Signs and reality

1. One, two, three

After thousands of years of debate, philosophers have inherited a large body of terminology from competing schools of thought with divergent ways of thinking and talking about what exists. They have all those terms at their fingertips when they write about ontology. To explain them, David Armstrong (1989) wrote an “opinionated introduction” that begins with the distinction between universals and particulars. His book is short (148 pages) and highly regarded by professional philosophers and Amazon reviewers, who gave it four or five stars. On page 1, Armstrong began with a cautionary note about the “Problem of Universals”:

So let me begin by saying what the problem is. It may turn out that it is really a pseudo-problem. That was the opinion of Wittgenstein and his followers, for instance. Quine is not far from thinking the same. But whether it is a real problem or not should not be decided in advance.

To illustrate the issues, Armstrong cited a “distinction that practically all contemporary philosophers accept…It is the distinction between token and type” by Charles Sanders Peirce. As an example, he noted that the phrase the same in the sentence Two ladies wore the same dress means the same type of dress, not the same token. In general, tokens are particulars, and types are universals. But Armstrong cited many more examples that show the complexities and ambiguities in any attempt to define precise identity conditions.

In discussing tokens and types, Armstrong did not mention and probably did not know that those terms are two-thirds of Peirce’s three-way distinction or triad of which the first term is mark:

A mark is anything perceptible at the earliest stage of sensation before it has been recognized, interpreted, or classified.

Peirce did not propose his trichotomies as categories of existence, but as phenomenological distinctions for analyzing, classifying, and relating observable marks. In any classification, an ontological category must answer one or more of three fundamental questions: What is something in itself? How is it related to something else? How does it relate other things to each other? Any answer to the first question may be represented as a one-place predicate or monad that classifies something by its observable quality or structure; to the second, as a two-place predicate or dyad that classifies something by its relation to something else. to the third, as a three-place predicate or triad by the way it mediates or relates other things to each other.

As an example, the words dog, pet, and gift might refer to the same individual. Both Peirce and Aristotle would say that the category Dog answers the question What is it? Peirce would add that the category Pet answers two questions, What is it? and How is it related to some person? He would add that calling the dog a gift classifies it by the mediating intention of a giver toward a recipient. If the giver hands the dog to the recipient, that is dyadic transfer. To be a gift, the triad requires a sign of intention, such as saying “happy birthday”.

Some philosophers would say that a dog is a member of a natural kind whose essence makes it a dog. But essences are problematical. The dog species, Canis familiaris, has recently been reclassified as a subspecies, Canis lupus familiaris, of Canis lupus, the gray wolf. The genome or DNA sequence is the most precise way of defining the essence of a species. But fertile hybrids of dogs with other members of the genus Canis are possible. Those hybrids would generate DNA sequences that do not exist in nature. Modern methods of genetic engineering provide even more options. Someone might insert a gene from an underwater creature to create a glow-in-the-dark dog. To call such an animal a member of a natural kind is problematical, but it’s just as problematical to call it an artifact. Peirce’s categories are determined by phenomena that are observed or inferred from observations, not on debatable essences, substances, or natures.

The category Pet is a role that classifies an animal by its relationship to someone who plays the complementary role of pet owner. But the variety of pet relationships is open ended. Koko the gorilla, for example, had a pet cat that she named All Ball, using a version of American Sign Language. The role of pet can vary on a continuum from friend to livestock. Some people say that they adopted a pet and call themselves pet parents. Nearly every word that refers to a role has a similar continuum: employee, teacher, cook, tool, foundation, or dwelling. The Canadian census classifies tepees and igloos as dwellings. When the census takers found a man who lived in a sewer, they had to get an official ruling to allow a sewer to be called a dwelling. Like the monadic quality, the dyadic role is determined by phenomena that indicate the kind of relation.

