Module 3: Aristotelian Logic
Aristotelian Logic Overview
The deductive logic that is the subject of this module was developed by Aristotle nearly 2,500 years ago, and we’ll refer to it simply as “Aristotelian Logic”. Aristotelian Logic seeks to tame natural language by restricting itself to a well-behaved, precise portion of the language. It only evaluates arguments that are expressed within that precisely delimited subset of the language referred to as “categorical propositions”.
Our study of Aristotelian Logic will demonstrate how the three essential tasks for a deductive logic are accomplished:
- Tame natural language to render arguments precise and suitable for evaluation (task 1).
- Precisely define an explicit structure for argument forms (task 2).
- Establish a technique to test logical forms for validity (task 3).
Learning Objectives
After successful completion of Module 3, you will be able to:
- Identify the four types of categorical propositions and represent them graphically with Venn diagrams.
- Use the relationships in the square of opposition to test inferences.
- Determine the obverse, converse, and contrapositive forms of categorical propositions and their resulting truth value.
- Explain what is meant by ‘existential import’ and the problem that arises with empty classes.
- Arrange categorical syllogisms in standard form, and use Venn diagrams to test their validity.
Module 3 Roadmap
- Section 3.1: We lay out the precisely delimited subset of language used in Aristotelian logic. Starting with the fundamental logical unit of Aristotelian logic – a
class
(also known as acategory
), we learn how categorical propositions are used to define relationships between two classes of things. Venn diagrams are introduced for graphically illustrating relationships between classes. - Section 3.2: Next we study the Square of Opposition, which defines truth relationships between different types of propositions.
- Section 3.3: Our next topic involves three operations that can be performed on categorical propositions: Conversion, Obversion, and Contraposition.
- Section 3.4: Then we look at some issues with the Aristotelian Square of Opposition created by the possibility of empty classes and how 19th Century English logician George Boole attends to the problem.
- Section 3.5: Finally, we work with the argument form that is the centerpiece of Aristotelian logic — categorical syllogisms; we learn how to test these arguments for validity.
Key Terms
- categorical proposition
- category
- categorical syllogism
- class
- class complement
- class term
- contradictory
- contrary
- conversion
- copula
- existential import
- empty class
- figure
- inferential relationship
- logical form (Aristotelian)
- major premise
- major term
- middle term
- minor premise
- minor term
- mood
- obversion
- partial inclusion
- particular affirmative
- particular negative
- predicate term
- quality
- quantifier
- quantity
- standard form
- subaltern
- subcontrary
- subject term
- universal affirmative
- universal negative
- whole inclusion
Definitions for these terms are available in the course Glossary.
Candela Citations
CC licensed content, Shared previously
- Retrieved from: https://open.umn.edu/opentextbooks/textbooks/fundamental-methods-of-logic. License: CC BY: Attribution
