group: a number of people that work together or share certain beliefs
organization: a group of people who form a business, club, etc. together in order to achieve a particular aim
b is an object aggregate means: b is a material entity consisting, at any time t at which b exists, exactly of a plurality of objects as member_parts at t.The member_part_of relation is given this definition (Note: "<=" means "less than or equal to"):
b member_part_of c at t =Def. b is an object & there is at t a mutually exhaustive and pairwise disjoint partition of c into objects x(1), ..., x(n) (for some n > 1) with b = x(i) for some 1 <= i <= n.
Later and by example, the BFO Guide offers additional guidance on 'object aggregate'.
Different sorts of examples of object aggregates satisfy further conditions. For example, example (object aggregate) [an organization is an aggregate whose member parts have roles of specific types (for example in a jazz band, a chess club, a football team); a swarm of bees is an aggregate of members who are linked together through operations of their motor and visual systems]; and so on.
Object aggregates may be defined through physical attachment (e.g., the aggregate of atoms in a lump of granite); defined through physical containment (e.g., the aggregate of molecules of carbon dioxide in a sealed container; the aggregate of blood cells in your body). Object aggregates may be defined by fiat (e.g., the aggregate of members of an organization]; or defined via attributive delimitations (e.g., the patients in this hospital; the residents of Palo Alto; your collection of Meissen ceramic plates.
[76] provides a formal treatment of aggregates (there called 'collections') that is broadly consistent with the above except that it assumes that membership in a collection is fixed over time. However, as is true for many material entities, note (object aggregate) [object aggregates may gain and lose parts while remaining numerically identical (one and the same individual) over time. This holds both for aggregates whose membership is determined naturally (the aggregate of cells in your body) and aggregates determined by fiat (a baseball team, a congressional committee).]
Lastly, the BFO Guide states this about aggregates across BFO:
Object aggregate is to be treated as a close analogue of set of objects, in the mathematician's sense; thus an object aggregate has no parts other than the objects that are its members. In this document we concentrate on the use of 'aggregate' as it appears in the term 'object aggregate'. However, 'aggregate' should be understood as being generalizable to all continuant BFO categories. Thus for each BFO category X, the user of BFO as at his disposal also the category aggregate of X. [51].
[51] Kerry Trentelman, Alan Ruttenberg and Barry Smith, "An Axiomatisation of Basic Formal Ontology with Projection Functions", Advances in Ontologies, Proceedings of the Sixth Australian Ontology Workshop, Adelaide, 7 December 2010, Kerry Taylor, Thomas Meyer and Mehmet Orgun (eds.), 2010, Sydney: ACS, 71-80.
Questions:
"Object aggregate is to be treated as a close analogue of 'set of objects',
in the mathematician's sense; thus an object aggregate has no parts
other than the objects that are its members. In this document we
concentrate on the use of 'aggregate' as it appears in the term 'object
aggregate'. However, 'aggregate' should be understood as being
generalizable to all continuant BFO categories. Thus for each BFO
category X, the user of BFO has at his disposal also the category aggregate of X. [51]."
While 'object aggregate' defines class membership for 'object', the BFO Guide constrains membership to 'objects' with the same-typed 'role(s)'. The 'object aggregate' set-theoretic construct is ontologically constrained by the member part role type(s), as it is ontologically constrained through its specialization of 'material entity'. However, this raises an interesting point. If 'object', 'object aggregate' and 'fiat object part' do not exhaustively close 'material entity' and if a BFO user has "category aggregate of X" at his disposal, then would it not follow that no part of BFO exhaustively closes? If we consider 'aggregate' merely as a set-theoretic construct, then, for example, cannot there be an aggregate of 'Entity' at the top-most level? I suppose one cannot impose an aggregate of, for instance, 'Material Entity' and 'Process' (category X does not resolve to the same immediate parent) but can define an aggregate of 'Material Entity' and 'Immaterial Entity' (category X resolves to the 'Independent Continuant' immediate parent).
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> group = an object aggregate whose member-parts are persons who act together
This implies a trans-ontological, specific dependence relation between 'person member parts' and 'process', whereby the person member parts participate in some process at some point in time (either temporally contiguous or temporally discontiguous). Acting together is to be concurrently and/or co-dependently engaged in some act (i.e., 'process'). Is this relation mandatory for defining a 'group'? Cannot a group simply be an ad-hoc collection of spatially co-located people? For example, a group instance could be an 'object-aggregate' particular of people who are demarcated by some fiat boundary at the intersection of 57th Street and 3rd Avenue in New York, NY 10021 on Thu, 20 Aug 2015 @ 1:00 PM (EDT). This group is defined by 'attributive deliminations'. As the group awaits a traffic light change, it can gain or lose parts over time as people step into or out of the group's fiat boundary.
> organization = a group in which some member-parts have specifically defined roles
If one considers 'organization' to specialize the more general 'group', then the same points apply here. Your proposed definitions present this generalization-specialization relationship.
By comparison, here again are the proposed definitions of 'group' and 'organization'.
[BS] group: an object aggregate whose member-parts are persons who act together
[AP] group: an ad hoc assemblage of people for which the assemblage has no prescribed purpose.
[BS] organization: a group in which some member-parts have specifically defined roles
[AP] organization: a prescribed and contractually obligated assemblage of people for which the assemblage has one or more prescribed purposes for achieving one or more prescribed goals.
In your proposed definitions, the differential is having specifically defined roles. With my proposed definitions, the differentia are (a) a qualification on the assemblage of people and (b) a qualification on purpose. This takes me back to a question I asked a long time ago on the Aristotelian definition structure (i.e., A is a B that C, where 'C' presents the differentia). With tangible objects, which physically occupy three-dimensional space, the differentia can be scientifically classified, for instance, down to the molecular level, and verdicality can hold at other 'ontologically zoomed', yet orthogonal, views of reality. This proves to be tricky with intangible objects. The 'group' and 'organization' terms do not present physical entities. What specific criteria must be applied for their differentia?
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Barry,
What are your thoughts on the relation between organization as you have defined here (organization = a group in which some member-parts have specifically defined roles) and a corresponding legal entity?
For example, if "Apple Computer Organization" as an instance of "organization" then I assume there will be a distinct corresponding "Apple Computer Legal Entity" that is responsible for paying taxes, paying employees, etc...
Where should "Apple Computer Legal Entity" be classified (i have seen other discussion threads leaning toward generically dependent continuant)?What is the relation between the "Apple Computer Legal Entity" and "Apple Computer Organization"?
-joe
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