(…) Mathematical and logical truths are about the design of building arguments, structures and systems, making sense of their pattern or layout, combination, arrangement, order, all that towards reaching conclusions, in the affirmative or in the negative, regardless of their semantic content. That may be a material of reality in the sciences, but quite outside mathematics and logic. Besides, in all languages, truth or Latin veritas or Greek alētheia also has a second associated meaning, which is the antonym of a lie, as in the expression telling the truth; this is not the same as reality or Latin realitas or Greek prāgmatikotēs, i.e. rapport to the imprints of things as they actually do exist and function in the world. It is really a question, worth contemplating, why two concepts that are so dissimilar become confused and identified in the minds of so many people.
The true issues in mathematics are things like definitional aptness, elegance, decidability, consistency, completeness, clarity vs. ambiguity, systemic coordination, theoretical productivity. None of these totally abstract features touch upon things like reality, concrete features regarding the material world, nature, physics or metaphysics.
Truth, as it appears in logic and mathematics, is abstract and regards scheme of train of thought; it has no bearing to meaning or reference to the world. Telling something like “it is”, logical concepts as if… then…, therefore, contradiction, equal, set, subset, and/or, for all, one, five, plus, equals, unit, longer, ratio, infinity etc. are not material of materialism or naturalism, metaphysical or otherwise.
For the rest, one is totally welcome to check the sciences. But, there, logic and mathematics serve as abstract borrowed modeling devices towards applications and descriptions. They do not “exist” or “reside” somewhere; so, they lie outside the administrative realm of materialism and naturalism and anything of the sort. (…)
Epistēmēs Metron Logos Journal No 3 (2020)
DOI 10.12681/eml.22106 ISSN 2585-2973
Konstantinos G. Papageorgiou, D. E. Lekkas