Philosophy might be our largest field of science, belief and thinking. Here we will focus on what is often referred to as mathematical philosophy and on language philosophy.
Mathematics can be regarded as a kind of language, but with the difference from natural languages that the referents of mathematical statements always has an internal or mental nature, i.e. the mathematical objects exist only as mental objects. What differences between mathematics and natural languages does this entail?
If something has the ontological status to be a mental object, then we should by definition treat this object as constructed, i.e. we are looking at an instance of constructivism.
But, on the contrary, if something has the ontological status of being a physical object, or any other non-mental object, we should equally regard this object as being absolute. This means that we in these cases cannot have constructed them. This means that we should not talk about constructivism concerning facts.
Theorem:
1. A use of language with physical or other non-mental objects as referents never constitutes an instance of constructivism.
2. A use of language with mental objects as referents always constitutes an instance of constructivism.
This theorem is often not universally accepted. On universities worldwide mathematics constructivism is regarded as a deviation or a sub-division of classical mathematics, which give rise to contradictions. Maybe this view is not universal, but also the existance of it in certain mathematical contexts still gives rise to contradictions, which is problematic for mathematics as a whole.
If we hold this theorem to be true, then it follows that mathematics must be constructivist to its nature (there are almost never any empirical evidence to ensure the truth of a mathematical statement), whereas i.e. natural languages cannot be constructivist (we most often have empirical evidence granting the truth).
(The text above is subject to ongoing changes, updated June 27th 2021)
Here is an essay treating aspects of the language philosophy of Wittgenstein, that are relevant for our discussion about meaning and logic (in Swedish):
Den ontologiska distinktionen och frågan om objektens status och roll i Wittgensteins Tractatus