Is it a necessary non-epistemic truth? After all, it has a very lengthy partial proof in Principia Mathematica, and maybe they got something wrong. Perhaps you should check?
But then maybe you’re not using a formal system to prove it, but just taking it as an axiom or maybe as a definition of what “2” means using other symbols with pre-existing meanings. But then if I define the term “blerg” to mean “a breakfast product with non-obvious composition”, is that definition in itself a necessary truth?
Obviously if you mean “if you take one object and then take another object, you now have two objects” then that’s a contingent proposition that requires evidence. It probably depends upon what sorts of things you mean by “objects” too, so we can rule that one out.
Or maybe “necessary non-epistemic truth” means a proposition that you can “grok in fullness” and just directly see that it is true as a single mental operation? Though, isn’t that subjective and also epistemic? Don’t you have to check to be sure that it is one? Was it a necessary non-epistemic truth for you when you were young enough to have trouble with the concept of counting?
So in the end I’m not really sure exactly what you mean by a necessary truth that doesn’t need any checking. Maybe it’s not even a coherent concept.
Is it a necessary non-epistemic truth? After all, it has a very lengthy partial proof in Principia Mathematica, and maybe they got something wrong. Perhaps you should check?
But then maybe you’re not using a formal system to prove it, but just taking it as an axiom or maybe as a definition of what “2” means using other symbols with pre-existing meanings. But then if I define the term “blerg” to mean “a breakfast product with non-obvious composition”, is that definition in itself a necessary truth?
Obviously if you mean “if you take one object and then take another object, you now have two objects” then that’s a contingent proposition that requires evidence. It probably depends upon what sorts of things you mean by “objects” too, so we can rule that one out.
Or maybe “necessary non-epistemic truth” means a proposition that you can “grok in fullness” and just directly see that it is true as a single mental operation? Though, isn’t that subjective and also epistemic? Don’t you have to check to be sure that it is one? Was it a necessary non-epistemic truth for you when you were young enough to have trouble with the concept of counting?
So in the end I’m not really sure exactly what you mean by a necessary truth that doesn’t need any checking. Maybe it’s not even a coherent concept.