Averroes wrote: ↑Mon Oct 05, 2020 9:21 am
Immanuel Can wrote: ↑Mon Oct 05, 2020 3:11 am
Averroes wrote: ↑Mon Oct 05, 2020 1:54 am
mathematical linguistic
No, it's either a mathematical placeholder OR a linguistic one. It's not both.
I understand your statements and wishes, but that's not how it works out in real life.
Actually, it is. Mathematics is a universal code system. It works the same in all languages and cultures. "Natural languages," as you call them, do not. That's one of the big differences between linguistics and mathematics. They are not interchangeable, and to call maths a "language" is to mistake a metaphor for a reality. It's not actually a "language": it's a universal code for quantities.
That's why people who, say, study in other countries often prefer to study mathematical subjects like computers, engineering or physics, and often shy away from linguistic ones like the Humanities. It's because maths is, if not any easier, at least accessible universally, across all languages and cultures; but subject dependent on natural languages are far more difficult and inaccessible cross-culturally. Math does not require things like linguistic competency, cultural awareness, idioms, metaphors, implications, mythologies, vocabularies, morphologies, syntactics, social dynamics, grammar and pronunciations.
Alright, I read what you wrote. May I now please ask you whether you consider the sequence of strings/symbols "¬(P∧¬P)" to be part of natural language or not?
No, it's not strictly part of natural language. No natural language contains it, and person unfamiliar with the linguistic content or the symbology of this logical system is going to understand what it means. And unlike, say, a sentence in English, it lacks the syntactic-grammatical and cultural elements required of English.
Instead, it contains both placeholders for concepts, such as "¬" and mathematical symbols, like brackets, and linguistic placeholders, such as "P." But "P" there is not algebraic. It stands for "proposition." It's linguistic. So symbolic logic is neither purely maths nor purely linguistics: it's an artificial hybrid, designed to try to impose mathematical precision on linguistic contents.
And what practitioners of symbolic logic always discover is that
the more precision is imposed, the less real-world connection there is in symbolic logic. As the operations become too formal, they become increasingly removed from the empirical realities and natural vicissitudes they are intended to represent and manage. To a degree, they help impose rigour on linguistic operations; but there is clearly a limit to their applicability. And were it not so, then all philosophy after Quine et al. would surely have become nothing but a matter of symbol systems; for why would one not opt for the maximally-rigorous formulations, if they always also worked better in reality?