In the whole of mathematics, it is the bits “in between the symbols that are written on the page” that are the most important.
The symbols on the page are, in one sense, arbitrary: it is the pre-existing consciousness and agency of mathematicians that is the ONLY necessary part of mathematics (1).
These necessary aspects of a mathematical system can only potentially be represented algorithmically. And these aspects of a mathematical system, that can only be represented algorithmically, are the causal aspects of the system.
Similarly, in the physics of the world, it is aspects of the real-world mathematical system, that can only potentially be represented algorithmically, that are the causal aspects of the real-world mathematical system.
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- And, of course, it is the same with word and sentence symbols: it is the pre-existing consciousness and agency of the reader/ writer/ speaker/ listener that is the ONLY necessary part of language use: the symbols themselves are, in one sense, arbitrary.