"The greatest certainty is found in the greatest abstraction" (Plato).
"The world of universals can be described as the world of being" (Bertrand Russell).
The Problem of Universals
The problem of universals is one of the most important philosophical problems of all times. Raised mainly since Plato and Aristotle, it became widespread thanks to Boethius' (480-524) early translations of Aristotle's works, together with his commentaries on the Stagirite's philosophical categories. The problem was discussed particularly intensely during the Middle Ages.
A universal is a type, class, or category of objects which, although distinct, share one or more properties. Each universal has a name associated with it, such as: man, animal, house, apple, table, color blue, etc. For example, Socrates and Plato are two instances of the category "man"; the sea and the sky share the property "color blue", etc.
Among the questions raised by the problem of universals are:
Do universals really exist? If they exist, what is their ontological status? Are they real or imaginary entities? Are they objective or subjective? Are they mental contents or outside the mind? Are they corporeal or incorporeal? Are they linguistic entities? Are they abstract entities? Are universals the concepts?
Do they reside in particulars (immanently) or outside of particulars (transcendently)?
What exactly is the ontological nature of the relation between universals and particulars?
How is it possible for a universal to be in several particulars at once?
What is the role of consciousness in the relation between universals and particulars?
Are there hierarchies of universals? Is a particular a last level universal?
An important question is whether or not abstract objects (such as the mathematical entities of number, set, polygon, etc.) are universals or whether or not they are a type of universals. What can be said is:
A universal can be instantiated in a particular, in a downward process or action. For example, the universal "color" can be instantiated into "green".
An abstract object is a generalization or abstraction of several particular objects in a bottom-up process or action. In turn, the abstract object can also be instantiated. For example, the abstract object "number" can be instantiated into a concrete number such as 37.
A universal can also be considered an abstraction of particulars and, therefore, would be a bottom-up process. Traditionally, universals have been called "abstract entities" or "generic notions. It is common to consider the universal as abstract, while the particular is concrete.
In general, the universal and the particular are considered to be opposed concepts and equivalent to the opposition between the abstract and the concrete. Therefore, universal and abstract object can be considered equivalent concepts, and the concepts of particular and concrete are also equivalent.
According to Hegel, a universal can be abstract or concrete. A concrete universal is a universal with its own or immanent content.
The subject of universals constitutes a capital question, since it affects not only basic philosophical disciplines (ontology and epistemology), but also affects other fundamental disciplines such as mathematics, logic, linguistics and psychology.
Faced with the problem of universals there have been several proposals. The two main positions are realism (universals exist) and nominalism (universals are just names that we assign to concepts).
Realism
Realism accepts the existence of universals. Without universals it is not possible to understand any of the particular things. They are not corporeal, for if they were, they would not be universals, but particulars.
There are basically two forms of realism:
Radical or extreme realism.
This is the view of Plato, who defended the existence of an objective realm of Ideas or universal or abstract forms, existing a priori, by themselves, outside of space and time; a realm superior to the phenomenal sensible world and independent of the physical world, an ideal, necessary, perfect and absolute realm. Mathematical entities dwell in this ideal realm (it is mathematical realism), which can be discovered, but not created.
The sensible world contains only the contingent, the particular, the changeable. The particulars are imperfect manifestations or projections on the physical plane of the universals.
Plato staged the universal-particular dialectic by means of a myth, which he expounds in The Republic. Gods and giants argue about the existence of universals. The gods affirm that they exist and that they are more real than the particulars. The giants argue that only particulars exist. The gods see the earth as a bad copy of heaven. Giants see heaven as an idealization of earth.
Moderate realism.
Universals exist, but only immanently, in particulars. This is Aristotle's position. For the Greek philosopher, matter and form are inseparable and constitute a unity called "substance". Matter and form represent the particular and the universal of substance, respectively.
John Duns Scotus is considered the highest representative of the immanent realism of universals. William of Occam and Scotus were the most prominent figures in the Middle Ages in the speculative debate on universals, both defending different positions. For Scotus, the truly real are the particulars, but there is a common nature that is present in all particulars. The universal is in the object (universal in re) before being grasped by the understanding (universal in mente). The understanding grasps directly the particular, and abstractly the universal. In the particulars there are various "formalities", which are degrees of being of an objective type. Scotus was called "Subtle Doctor (Doctor Subtilis)" because of the subtlety of his analysis. His moderate realism can also be considered close to nominalism.
Nominalism
According to the nominalist doctrine, only particulars exist. There are neither universals nor abstract entities, neither immanently nor transcendently. Universals are only names that we assign to concepts, general ideas, predicates, classes, categories, relations of similarity, etc. They are mere verbal designations that serve as labels to collections of things.
Conceptualism is a moderate nominalism. It asserts that universals do not exist at the objective but at the subjective level, for they are creations of the mind. Conceptualism can also be considered a moderate realism. It can be said that conceptualism is situated between realism and nominalism.
Mathematical nominalism holds that mathematical entities do not exist. Its opposite is mathematical realism.
