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Location: http://www.cs.mun.ca/~ulf/gloss/obj.html. By Ulf Schünemann since 2002. Please mail any comments.

1. Analysis of Concrete Objects
2. Bottom-Up Analysis: Physical + Abstract (object = matter + form OR particularity + separation)
3. Top-Down Analysis: Objects have Properties (object = substance + properties)
4. Formal Model of Concrete Objects

Substance theory: An object is something over and above the properties that inhere in it [wiki]

1. Platonism: Besides his panta rhei, «Heraclitus also emphasized the intangible logos ... "all things (panta) come into being according to this logos"» [TOC 673]. «A century later, Plato adopted Heraclitus' distinction between the ever-changing flow of all things and the intangible logos that determines that flow. ... Plato proposed the intangible, unchanging mathematical forms or ideas as the true reality, which is reflected in the changeable, illusory flow of physical things. Aristotle ... considered the physical world to be the ultimate reality and treated the forms as abstractions learned through sensory experience. ... In ... Process and Reality, Whitehead adopted a Platonic ontology with the ever-changing physical processes distinguished from the eternal mathematical, logical forms» [TOC 673].
   That is, in an analysis of "objects" which starts from the flow of physical particularity, an object can be decomposed into that what is in flow, abstracted from the form it takes, its matter, and its form. See Type for how the two relate.

   concrete object = formless matter [physical] (what flows) + form [abstract] (how it flows)

2. Alternatively, not Platonic forms cooky-cut objects out of the matter, but the observer does, by way of stabilization against the flow, involving abstraction from changes [OOO] -> more

   concrete object/individual = physical particularity (fuzzily patterned) + separation & stabilization & abstraction

   Caveat: Smith here makes a non-standard distinction between particularity and (material or abstract) individuals.
   - Particularity and individuality are «two overarching metaphysical characteristics ... that are essential to our everyday conception of at least ordinary material objects. Both ideas ... come together when we conceive of a stable and enduring thing, such as a table, an old notebook, or a favorite bristelcone pine. ... It is helpful to separate them, however, not only because they have different conceptual structures, but also because ... they stem from different sources.» [OOO 117]
   «The whole point is «to separate the sense of the very specific or local or "peculiar," to be associated with particularity, from the quite different sense of being discrete or chopped up into distinct units or wholes, to be associated with individuality» [OOO 120]. «[P]articularity and individuality, as I am using the terms, are conceptually orthogonal. This can be seen by observing that they occur differentially, or at least potentially occur differentially» [OOO 124].
   «It is non-standard to distinguish particularity and individuality ... The traditional treatment is ...: particulars are viewed as a kind of individual ... Non-particulars, however - like generics, for example, and/or abstract entities - are (or at least can be) counted as individuals, but not as particulars ... Thus [the tiger] that snarled at your Land Rover yesterday, would be a (bare) particular ... The type tiger, being abstract, would still be individual, but ... not a particular ... The same would be true of the generic tiger, the tiger that is threatened with extinction.
   It is traditional, in other words, to take the word `individual' to be essentially synonymous with `object' or `entity' - i.e., as denoting the most general class, of which particular are taken to be an important, or even the paradigmatic, species.» [OOO 123f]
   - Particular. «By `particular' ... I mean something like `occurrent': something that is located or that happens, something that is embodied ... If one is a physicalist ... a possible alternative for `particular' might be `concrete.' [OOO 117ff]
   - Individual. «By individuality ... I mean whatever it is about an entity that supports the notion of individuation criteria - something that makes `object' a count noun, something that makes objects discrete. Somehow or other, an individual object is taken to be something of coherent unity, separated out from a background ...
   Etymologically, individual means indivisible: not to be divided. That should not be taken as implying that individuals cannot be chopped up at all ... Rather, it is to imply that, qua individuals, they have an overall integrity or unity that is liable to be violated by taken them apart. Because they are discrete, in other words, individuals support the notion of half, as well as of two. Unlike water, if you put individual and individual together, you get two individuals, not just more. By the same token, if you taken an individual apart, you get parts or fragments, not just less.« [OOO 119f]
   - Individual vs identity: «Because objects (individuals) play such a central ontological role ... questions of identity are often assumed, by default, to be questions about the identity of an individual. ... In practice, however, it is easy to see that it is not always justified. Diffusions (such as fog), abstractions (such as melancholy), and collectives (such as of people) can have identities without necessarily being individuals, or supporting individuation criteria.» [OOO 132]
   «Identity ... is simply the property of being the individual in question; it is not a feature or property relevant to whether it is the indivudal in question.»

