Relation-Theory: takes belief to be a relation to internal objects (entities). Virtually all authors are against the assumption of thoughts as internal objects. See also intensional objects, intensions, propositional attitudes, mentalism.
Relational Theory/Bigelow/Pargetter (Science and Necessity Cambridge University Press 1990 p55) assumes universals (e.g. sets, numbers, properties) and relations between them in order to explain the problem of quantities. See also change, motion, quantities, universals, Platonism, nominalism._____________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.
Quantity/relational theory/Bigelow/Pargetter: Quantities are general relations between objects. They seem to be consequences of the intrinsic properties of objects. But one would not have to postulate an intrinsic relation "greater than", but only e.g. the size.
Greater than/relational property/problem/Bigelow/Pargetter: one might wonder if there really is an intrinsic property to be that and that big.
Relational property/Bigelow/Pargetter: one might be tempted to assume that everything is based on relational properties, rather than vice versa. But we are not going to go into that here.
Intrinsic property/Bigelow/Pargetter: we think that in the end they can be defended against relational properties as a basis. Nevertheless, we certainly need relational properties, e.g. for the order of events. These do not just stand in time. So we definitely need relations.
Relations/Bigelow/Pargetter: we definitely need relations. Because events never stand for themselves.
Also for expressions such as "twice the size" etc.
Quantity/Bigelow/Pargetter: Quantities cannot be based on properties alone, but need relations. For example, having this or that mass is then the property of being in relation to other massive objects.
Participation/BigelowVsPlato: Plato has all things in a more or less strong relation to a single thing, the form. We, on the other hand, want relations between things among themselves.
BigelowVsPlato: we can then explain different kinds of differences between objects, namely that they have different relational properties that other things do not have. E.g. two pairs of things can differ in different ways.
Relational Theory/Bigelow/Pargetter: can handle differences of differences well.
Question: can it cope well with similarities? For example, explain what mass is at all?
Problem: we need a relation between a common property and many relations to it. There are many implications (entailments) which are not yet explained.
Property/Bigelow/Pargetter: 1. in order to construct an (intrinsic) property at all, we must therefore specify the many possible relations it can have to particalur.
Solution: one possibility: the sentence via the property of the 2nd level.
2. Problem: how can two things have more in common than two other things?
Ad 1. Example Mass
Common/Commonality/Bigelow/Pargetter: must then be a property of relations (of the many different relations that the individual objects have to "mass").
Solution: property of the 2nd level that is shared by all massive things. For example, "stand in mass relations".
Entailment/N.B.: this common (2nd level property) explains the many relations of the entailment between massive objects and the common property of solidity.
Problem/Bigelow/Pargetter: our relational theory is still incomplete.
Problem: to explain to what extent some mass-relations are closer (more similar) than others.
Relations/common/Bigelow/Pargetter: also the relations have a common: a property of the 2nd level. Property 2.
Level/difference/differentiation/problem/Bigelow/Pargetter: does not explain how two things differ more than two other things.
It also does not explain how, for example, differences in masses relate to differences in volume.
For example, compare the pairs
between which there are differences in thicknesses with regard to e.g. length.
Then two of the couples will be more similar in important respects than two other pairs.
Solution/Bigelow/Pargetter: the relation of proportion. This is similar to Frege's approach to real numbers.
Real numbers/Frege: as proportions between sizes (Bigelow/Pargetter corresponds to our quantities).
Bigelow/Pargetter: three fundamental components
(2) Relations between individuals
(3) Relations of proportions between relations between individuals.
Proportions/Bigelow/Pargetter: divide the relations between individuals into equivalence classes:
Mass/Volume/Proportions/N.B./Bigelow/Pargetter: all masses are proportional to each other and all volumes are proportional to each other, but masses and volumes are not proportional to each other.
Equivalence classes/Bigelow/Pargetter: arrange objects with the same D-ates into classes. So they explain how two things ((s) can be more similar in one respect, D-able) than in another.
Level 1: Objects
Level 2: Properties of things
Level 3: Proportions between such properties.
Proportions/Bigelow/Pargetter: are universals that can introduce finer differences between equivalence classes of properties of the 2nd level.
Different pairs of mass relations can be placed in the same proportion on level 3. E.g. (s) 2Kg/4kg is twice as heavy as 3Kg/6Kg.
N.B.: with this we have groupings that are transverse to the equivalence classes of the mass relations, volumetric relations, velocity relations, etc.
Equal/different/Bigelow/Pargetter: N.B:: that explains why two relations can be equal and different at the same time. E.g. Assuming that one of the two relations is a mass relation (and stands in relation to other mass relations) the other is not a mass relation (and is not in relation to mass relations) and yet...
...both have something in common: they are "double" once in terms of mass, once in terms of volume. This is explained on level 3.
Figures/Bigelow/Pargetter: this shows the usefulness of numbers in the treatment of quantities. (BigelowVsField).
Real numbers/Frege: Lit: Quine (1941, 1966) in "Whitehead and the Rise of Modern Logic")
Measure/Unit/Measuerment Unit/To Measure/Bigelow/Pargetter:"same mass as" would be a property of the 2nd level that a thing has to an arbitrary unit.
Form/Plato/Bigelow/Pargetter: his theory of forms was not wrong, but incomplete. Objects have relations to paradigms (here: units of measurement). This is the same relation as that of participation in Plato.
Level 3: the relations between some D-ates can be more complex than those between others. For mass, for example, we need real numbers, other terms are less clear.
Quantities/Bigelow/Pargetter: are divided into different types, which leads to interval scales or ratio scales of measurement, for example.
Pain/Bigelow/Pargetter: we cannot compare the pain of different living beings.
Level 3: not only explains a rich network of properties of the 2nd level and relations between objects,...
...but also explain patterns of entailments between them.
NominalismVsBigelow: will try to avoid our apparatus of relations of relations.
BigelowVsNominalism: we need relations and relations of relations in science.
Realism/Bigelow/Pargetter: we do not claim to have proven it here. But it is the only way to solve the problem of the same and the different (problem of the quantities with the 3 levels).
Simplicity/BigelowVsNominalism: will never be as uniform as our realistic explanation. Nominalism would have to accept complex relational predicates as primitive. Worse still, it will have to accept complex relations between them as primitive._____________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