William of Occam is considered the highest representative of nominalism. However, his philosophy can also be regarded as conceptualist and also as a form of moderate realism:
Universals do not exist in an objective sense, nor do they have metaphysical reality. To assert the existence of the universal is a contradiction, since everything that exists is singular. If the universal existed it would also be something singular.
Universals are subjective mental objects. They are only creations or abstractions of the human mind to refer to a set of individual things that have among themselves some similarity. Universals and abstractions do not exist in nature and have no basis outside the mind. Universals are mental representations. The universal is only mental.
A concept is a "sign" (signum) or "term" (términus) which has no real objective existence. Universals are conceptual terms that signify individual things and are represented in propositions.
Contrary to popular belief, Occam did not use his famous razor to deny the existence of universals. The principle of Occam's razor affirms that one should not multiply things without necessity, that one should always seek maximum simplicity in the theories that explain things, eliminating unnecessary concepts.
Theory of tropes
A contemporary version of nominalism, with connections to modern analytic philosophy:
There are no universals. The world consists only of particulars. What are usually called "universals" are really properties and relations, which are also particulars.
A trope is a particular property or relation of a thing. For example, in a leaf of a plant, its green color is a particular property of that leaf. And if a person is of a particular height (e.g., 6 feet tall), a relationship is established with a unit of measurement (the meter). But the fact that something has a property or relation does not imply that it is an "instance" of a universal. That is why the term "trope" is used instead of "instance".
A particular object is a system made up of coexisting tropes, i.e. it has multiple properties or relations. If an object a has property p, it means that the trope p is part of the system of tropes that make up the object a. Therefore, a is not an instance of a hypothetical universal entity p.
A universal is a system of tropes that resemble each other. Particular and universal are secondary concepts of the primary concept "trope".
The theory of tropes was born with Donald C. Williams' article "On the Elements of Being" [1953], a theory that was later developed further by Keith Campbell in his book "Abstract Particulars" [1990].
Other views and theories
For Neoplatonists such as Plotinus and Augustine of Hippo, universals are in the mind of God.
For positivists, there are no universals. They are only terms associated with collections of particular ideas.
Peirce was an extreme realist, close to Platonism. He spoke of "type" (the universal) and "tokens" (the particulars). The laws of nature are types, laws of being, which are real and objective. The tokens are manifestations of the types.
For Peirce, there are three philosophical categories: the firstness is being, the secondness is an aspect of being, and the thirdness is the relation between the two previous categories. Thirdness is the category of the relation between universals and particulars.
For Frege, there is an inner world (to which mental or psychological facts belong) and an outer, real world (to which physical objects belong). There is also a third realm of ideal entities, which is objectively real, which is above the mental and physical worlds. In turn, the mental world is ontologically superior to the physical world.
G.E. Moore and Bertrand Russell were realists in the sense that they considered universals to be necessary entities for scientific knowledge.
For David Lewis, universals are the possible kinds, which can manifest themselves in every possible world. This is the so-called "modal realism".
Quine [1962] defends the holism of science: "The unity of empirical meaning is the totality of science". This holism implies accepting everything in science, whether concrete or abstract. For Quine, it is necessary to admit the existence of abstract mathematical entities for our best scientific theories to be true. This is his famous "argument from indispensableness," which is usually taken as an argument from mathematical realism.
For Daniel Dennett, universals do not exist in the real world. What exist are only brain reactions to words like "blue", "man", etc.
For Nelson Goodman, there are individual entities (concrete or abstract) that have no parts, just as there are collections of individual entities.
David Armstrong wields against nominalism the "truthmaker" principle. This principle says that for every true (extrinsic) sentence there must be something intrinsic that makes it true, which is the "truthmaker". For it to be false, a qualitative change in the "truth-maker" is needed. The world has an intrinsic and an extrinsic nature. The "truth-maker" is of an intrinsic, necessary and essential kind. Nominalism does not hold because it has no intrinsic support, it is superficial, it has no ontological support.
It also rejects abstract objects because it defends naturalism: nothing exists except Nature, the only all-encompassing system.
Realism and nominalism in mathematics
According to Quine [1962], the three classical views regarding universals (realism, conceptualism, and nominalism) are essentially the same doctrines that reappear in the twentieth century in the philosophy of mathematics under new names: logicism, intuitionism, and formalism, respectively.
Logicism −represented by Frege, Russell, Whitehead, Church and Carnap− admits universals, like philosophical realism. Universals and abstract entities exist independently of the mind. With logicism/realism, ideas are discovered.
Intuitionism −represented mainly by Brower, Weyl and Poincare− does not admit objective universals, but only universals produced by the mind, like conceptualism. With intuitionism/conceptualism, ideas are created or invented.
Formalism −whose highest representative is Hilbert− does not admit universals or abstract entities, like nominalism. Names have no meaning or reference (or the reference is themselves). Mathematics is just manipulation of meaningless symbols by means of formal axioms and rules of inference. Mathematics can be done without assuming the existence of mathematical entities such as numbers or sets.
