Update: See the comment by philh. These logical operations are matters of convention, but the way that it is defined is less arbitary than I thought!
I want to start this sequence with a very basic example - the word "if".
I expect that most people here already know that there are two definitions of "if":
- Logical if: "If A then B" is true is equivalent to "B OR NOT A"
- Counterfactual if: "If A was true, then B" means consider a world or a set of worlds like ours, but with A being true. In all these worlds, B is true as well".
In this post we'll discuss the logical if and counterfactuals will wait until another post. Someone might naively think that this logical if is in the territory, but it is actually in the map.
Consider the sentence, "If pigs can fly, then Trump is Queen of England". Both components are false and when this occurs, the if-statement is considered true.
However, this is purely a matter of convention. There's no reason why we couldn't consider these sentences where the condition is false to be false or undefined. It's a mistake to ask why this is the case as though it were necessarily the case, but not a mistake to ask why we chose for it to be the case.
These statements being false isn't part of the territory (of relations between propositions), but is rather a result of how we've drawn our map (of relations between propositions).
Note that I haven't said what relations between propositions are - whether these are abstract objects or purely exist in our minds. But whatever they are, "if" is in the map of relations between propositions.