contraposable
To subject a logical proposition to contraposition, which involves negating both the subject and the predicate and reversing their order. This operation is used in formal logic to derive a statement that is logically equivalent to the original conditional statement.
Examples
3 of 5If you want to understand the logic, try to contrapose the statement: 'If it rains, the grass is wet' becomes 'If the grass is not wet, it did not rain'.
To understand the logic, swap and negate the parts: 'If it rains, the grass is wet' becomes 'If the grass isn't wet, it didn't rain'.
The philosopher sought to contrapose the central axioms of the theory to test for any internal logical inconsistencies.
The philosopher tried to invert and negate the theory's main rules to check for logical errors.
So, if we contrapose that idea, you're basically saying that if we don't finish this now, we'll definitely fail later.
If we look at the logical opposite, you're saying that failing to finish now leads to certain failure later.
Word Family
Memory Tip
Think of 'Contra' (against/opposite) and 'Pose' (place). You are placing the 'opposite' (negated) version of the terms in the opposite order.
Quick Quiz
To verify the truth of the conditional statement, the logician decided to ________ the premise.
Correct!
The correct answer is: contrapose
Examples
If you want to understand the logic, try to contrapose the statement: 'If it rains, the grass is wet' becomes 'If the grass is not wet, it did not rain'.
everydayTo understand the logic, swap and negate the parts: 'If it rains, the grass is wet' becomes 'If the grass isn't wet, it didn't rain'.
The philosopher sought to contrapose the central axioms of the theory to test for any internal logical inconsistencies.
formalThe philosopher tried to invert and negate the theory's main rules to check for logical errors.
So, if we contrapose that idea, you're basically saying that if we don't finish this now, we'll definitely fail later.
informalIf we look at the logical opposite, you're saying that failing to finish now leads to certain failure later.
In introductory logic, students are taught to contrapose a conditional 'if P then Q' to 'if not Q then not P' as a valid form of inference.
academicLogic students learn that switching and negating 'if P then Q' to 'if not Q then not P' is a valid way to reason.
We need to contrapose our growth projections against the risk factors to see if the inverse logic still supports our investment.
businessWe should evaluate our growth plans by looking at the negative conditions to see if the investment still makes sense.
Word Family
Common Collocations
Common Phrases
contrapose the premise
to logically reverse the starting assumption
contrapose the conditional
to apply logic to an if-then statement
unable to contrapose
when a statement cannot be logically inverted
Often Confused With
Juxtapose means to place things side by side for comparison, while contrapose is a specific logical operation of negating and reversing.
Transpose means to switch the positions of two things, but contrapose also requires the negation of those things.
Usage Notes
The term is primarily used in the fields of mathematics, philosophy, and formal logic. It is a transitive verb, meaning it requires a direct object, usually a statement or proposition.
Common Mistakes
Learners often use 'contrapose' when they simply mean 'contrast' or 'contradict'. Remember that contraposing a statement creates a new statement that is logically identical in truth to the original.
Memory Tip
Think of 'Contra' (against/opposite) and 'Pose' (place). You are placing the 'opposite' (negated) version of the terms in the opposite order.
Word Origin
Derived from the Latin 'contrapositus', the past participle of 'contraponere', meaning 'to place against' or 'to set opposite'.
Grammar Patterns
Cultural Context
This term is central to Western formal logic and the 'Square of Opposition', a framework used since the time of Aristotle to teach deductive reasoning.
Quick Quiz
To verify the truth of the conditional statement, the logician decided to ________ the premise.
Correct!
The correct answer is: contrapose
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