# Constructivism: systems perform operations on both physical objects and abstract objects.

The next thing that must be considered in the system ontology relying on physics is the ontology of physics and mathematics. Such an ontology is proposed in many works, but let's highlight the work of Deutsch^{[1]}, which proposes considering **physics as a science of real objects**, **mathematics as a science of mental/abstract/mathematical objects, and computer science** as **an experimental science of evidence that the behavior of physical objects can somehow reflect the behavior of ideal/abstract/mathematical objects** (i.e., the science of **universal computers** as physical devices capable of performing **computations/reasoning/inference**—traditional electronic, quantum, etc., including computations/reasoning of humans or even human collectives together with their computers). These ideas imply a shift from discussion on **models** and **data** to **universal computers** as physical devices that interpret such data and change the state of the **environment** depending on these computations (inputting data for computations and outputting results in symbolic form being just a specific case here. The perception of the surrounding world and changing the surrounding world and/or "self" as an embodied computer/constructor—that's just a more general case). Central to this **approach** will be the concept of **creator/constructor**—a physical device that can interact with the environment, carrying out multiple operations therein according to descriptions, while maintaining its stability (for example, a catalyst molecule, robot, or human). So, we have some approach to the formal description of second-generation systems: systems of varying **degrees of agency/rationality** (from cosmic matter to robots, rational agents, and various hybrids) create target systems based on some descriptions, and then we can discuss everything as in the first-generation systems approach, where target systems operate within their environment.

A similar approach integrating physics, topology, logic, and computer science with a **shift of focus to operations on objects** instead of considering objects in their static relationships was proposed by Baez and Stay in the Rosetta stone approach^{[2]}. After transitioning from describing system interactions as **processes in networks** (electrical, hydraulic networks, as well as **interaction networks in system dynamics**, usually associated with functional representations of the system, i.e., representations of the functional runtime, the first-generation systems approach), Baez proposes using the formalism of **symmetric monoidal category theory** to describe not just processes, but **open systems**, implying interaction with the environment^{[3]}. Once again, we see a move towards using category theory as a foundational ontology for a system, with the main shift being from expressing ontology in **static relationships** to **morphisms, changes**. This logical move corresponds to the move towards **constructivism in mathematics**, where from "eternal classes" and their relationships, we move to **operations** **of construction/construction**^{[4]}. This allows for a **constructivist reformulation of mereology** to become a central ontological discipline of the systems approach because it examines **part-whole** relationships^{[5]}.

Another move in this direction of constructive mereology is the ideas by Fine on mereology, including abstract objects^[Kit Fine, Towards a Theory of Part, 2010, https://as.nyu.edu/content/dam/nyu-as/philosophy/documents/faculty-documents/fine/accessible_fine/Fine_Theory-Part.pdf. It suggests **operations of constructing a whole from physical and abstract parts** (for example, constructing a set from its elements). Although Fine does not explicitly state this, defining construction operations (as well as morphisms of category theory) as being performed as if by "no one," but behind these operations, one can easily see a physical device-constructor from constructor theory, including for abstract parts—a physical device embodying a "universal computer," including a quantum computer, and a living mathematician—they are computationally equivalent and physic...

David Deutsch, The Beginning of Infinity, 2011, https://www.thebeginningofinfinity.com/ ↩︎

John Baez and Mike Stay, Physics, topology, logic, and computation: a Rosetta Stone (2011), in "New Structures for Physics", ed. Bob Coecke, Lecture Notes in Physics vol. 813, Springer, Berlin, 2011, pp. 95-174, https://arxiv.org/abs/0903.0340 ↩︎

John Baez, Symmetric Monoidal Categories: a Rosetta Stone, https://johncarlosbaez.wordpress.com/2021/05/28/symmetric-monoidal-categories-a-rosetta-stone/ ↩︎

Constructive Mathematics, https://plato.stanford.edu/entries/mathematics-constructive/ ↩︎

Mereology, https://plato.stanford.edu/entries/mereology/ ↩︎