   navigation bar: Universals (properties, attributes, features, forms, types)

   object = universals (shared) + X (unshared)

   concrete obj.: properties <-> concept: attributes

   individual: properties <-> particular: features

   properties <-> classes

   ontological status of universals

   attributes denote properties

   «As an example of particularity without individuality [individual objecthood], consider Strawson's analysis of the reference or content of what he calls feature-placing sentences, such as "it is foggy" or "it is raining." ... If it rains, and, noticing that facts, you say, "It's raining" ... then what you are saying is that the feature "raining" is being exemplified, around here and about now. You do so, however, without identifying or individuating any object or individual of which that feature or quality holds."What's raining?" is not a sensible question to ask. It cannot be answered, indeed it has no answer, because the `it' in "It's raining" does not refer. In this construction, to say the same thing in a different way, rain is not a property. It is not a property because it is not being predicated of any (individual) object» [OOO 124].
   «I will follow Strawson in using the word `feature' for the sorts of thing, like rain, that in this way do not require individual objects for their exemplification, and `property,' in contrast, for the more familiar notion of something that does require an object. ... Features, on this analysis, are thus in some metaphysical sense simpler than properties - and perhaps, though it is less clear on what metric, more basic as well» [OOO 124f] «It would be a mistake ... to cast the feature-property distinction into stone. ... [S]uppose ... that in response to a woman's saying, "It is foggy" (feature-placing), a man agrees by replying, "Yes, I guess the fog has come in." ... In virtue of saying "the fog," [the man] commits an additional act of individuation ... But what is the man reffring to, and how does that relate to what the woman said? That is not so clear.» [OOO 127]
   «[W]hat is particular but not individual [not a discrete object] is the metaphysical path or disturbance or stuff in the world that warrants the feature placement. Thus suppose that last night you drove for three long hours through the rain. There is no denying that the rain ... was concrete (and thus particular). Suppose, however, that ... you thought "it's too bad that it is raining" - thereby engaging in an intentional act of feature placing. ... What is particular-but-not-individual ... is that towards [which?] your feature-placing was directed. Or so at least we theorists or observers would say, although to do so is distracting, in a way, because it is so tempting for us, from our different theoretical position, simply to call that towards which your feature-placing is directed "the rain." But nothing follows from that; all it means ... is that we theorists have individuated the rain, not that you have."Alternatively, one could say: "It is what makes a (particular) act of feature-placing true that is [a] particular but not [an] individual."» [OOO 125f]

C. Aristotle's linguistic approach

a) Hence, in terms of a compositional semantics of statements, there must not only be things (objects) denoted by the subject and argument expressions in the statement, but there must also be something meant by the predicate in the statement. For instance, in case of the statement "the apple is red" there must be some "apple" and something like the "red-being" or "redness".

b) Psychologically, in order to use and reason about such a statement, one must know a referential concept "apple" and a predicable concept "red-being". «Referential and predicable concepts are not the same, but rather are complementary, types of cognitive structures ... That is, predicable concepts, as unsaturated cognitive structures based upon capacities to identify, characterize, and relate objects in various ways, are complemented in speech acts by referential concepts as cognitive structures that enable us to refer (or purport to refer) to the objects that we characterize and relate to one another. And, just as it is the exercise of a predicable concept that informs such an act with a predicable nature, so it is the exercise of a referential concept that informs that act with a referential nature» [KRCR].
«Referential concepts are initially developed not in terms of reference to objects in general but to objects of a sort--where, by a sort (or sortal concept) [^], I mean a type of concept (such as Raven, dog, horse, car, tomato, etc.) whose use in thought and communication is associatated with certain identity criteria, i.e. criteria by which we are able to distinguish and count objects of the sort in question» [KRCR] -> [IC].