The mediating intention of a triad also depends on an observable sign, such as a promise, a handshake, a signature, or a habitual pattern of behavior. But not all triadic relations involve a mediating intention. The relation Between ( x , y , z ) , for example, is equivalent to a conjunction of two dyads, such as Before ( x , y ) and Before ( y , z ) . Any number of such dyads could be linked together to form a chain, but each one is independent of the others. In an act of giving, a mediating intention binds the giver, gift, and recipient. Removing any one of the participants destroys the act of giving. But a chain of items linked by dyadic relations can be broken at any link without affecting the other relations in the chain. Peirce called a triad defined by a pair of independent dyads a degenerate triad.

Yet the triadic relation Give ( x , y , z ) may be defined in terms a nominalized verb Giving ( w ) and three dyads that link w to each of the participants: Agent ( w , x ) , Theme ( w , y ) , and Recipient ( w , z ) . But those dyads are not independent. The three variables linked to the variable w form a triadic connection, which requires the dyads Agent, Theme, and Recipient as obligatory links. For a genuine triad, such as Give or Giving, the nominalization of the verb is a purely syntactic transformation that does not affect the semantics.

This transformation raises serious questions about Quine’s claim “To be is to be the value of a quantified variable.” The syntactic transformations may increase the number of variables without changing the semantics: any triad may be translated from a three-variable predicate to a four-variable expression without affecting the truth value. But the four-variable expression increases the flexibility because it allows more relations to be linked to the fourth variable w. If new relations are linked to w, it’s no longer possible to translate the four-variable version back to three variables without discarding some of the information.

As these examples show, Peirce’s phenomenological categories distinguish reality from theories about what exists. Although reality is independent of what we may think, we can talk about the same phenomena at different levels of detail from different perspectives with different choices of types and different numbers of existential quantifiers. There is no limit to the variety of perspectives, purposes, questions, answers, decisions, actions, social interactions, and metaphysical explanations.

2. The theory of signs

Plato’s dialogs show that puzzles about signs, language, and logic were a common topic of debate in the Academy. Aristotle began the systematic study of signs in the first paragraph of his book On Interpretation (16a1). He related the basic principles of signs to language, but he made no assumptions about the psyche other than its existence as a repository for signs:

First we must determine what are noun and verb and after that, what are negation, assertion, proposition, and sentence. Those in speech are symbols (symbola) of affections in the psyche, and those written are symbols of those in speech. As letters, so are speech sounds not the same for everyone. But they are signs (sêmeia) primarily of the affections in the psyche, which are the same for everyone, and so are the objects of which they are likenesses. On these matters we speak in the treatise on the psyche, for it is a different subject.

By using two different words for sign, Aristotle recognized two distinct ways of signifying: sêmeion for a natural sign and symbolon for a conventional sign. The word sêmeion, which was used for symptoms of a disease, implies that a speech sound is primarily a natural sign of a mental affection or concept and secondarily a symbol of the object it refers to. That triad of sign, concept, and object is the meaning triangle, for which Ogden and Richards (1923) contributed the name and the diagrams.

From the 12th to the 16th centuries, the Scholastics developed semiotics in great depth and subtlety. They called the concept at the top of the meaning triangle the signification (significatio) and the intended object on the right the supposition (suppositio). They recognized that the supposition of a sign might not exist: it may be a hypothesis, a mythical beast, or something expected in the future. With his theory of terms, Ockham (1974) developed one of the most detailed versions, which generalized Aristotle’s option of allowing signs to refer to other signs. In Fig. 1, a sign whose supposition is a physical entity is called a first intention (intentio), and a sign whose supposition is another sign is a second intention.

OPEN IN VIEWER

Fig. 1.

Ockham’s meaning triangles.

For the signification at the top of a triangle, the usual Latin term was conceptio (concept). The sign at the lower left could be a word, an image, or a concept of a concept. The supposition at the lower right could be something physical, something imagined, or another sign. For his theory of propositions, Ockham (1980) developed the syntax and semantics for a significant subset of Latin: Aristotle’s four sentence types for simple sentences and arbitrary Boolean combinations for complex sentences. For that subset, Ockham’s semantics is consistent with the symbolic version by Tarski (1933). In fact, there may have been some influence since Tarski’s colleague, Jan Łukasiewicz, had published several articles on the history of the logic Simons (2014).

