Definition:Truth Value

From ProofWiki
Jump to: navigation, search


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:

$\mathrm T$ 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.