The False Subtlety of the Four Syllogistic Figures Proved (German: Die falsche Spitzfindigkeit der vier syllogistischen Figuren erwiesen) is an essay published by Immanuel Kant in 1762.
General conception of the Nature of Ratiocination [Vernunftschlüsse] A judgment is the comparison of a subject or thing with a predicate or attribute [also called a "mark"].
The intermediate predicate is called the middle term of a rational inference.
Note: Kant's examples utilized obscure subjects such as Soul, Spirit, and God and their supposed predicates.
These do not facilitate easy comprehension because these subjects are not encountered in everyday experience and consequently their predicates are not evident.
The dictum de omni is the highest principle of affirmative syllogisms.
For example, the ratiocination is only valid if the fourth proposition Therefore, no man is immortal is covertly thought.
This is a mixed ratiocination because an unexpressed proposition must be added in thought in order to arrive at the conclusion.
An example of a syllogism of the third figure is: This validly follows only if an immediate inference is silently interpolated.
Kant claimed that the fourth figure is based on the insertion of several immediate inferences that each have no middle term.
The affirmative mode of this fourth figure is not possible because a conclusion cannot be derived from the premises.
In order to be valid, the negative mode ratiocination: must become: The Logical Division of the Four Figures is a Mistaken Subtlety.
Previous logicians incorrectly considered all four figures as being simple and pure.
The four figures were created by playfully changing the middle term's position.
The first figure yields a correct inference in a simple, direct manner.
Non-human animals can have clear representations of things that are predicates of a subject.
The higher knowledge of a human is based on the ability to make our own ideas the object of our thoughts.
Judgments in which identity or contradiction is immediately known cannot be proved (See Section II).
Kant summed up his thoughts on this topic in a short footnote that appeared in the second edition of the Critique of Pure Reason, B141.
In his footnote, Kant asserted that the lengthy and detailed doctrine of the four syllogistic figures concerned only categorical syllogisms or inferences.
He stated that this doctrine is only an artifice or trick for giving the appearance that there are three more kinds of inference or modes of drawing a conclusion than that of the first figure.
This is done surreptitiously by secretly concealing immediate inferences[1] in the premises of a pure syllogism.