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Truth is what is real. A thing is true if it is a fact. The English word truth is from Old English tríewþ, tréowþ, trýwþ, Middle English trewþe. Aristotle said: “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true”.
Something untrue is false. A half truth is something true mixed with something false, or where something is partly true but you do not tell the whole story.
If the things you say are true, then you are speaking the truth, or speaking truly. Saying something that is untrue can be called 'a lie', if the person who is saying it knows it is untrue. A person who says something untrue is often called a "liar".
True & false in logic and philosophy
Aristotle was the first to put logic into a formal framework. His version is called propositional logic (see also syllogism and deductive reasoning). Other forms of logic use types of mathematics (mathematical logic) or symbols. Boolean algebra is about things being true and false.
- David, Marion (2005). "Correspondence Theory of Truth" in Stanford Encyclopedia of Philosophy