Relations between concepts in logic

Main thing

Relations between concepts in logic describe how different concepts are connected or associated with each other. There are two broad categories of relations: compatible and incompatible.

Compatible relations occur when the concepts can coexist without conflict. This includes:

1. Equivalence - Two concepts have exactly the same meaning and scope, representing the same set of instances. For example, 'bachelor' and 'unmarried man' are equivalent concepts.

   

2. Intersection - The concepts overlap partially, sharing some common instances but each also having some unique instances. Like 'vegetables' and 'green foods' - some vegetables are green foods, some are not, and some green foods are not vegetables.

   

3. Subordination - One concept is a specific type or subset contained entirely within the broader, more general concept. For instance, 'square' is a subordinate of the concept 'rectangle'.

   

Incompatible relations occur when the concepts cannot logically coexist or are contradictory. This includes:

1. Co-subordination - Two concepts are separate, distinct subsets of a broader concept with no overlap between them. For example, 'red' and 'blue' are co-subordinate under the concept of 'color'.

   

2. Proto-displacement - One concept originated from the other but has taken on a new, distinct meaning over time. Like 'awful' originally meant 'inspiring awe' but now means 'extremely bad/unpleasant'.

   

3. Contradiction - The concepts are mutually exclusive and cannot be jointly true. Such as 'living' and 'dead' for a single organism.

   

Terms

• Concept - An abstract idea or mental representation of a group of instances/objects that share common characteristics. Example: The concept of 'chair' represents the idea of a seat with a back support.

An analogy

Relations between concepts are like relationships between people - some get along compatibly, others conflict. Just as friends are compatible, enemies contradict each other.

A main misconception

Many confuse intersection with equivalence. For example, thinking all vegetables are green foods and vice versa. But some vegetables are not green, and some green foods are not vegetables.

The history

1. Ancient Greek philosophers like Aristotle (384-322 BC) first systematically studied relations between concepts.

2. In the 9th century, Muslim logicians like Al-Farabi expanded on Aristotle's work.

3. In the 13th century, European scholastic philosophers further developed the topic.

4. In the 19th century, developments in symbolic logic by Gottlob Frege and others allowed more precise analysis.

5. In the 20th century, logicians like W.V.O. Quine made key contributions to understanding relations.

"Logic is the anatomy of thought." - John Locke, influential Enlightenment philosopher

Three cases how to use it right now

1. Classifying items in a grocery store based on their relations (e.g. putting all vegetables together as subordinates of produce).

2. Resolving conflicting instructions by identifying contradictory concepts (e.g. cannot open and close a door simultaneously).

3. Designing a product taxonomy for an e-commerce website by organizing concepts into compatible and incompatible groups.

Interesting facts

• The word "concept" derives from the Latin "concipere" meaning to conceive or take in.

• Venn diagrams, invented in 1880, are widely used to visualize relations between concepts.

• The philosophical problem of universals concerns the metaphysical status of abstract concepts.

• Thesauruses group words based on semantic concept relations like synonymy and antonymy.

• Conceptual metaphors allow humans to understand abstract concepts in terms of more concrete ones.