# Definition:Truth Value

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## Definition

### Aristotelian Logic

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 represented in one of two ways:

There are advantages for both notations. In particular, the second lends itself to extending the discipline of logic into that of probability theory.

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## Sources

- 1944: Eugene P. Northrop:
*Riddles in Mathematics*... (previous) ... (next): Chapter One: What is a Paradox? - 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): Chapter $\text I$ Introductory: $3$. Logical Form - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**truth value** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**truth value**