|Universals: universals are expressions for what objects may have in common, e.g. a certain color. Examples for universals are redness, roundness, difference, value. The ontological status of universals as something independent of thought - that is, their existence - is controversial. Nevertheless it is undisputed that we form terms for generalization and successfully use them. See also general terms, general, generalization, ontology, existence, conceptual realism, realism, ideas, participation, sortals, conceptualism, 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. |
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Universals/Bigelow/Pargetter: pro: they help to create a unified picture and to understand probabilities. They help to establish a unified theory of modalities (possibility, necessity) that we find in science.
Universals/science/Bigelow/Pargetter: we have encountered universals that are useful for physics, now we are looking at those that are useful for chemistry:
Chemical components: are structures made up of elements.
Universal: is the property of having a certain structure, which in turn is related to the universals that determine the elements.
These are structural universals.
Structural universals/Bigelow/Pargettesr e.g. expressed by the predicate "to be methane" or "Methane"; Instantiated: by a carbon atom and four hydrogen atoms in a certain constellation. This constellation is an essential property.
Instantiation: by methane molecules.
N.B.: this universal is intrinsically connected to other universals: the universals, being hydrogen, being carbon and be bound.
Level 1: material individuals who have the property of being butane or methane, etc. These are then methane molecules, etc. These individuals have parts with different properties and relations.
Level 2: Properties and relations of the individuals of the 1st Level.
Property: For example, the property to be methane.
Level 3: Relations or proportions between properties or relations between individuals, no matter whether they are properties of the 1st or 2nd level (sic) of these individuals. For example,"having the same number of instances as".
Cardinal numbers/Frege: Frege needed this construction for the cardinal numbers.
Family: this relation between properties have the form of a family, including e.g. "having twice as many instances","having four times as many instances", etc.
Proportion: these "numerical" proportions will also exist between more complex properties of the 2nd level: e.g. "conjunctive property: being carbon and be part of this molecule".
For example, if the molecule is methane, these two properties are in a ratio characterized by the proportion 4:1.
Structural universals/Bigelow/Pargetter: we can then characterize it as a relational property of an object. It relates the molecule to various properties. These properties are being carbon, being hydrogen and being bound.
Universal: e.g. being methane: is then identical with a highly conjunctive relational property of the 2nd level of an individual (molecule).
Property: the property of being methane stands in a pattern of internal proportions to other properties, e.g. being hydrogen, being bound, etc.
Mereology/Chemistry/Bigelow/Pargetter: but these relations are not mereological.
Relations/Bigelow/Pargetter: these relations are internal relations and they are essential.
Essentialism/Bigelow/Pargetter: pro: we need essential properties here. But this is better than seeking refuge in magic (see above).
Universals/Bigelow/Pargetter: could not exist as these universals if they were not in these relations with each other. These are the structural universals.
Universals/Bigelow/Pargetter: a full theory of universals needs a pre-semantic source for universals (pre-semantic/s): something that does not require 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 any existence of the 1st level without additional premises.
Causes as structural universals.
Fundamental Forces/Bigelow/Pargetter: are vectors.
Basic forces/Bigelow/Pargetter: are aggregates of vectors: thesis: they are structural universals.
For example, mass: each specific mass corresponds to a specific property. Nevertheless, massive objects have something in common: that they have mass. This corresponds to a relation of a higher level.
These relations are internal and essential, not external. That is, the particular mass properties could not be them if they were in different relations to other objects.
Common: this is the fact that all massive things are related to other massive things.
Property of the 1st level: Example: velocity in the plane.
Relation 1st level: For example, difference in velocity or direction. Therefore, there are two relations of the 1st level.
Forces/Bigelow/Pargetter: are more complex vectors, since they themselves are relations of the 2nd level. Fundamental forces can be of different sizes and directions.
They are thus in a cluster of internal relations of higher degrees to other fundamental forces. That makes sure that they are a family with something in common.
Necessary/Properties/Forces/Bigelow/Pargetter: the fact that one fundamental force is twice as great as the other, or perpendicular to another; it is not contingent.
Solution: they would otherwise be different from the forces they are.
On the other hand,
Contingent: whether things are connected by a force is contingent.
Structural Universals/Bigelow/Pargetter: (see above: methane example)
Forces: the constitutive properties of structural universals can also be fundamental forces, including vectors with size and direction.
Internal relations: there are many of them within a structural universal. And they also establish the connections to individuals.
Cause/Bigelow/Pargetter: we said it is local. So it cannot be a relation only between completely nonlocal universals.
Structural universals: must therefore have a local element.
Solution: their relational properties embed particulars as well as universals.
Fundamental cause/Bigelow/Pargetter: if it is a structural universal, it will be a conjunctive relation of a higher level between single events.
Causal relations/Bigelow/Pargetter: after all, they have a rich and essential nature. And they are not primitive basic concepts. They are explained by vectors and structural universals. They exist independently alongside causes and effects.
Modalities/Bigelow/Pargetter: some are essentially causal. But:
Cause/Bigelow/Pargetter: is not essentially modal for its part.
Universals/Bigelow/Pargetter: are things in the world like others. In particular, they are namable.
There is no essential connection between universals and predicates. I.e. universals can be in subject position. ((s) But can we quantify via them?). Therefore, we have no problem with higher-level logic (2nd level logic).
Universals: should not be dominated by semantic theory. They should not have to be arranged according to a hierarchy. Nevertheless, they have a hierarchical pattern with individuals as a basis.
Paradoxes: are avoided by prohibiting universals from instantiating themselves or other universals.
Self-reference/Bigelow/Pargetter: however, this is only a problem if mathematics is based a priori on logic alone. And we do not want that. For example, we do not assume that each linguistic description determines a quantity._____________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