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Not sure where to even begin, which is why I stated the issue in such a nonspecific way. I guess to hone in on the crux of the matter: how do we define "abstract" vs. "symbolic" vs. "technical" concepts?

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I suppose I'm ideally looking for a partial synopsis of what recent philosophy has argued, some kind of brief reference to current consensus or demarcation of the topic.

The dictionary says abstractions are thoughts or ideas that do not have a physically concrete existence. Symbols are languagelike or material representations of ideas. "Technical" is defined as the constituent characteristics and techniques of a subject, art or craft.

You or anyone know of some theoretical or experiential angle clarifying how symbols participate in the interaction between abstract ideation and its instantiation in technical practice, either generally or within specific domains like communications, formal logic, math, scientific modeling or philosophical justification for instance? Even armchair or informal speculating is welcome, a perspective with any degree of focus to give me some traction on objectivity.

A real world example of how the language game concept applies might be helpful.

In mathematics one learns the concept underlying a symbol, then develops a skill for manipulating it. I once read of a prominent mathematician saying that the most valuable competency he had acquired was how to mechanically manipulate elementary calculus as if without thinking.

What is the relationship between abstract, symbolic and technical thinking? — Enrique

Deductive manipulation-substitution (i.e. syntactics) of tautologies. Much more calculating (i.e. computational) than "thinking" (i.e. reflective).