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Definition Determinable/Bigelow/Pargetter: what the objects have in common, but what is differently strong in them. For example, mass.
Definition Determinate/Bigelow/Pargetter: is the special property that distinguishes the objects (simultaneously). For example a mass of 2.0 kg.
Both together show what is common and what is different. (> Problem of Quantities, Participation/Plato).
Quantities/Bigelow/Pargetter: Problem: the approach is still incomplete:
Either the relation between determinates and determinables is objective or it is not objective.
A) objective: if it is objective, we need an explanation in which it exists.
B) non-objective: then it is arbitrary to assert that objects that have different Determinates fall under that same Determinable.
W.E. Johnson: our approach is based on one of Johnson's: in it, both are Determinables and also Determinate properties of individuals.
Bigelow/Pargetter: Variant: we can start with a special property for each individual (Determinate, e.g. color shading). Then we define the common: color, this commonality is a property of 2nd level
Definition 2nd degree property/Bigelow/Pargetter: E.g. the commonality of all shades of a color.
Hierarchy: can then be continued upwards. E.g. to have a color at all is one level higher.
E.g. pain: is having a 2nd level property.
Functional role/Bigelow/Pargetter: is a commonality, so there is a property 2nd level to have a certain functional role.
Hierarchy: then consists of three sets of properties.
1. Property 1st level of individuals. All other properties supervene on them.
2. Properties of properties 1st level: = properties of 2nd degree (commonality of properties)
3. Properties 2nd level of individuals: = the property to have that or that property of the 1st level which has that or that property of the 2nd degree.
Problem of Quantities/Solution/Bigelow/Pargetter:
1. Objects with different Determinates are different because each has a property of 1st level that another thing does not have.
2. they are the same because they have the same property of 2nd level.
Determinables/Determinates/Johnson: are in close logical relations: to have a Determinate entails to have the corresponding Determinable.
But not vice versa! Having a Determinable does not require possession of a particular Determinate! But it requires some Determinate from the range.
BigelowVsJohnson: he could not explain the asymmetry.
Solution/Bigelow/Pargetter: properties of 2nd level.
Problem: our theory is still incomplete!
Problem: to explain why quantities are gradual. This does not mean that objects are the same and different at the same time.
New: the problem that we can also say exactly how much they differ. Or, for example, two masses are more similar than two others.
Plato: Plato solves this with the participation.
Bigelow/Pargetter: we try a different solution: > Relational theories._____________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