Charles Sanders Peirce (1839-1914), the founder of pragmatism, spent 4 decades on the investigation of induction and deduction, models of thinking well established in logic, and supplemented them by an inferential procedure which he called abduction. He distinguished 3 kinds of inference: deduction, induction, and abduction. The abductive form was first called hypothetical, then abductive, than retroductive, and only at a later stage abductive consistently. In a semiotic theory of cognition abduction plays a decisive role because only by abduction can we add to our knowledge of the world. Peirce introduces the new kind of inference as "reasoning a posteriori," thus setting it apart from deduction a priori, and he replaces the three classical terms, major premise, minor premise, and conclusion, by his own terms: rule, case, and result. In this way, the sequential order in which the premises and the conclusion are known may be taken into account. Thus each of the 3 statements of the classical syllogism could in principle take any of the 3 positions, whether they are rule, case, or conclusion. The minor premise (the second premise of the classical syllogism), for example, may become the inferred conclusion, as is the case in abduction. The major premise which contains the predicate may naturally also be formulated as a rule (law): All humans are mortal. If X is human, X is mortal. Here it is the most famous of all syllogisms, the Modus Barbara, the deductive model of inference of the figure, the best-known instance of which has to do with the immortal Socrates

Major Premise (rule): All humans are mortal..................(MaP)

Minor Premise (case): Socrates is human......................(SaM)

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Conclusion (result): Socrates is mortal......................(SaP)

The categorical syllogism relates 3 concepts, S (subject), P (predicate), and M (middle), in 3 statements (major premise, minor premise, conclusion) in order to examine their validity. In Peirce's view, the goal of all inferential thinking is to discover something we do not know and thus enlarge our knowledge by considering something we do know.

Boxes with continuous lines contain that which is presupposed as given/true; boxes with dotted lines hypotheses that are inferred

In logic as well as in the philosophy of science a valid deduction is considered to be truth-conserving; if the premises are true, the conclusion must be true, too. The price to be paid for this necessary truth, however, is that the information content of the conclusion is already implicitly contained in the premises. The "mortality of Socrates," the conclusion supplied by Modus Barbara, is nothing new, it was completely contained in the premises. Deduction, therefore, is not synthetic (content-increasing), does not lead to new knowledge. It is analytically true (redundant) and has, therefore, been considered to be merely an "explanatory statement" in the more recent discussion. Deductive thinking proceeds from the general (the rule), through the subsumption of the singular case under the rule, to the assertion of the particular (the result), as the arrows in the figure indicate. In the case of induction the premises (the initial basis) are observational statements, and an inferred conclusion (e.g., a hypothetical rule: All M are P) is considered to be content-increasing, but not truth-conserving because the inference is only a hypothesis that cannot be proved with ultimate certainty. Induction -- the converse of deduction -- progresses from the particular to the general. Therefore the arrows point "from the bottom to the top."

For a long time, Peirce classified induction as a synthetic inference until he had an insight of the greatest relevance to the philosophy of science, namely, that a valid induction already presupposes as a hypothesis the law or the general rule (M is P) which it is supposed to infer, in the first place. For Peirce inductive inferences, must satisfy 2 conditions in order to be valid: the sample must be a random selection from the underlying totality, and the specific characteristic that is to be examined by means of the sample must have been defined before the sample is drawn. The significance of this requirement, called "pre-designation" by Peirce, for the definition of inductive inference is that the predicate P must already be known before the sample (S', S'', S''') is selected from the totality (M). If however, the property to be examined must be defined before the sample is selected, this is only possible on the basis of a conjecture that the property exists in the corresponding totality before the inductive inference is made. How else could the property be known in advance of sample selection? Valid induction, therefore, already presupposes as a hypothesis the conclusion that is to be inferred. More precisely, inductive reasoning is based on a given hypothesis (M is P) and then, by means of samples (S', s"), seeks to establish the relative frequency (p) of the property (P) in the totality (M) with regard to that hypothesis... The condition that the property to be examined must be pre-designated in advance of sample selection makes Peirce conclude explicitly that induction cannot lead to new discoveries. This could mean that the scientist is bound to know already (implicitly) what he does not, in fact, know that he knows.

As it is logically excluded that there can be knowledge before knowing, the cognizing subjects must invent hypotheses on their own before any experience or experimentation takes place. Peirce's logical analysis shows, on the one hand, that induction does not belong among the synthetic forms of inference that, in one way or another, may enlarge our knowledge of the world. On the other hand, any kind of induction is dependent upon hypotheses which must have been constructed beforehand by cognizing subjects. And this process of construction is abductive, as far as its logical form is concerned. If, however, neither induction nor deduction enlarge our knowledge of the world, then abduction as the only knowledge-generating mechanism needs to become the central focus of discussion.