Occam's "mental language"
Occam postulated the existence of an inner, common and universal language in all human beings. Although Aristotle and other philosophers had previously made reference to this subject, Occam was the first philosopher to develop in some detail the notion of "mental language."
Human thought is a language. Mental concepts are structured as language. This language is reflected at the syntactic level in grammatical categories such as noun (singular and plural), verb and adverb.
At the semantic level the concepts of signification, connotation and supposition operate. The meaning of a term is an index that connects the internal (the concept) with the external (the object); it is to present a form to the understanding. A connotative term is a qualitative or relational term. The presupposition of a term is the meaning associated with the context of a proposition.
Written words are subordinate to spoken words, and spoken words are subordinate to mental units called "concepts" or "mental terms", which have meaning and are "natural signs". Words are "artificial signs". The human mind has the capacity to intuitively associate a particular object with a sign.
The meanings of spoken or written terms are conventional and relative, can mean anything (even non-existent things) and can be changed by agreement. But the meanings of mental terms cannot be changed, they are absolute, because they have been established by nature.
Concepts can be combined to form mental propositions, which are structured in the same way that words (spoken or written) combine to form sentences (audible or visible).
There are two types of definitions: real and nominal. A real definition is one that expresses the structure or nature of a thing. A nominal definition expresses the meaning of a term.
The primary function of language is not so much to communicate thoughts from one mind to another, but to discover the structure of reality.
Some authors consider Occam the father of modern philosophy and especially of what would later be called "analytic philosophy" or "philosophy of language", being six centuries ahead of Frege, the considered "official father" of analytic philosophy.
Realism and Nominalism in MENTAL
MENTAL integrates and reconciles realism and nominalism in a simple way, following two principles: the principle of downward causality and the principle of Occam's razor:
The universal semantic primitives of MENTAL are primary universals of an abstract kind. They are also linguistic, philosophical and deep psychological universals (archetypes).
MENTAL is realistic in the sense that universal semantic primitives have real existence, but reside in a metaphysical, transcendent, deep, primary, universal, abstract, absolute, timeless and inaccessible world. We can only access that world by intuition.
MENTAL is nominalistic because we can access the superficial manifestations of the universals, that is, the concrete formal expressions or representations. Particular expressions connect us with the universal, they allow us to intuit the universal.
The same universals are present in lexical semantics and in the structural semantics of language.
The particulars are supported by the universals. Without the universals, the particulars could not exist. Or −according to David Armstrong's terminology− intrinsic (or deep) nature supports extrinsic (or superficial) nature.
All expressions participate, to a greater or lesser extent, in the same universals. All possible particulars are determined by the combinatorics of the primary universals.
The universals-particulars connection is what makes the world comprehensible, simplifying it. This connection between both poles, between the deep (universal) and the superficial (particular) is the basis of consciousness. The universal corresponds to the mode of consciousness of the right hemisphere (HD) of the brain, and the particular corresponds to the mode of consciousness of the left hemisphere (HI).
Universals manifest and are present at all levels of reality: abstract, mental, linguistic and physical. The abstract level is the level closest to the universals, and the farthest level is the physical level.
There is a hierarchy of universals. The universal semantic primitives (the primal universals) are the highest ranking, the supreme level of reality.
A universal can be instantiated in a particular or in a universal of lower rank. For example, dark blue: (blue/dark).
In general, a particular cannot be instantiated, but in MENTAL any particular expression can be instantiated or substituted for any other. In this sense, every expression is potentially universal.
MENTAL represents a "semantic holism". Primitives only make sense within the language as a whole.
Regarding Occam's "mental language," there are several overlaps with MENTAL:
Mental concepts or terms, the "natural signs" are at a higher level. The human mind has the ability to intuitively associate a particular object with a sign.
Concepts can be combined to form mental propositions.
The meanings of mental terms are absolute, because they have been established by nature.
The main function of language is to discover the structure of reality.
Bibliography
Armstrong, David M. Los universales y el realismo científico. UNAM, México, 1989.
Armstrong, David M. Nominalism and Realism. Cambridge University Press, 1978.
Armstrong, David M. A Theory of Universals. Cambridge University Press, 1978.
Armstrong, David M. Universals: an Opinionated Introduction. Westview Press, 1989.
Gilson, Étienne. El espíritu de la filosofía medieval. Ediciones Rialp, 2009.
Grabmann, Martin. Historia de la filosofía medieval. Editorial Labor, 1928. Disponible en Internet.
Keith Campbell, Keith. Abstract Particulars. Blackwell, 1990.
Ockham, William. Ockham's Theory of Terms: Part I of the Summa Logicae. St. Augustines Press, 2011.
Ockham, William. Ockham's Theory of Propositions: Part II of the Summa Logicae. St. Augustines Press, 2011.
Quine, Willard Van Orman. Desde un punto de vista lógico. Paidós Ibérica, 2002.
Russell, Bertrand. Los Problemas de la Filosofía. Editorial Labor, 1991. Disponible en Internet.
Williams, Donald C. On the Elements of Being. The Review of Metaphysics vol. 7, no. 1, pp. 3-18, Sep. 1953.