Properties and property-spaces «The properties an object may have fall into natural groups or spaces of contraries. ... Provided we speak only of fully exact properties, in each of those spaces no object can simulataneously have more than one property-- it cannot have two masses, temperatures, etc. ... Such spaces of properties are often known by their own names, like `mass', `volume', and so on ... Following Johnson, we call mass, volume and the like determinables and the precise properties making up such a space determinates. So for the determinable mass there are indefinitely many determinates, including 1gm, 2gm, 3.78gm, and so on, and similarly for other determinables. Determinables are sometimes called `attributes' and their determinates `values' of these attributes. ... There are also multi-placed determinates, like distance (always of one thing to another) and angle (of one thing to another with respect to a third). By plugging gaps in multi-placed determinables we get determinables of fewer places, e.g., distance from Rome.» [Parts 343f] Property-space ("general property") P represented by propositional function S->P «A substantial property must ... be representable as a propositional function, or predicate, on a domain that somehow includes S [the set of substantial individuals]. The function will represent the property in general, e.g. age; and its value for a particular individual, the given property of the individual concerned, eg. its age. ... For example, mass is representable by a certain real valued function M on the set of quadruples <body, reference frame, time, mass unit>» [MB3 63].

c) Ontologically, one may say that "redness" refers to something in the "apple" object, something called a property (or attribute) of the object. Although (some) objects are intuitively perceived as wholes (e.g., the apple), an analysis (= "decomposition") of the object is still possible and can identify properties (attributes) of the object like shape, color, texture, taste, and so on, which can be predicated of the object. Properties are different to objects. First, to explain the world (with objects) one needs more than (a bundle of) properties. «An entity possesses properties but is not a bundle of properties. That entity b possesses properties P₁, P₂, ..., P_n, ... does not entail that b = {P₁, P₂, ..., P_n, ...}. If it did we would have to define properties independently of any individuals, and condone absurd expressions such as `{P₁, P₂, ..., P_n, ...} possesses P₁'» [MB3 64].
Second, properties exist in a fundamentally different way to how objects exist. Properties exist (in a perceiveable way) only through the (perceived) existence of objects. This lead Aristotle to distinguishing two modes of being [x] of "whatever is" [AUOOP]: that which exists in itself, and that whose existence logically dependent upon that of something else (so that it can be predicated about this "something else"). «Aristotle designates these two modes of real being as substance and accident» [AUOOP]. (see subclassification of accidents into categories; see concrete vs abstract mode-of-being).

Object [referenced by term] = mutable properties [predicated] + substance [basis of identification] physical object (substantial individual) = substantial properties + substance conceptual object = formal properties (attributes) + substance

In order to be able

1. to compare two objects not only for identity but w.r.t. certain aspects only (e.g., a green banana object and a yellow banana object),
2. to «speak of an object remaining the same yet different, invoking the idea of change», and
3. to explain intra-active and interactive aspects of the existence of objects,

1. «on to which the attributes which [the object] shoulders, and with respect to which [objects] can be compared, are grafted» [x].
2. It is that aspect of an object which persists through a change (also called `prime matter') [x]. «[S]ubstance is ... the ground which enables an object to be the same in spite of the newness of its features» [x].
3. Substance «imbues an object with the active power to initiate change in itself (Leibniz) or in another object (Locke and Kant) and the passive power to allow change to be initiated in it (Locke and Kant). In this sense, substance is seen as the ultimate centre of force used in grounding change-producing actions and causalities.» [x].

D. Bunge's approach (for concrete objects only)

Assembly theory: two modes of association:
a. physical sum (juxtaposition, eg. two things placed side by side),
b. physical product (superposition, eg. the mixture of two fluids)

Bare individuals and non-individual properties are fictions: «entities deprived of most of their properties [except for their association], forms without a definite stuff. However, we warned that these are fictions and anticipated that they would enable us to construct the notion of a real thing as a fully qualitied individual. This is indeed what a concrete or material object, such as a radio wave or a person or a society is: namely an entity endowed with all its properties, both intrinsic and mutual, permanent and transient» [MB3 110]
«The set of (unarized dichotomic) properties of individual xT is called
p(x) = {PP | x possesses P}» [MB3 72].

«Definition 3.1 ... The individual together with its properties is called the thing (or concrete object) X» [MB3 111].

A formal object model based on this definition comes next

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Formal Model of Concrete Objects

Recall «Definition 3.1 ... The individual together with its properties is called the thing (or concrete object) X» [MB3 111].

If "x's properties" for a substantial individual xS is formalized as the set p(x)P of properties,
and if "A together with B" is formalized as the tuple <A,B>
then concrete object X can be formalized as <x,p(x)>.

But note that «X =_df <x,p(x)> ... characterizes a concept of a thing rather than being the "real definition" of a thing» [MB3 112]. <x,p(x)> is a formal model of concrete object X, not X itself: a concrete object is not a tuple (ie. a mathematical, not concrete, concept), nor does it comprise a set (which is another mathematical, not concrete, concept).

