Categories

F_bx = x falls on b.
If we change the value of the parameter, say to c!=b, we obtain another predicate, namely F_c ... In this way the single binary predicate F is replaced by an infinite set of unary predicates F_z. ... There is of course no economyat all in the unarization procedure: this is just a trick allowing one to speak, although at greater length, of any property of an individual as if it were intrinsic. Therefore it has nothing to do with Bradley's attempt to eliminate relations in favor of monadic predicates or "internal relations" (Bradley, 1893)» [MB3 70].
«Every one of [the unarized predicates] may be taken to represent an intrinsic property and moreover an individual [ie. dichotomic/Boolean] one, for it is either possessed or not possessed by the corresponding substantial individual» [MB3 71].

4. Resultant and Emergent Properties

«Let Pp(x) be a property of an entity xS with composition C(x) [SUPER] {x}. The P is a resultant or hereditary property of x iff P is aproperty of some components yC(x) of x other than x; othewise P is an emergent or gestalt property of x» [MB3 97]. 

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Cf. Phenomenology: «Phenomenology distinguishes sharply between perceptual properties on the one hand, and abstract properties on the other. Consider two white billiard balls, called A and B. The white colour of A, which one can see with one's eyes, is said to be located in space where A is. The white colour of B, similarly, is taken to be located where B is. Furthermore, it is maintained that the colour of A is not identical with the colour of B, since they are located at two different places. The same shade of colour, according to this analysis, divides into as many 'colour instances' of that shade as there are individual things with this colour shade.
However, all of these instances are instances of the same colour shade. There exists, therefore, according to phenomenology, also the abstract colour shade of which the instances are instances. Let us call this abstract colour the 'universal whiteness'. Phenomenology asserts that there is not only a direct perception of instances of whiteness, but also a sort of direct perception of the universal whiteness. This perception is called 'eidetic intuition'. By means of eidetic intuition we have knowledge of the essential features of the world. Phenomenologists call such universals essences.» [x]

health .--------------------. model | .------v | care Person---------| Well Sick<---|--------Doctor ^ | A ^------' A | ^ : `---|----------|-----' : : | | : : «instance» | | : «instance» : | | : : health .---|----------|-----. : : model | | .------v | | : John-----------| JohnWell JohnSick | : | ^------' ^ | : `----------------:---' : : : «instance» : : : care : JohnSick#23<-------Susan

Individual states in object-oriented modeling have been proposed by Bock [Conrad Bock: A More Object-oriented State Machine; JOOP Jan 2000]. He describes an object-oriented model of Persons whose health state is modeled as a state machine were states Well and Sick can alternate. In the Sick state only, the Person is taken care of by a Doctor. On the instance, an individual Person like John has a corresponding individual instance of the state model with its individual states JohnWell and JohnSick/ JohnWell and JohnSick are considered state types (classes) which are specializations of Well and Sick. An instance of state JohnSick is, e.g., the 23rd time when John was in state JohnSick. In that state instance JohnSick#23, John was/is taken care of by Doctor Susan.

2. Properties/universals can be substantial, or formal

P is a substantial property, PProp, iff some substantial individuals possess P, ie., (Ex)(xS & x possesses P) [MB3 71].

1. Property PProp is a (substantial) universal in a set TS of entities iff P's scope S(P) = T. (cf. scope)
2. Attribute AAttr is a (conceptual) universal in a set TC of constructs iff A's extension E(A) = T. [MB3 105]

Concrete objects have no (unary) formal/conceptual properties (hence mathematics cannot illucidate them): «[C]oncrete objects (things) have no intrinsic [ie. unary] conceptual properties, in particular no mathematical features. ... What is true is that some of our ideas about the world, when detached from their factual reference, can be dealt with by mathematics. ... not the world but some of our ideas about the world are mathematical.» [MB3 118f].
«[T]he so called formal properties of things, such as number and shape, appear to be full fledged conceptual universals inherent in concrete entities and thus defy the substantial/conceptual dichotomy ... Thus numerosity is a property of any collection whatever the nature of its components. True, but then a set is a concept. Surely dogs are normally four legged, this being a substantial property of theirs. The corresponding mathematical property is the cardinality of the set of legs of a dog. On other words four leggedness is a substantial property to be distinguished from the mathematical property of the set of legs of a quadruped» [MB3 106].

