The provability of the existence of truth in an objective sense is one of the most fundamental problems when it comes to the study of the conceptions of truth in the field of epistemology, for the verification of such an entity is always contrained by the degree of cognitive tangibility of that entity and the possiblity of errors in your interpretation. But based on whatever little I have read about the conceptions of truth, it seems to me that both the issues can be resolved by resorting to the correspondence theory of truth with a hint of fallibilism thrown into it.
The basic idea here is to see each correspondence(C_i_j) between the abstraction(A_i) and the reality(R_j) as remappable with a fungibilty quotient(fq). The fungibility quotient(fq) can be then used to determine the degree of cognitive tangibility, whereas the remappabilty can be used to enforce the popperian/darwinian/deutschian notion of variation and selection(a.k.a conjecture and criticism) to enable error-correction.
- An abstraction(A_i) need not necessarily represent reality(R_j). Multiple abstractions can also represent a single reality, but a single abstraction cannot represent multiple realities — a strict constraint to discourage probability calculus(See Fuzzy Logic) and other many-valued states(See Many Valued Logic) as a means to represent the truthhood or falsehood of a statement(proposition/assertion?).
- I have been made aware by some of my programmer friends that fungibility quotient(fq) is just an encoding scheme here and that it doesn't contribute anything to the solution in any fundamental way, but I have a feeling that they are confused here. Needs further discussion.
- I might have got some set theory notions wrong here, that is, remappability might not be a viable idea based on the principles of set theory. Needs further Investigation.
- Tarski, A. (1944). The Semantic Conception of Truth: And the Foundations of Semantics. Philosophy and Phenomenological Research, 4(3), 341-376. doi:10.2307/2102968
- David, D. (2021). In conversation with David Deutsch: musing about statements, propositions, and truth
- Kolenda, K. (1979). Truth and Fallibilism. Transactions of the Charles S. Peirce Society, 15(3), 251-258. Retrieved May 8, 2021, from http://www.jstor.org/stable/40319611
- Massimo Dell'Utri. (2005). Truth and fallibilism: a dubious combination in Robert Nozick's philosophy
- Massimo Dell'Utri. (2014). New Frontiers in Truth
- Bertrand Russell. (1912). Problems of Philosophy