Centrality of syllogism in ordinary language

Classical logic considered itself to be the science of correct thinking, and the syllogism is the foundation of propositional logic and, symbolicallyhe, its core. If humans are rational beings, then logic defines humans.
However, the mathematisation of logic and the emergence of observational and experimental sciences have completely transformed this view of logic as the ‘art of thinking’.

Argumentation seeks to define itself in relation to logic, particularly mathematical logic. Perelman and Olbrechts-Tyteca contrast argumentation with logic, and the syllogism disappears from the theory of argumentation.
The classical syllogism employs set theory (see the evaluation method using Venn diagrams). Categorization corresponds to the syllogism with a concrete subject. The legal syllogism is a form of this type of syllogism used in law.

A syllogism with a concrete subject governs the categorization of a being and may be the fundamental operation of ordinary reasoning carried out using only the resources of ordinary language.
Classical texts translated from Chinese contain explicit examples of classical syllogisms (section 2) and syllogisms with concrete subjects (section 3).

A Chinese syllogism

Consider « this curiously familiar-sounding syllogism of Wang Ch’ung (*):

‘Man is a thing: though honored as king or noble, by nature he is no different from other things. No thing does not die, how can man be immortal?‘
(Graham  1989, p.  168; see arguing without argumentation theory)

Wang Ch’ung uses a valid syllogism, that combines true propositions to arrive at a sound conclusion, « Humans are beings, no being is immortal, no human is immortal.” In the unfriendly language of traditional logic, this reasoning is described as a syllogism of the fourth figure, said Galenic, and in the Camenes mode: « all H are B; no B is I; therefore no H is I. »
Wang Ch’ung presents this incontrovertible conclusion as a so-called “rhetorical » question, which is a challenge to any opponent (Toulmin, 1958: 97); this introduces a dialectical movement within syllogistic reasoning.

(*) Wang Ch’ung, c. 27 – c. 97 ce