Final answer:
Pairs of propositions like 'It is a possible truth that p' and 'It is possibly true that p' mean the same; both imply a scenario where 'p' could be true. Similarly, necessary truth propositions indicate 'p' must be true in all contexts, and simple truth affirmations directly declare 'p' as true. Theories of truth, such as Aristotle's and the redundancy theory, help illuminate these concepts.
Step-by-step explanation:
Within metaphysics, the truth of propositions can often seem confusing due to their phrasing, but essentially the pairs of propositions you've mentioned share the same meaning. For (a.1.) 'It is a possible truth that p' and (a.2.) 'It is possibly true that p', both suggest that there is a scenario where 'p' could be true. Similarly, (b.1.) 'It is a necessary truth that p' and (b.2.) 'It is necessarily true that p' both indicate that 'p' must be true in all possible worlds. Lastly, (c.1.) 'It is a truth that p' and (c.2.) 'It is true that p' are direct affirmations that 'p' is indeed true.
Indeed, the concept of truth lies at the heart of metaphysical inquiry. Aristotle's classic formulation that a true statement aligns with reality supports our understanding that 'A is B' is true if and if only A is B - without the need for quotation marks around the proposition. The correspondence theory of truth states a proposition is true if it corresponds to a fact. The redundancy theory states claiming a proposition is true is superfluous; it adds nothing beyond the affirmation of the proposition itself.
Overall, a proposition is a claim about the world that can be judged either true or false, and truth is not relative; contradictory claims cannot be true simultaneously. The philosophy around truth is crucial in understanding how we relate to the world and construct knowledge.