Deduction

Deduction cannot be considered a pure Class of Sign but an analytical method that makes a special use of other signs, mainly Abduction and Induction (cf. CP 5.581). The role of Deduction is to build a Metaphor in the form of a Diagram that represents hypothetically the relations among the general predicates involved in a determined state of information. In such Diagram, Metonymies are applied to indicate the Subjects (Objects) of the diagrammatic relations.  Once this is done, it is possible to observe, by abductive and inductive procedures, relations that had not been noticed before – although they were already apparent in the Diagram. To this Deduction, result of a simple attention paid by the interpreter, Peirce gives the name of Corollarial. Relations that are not “easily at sight” can still be revealed by the introduction (hypothetically) of some new relations on the original Diagram. The result of this manipulation is a newly and purely abductive hypothesis, which now must be tested by Induction to be proven correct. Peirce calls Theorematic (EP 2:502) this second and more complex type of Deduction. In the words of Peirce: “Deduction is really a matter of perception and of experimentation, just as induction and hypothetic inference are; only, the perception and experimentation are concerned with imaginary objects instead of with real ones. The operations of perception and of experimentation are subject to error, and therefore it is only in a Pickwickian sense that mathematical reasoning can be said to be perfectly certain. It is so only under the condition that no error creeps into it; yet, after all, it is susceptible of attaining a practical certainty. So, for that matter, is scientific reasoning; but not so readily. Again, mathematics brings to light results as truly occult and unexpected as those of chemistry; only they are results dependent upon the action of reason in the depths of our own consciousness, instead of being dependent, like those of chemistry, upon the action of Cosmical Reason, or Law. Or, stating the matter under another aspect, analytical reasoning depends upon associations of similarity, synthetical reasoning upon associations of contiguity”  (CP 6.595).