The IF-THEN Implication
Learn about IF-THEN implications.
Contingent situations and language
A lot of human situations are contingent, and in natural language, they usually get represented through conditional sentences.
Contingent Situations
Contingent Situations Represented by Conditional Sentences |
If the alarm rings, the students will evacuate the building. |
When the traffic light turns red, vehicles must come to a stop. |
You will pass the course if you study conceptually. |
Metal expands when heated. |
In the examples above, it’s obvious that some phenomenon is waiting to happen subject to the meeting of appropriate condition(s). For example, the vehicles must come to a stop
The IF-THEN implication in formal logic
Human expression is diverse, but for consistency, we’ll stick to the following formal syntax and semantics in our simple binary logic language.
Syntax
As far as correct syntax (or structure) of a sentence goes, the following rules apply for an implication:
IF Proposition 1, THEN Proposition 2.
Proposition 1 is termed as the antecedent; Proposition 2 is termed as the consequent.
It’s represented by an arrow (
) symbol between the antecedent and consequent
This particular compound arrangement of propositional statements is termed in logic as a conditional statement or implication, represented as:
Proposition 1
Proposition 2.
Examples
Natural Language | Translation Step | Implication |
When the traffic light turns red, vehicles must come to a stop. | IF the traffic light turns red THEN vehicles must come to a stop. | The traffic light turns red → Vehicles come to a stop |
Metal expands when heated. | IF metal is heated THEN the metal expands. | Metal is heated → The metal expands |
You will pass if you study the course conceptually. | IF you study this course conceptually THEN you will pass. | You study this course conceptually → You pass the course |