Definition:Truth Value
Disambiguate with Definition:Boolean Interpretation/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.
Other logic types
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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): $\S 1.3$: Logical Form
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: truth value
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: truth value