INFERENCE
1. A primitive concept
The concept of inference is a primitive concept, that is, it can be defined only on the basis of concepts of an equal complexity, or by an example of inference taken from a special field, logic. For example, inference is “the derivation of a proposition (the conclusion) from a set of other propositions (the premises)” (Brody 1967, pp. 66-67). Inference is used to establish a new truth on the basis of truths already known; in an extended version: to base the acceptance of a new proposition on the prior acceptance of other propositions.
Strict inference and immediate inference — There are two types of inference, inference strictly speaking and immediate inference.
— In immediate inference, the conclusion is derived from a single proposition, see Proposition, §4.
— Strict, or direct inference is based on two propositions, its premises, see Syllogism
2. Deductive and inductive inference, analogy, conduction
Traditional logic distinguishes between deductive inference (deduction) and inductive inference (induction).
In Aristotle’s view of rhetoric, the enthymeme is the argumentative counterpart of deductive inference and the example is the counterpart of inductive inference, S. Enthymeme; Example.
Analogical inference is accepted only as a heuristic tool, it has no evidential value, S. Analogy.
Deduction and induction are traditionally opposed on two grounds.
1) The particular / general orientation. Deduction and induction are seen as two complementary processes, with induction going from the general to the most general:
« This Syldavian is red-haired, so Syldavians are red-haired. »
Whereas, the deduction would go from the most general to the least general:
« Men are mortal, so Socrates is mortal. »
But syllogistic deduction can be generalizing:
« All horses are mammals, all mammals are vertebrates, so all horses are vertebrates. »
2) The degree of certainty. The valid conclusion of a syllogistic deduction from true premises is apodictic, i.e., necessarily true, while induction concludes only in a probable way.
Analogical reasoning is accepted only as a heuristic tool, it has no probative value, see analogy.
Conduction is considered by Wellman (1971) to be a special kind of inference on a par with deduction and induction.
3. Direct inference and analytic statements
An analytic proposition is a proposition that is true “by definition”, i.e., by virtue of its meaning. Good definitions are analytically true “a single person is an adult unmarried person”. Whereas direct logical inference is based on quantifiers or “empty words”, immediate analytical inference operates upon the meaning of the “full words” of the basic proposition:
He is single, so he is not married.
In arguments such as, “this is our duty, so we must do it”, the proposition introduced by so, “we must do it” is contained in the argument “it is our duty”; by definition a duty is something people must do. The conclusion, if it is a conclusion at all, is direct.
More generally, an analytic inference is one in which the conclusion is somehow embedded in the argument; the conclusion merely develops the semantic content of the argument. If I’m told that my colleague recently “quit smoking” I can analytically infer that he or she smoked in the past, S. Presupposition.
Consider the example:
You talk about the birth of the gods; this implies that at one time the gods did not exist. This is just as impious as talking about the death of gods, for which your colleague was recently sentenced to death.
Birth is defined as the “beginning of life”. The conclusion does not follow directly from the definition of the word; an additional step is required to make explicit the meaning of “beginning”, which is chosen to imply equivalence between the time after death with the time before birth. For this reason, the conclusion does not seem as obvious as in the previous cases.
3. Pragmatic inference
The concept of pragmatic inference is used to explain the interpretation of utterances in discourse. In the dialog:
S1 — Who did you meet at the party?
S2 — Paul, Peter and Mary
From S2’s answer, S1 will infer that S2 did not meet any no other person they both know. This inference is based on a transitional law, the maxim of quantity, or completeness: “When you are asked a question, give the best information you have, both quantitatively and qualitatively”. If S2 met Bruno at the party, a person known to S1, then S2 can be said to have lied to S1 by omission, S. Cooperation.