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Symbolic Logic and Reasoning
Contingency
A contingency is a proposition that can be true under some assignments and false under others.
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Contingency
Definition
A contingency is a proposition that is sometimes true and sometimes false, depending on the truth values of its parts.
Example:
P AND Q
This is true when both P and Q are true.
It is false in other cases.
Contingency = truth depends on the case.
Truth Table Example
Truth table:
P Q P AND Q
true true true
true false false
false true false
false false false
The final column is not always true.
It is also not always false.
So the expression is contingent.
A contingent statement has mixed truth table results.
Contingency vs Tautology
A tautology is always true.
Example:
P OR NOT P
A contingency is not always true.
Example:
P AND Q
It depends on whether P and Q are true.
Tautology is always true; contingency depends on assignment.
Contingency vs Contradiction
A contradiction is always false.
Example:
P AND NOT P
A contingency is sometimes true and sometimes false.
Example:
P OR Q
This can be true or false depending on the case.
Contradiction is always false; contingency varies.
Why Contingency Matters
Most useful factual claims are contingent.
Example:
It is raining.
This is true in some situations and false in others.
Logic needs to distinguish contingent truth from truth guaranteed by form.
Contingency captures statements whose truth depends on the situation.
Final Summary
- A contingency is sometimes true and sometimes false.
- Truth tables can identify contingencies.
- A contingency is different from a tautology.
- A contingency is different from a contradiction.
- Many factual claims are contingent.
- Contingency means truth depends on assignment or interpretation.
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Universal Quantifier