Quick Answer
A corollary is a logical consequence of something already known. Think of it as an unavoidable "because X is true, then Y must also be true." It matters because recognising these natural outcomes allows us to anticipate what's coming next, helping us make smarter decisions and prepare for the ripple effects.
In a hurry? TL;DR
- 1A corollary is a natural, direct consequence of an existing fact or proposition, often requiring minimal additional proof.
- 2It's an inseparable, predictable companion to a primary event, unlike a random fluke or accidental side effect.
- 3Recognizing corollaries helps predict secondary effects of changes, improving strategy and communication precision.
- 4In logic and math, corollaries act as immediate insights that logically extend an already proven theorem.
- 5The term highlights the inherent, built-in realities that follow from a specific choice or decision.
- 6Corollaries are like 'freebies' of knowledge—once you accept the initial premise, the secondary truth arrives automatically.
Why It Matters
Understanding corollaries helps us see the unavoidable knock-on effects of any decision, making us better at planning and explaining things precisely.
A corollary is a direct consequence or result that stems naturally from an existing fact or proposition. In logic and mathematics, it refers to a theorem that requires little to no proof because it follows so obviously from one already established.
Why It Matters: Recognising a corollary allows you to predict the secondary effects of a change before they happen, making you a sharper strategist and a more precise communicator.
The Definition
KOR-uh-ler-ee (/ˈkɒrələri/)
Part of Speech: Noun Meaning: A proposition that follows from one already proved; a natural consequence or result.
The Logic of the Inevitable
A corollary is not just any random result. It is an inseparable companion to a primary event. When you change one variable in a complex system, the corollary is the shadow that moves with it. Unlike a fluke or an accidental side effect, a corollary is predictable and logically bound to its predecessor.
The word fills a specific gap in our vocabulary by distinguishing between a direct cause-and-eye effect and a secondary, self-evident truth. If a company doubles its staff, a budget increase is the direct action, but a more complex office culture is the corollary. It is the baked-in reality of a previous choice.
In contrast to a mere consequence, which can be negative or chaotic, a corollary often feels like a formal extension of a rule. It is the fine print written by nature or logic. Scientists use the term to describe phenomena that must exist if their primary theory holds water.
Etymology: From Flowers to Logic
The origin of the word is surprisingly delicate for a term now associated with cold logic and mathematics.
Contextual Examples
- Digital Fatigue: As remote work became the standard for many, the corollary was a sharp rise in digital fatigue and the blurring of home-office boundaries.
- Economic Growth: High consumer confidence is often a corollary of low unemployment rates and steady wage growth.
- Urban Planning: When a city invests heavily in public transport, a corollary is usually a rise in property values near new transit hubs.
Synonyms and Antonyms
- Synonyms: Consequence, byproduct, spin-off, result, aftereffect.
- Antonyms: Cause, origin, foundation, antecedent, premise.
Practical Usage Tips
Use corollary when you want to sound analytical rather than accusatory. Saying "the corollary of your plan is X" sounds like a neutral observation of logic, whereas saying "the consequence of your plan is X" often carries a hint of blame or warning. It is a useful tool for highlighting hidden costs or logical inconsistencies without becoming emotional.
Related Concepts
- Success: Why the corollary of fame is often a loss of privacy.
- Causality: Understanding the difference between a corollary and a coincidence.
- Mathematics: How Euclid shaped the way we use logical deductions.
Key Takeaways
- A corollary is an inevitable secondary result.
- It originates from the Latin word for a floral gift or "bonus."
- It is most commonly used in technical, logical, and formal contexts.
- Use it to describe results that are baked into a situation by logic.
Example Sentences
"A direct corollary of increasing the minimum wage is often a slight rise in consumer prices."
"The surge in online shopping has led to a corollary decline in footfall traffic at high street retailers."
"His incredible work ethic was a natural corollary to his ambition to succeed in his chosen field."
"The theorem states that all perfect squares are positive, and a corollary is that their square roots are real numbers."
"One regrettable corollary of rapid urban development is the loss of natural habitats for local wildlife."
