In Propositional Logic, a proposition is a sentence or statement that has a value of either True or False. Propositions are also used in other logics such as Predicate Logic.
Propositions are represented by symbols, and it is tradition, when appropriate, to use p and q, specifically:
- p is called the antecedent
- q is called the consequent
A curious question…
We found the following and in a way, we can agree with it, mostly, but we still have questions…
“Similarly “x = x” is not a proposition because we don’t know what “x” represents hence what “=” means. “
Hmmm… We would argue the exist of a generalized “equals” and a generalized “variable”, and thus x has to be equal to something. Now, if we accept Common Notion One, then the first x is equal to something and the second x is also equal to that something, and Common Notion One tells us that two things equal to a third are equal to each other. That would make “x = x” true, and a sentence having a value of true or false is a proposition.
We have seen discussions of propositional logic that use the word statement rather than the word proposition.
Rob Sterling 