I understand how in propositional logic, every proposition is a statement that is either TRUE or FALSE, and we can make use of logical connectors to turn separate propositions into fromulas which intern are more complex propositions.
My question is, just to see if i get this right: Is any proposition (be it a compound of predicates with quantors or just the basic well-formed formula), that's written down without any indication of its truth value, assumed to be true?
This would clarify why in higher level math topics (depending on formal logic and axiomatic set theory, like real analysis, linear algebra, etc..), when we state a theorem, we only write down a proposition without specifying truth values.
Best Answer
Yes: in non-formal logic, issued statements are tacitly understood—rather than assumed— as true, just like the first four words in “It is true that I went to the cinema” are typically omitted except for emphasis.
Side point: some philosophy texts seem to distinguish statements from propositions in that the former express/interpret the latter over a domain of discourse.