Euler Circles for Categorical Syllogisms
Euler Circles for Categorical Syllogisms
This Demonstration shows representations of categorical syllogisms [10] by Euler circles (or Euler diagrams). These are equivalent to Venn diagrams, except that Euler circles for disjoint sets do not touch. The Demonstration produces a random syllogistic form, and the user must show whether the form is a valid syllogism or not by moving circles and adapting their radii. The Demonstration simultaneously calculates values of propositions.
Aristotelian logic, or the traditional study of deduction, is based on the following four so-called categorical (or subject-predicate) propositions:
SaP⇔
S
P
SiP⇔
S
P
SeP⇔
S
P
SoP⇔
S
P
The categorical propositions A, E, I, and O are designated the mood of a syllogism. is called the subject (or minor) term, and is called the predicate (or major) term of the proposition. A categorical syllogism is a deductive argument about categorical propositions in which a conclusion is inferred from two premises. The term that occurs in both premises is called the middle term. An example of a syllogism is , ⇒ . There are 256 possible triples of categorical propositions, but only 24 of these are valid syllogisms.
S
P
M
MaP
SiM
SiP
A valid syllogism is found by choosing true premises, which imply true conclusions. To run the Demonstration, click for a new syllogistic form, then move the three circles (using the mouse) into the corresponding configuration. You can vary the size of each circle to enable one to contain another.
To show that the appeared form is not a valid syllogism, move or adopt radii of circles so that the first two propositions (premises) are true and the third (conclusion) is false.