Many theories of signs are limited to first-intentional triangles. Frege, for example, used the terms Zeichen, Sinn, and Bedeutung (usually translated sign, sense, and reference), but he did not let the reference of one sign signify another sign. Franz Brentano (1874), who had studied Scholastic logic, adopted the word intentio as the basis for his theory of intentionality, which he defined as the directedness (Gerichtetheit) of thought toward some object, real or imagined.

Peirce had studied Scholastic logic and lectured on Ockham and Duns Scotus at Harvard. For his theory of signs, Peirce elaborated the option of signs of signs. His term for the concept at the top of the meaning triangle is interpretant. Following is one of his most often quoted definitions:

A sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody, that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign. That sign which it creates I call the interpretant of the first sign. The sign stands for something, its object. It stands for that object, not in all respects, but in reference to a sort of idea, which I have sometimes called the ground of the representamen. (Peirce, CP, 2.228)

A pattern of green and yellow in the lawn, for example, is a mark, and the interpretant is some type, such as Plant, Weed, Flower, SaladGreen, or Dandelion. The guiding idea that determines the interpretant depends on the context and the goals and interests of the observer. The interpretant determines how the observer thinks or talks about the object of the sign.

As Peirce noted, a listener who is an expert in the subject matter can often derive a richer interpretant than the speaker. In effect, an expert can “read between the lines.” That variability is essential for flexibility and creativity in language, but many philosophers deplore the lack of precision. Mohanty (1982) remarked “Not unlike Frege, Husserl would rather eliminate such fluctuations from scientific discourse, but both are forced to recognize their recalcitrant character for their theories and indispensability for natural languages.” Creative scientists like Einstein and Bohr could often derive more meaning from scientific language than the original authors had intended.

Like objects, events can also be classified by what aspect they describe: a directly observable event (monad); a causally related effect (dyad); or a mediating intention (triad). The next three sentences describe the same event in each of those ways:

An act of stabbing can be recognized at the instant it happens. It can be classified by immediate observation of the event. But an act of stabbing cannot be called killing unless a second event of dying occurs. Murder involves a triad because the stabbing (1) is related to the dying (2) by the intention (3). Determining whether an act of stabbing that resulted in killing should be considered a murder depends on subtle clues, whose interpretation may require a judge, a jury, and a lengthy trial.

Peirce developed a rich combinatorial system for classifying signs, of which the most widely used subset is summarized in Fig. 2. The labels at the top indicate how a sign directs attention to the object: quality is some aspect of the mark itself, indexicality is some causal or pointing relationship, and mediation involves some law, habit, or convention.

OPEN IN VIEWER

Fig. 2.

Peirce’s triple trichotomy.

Over the years, Peirce had introduced synonyms for some of his more technical terms. The choice of terms in Fig. 2 is based on a letter by Peirce (EP, 2:488) to Lady Welby. In other writings, he used the words qualisign, sinsign, and legisign for the top line. He had also used the word tone for mark, but that word is too closely tied to auditory sensations. The word mark can be used as a more general term. For the bottom line, he also used rheme for predicate and dicent sign for assertion. In 1908, Peirce (EP, 2:483) extended his framework to ten trichotomies, but the nine terms in Fig. 2 are sufficient for most purposes. The following examples, adapted from Sowa (2010), illustrate each of the nine kinds of signs:

Peirce coined the term indexical for a word like this or that, which has the effect of a pointing finger. Instead of being troublesome exceptions, as they were for Frege and Russell, indexicals are an integral part of a systematic framework.

The three triads in Fig. 2 make finer distinctions than most definitions of signs, and they cover a broader range of phenomena. Anything that exists may be a sign of itself (token or sinsign). Shortly after the Big Bang, there were no living things that could interpret the marks of any event. But as soon as some living thing invented instruments that could detect ancient light, they became tokens of types.

