Definition:Truth Value

Definition

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.

The statement:

"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 defined 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.

Also see

• Boolean Domain

Sources

• Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning (1964): $\text{II}: \S 6$
• Alan G. Hamilton: Logic for Mathematicians (1978): $\S 1.1$
• D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.3$
• Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems (2000): $\S 1.4$: Definition $1.28$