Unit 3 of Logic – I (syllabus: Module III — kinds of inference; the opposition of propositions and the square; conversion and obversion; the derived eductions and other immediate inferences). Below: what the unit covers, the provisions it turns on, and the cases an examiner expects you to name.
What this unit covers
- What is opposition of propositions, and what are its four kinds?
- What follows from the truth or falsity of each of the four propositions?
- Why is the opposition of two singular propositions contradictory and not contrary?
- What are the rules of conversion, and why has an O proposition no converse?
- What is obversion, and why has every proposition an obverse?
- How are the five derived eductions built, and where do the gaps come from?
- How is an immediate inference tested for validity?
- What are the four other immediate inferences, and why are they treated separately?
Treat that list as a self-test: recite each topic's rule from memory before you open its cases.
Provisions
- The square of opposition, s. Module 3, head 3.2
- Inference by opposition of propositions, s. Module 3, head 3.2
- Opposition of singular propositions, s. Module 3, head 3.2
- Eduction: rules of conversion, s. Module 3, head 3.3
- Eduction: obversion, s. Module 3, head 3.3
- Eduction: obverted converse, contrapositive and inverse, s. Module 3, head 3.3
- Testing the validity of immediate inferences, s. Module 3, head 3.3
- Other immediate inferences, s. Module 3, head 3.4
Leading cases
- Aristotle
- Keynes
- Aristotle for the operation; the complement of a class is the modern logicians' explanation of it
- Bain