Introduction to Categorical Logic PHIL 121: Methods of Reasoning February 18, 2013 Instructor:Karin Howe Binghamton University.

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Presentation transcript:

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: 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