In Aristotelian logic, a statement can be either true or false, and there is no undefined, in-between value.
Whether it is true or false is called its truth value.
Note that a statement's truth value may change depending on circumstances.
Thus, the statement:
- It is currently raining on the grass outside my window
has the truth value false, whereas it had the truth value true last week.
- I am listening to Shostakovich's 4th symphony
is currently true, but that will last only for the next twenty minutes or so as I type.
The truth values true and false are usually represented in one of two ways:
- $\mathrm T$ for true and $\mathrm F$ for false;
- $1$ for true and $0$ for false.
There are advantages for both notations. In particular, the second lends itself to extending the discipline of logic into that of probability theory.