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)