Conceptual objects represent concrete objects. «The relation between the predicate and the corresponding property is that of representation: the former represents the latter ... [N]ot things but our models of them have mathematical properties, and this because we conceptualize substantial properties as functions. This mode of representation is so deeply ingrained in our habits of thought that we often mistake the deputy for his constituency» [MB3 106].
«Intrinsic [ie. unary] properties are either of [physical] things or of [abstract] constructs. One the other hand a mutal [ie. relations] (e.g. binary) property can link things with constructs. An example of a mutual property of this kind is that of representation, such as it occurs in the statement `Proposition p represents thing b'» [MB3 118].
-> continue quote: A concept (with attributes) represents a substantial individual (with properties).
-> substantial properties must be representable by propositional functions

3. Aggregates =/= Sets

T S

The Stoics had a list of four categories: substrate, qualified, disposed, relatively disposed [x]

Dölling's categories

Grossmann's categories and STATE OF AFFAIRS

Individual / Role / Context

A somwhat similar distinction between the individual object, its role towards others, and that relating context in which objects have roles towards one another seems to be expressed in Peirce's Firstness, Secondness, Thirdness (1891) [from TOC 677f]: «"First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction with, something else. Third is the conception of mediation, whereby a first and a second are brought into relation"

As Firstness, the type Woman represents a kind of person existing independent of anything else. But the same individual could be considered relative to or in reaction with many other things, as in the concept types Mother, Attorney, Wife, Pilot, Pedestrian, or Employee. These roles are examples of Secondness. They represent the individual in relation to another type, such as Child, Client, Husband, Airplane, Street, or Employer. Thirdness is a conception of mediating circumstances that bring the first and second into relation. Motherhood, which comprises the act of giving birth and the subsequent period of nuturing, relates the mother and the child. The legal system gives rise to the roles of attroney and client. ... These mediating situations are examples of Thirdness, whether they are traditionally recognized categories like Motherhood and Aviation or whether they are unnamed categories like walking-where-other-people-are-driving.

Firstness is independent, Secondness reacts to something else, and Thirdness involves some mental mediation. As an example, a human may make an animal (Firstness) into a pet (Secondness), by establishing a contract (Thirdness) with it. ... Peirce's categories apply equally well to actions ... :

1. Brutus stabbed Caesar.
2. Brutus killed Caesar.
3. Brutus murdered Caesar.

An act of stabbing is a Firstness that can be recognized by objective criteria at the instant it happens. No other events or mental attitudes need to be considered in identifying an act of stabbing. Killing is a Secondness that depends on whether the victiim dies. ... [T]he act of stabbing does not become a killing unitl after the event of dying. Murder is a Thirdness that depends on the motives of the agent. ...»

	physical things	information things	sign
Firstness	entity	form	representamen
Secondness	role	proposition	object
Thirdness	circumstances	theory	interpretant

Event. «An event is sometimes defined as a change (for example, the loss or acquisition of a property by something) ... However, many theories of events include states that consist in things' having (or retaining) properties (e.g. the lawn's staying wet) as well as changes that consist in their acquiring or losing them (e.g. the lawn's becoming dry)» [x].
Events can be regarded as identical iff they have exactly the same causes and effects (Davidson's first answer), or iff they occupy exactly the same places at the same times (Quine and Davidson's second answer), or iff they consist in the same objects' having the same properties at the same times (Jaegwon Kim). [x].

«Every collection of events is a set of changes in some thing or other. We have found no use for the fiction that the are changes that fail to consist in modifications of the states of some thing or other. Anyone claiming that there are such changes in reality should exhibit empirical evidence to this effect and proceed to build a theory of such thingless (or immaterial) changes.
Nevertheless once in a while philosophers and even scientists are found claiming that there are such thingless changes. ... One of them is the information process, sometimes regarded as not being based on the transport of matter or the propagation of fields. The reason for this misconception is that statistical information theory is a black box or phenomenonological theory so general that it disregards the precise kind of signal carrying the information, the information transmission mechanism, and the kind(s) and quantities of energy involved. For this reason information theory is a nonphysical theory: it is instead a theory qualifying as a piece of scientific metaphysics, since it deals in an extremely general way with a genus of conrete things. But, of course, information is a property of certain physical (or chemical or biological) processes, namely signals, which are processes of a kind. No signal, no information transmission. And signals, let us repeat, are chains of events occuring in concrete things: the transmission of information consists in events propagating across space and carrying energy. Remove such real processes and only parapsychological anecdotes remain» [MB3 271f, underlining added].