but it leaves lower level intricacies inaccessible - particularly in real and complex analysis, the latter being very important in QT. — jgill
In what sense inaccessible? Do you mean that generalisation actually ends up cutting its connection to the particular?
That shouldn’t happen if it is being done right. This would be a reason why I say that the systems view - which is based on the living relation between the general and the particular - is the proper logic of metaphysical inquiry.
Vagueness, dichotomies and hierarchies. They are the triad on which metaphysics was originally founded. Anaximander’s Apeiron was already there with that.
But then of course the value of atomism as an opposing metaphysics took over. Maths, logic and science shifted to an ontology of bottom up construction and “othered” the metaphysics of holism with its talk of downward acting formal and final constraints.
Nature became understood to be a machine. An engineered cosmic device.
No wonder the atomistic view of metaphysics felt so broke that it’s adherents felt the need to reject metaphysics in its entirety. Metaphysics of the original holistic kind was made the unspeakable.
A scientist or mathematician would seem to need no training in holistic reasoning. What would be the point if it made them uncomfortable about their mechanistic worldview that paid the bills?
With category theory, you do have that effort to return mathematics to some kind of holistic metaphysical foundation. Hegel and Peirce get dragged in as systems exponents.
But I just don’t find category theory a success. I think it lacks the third essential ingredient of a logic of vagueness.
The same applies to quantum theory - at least in the discomfort folk have with its interpretation. The maths itself is all about the inability to have literally a nothingness. There is always an indeterminate potential. Or in other words, there is an everythingness that is a nothingness and so the deeper thing of a foundational vagueness. An Apeiron.
So every conversation must circle back to this schism in metaphysics. Holism produced its antithesis of Atomism. And instead of that then demonstrating the triadic or systematic integrity of the full holistic model, it became the argument for simply rejecting downwards causation, and building a world as understood in terms of upwards construction - a world of nothing but material and efficient cause.
That is how we ended up as Homo technologicalus - living mechanised lives in a mechanised world … bemoaning the loss of something that was forever hard to put our finger on. Something organic, authentic, “spiritual”, in the way it spoke to the ontological reality of formal and final cause.
Holism is a theory of how top down constraints shape bottom up degrees of freedom as a virtuous - or at least self-creating and self-maintaining - closed cycle of activity. A cybernetic system. A dynamical balancing act.
In sharpening our epistemic models of the bottom-up construction part, that should have led to a sharper view of the top-down constraints. But the new mechanical view simply shoved all that metaphysics out of sight. Global constraints became laws that floated off to some place transcendent like mathematical Platonia or science’s “mind of God”.
Hence the metaphysical conversation stalled. One room got renovated and vastly enlarged. The other became some kind of attic full of forgotten relics. The basement - the grounding notion of vagueness or pure potentiality - was forgotten even to exist and became unvisited.
This sounds pretty pessimistic. But the realm of human discourse is also vast. The systems view does exist in every field. There is always plenty being said if your ears are attuned to it. It isn’t the mainstream, but it quietly flourishes.