INTEGRATED PLURALISM

Definition 1. H is a hierarchy if and only if it is an ordered triple H=(S,b,D) where S is a non-empty set, b a distinguished element of S and D a binary relation in S such that H1 S has a single beginner, namely b (that is H has one and only one supreme commander). H2 b stands in some power of D to every other member of S, (that is no matter how low in the hierarchy an element of S may stand, it still is under the command of the beginner). H3 For any given element y of S except b, there is exactly one element x of S such that Dry (that is, every member has a single boss). H4 D is antisymmetric and transitive. H5 D represents (mirrors) domination or power. (That is S is not merely a partially ordered set with a first element: The behavior of each element of S save its beginner is ultimately determined by its superior),

This description of hierarchical systems is determined primarily by his initial definition of a hierarchy as a system that includes dominance-subordinance properties.

The five preceding statements constitute the axiomatic foundations of the micro theory of hierarchies Any specific structure has to satisfy the above axioms if it is to qualify as a hierarchical structure--by definition of "heirarchy".

Simon deduced his concept of hierarchy from an empirical observation of nature. Bunge derived his specifically from the dictionary definition. There may very well be systems that would, from Simon's point of viewú, qualify as hierarchies and would not from Bunge's, With this in mind, we can examine Bunge's discussion of level structures.

Definition 4.

L is a level structure if and only if it is an ordered pair L=(S,ES wúhere S is a family of sets of individual systems, E is a binary relationship in S such that

L1 Every member of S is a set of systems that are equivalent in some respect,

L2 E is a one-many reflexive and transitive relation in S.

L3 E represents (mirrors) emergence or coming into being of novelty of qualitatively new systems in a process.

Emergence is a concept that has been ill-defined in systems literature. Here we see it as "mirrored" by that relationship that united the elements to form a system, or in this case a level structure. Bunge defined "level structures" in terms that were not in violation of the principles Simon used to define hierarchies, he continued by giving more explicit definitions of the concept of emergence,

Definition 5.

A set of individual systems is (constitutes) a level if and only if it is a member of a family S of a level structure I.

Definition 6.

A level is newer than another level of the same level structure if and only if the former has emerged from the latter.

Emergence, then, as seen by Bunge, is a temporal property. One level emerges from another if and only if it arrives later in timeo A level can be described in his words as; "A collection of systems characterized by a definite set of properties and such that it belongs to an evolutionary line, though not necessarily to a line of: biological descent."

Bunge's ontology is one that is consistent with what he called "integrated pluralism", an ontology that proclaims both the "diversity and the unity of the world". He presented five theses of integrated pluralism.

01 Reality (=the wúorld) is a level structure such that every existent belongs to at least one level of that structure. 02 In the course of every emergence process (self-assembly or evolution) some properties, hence also some laws, are gained while others are lost. 03 The newer levels depend on the older ones both for their emergence and for their continued existence. 04 Every level has, within bounds, some autonomy and stability. 05 Every event is primarily determined in accordance with the set of specific laws that characterize its own level(s) and the contiguous levels.

Assuming these hypotheses to be true, and reality is organized in levels and is knowúable, then that structure, the author maintained, must be mapped in our scientific knowledge. "That is," as he put it, "the ontological theses concerning levels, if true, must have epistemological partners that can be checked by examining knowledge itself." He suggested the following epistemological principles.

E1. The real level structure is knowúable and scientific knowledge is a level structure that matches the former. E2 Every newúly formed science has its peculiar objects and special methods. And, although every science retains some of the ideas typical of the parent science(s) it does not preserve them all and it introduces new concepts absent from the latter. E3 The understanding of any level is greatly deepened by research into the adjacent levels particularly the underlying ones. E4 Every level of science has, within bounds, some autonomy and stability. E5 Every system and every event can be accounted for (described), explained, or predicted as the case my be) primarily. in terms of its own levels and the adjoining levels without necessarily involving the whole level structure.

In summary, the most important point about integrated pluralism is that it is logically plausible and in practice it is fruitful, As he ends his paper, "Integrated pluralism is worth being further explored as a candidate to the metaphysics of science that acknowledges the existence of distinct but interrelated levels of organization.