This is a guest post by Eric Steinhart, Professor of Philosophy at William Paterson University.
Over the next few posts, I’m going to do some heavy metaphysics. So a bit of background is necessary. An ontology is a taxonomy of categories (usually at a very high level of generality). To avoid misunderstanding, the ontology I’m working with is outlined below. This ontology is naturalistic in exactly the sense that objects in all its categories are found in our best scientific theories.
Material Things – Material things are either simple or complex. Simple material things are instances of the types of particles found in the Standard Model of Matter. For instance, they are quarks or leptons or bosons. Complex material things are wholes composed of simple or less complex material things. For instance, protons, planets, and people are complex material things. All material things are physical things. Also, they are particulars. Scientific theories refer to material things. But scientific theories also refer to lots of non-material things – materialism is an incomplete ontology.
Geometrical Things – Geometrical things include space-time points and regions. Regions are wholes composed of space-time points. Our best current physical theories (e.g. field theories) refer to points and regions. They are physical but not material. Points have properties like force vectors and points participate in distance relations. All geometrical things are particulars. Scientific theories refer to geometrical objects. The theories of relativity as well as quantum field theories refer to points.
Mathematical Things – Mathematical things include all the objects of mathematics. These are numbers, sets, functions, vectors, etc. It’s common to define all mathematical things in terms of sets. So, in my ontology, all mathematical things are sets. Sets are defined using some standard set theory like ZFC. Sets are not physical. Sets have properties (e.g. their cardinalities) and participate in relations (e.g. the membership or subset relations). Sets are particulars. Scientific theories refer to mathematical things. Scientific theories refer to numbers, vectors, tensors, functions, matrices, and on and on. If you’re looking for arguments justifying the existence of mathematical objects on scientific grounds, a great book is Colyvan’s The Indispensability of Mathematics.
Particulars – Any particular is either a material, geometrical, or mathematical thing. I’ll often use the term “thing” to refer to particulars. The term “thing” is more specific than terms like “object” or “entity”. Particulars have properties and participate in relations. Physical things participate in spatial, temporal, and causal relations.
Properties – Some properties are features of things. These include: being-square, being-liquid. Some properties are types of things. These include: being-an-electron, being-a-silicon-atom, being-a-human, being-a-man. Mathematical properties include being-empty or being-prime or being-infinite. Properties are usually given abstraction suffixes like “ness” or “hood”. Thus “treeness” is the property of being a tree, “emptiness” is the property of being empty, and “motherhood” is the property of being a mother. The essence or forms of things are properties. Properties are not particulars and thus are not things (but they are objects or entities). Properties are universals.
Relations – Pluralities of objects participate in relations. Examples of relations include loving, being-heavier-than, being-a-subset-of, and so forth. Relations are not particulars; hence they are not things. On the contrary, they are universals.
Patterns – Patterns are also known as structures or forms. They are described by logical templates involving lots of variables. An example of a pattern is the simple family pattern. It has three slots or variables x, y, z. The pattern is: x is male; y is female; x is married to y; x is the father of z; and y is the mother of z. Some of the variables in a pattern may be bound with quantifiers. The laws of nature are patterns. Computer programs are patterns. Scientific theories and mathematical axiom systems are propositions. Aristotle said that the soul is the form of the body (De Anima, 412a5-414a33). If he’s right, then souls are patterns. Patterns are not particulars, they are universals.
Universals – Universals include properties, relations, and patterns. Universals are not things. However, they are objects or entities. Obviously scientific theories refer to universals (such as mass, charge, spin, distance). And scientific theories themselves are universals. There are good arguments to justify the existence of universals. You can find them in in David Armstrong’s Universals and in Michael Loux’s wonderful book, Metaphysics: A Contemporary Introduction. Universals are here understood as immanent universals rather than as transcendental universals (they are universalia in re rather than universalia ante rem). Universals are not things.
Possibilia – Since our best current physical theories talk about other possible universes, the ontology includes possible particulars and universals. These exist at other universes. David Lewis says his ontology “consists of possibilia – particular, individual things, some of which comprise our actual world and others of which are unactualized – together with the iterative hierarchy of classes built up from them” (1983: 9). Add immanent universals, and the result is the ontology I’ll be using going forward.
Armstrong, D. (1989) Universals. Boulder, CO: Westview Press.
Colyvan, M. (2001) The Indispensability of Mathematics. New York: Oxford University Press.
Lewis, D. (1983) New work for a theory of universals. In D. Lewis (Ed.) (1999) Papers in Metaphysics and Epistemology. New York: Cambridge University Press.
Loux, M. J. (2006) Metaphysics: A Contemporary Introduction. Third Edition. New York: Routledge. ISBN 0-415-26107-4.
Other posts in this series: