|Property: what can be ascribed to an object in order to distinguish it from other objects. In philosophy, there is debate about whether properties exist or whether "bare particulars" exist. Expressions for properties are predicates. Not every predicate will refer to a property. See also quantification over properties, 2nd order logic, HOL, completeness._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Property/Relation/Universals/Bigelow/Pargetter: there is an ambiguity:
For example, Russell admires wisdom: this is a relation between individual and wisdom instantiated by a pair of things, the second being a property. So the relation is a universal from the set
On the other hand,
Wisdom: we can also consider it as a relation, rather than as a property of individuals. For example, as a love of knowledge.
Problem: knowledge can be defined differently again, whereby the grouping into the hierarchy is changed. We are not dealing with a simple representation of words on universals.
For example: Merit/virtue/Bigelow/Pargetter: is a property of properties. For example, Russell admires merits:
logical form: is then not (o,(o)) as above but:
Question: does this mean that a thing belongs to several sets at the same time?
Solution/Bigelow/Pargetter: we need to define the sets (o),((o)), (o,(o)), etc. more precisely:
For example (o) is a set of things instantiated by individuals, but do they only have to be individuals, or can they also be non-individuals as instances? (Example: Property of Property)
Universal/Universals/Bigelow/Pargetter: we define them as belonging to at least one type, but perhaps also to several types.
Definition "multigrade" relation/Bigelow/Pargetter: a relation that can exist between individuals, but also between sets of individuals or between an individual and a set of individuals.
For example: living together: can be applied to individuals and groups of individuals.
Definition "multigrades" Universal/Bigelow/Pargetter: a universal that belongs to more than one type.
Properties/Relations/Bigelow/Pargetter: correspondingly, there are two types:
a) those where we can simply say whether things have them or not. ((s) > extensionally characterizable).
b) those where this is not enough: for example fun: we cannot simply characterize it with which individuals belong to it? ((s) Non-extensionally characterisable). Example: mass, e.g. charge ((s) generic properties). For example, relative speed.
Property/Bigelow/Pargetter: Problem: Instantiation: Assuming an individual has a property. Then what has to be in the world for it to be like this? The individual and the property. But that is not enough. Both could exist without one instantiating the other. That is, it is not enough for having a property that thing and property coexist side by side in the world.
Wrong solution: to postulate instantiation as a relation: this only shifts the problem. The relation could exist in the world, without that certain thing having that certain property. Or without the thing being related to anything.
Instantiation/Bigelow/Pargetter: the problem lies in a wrong conclusion of quantification of the 2nd level to quantification of the 1st level.
"Somehow" is not "any".
For example, property F: in order to have it, it must be somehow in relation to it. ("there must be somehow that the individual stands to the property").
(Eψ)(ψ (a, F))
This "somehow" is not a "something". I.e. we must not conclude:
(Ex)(Eψ)(ψ (x, a, F))
Problem: this would lead to a regress. This has always threatened the universals.
Solution/Bigelow/Pargetter: Quantification of the 2nd level should not be taken so seriously that it makes the "somehow" into a "something".
Universals/Bigelow/Pargetter: a full theory of universals therefore needs a pre-semantic source for universals (pre-semantic/s): something that does not require any truthmakers.
Solution/Bigelow/Pargetter: we need something that instantiates something without ever being instantiated.
Existence of 2nd level/Bigelow/Pargetter: is also required by a theory of universals. From which, however, you cannot deduce an existence of the 1st level without additional premises._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990