Final answer:
The mathematical context is missing which is necessary to discuss absolute convergence. In mathematics, absolute convergence of the sum of two series is guaranteed if each series converges absolutely. The philosophically inclined question addresses different aspects of truth and evidence but does not provide the foundation for a discourse on mathematical convergence.
Step-by-step explanation:
The question seems to miss the necessary mathematical context to provide an answer about convergence of series or sequences. Instead, the question drifts into philosophical claims about the truth and nature of reality. To accurately answer questions about the absolute convergence of series, we require specific mathematical series or sequences to discuss. In mathematics, a series or sequence is said to converge absolutely if the series of absolute values of its terms converges. That means, given two series ∑a_n and ∑b_n, if both series converge absolutely then the series ∑(a_n + b_n) will also converge absolutely. A counterexample to disprove a claim about absolute convergence would involve providing two absolutely convergent series whose sum does not converge absolutely, but such a counterexample cannot exist as per the triangle inequality we use to establish the absolute convergence of the sum of two absolutely convergent series.
When discussing empirical claims and their relation to the truth, evidence supports the probability of a hypothesis rather than proving it absolutely. Truth, as the question suggests, does not have degrees; a statement is either true or it isn't. This fact underscores the importance of evidence in supporting claims and highlights the impossibility of contradictory claims, like the flat and spherical Earth, being true simultaneously.