Introduction to Categorical Logic PHIL 121 Methods of
- Slides: 10
Introduction to Categorical Logic PHIL 121: Methods of Reasoning February 18, 2013 Instructor: Karin Howe Binghamton University
Issues from Part I that are still highly relevant • Statement or proposition • Arguments, specifically deductive arguments • Validity/invalidity
Most importantly … • Putting arguments into standard form • Standard form categorical propositions • Categorical syllogisms
Categorical Logic: A Brief History • Categorical logic was invented by Aristotle over 300 years BCE (Aristotle: 384 -322 BCE) • Categorical logic was the logic used by medieval logicians • They studied it in a more systematic fashion than Aristotle (more formalized)
Medieval logic? Why are WE studying that? • Historically interesting part of the study of logic and reasoning • Nice bridge between the less formal parts of this course (Part I) and the more formal parts of the course (Parts III and IV) • Amazingly powerful and fairly intuitive tool (again, a nice bridge in terms of accessibility to the non-specialist)
However, we're not going to do it exactly like the medieval logicians • Aristotle got some things wrong • Problem: in Aristotelian logic, universal propositions implied existence • The statement "All unicorns are white" implied the statement "Some unicorns are white. "
Boolean Interpretation of Categorical Logic • Solution: make that no longer the case • Now "All unicorns are white" no longer entails that unicorns exist • A small change that makes BIG differences
Brief overview of new things we will be learning • Categorization of categorical propositions into four distinct types, and their associated Venn diagrams • How to place these four types of propositions on the (Boolean) Square of Opposition and determine things about their relationship based on this square
• How to make certain inferences in categorical logic (transform propositions into their logical equivalents) • Determining validity and invalidity using the Venn Diagram technique • How to recognize certain formal fallacies in categorical syllogisms • Other stuff, depending on time
- Categorical syllogism
- Categorical logic in nursing
- Categorical syllogism
- First order logic vs propositional logic
- First order logic vs propositional logic
- Third order logic
- Combinational vs sequential logic
- Cryptarithmetic problem logic+logic=prolog
- 캠블리 단점
- Is it x y or y x
- Combinational logic sequential logic 차이