In other writings, Peirce used the term quasi-mind to emphasize the generality. A dog, like its owner, could experience a ringing sound as a mark and recognize it as a token of a familiar type. An intelligent dog might discover that a ringing phone is an index of its owner’s habit of answering it. A language of some kind is a prerequisite for signs at the formal level of predicates, assertions, and arguments. Apes that have learned a human sign language have some of that ability. Whether the signs they use among themselves are comparable is still an open question.

As an example, Fig. 3 illustrates the concept of representation with two meaning triangles. The first-intentional triangle at the bottom shows that the name Yojo refers to a cat illustrated by an image at the bottom right. The peak of that triangle is a concept illustrated by the same image enclosed in a balloon. The second-intentional triangle at the top, shows that the symbol [Cat: Yojo] refers to the same concept that is shared with the peak of the first-intentional triangle. The uppermost balloon illustrates a concept of representation that relates the symbol [Cat: Yojo] to a concept of the same cat.

OPEN IN VIEWER

Fig. 3.

Meaning triangles for the concept of representation.

Of the five signs shown in Fig. 3, three have physical marks and two are mental concepts, which are enclosed in balloons. Although mental concepts are not directly observable, no introspection is needed to infer their existence. The triangles are based on semiotic principles, which, as Peirce said, would hold for any living thing. The simplest kinds, such as bacteria, would respond according to the first triad: they would move away from acid and move toward sugar. Those responses are determined by their genes, but the genes themselves are very complex signs.

As these examples show, the Scholastic theory of signs and Peirce’s further developments are far richer than just the first-intentional triangle by Ogden and Richards. The most important aspect of Peirce’s theory is its dynamic nature: any node can spawn another triangle to show more relationships to the entity represented by that node. In Fig. 3, for example, the concept of the cat Yojo could be the left corner of another triangle that represents the concept of the cat Yojo. That triangle would be first intentional because its object would be the physical cat.

By avoiding any assumptions about the psyche, Peirce avoided psychologism. As he said, “Thought is not necessarily connected with a brain” (Peirce, CP, 4.551). Although every thought depends on some mind or quasi-mind, he emphasized that the quasi-mind need not be human:

I define a sign as something, A, which brings something, B, its interpretant, into the same sort of correspondence with something, C, its object, as that in which it itself stands to C. In this definition I make no more reference to anything like the human mind than I do when I define a line as the place within which a particle lies during a lapse of time. (Peirce, 1902)

Armstrong admitted that nearly all the philosophical terminology in his book is controversial. But he made two exceptions. On page 1, he wrote that Peirce’s “distinction between token and type” is accepted by “practically all contemporary philosophers”. On page 135, he wrote “the real existence of properties and relations” is “the most secure”. With his “logic of relatives”, Peirce (1870) developed a notation for representing both monadic properties and N-adic relations. Frege (1879) adapted it to his version of first-order logic. Peirce (1885) adapted it to his algebraic notation for first-order and higher-order logic. Those aspects of Peirce’s logic and semiotic would be the least controversial part of any foundation for ontology.

As another argument for Peirce’s semiotic, two classics of formal ontology failed to define more than a small subset of the categories required for applied ontology: The Logical Construction of the World by Carnap (1928) and The Structure of Appearance by Goodman (1951). The only formal specification in Carnap’s book is the 16-page Chapter IV A on autopsychological objects. Those are prerequisites that any self (autos) would require. To define them, Carnap assumes the logic of the Principia and the development of mathematics by Whitehead & Russell (1910). Then he attempts to define everything in terms of single relation: similarity of elementary experiences (Elementarerlebnisse). To combine them, he uses logic plus a version of mereology. But he ends Chapter A with an admission that these definitions are “examples” of what should be elaborated into a complete system. Chapter B on physical objects is an “outline” with no formal notation of any kind. It ends with a vague discussion of biological objects, which include something called “my body”. Chapter C on heteropsychological objects is an even vaguer discussion of social relations of one body to another (heteros).

