# Inference

The concept of inference is a primitive, that is, it can be defined on the basis of concepts of an equal complexity, or by an example of inference taken from a special field, logic: an inference is “the derivation of a proposition (conclusion) from a set of other propositions (the premises)” (Brody 1967, p. 66-67). Inference is used to establish a new truth on the basis of truths already known or accepted.

There are two kinds of inference, inference strictly speaking and immediate inference.

— In immediate inference, the conclusion is derived from a single proposition, S. Proposition.
— Strictly speaking, inference is based upon several propositions, its premises. Traditional logic distinguishes between deductive inference (deduction) and inductive inference (induction). In Aristotle’s vision of rhetoric, the enthymeme is the argumentative counterpart of deductive inference and the example is the counterpart of inductive inference, S. Enthymeme; Example.

# 1. Analogy, deduction, induction and conduction

Analogical inference is accepted only as a heuristic instrument, it has no probative value, S. Analogy.

Deduction and induction are traditionally opposed on two bases.
— The particular / general orientation. Deduction and induction are considered to be two complementary processes, induction going from the general to the most general:

This Syldavian is red-haired, so all 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, therefore all horses are vertebrates.

— The degree of certainty. The valid conclusion of a syllogistic deduction from true premises is apodictic, i.e., necessarily true, while induction only concludes in a probable way.

Conduction is considered by Wellman (1971) as a specific kind of inference on a par with deduction and induction.

# 2. Immediate inference and analytic statements

An analytic statement is a statement deemed true “by definition”, i.e., in virtue of its meaning. Good definitions are analytically true “a single person is an adult unmarried person”. While logical immediate inference proceeds from quantifiers or “empty words”, immediate analytical inference operates upon the meaning of the “full words” of the basic utterance:

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 a conclusion at all, is immediate.
More broadly, an analytic inference is an inference where the conclusion is some way embedded in the argument; the conclusion only develops the semantic contents of the argument. If I’m advised that my colleague recently “quitted 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 directly follow from the definition of the word; an additional step is needed to make explicit the meaning of “beginning”, chosen so as to imply equivalence between the times after death with the times before birth. For this reason, the conclusion does not seem so obvious as in the preceding cases.

# 3. Pragmatic inference

The concept of pragmatic inference is used to account for the interpretation of utterances in discourse. In the dialogue:

S1    — Whom did you meet at the party?
S2    — Paul, Peter and Mary

From S2’s answer, S1 will infer that S2 encountered no other person they both know. This inference is based on a transition law, the maxim of quantity, or completeness: “when you are asked something, give the best information you have, both quantitatively and qualitatively”. If S2 met Bruno at the party, a person well-known to S1, then S2 can be said to have lied to S1 by omission, S. Cooperation.