Functional schema «Theoretical science and ontology handle not concrete things but concepts of such, in particular conceptual schemata sometimes called model things. Our construal of a thing as a substantial individual together with the set of its properties ... is of course such a model thing - albeit a rather poor one. A richer characterization of a thing is given by a set equipped with specified relations, such as functions or operations. For example, if the thing represented is a force field, then the set will be a portion of a geometrical manifold M - e.g. a region in Euclidean three space - together with a tensor field F on M. Briefly, <M,F> ^= field» [MB3 119, underlining added]. «We shall adopt this mode of representation by making

Definition 3.6 Let X = <x,p(x)> be a thing of class TThing. A functional schema X_m of X is a certain nonempty set M together with a finite sequence F of nonpropositional functions on M, each of which represents a [general] property of T's. Briefly,

X_m =_df <M,F>, where

F = <F_i | F_i is a function on M & 1 =< i =< n < >» [MB3 119]

«The base set M will be denumarable or nondenumerable, as the case may be. It may or may not be thought of as mapped on a subset of physical spacetime. ... The finiteness of the set of components of F agrees with the part of Postulate 2.3 specifying that there are finitely many general properties [aka. property spaces, cf.] (such as length or longevity). And it does not contradict the second part of that postulate, according to which p(x) is nondenumerable for each xS. Indeed, ... a single continuous general property, such as age, gives rise to infinitely many individual properties (such as successive ages) as the property in question takes values. ...
Example 1 The simplest functional model of a corpuscle with variable mass is the classical mass point. Here M=F×T, where F is the set of referenceframes and T=R the real line, everypoint of which is interpreted as an instant of time. And F=<mu,pi,psi> is a triple of functions on M=F×T, such that mu(f,t) represents the mass, pi(f,t) the position, and psi(f,t) the force acting on the corpuscle, relative to frame fF, at time tT» [MB3 120].

State functions «The components F_i of the list F of functions in a functional schema are usually called state variables [or state functions] because their values contribute to characterizing or identifying the states the thing of interest is in» [MB3 125]. The F_i: M->V_i have unspecified co-domains. They represent the property spaces of X ("general properties"). Each value of F_i at a point mM represents an ("individual") property of X.
F is called the total state function for X, and its value F(m) = <F₁,F₂,...,F_n>(m) = <F₁(m),F₂(m),...,F_n(m)> for mM represents the state of X at m in the representation X_m [MB3 127].

«Notice the cautious expression `in the representation X_m'. The reason is that there is no such thing as the absolute statefunction for a given thing: indeed there are as many state functions as functional schemata of the thing can be conceived» [MB3 127]. «The various functional schemata of a given thing need not be equivalent: for example they may exhibit different amounts of structure» [MB3 121]. «It goes without saying that things belonging to the same natural kinds - e.g. electrons, neurons, peasant societies- are represented by the same functional schemata. In particular, indiscernables are representable by the same model things. In other words, for theoretical purposes we may treat indiscernibles as if they were identifical - which of course they are not» [MB3 122].

For systems: «The domain A of the state function F os systems of kind K is the cartesian product of certain sets, such as K, the family 2^E of sets of environmental items with which the members of K are coupled, the set F of reference frames, the set T of time instances, and so on» [MB4 20].

State space «Every theoretical model of a thing is concerned with representing the really possible (i.e. lawful) states, and perhaps also the really possible (lawful) changes of state, of the thing» [MB3 131]. «If we form the cartesian product of the codomains of the various components of F ... we obtain the codomain V of F itself, a set that will be called the conceivable state space for the thing represented ... However, a state function may not take values in its entire codomain but may be restricted to a subset of the latter, by virtue of some law ... In other words, because the laws impose restrictions upon the state functions and their values, hence upon the state spaces, only certain subsets of the latter are accessible to the thing represented. We shall call the accessible part of the state space the lawful state space of the thing in the given representation and relative to a given frame» [MB3 133]. «[F]ar from being something out there, like physical space, a state space for a thing [in the representation X_m] stands with one leg on the thing, another on a reference frame, and a third on the theoretician (modeller)» [MB3 132]. («While in most of general system theory the state space is assumed to be finite dimensional, the state (or Hilber) spaces occurring in the quantum theories are infinite dimensional. Every point in such spaces can be analyzed into infinitely many components, namely those along the axes constituted by the orthonormal eigenfunctions of an arbitrary hermitian operator in the Hilbert space» [MB3 136].)

