content: their theoretical characterization (under the conceptual role
theory) must be purely SYNTACTIC.
See also NORMATIVE, RATIONALITY