Critical Thinking: Categorical Logic
Introduction to Categorical Logic
- Categorical logic is one of the oldest forms of logic, dating back to ancient Greeks and Aristotle.
- It's foundational in logic studies, similar to how addition and multiplication are to algebra.
Building Blocks of Categorical Logic
- Categorical Propositions: Basic units of categorical syllogism, analyzing relationships among categories or classes.
- Affirm or Deny: Propositions can affirm or deny that one class is partially or wholly included in another.
- Types of Propositions:
- Universal Affirmatives (A)
- Universal Negatives (E)
- Particular Affirmatives (I)
- Particular Negatives (O)
Components of Categorical Propositions
- Subject Term: What the assertion is about.
- Predicate Term: What is asserted about the subject.
- Copula: Verbs like 'is', 'are', 'was', or 'were' that join subject and predicate.
- Quantifier: Indicates the extent (all or some) of the category discussed.
- Quality: Indicator if a proposition is affirmative or negative.
- Quantity: Universal ('all') or particular ('some').
Visual Representations
- Euler Circles: Used to illustrate relationships between subject and predicate terms.
- Five Possible Diagrams: Represent the various types of categorical propositions.
Translation of Ordinary Sentences
- Singular Subjects: Treated as a class with one member.
- Non-Standard Propositions: Translate into standard categorical form.
Key Translation Techniques
- Singular Subjects: Use quantifier 'All' for singular objects.
- Missing Copula: Replace other verbs with forms of 'to be'.
- Ambiguous Quantifiers: Translate words indicating quantity into 'all' or 'some'.
Examples of Translations
- "Anyone without hair is bald" translates to "All people without hair are people who are bald."
- "The dolphin is an aquatic mammal" translates to "All dolphins are aquatic mammals."
- "All dogs are not black" should translate to "Some dogs are not black."
Special Propositions
- Exclusive Propositions: Translate using universal quantifier 'All' and reverse subject/predicate.
- Negative Propositions: Use 'No' to indicate universal negatives.
- Acceptive Propositions: Require two claims, a universal affirmative and a universal negative claim.
Conclusion
- Translation Skills: Essential for understanding and rendering logical arguments clear.
- Next Topics: Square of opposition and immediate inference.
Remember, logic involves translating the meaning, not just words, to convey clear and logical arguments.