Frank Rissanen
Is truth relative to your level of your understanding? For example, is 1+1=2 always true, or are there legitimate paradigms from wich that equation is false?
Richard A. Nichols III
There are no paradigms from which that equation is false, unless you change the definitions/meanings of the symbols 1, +, =, and/or 2, but that would trivialize the question, because it's functionally the same as simply using different symbols (and defining them, if the necessary symbols/definitions don't already exist) and hence writing a different equation.
Or you could say the paradigm includes how you relate or manipulate those symbols relative to each other, thus the paradigm can determine its truth value, but there's no clear distinction between that being an aspect of the paradigm strictly outside of the meanings of the symbols themselves, or being embedded in them/inextricable from them.
But the bigger problem here is that this is a math problem, and math and formal logic are the only two categories of supposed "knowledge" or "truth" in which there is an objective, incontrovertible, by-definition way of determining the truth value of a proposition. So it's not really that relevant to the general question of whether truth is relative to your level of understanding or to your paradigm.
IMO, it's questionable whether the "truths" of math are even really truths, as they say nothing about anything substantively extant. For them to speak on anything substantive, they would have to be at least partially informed by empirical observation or some other active observation of reality, and that would imply that the "truths" could conceivably have been different from what they are, because you don't necessarily know what you'll discover in reality until you look. Whereas the "truths" of math can't have been any other way because they're the only logically/cognitively coherent possibility (given the particular set of fundamental axioms).
But to the real question of whether truth in general is subject to level of understanding or paradigm, as truth is classically/typically understood, the answer should be no, because truth is thought to be objective and universal. So if two paradigms or levels of understanding render two different contradicting truths, at least one of the paradigms should be wrong.
But there is the confounding factor that what paradigm you're using could be inextricable from the particular meaning of the given proposition or belief within it, so if that proposition/belief has the opposite truth value under a different paradigm, you can't really say it contradicts it because it's actually not the same proposition/belief.
But anyway, personally, I think truth as an objective thing is problematic. The only thing the notion of truth being objective really has going for it is that the term "truth" is *defined* as being objective, which makes it somewhat problematic to argue against it. However, it can still be done, because you can either show that there simply isn't such a thing as truth under that definition because objective truth is impossible, or you can argue that the definition is mistaken, as in it's misrepresentative of the meaning of the word according to its popular usage, and dictionary writers intend for their definitions to be *descriptive* of popular usage rather than *prescriptive* of it.
Though actually, to be fair, the definition of truth being objective comes from how it's widely instinctively regarded, so it's not merely a matter of the definition. And either way, the argument that the definition is mistaken is problematic because, due to the well-known and commonly accepted definition of truth as being objective, the definition is in some sense a part of its usage, so saying that the definition of it being objective is misrepresentative of actual usage can only be partially true at best; i.e., you can show that their usage of the term is inconsistent with itself, or inconsistent with their belief in how it should be formally defined, or you could argue that the logical consequences of what they suppose is the nature of truth are self-contradictory, or at least contradictory of reality, though that would be problematic because reality could be defined as the set of all truths...i.e., if there's no objective truth, reality could be anything.
And also, you could argue that if the logical consequences of what they suppose is the nature of truth are self-contradictory or contradictory with reality, then that's not a proof that truth isn't actually objective so much as, again, a proof that there's no such thing as truth. Except that it's really not, because truth as objective isn't the *only* aspect of their idea of the nature of truth; there are more, and if they're still valid then the spirit of the concept of truth could still be valid while that one aspect of the concept isn't.
So, anyway, here's my essay showing why the concept of truth as being objective is problematic: https://philosophy.inhahe.com/.../is-there-objective-truth/ I also write why truth is not really a property of external reality here: https://philosophy.inhahe.com/.../the-truth-is-not-out.../