«Any restriction of the posssible values of the components of F and any relation among two or more such components is called a law statement iff (i) is belongs in a consistent theory about the X's and (ii) it has been confirmed empirically to a satisfactory degree» [MB3 129].
«If a law statement concerns a certain thing x, we call it L(x), and we may call L(x) = p(x)L the totality of laws, or rather law statments, for x. ... This is not a mere matter of notation for ... laws are properties. And, being properties, they are representable as functions, Indeed, a law statement may be construed as the value of a certain function - a law function - with domain the class T of things concerned, and codomain the set of law statements of the form L(x). In short,

If TThing, then L:T -> L(T)» [MB3 129].

The lawful state space S_L(X) of thing X in representation X_m is

S_L(X) = {<x₁,...,x_n> V₁ × ... × V_n | F statisfies jointly every member of L(X) }
«and every point of S_L(X) is called a lawful (or really possible) state of X in the representation X_m» [MB3 134].

«If during the existence of a thing (e.g. when it is being observed), only some components of its state function change their values, one says that the remaining components are ignorable and the study of the thing can be restricted to the state subspace spanned by the active state variables. This subspace may be called the reduced state space» [MB3 136].

«Every state is a state of some concrete object or other: there are no states in themselves. And conceptual objects are in no states whatsoever. Therefore a thing could be defined as whatever is insome state or other. Things differ by the states they are in, and their changes are changes of state. But all the things of a given (natural) kind share the same (lawful) state space - which is a way of saying that they share the same general properties. In sum, states serve to characterize not only individual things but also natural classes of things - hence the centrality of the state concept» [MB3 139f].

Change «Whatever changes may be thought of either as turning into a different thing or as going into a different state. In the former case the change of interest can be construed as the ordered couple <x,x'>, where x and x' are the initial and the final things respectively. However, since names or singular terms such as `x' and `x'' are not descriptive, this representation of change is unilluminating. Nesides, it forces an unnecessary multitude of the number of things. For this reason it is not used in science and we shall not employ it in ontology.
Far more information is conveyed if the name `x' is replaced by the sentence `thing x is in state s', where s is a point (or a set of points) in a state space S(x) for x. We can then construe a change of x as a transition from state s to some other state s'S(x). In other words, we adopt what may be called the principle of nominal invariance, or permanence of names through change, and describe change as changes of state. ...
Principle 5.1 A thing, if named, shall keep its name throught its history as long as the latter does not include changes in natural kind - changes which call for changes of name.
... This allows us to designate a given person at age 50 by the same name as at age 5 even though in between the person may have renewed every single atom in his/her body. In short, there are no self-identical things but only constant names helping us to keep track of the changes undergone by things» [MB3 221].

«Every point s belonging to a lawful state space S_L(x) of a thing x represents a possible state of the thing. The actual state of the thing is represented by what is called its representative point in the state space. An actual change of thing x is represented by a trajectory of the representative point; this trajectory is of course the graph of a certain function on S_L(x). It is convenient, through not indispensible, to express the curve with the help of a parameter, the standard interpretation of which is time. But one of the advantages of the state space representation of change is that it requires no explicit use of the time concept» [MB3 216f].

«Definition 5.27 Let F be a state function for a thing x relative to a reference f with states t in S(f), and let the latter be coordinatized by a certain function k: R⁴ -> S(f). Then the history of x relative to f is the set of ordered pairs

h(x) = {<t,F(t) | tS(f) }.
This is an elucidation of the concept of a life line, behavior line, or trajectory. The history of a thing is regared as the succession of its states but, instead of being represented by a line in the n-dimensional state space spanned by F, it is represented as a curve in the (n+4)-dimensional space R⁴×S_L(x)» [MB3 255].

«If there are considerable changes in the individual properties of a thing, but the thing neither acquires nor loses any general property, we may say that it undergoes a large change. If on the other hand a thing gains or loses general properties then it canbe said to undergo a deep change. Whereas in the first case the axes of the state space remain fixed, in the second some are added or removed. We obtain a smooth description of this sort of change if we build the state space will all the necessary axes and use at any given moment only those portions of the total space that concern the properties actually possessed by the thing at the moment» [MB3 219] (cf. redunced state space).
«The thing undergoes a qualitative change iff S_L(x) equals the union of at least two subspaces, eachof which is spanned by a different projection of F. Otherwise (i.e. if none of the components can be ignored during any stretch of the process), the thing undergoes only a quantitative change.

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Ulf Schünemann 120503