The algebraic recursive structure of countable languages of classical first-order logic with equality is analysed. all languages of finite undecidable similarity type are shown to be algebraically and recursively equivalent in the following sense: their boolean algebras of formulas are, after trivial factors involving the one element models of the languages have been excepted, recursively isomorphic by a map which preserves the degree of recursiveness of their models.

Using Evidence Logic (EL), a logic which is conceptually to Classical Logic and which is equipped with both gradational confirmatory predications and gradational refutatory predications, further investigation of some of the persistent problematic aspects of negation is facilitated. This perspective helps to illuminate distinction of “absence of evidence”, and may help further understanding of the semantics of negation.

We explicate the view that our ignorance of the nature of the real world R, more so than a lack of ingenuity or sufficient time to have deduced the truth from what is so far known, accounts for the inadequacies of our theories of truth and systems of logic. Because of these inadequacies, advocacy of substantial correctness of such theories and systems is certainly not right and should be replaced with a perspective of Explorationism which is the broadest possible investigation (...) of potential theories and systems along with the realization that all such theories and systems are partial and tentative. For example, the position of classical logic is clearly untenable from the perspective of explorationism. Due to ignorance regarding R and, consequently, the partial and evidential nature of our knowledge about R, an explorationist foundational logical framework should contain machinery which goes beyond that of classical logic in the direction of allowing for the handling of confirmatory and refutatory evidential knowledge. Such a foundational framework is described and analysed in terms of its ability to tolerate substantial evidential conflict while not allowing contraditions. (shrink)