Excursus 009 – On Induction, Deduction, and the Syllogistic Structure of Aristotle

Hossein Jorjani

First publication: 2026 – 06 – 30

In Aristotle’s theory of demonstrative science (epistēmē apodeiktikē), knowledge arises through necessary reasoning from first principles (archai). These principles are grasped intuitively by nous and form the foundation from which other propositions follow through deduction. The following outline summarizes the Aristotelian system of deductive reasoning:

• 1. There exists a finite number of basic propositions (archai or principia) that are posited without proof.
• 2. A proposition that is not basic may be asserted only if it has been derived from the basic propositions by logical inference.
• 3. The inferences proceed by means of the syllogistic structure—a triadic pattern of major premise, minor premise, and conclusion. Example:
•     3a. All B are C.
•     3b. All A are B.
•     3c. Therefore, all A are C.
• 4. The basic propositions are true and necessary.
• 5. The basic propositions possess absolute certainty or self-evidence, being apprehended directly by the intellect (nous).
• 6. The basic propositions of a demonstrative science are indemonstrable; no further reasons can be given for them.
• 7. These propositions are the objects of knowledge, and further truths become known as they are inferred from them through the syllogistic structure. The syllogistic structure therefore provides the vehicle of deduction, not its source: it conveys truth from principles already known but does not generate truth by its own form. This was Aristotle’s view and remained Bacon’s—both denied that formal logic alone could create knowledge.

In this framework, induction (epagōgē) supplies the first principles from experience, while deduction (apodeixis) draws necessary conclusions from those principles. Scholastic philosophy increasingly came to rely upon authoritative sources—such as Scripture, the Church Fathers, and canonical texts—as premises in many domains of inquiry, thereby displacing the empirical search for first principles that Bacon regarded as essential.

Bacon’s methodological reform aimed precisely to restore the balance between experience and reason: to make the ascent of induction and the descent of deduction interdependent. He thus called for methodical descent (deductio ad nova experimenta)—the logical application of inductively established axioms to new experiments—thereby allowing inquiry to move cyclically between observation and reasoning.