In logic, we see expressions like a lot.
- The symbol is read as ‘implies’ and is also called the material conditional.
- Logically/mathematically, it is a truth-function.
- I.e. it merely takes in two yes-or-no bits of information and deterministically spits out a bit of information.
- A simple characterization is to say that the only way to show that is false is to show that is false and is true.
- It is expressible as the following table:
- Its meaning, in brief, is an assertion that being true can be asserted if is true.
- There is a gap between these two characterizations, expressed in Lewis Carroll’s parable.
- A common example is: If is a bachelor, then is male.
- The relation is ‘truth functional’ - it only depends on the scenarios in which and are true and says nothing about and being related to each other in some deeper way. The following examples illustrate this:
- If , then more than 10 people live on Earth. (this is the first row of the table)
- If the moon is made of cheese, then . (the third row)
- If the moon is made of cheese, then . (the fourth row)