The ontology is that human endeavour to epistemologically verify ontes or being/existence. Taxonomy is that effort to create a taxon or categorisation/pigeon hole for everything. The two are motivated by different impulses the former to demonstrate existentiality in a logically consistent way, And taxonomy is the effort to tidy everything away so that nothing is missed or forgotten : taxis
in the end we can only know what everything is ultimately mad of through accepting what it is ultimately made of, and how it is ultimately structured through accepting how things are ultimately structured. The stability of our existential experiences are dependent on the stability of what we accept and the stability and firmness of our acceptance.
There is a feeling among philosophers that icons mislead the logical process. I find it written clearly in Schellings and Vollkerts analysis of the symbols of mathematics. This was an idea used in a devastating critique on the old guard of Academia by Russell, who chose to cloak it rather unwarrantable as an attack on Euclid.
The problem is that Vollkert and Schelling, and most early 19th century philosophers are under the mistaken assumption they know what they are talking about! At least they claim to have defined the topic of their discourse. Unfortunately, they had been sold a bill of goods. No one had bothered to check the " ontology" of the concept of a Mathematikos, or to establish if indeed it could be contrasted against a similarly under researched notion of Philosophy. Thus , concentrating on symbols and iconography has a wider context of relevance in human psychological reaction to existential concerns. The matter was fully dealt with by the So called Neo Platonists, and resulted in an increasing adoption of magical and mystical ritual as a consequence.
The current best practice with regard to this matter is found in the work of Bandler and Grindler, particularly in the Structure of Magic I and Ii. The much broader academic discipline, but in my view less effective s Cognitive Behavioural Therapy, in which these ideas are discussed in a standard academic way.
Thus to create a scale of generality based on whether the details are less confusing or misleading seems very odd, but this is what Schelling sets out. Geometry can mislead by its "reliance" on diagrams, arithmetic has no diagrams just magnitudes and is thus less misleading and finally Algebra has just ratios of magnitudes and is the least misleading!
Schelling declares his Leibnizian Agenda: the idea or form that through symbol or characterisation if not in mathematics then in some other universal system of Symbols or Characteristics that unambiguously discovers or reveals reality! This was a dream sought after by Leibniz which his contemporaries paid scant attention to. But Schelling saw in Kant's philosophy a way to devise or construct it based on symbols or characterisations. What he meant by that was described in his idea of the Zeichen. But the Zeichen had to be unambiguous, or else it would lead to mistakes. His argument was that it therefore could not be devised or constructed from Icons, it had to be devised from symbols or characteristics, and the purest form of that was the algebraic reliance on ratios of Ratios!.
While Schelling does not seem to have seen the next step he saw the first step taken by Kant. It seems that Justus Grassmann acting upon Schellings Characterisation of Algebra began to devise the next step in the program.
It is clear that Schelling was not attacking Academia as Russell used his ideas to do, but struggling to solve a problem posed by Leibniz, which required intellectualy taking charge and inventing a new paradigm from Mathematikos and philosophy. To do that he had to establish the hand of his followers to remove from their mind the Kantian limiter that only Mathematikos can be constructed! To fulfill Leibniz dream a new philosophy also had to be constructed and people had to believe this could be done . This philosophy was not constructed onquantity of magnitude, but on Symbols or Characterisations of magnitudes, to avoid the problems of using Icons Schelling insists it must have a purely algebraic formulation.
Justus Grassmann seems to have been inspired to tackle this issue, but his sons were the ones to complete his work.