Chapter C shows that Carnap had started at the wrong end. In Chapters A and B, he tried to construct everything from elementary experiences. But experiences are signs, and in Chapter C he admitted “The construction of [the sign] relation is more difficult than any of the others which we have hitherto undertaken”. As Aristotle, the Scholastics, and Peirce had shown, signs can be defined by a short specification that assumes a mind but makes no assumptions about its nature. The only requirement is that a mind can relate one sign to another and store some signs for future reference. Carnap mentions the word mind, but defines it only as an unobservable part of a body. That definition would be sufficient for him to adopt Peirce’s definition of sign. With that definition, he could state more precise and detailed definitions of experiences, similarity, languages, communication, and social relations.

Carnap (1967) noted that Goodman started with an assumption that physical objects exist. That approach enabled him to define a larger subset of relations for representing a visual scene. But neither Carnap nor Goodman defined an ontology that was adequate to specify movement and causality in physics, let alone chemistry, biology, languages, and social relations. Without those relations, it’s impossible to specify an ontology for business, finance, engineering, medicine, law, or life.

Philosophical Investigations by Husserl (1900) is another classic that has had a strong influence on formal ontology. Husserl covers a wider range of issues than Carnap or Goodman, including issues about language and intentionality that were influenced by Brentano. Husserl’s discussions of language have had a strong influence, but many philosophers have rejected his treatment of intentionality as “anthropomorphic”. There are three responses to that objection:

As these examples show, Peirce’s semiotic or something equivalent is necessary for any ontology that can support language, communication, and social relations. To show that it is sufficient to define all the terms that any philosopher might adopt is beyond the scope of this article. But a few examples can show how the nine terms in Fig. 2 can clarify and replace the large number of controversial terms that Armstrong discussed:

Since the traditional terms have been used in conflicting ways by many different philosophers, no formal definitions are possible. Peirce’s nine words are not sufficient to express all the details of an ontology, but it is better to represent the details by two kinds of terms: the terminology of whatever logic is used and the terminology of the subject matter that is being represented.

4. Ontology as science or engineering

As a branch of philosophy, ontology is the study of existence. But an applied ontology is an engineering specification of what exists or may exist in some domain. The domain may be as narrow as a particular application, or it may be the entire universe for all time. Traditional philosophical terms are important for relating new developments to the long history of the subject. But the index of Armstrong’s book has over a hundred terms that are unfamiliar to most programmers and systems analysts.

Peirce had studied philosophy ranging from the ancient Greeks and the medieval Scholastics to the early writings by Whitehead, Russell, and Husserl, nearly always in the original languages. But he was also a scientist who had published research in astronomy, chemistry, logic, mathematics, physics, and psychology. He had also been employed as an associate editor of the Century Dictionary, for which he wrote, revised, or reviewed over 16,000 definitions Sowa (2006). He had also published an article on logical machines Peirce (1887) in the American Journal of Psychology, and Minsky (1963) included it in his bibliography of artificial intelligence.

With that background, Peirce chose the nine terms in Fig. 2 as a precise, neutral framework for defining any word that might occur in an unabridged dictionary. It has the simplicity and generality for specifying an ontology for science, design, or engineering:

For both kinds of ontology, some guidelines are necessary for choosing the domain, the methods for analyzing it, and the ways of representing the specifications. They must address issues of logic, metaphysics, and terminology:

An ontology for a narrow domain, such as a program specification, may be able to specify everything in that domain precisely. But an ontology that includes anything outside the control of the designer must be an approximation. No ontology that claims to represent everything can be completed until every branch of science, including the social sciences, has answered every possible research question. Since no perfect universal ontology is possible, different kinds of ontologies for different purposes will require different approximations. Whatever may happen, one principle is certain: every ontology will consist of signs of signs, and every applied ontology must relate signs about the subject matter to the signs inside a computer system.