There are no paradoxes only grammatical errors.
If people err they do not speak the truth they speak only honestly or truthfully. That they conflate honesty with truthfully is merely another version of conflating preference “i like chocolate ice cream” with consensus “chocolate tastes good (to most of us)”, with truth (chocolate may taste good to many people).
Truth originated with the term testimony. We merely combine the word True with the copula “is” (meaning “i dont know how it exists”) and conflate the various positions on the truth spectrum out of convenience and ignorance. We eliminate these problems through speaking if full sentences in operational language (testable transactions)>
This is why all knowledge in science is forever contingent, and all scientists that have been taught sufficient understanding of their craft, rarely make truth claims, and almost always make contingent truth claims, with prevarications like “as far as we know” or “according to x it appears”, and “it’s hard to imagine otherwise”.
Right now my favorite example is the red shift that is hypothetically measuring that the universe is expanding faster than light, when it is just as likely it is a property of space itself that is causing the shift (distortion). We just don’t know. And we can’t observe directly. So we have to triangulate and deduce by some other series of observations. Even then we must eliminate all alternatives before we can make a truth claim – that’s what ‘truth’ means.
In the case of the shapes above, what are the observers testifying to? Their observation? Their shape of the shadow? The shape of the object casting the shadow? People conflate observation, effect, and cause.
|| Observation <- Effect <- Causes
One cannot testify to the shape of the object only to the observation of the shape of the shadow being cast (fact). One can hypothesize a shape of the object (hypothesis). One can speak honestly about that shape (honesty). One can perform due diligence that one does not err (theory) but in science all claims are contingent. One cannot testify to the unobservable, until he has eliminated all possible alternatives (due diligence). Since perfect knowledge is almost never possible outside of the reductio, once on has performed tests eliminating all alternatives (due diligence) one can testify he speaks truthfully of his theory. But in general we make only truth claims of an observation of change in state.
That people do such a thing regularly is simply a matter of ignorance, and the bad habits accumulated in ordinary language grammer – which any time in court will rapidly correct.
The fact that people say “aint” instead of ‘isn’t’, and ‘different than’ rather than ‘different from’, is no different from saying “It’s a shape X” rather than “The shadow I can observe is the shape X”.
It’s just ignorance, error, poor education, colloquial speech, or being verbally lazy.
TAUTOLOGICAL TRUTH: That testimony you give when you promising the equality of two statements using different terms: A circular definition, a statement of equality or a statement of identity.
ANALYTIC TRUTH: The testimony you give promising the internal consistency of one or more statements used in the construction of a proof in an axiomatic(declarative) system. (a Logical Truth).
IDEAL TRUTH: That testimony (description) you would give, if your knowledge (information) was complete, your language was sufficient, stated without error, cleansed of bias, and absent deceit, within the scope of precision limited to the context of the question you wish to answer; and the promise that another possessed of the same knowledge (information), performing the same due diligence, having the same experiences, would provide the same testimony. (Ideal Truth = Perfect Parsimony.)
TRUTHFULNESS: that testimony (description) you give if your knowledge (information) is incomplete, your language is insufficient, you have performed due diligence in the elimination of error, imaginary content, wishful thinking, bias, and deceit; within the scope of precision limited to the question you wish to answer; and which you warranty to be so; and the promise that another possessed of the knowledge, performing the same due diligence, having the same experiences, would provide the same testimony.
HONESTY: that testimony (description) you give with full knowledge that knowledge is incomplete, your language is insufficient, but you have not performed due diligence in the elimination of error and bias, but which you warranty is free of deceit; within the scope of precision limited to the question you wish to answer; and the promise that another possess of the same knowledge (information), performing the same due diligence, having the same experiences, would provide the same testimony.