The history of philosophy is replete with different metaphysical schemes of the ontological structure of the world. These schemes have generally been described in informal, intuitive terms, and the arguments for and against them, including their consistency and adequacy as explanatory frameworks, have generally been given in even more informal terms. The goal of formal ontology is to correct for these deficiencies. By formally reconstructing an intuitive, informal ontological scheme as a formal ontology we can better determine the consistency and adequacy of that scheme; and then by comparing different reconstructed schemes with one another as formal ontologies we can better evaluate the arguments for and against them, and come to a decision as to which system it is best to adopt.
1. Formal Ontology
Formal ontology,… is a discipline in which the formal methods of mathematical logic are combined with the intuitive, philosophical analyses and principles of ontology, where by ontology we mean the study and analysis of being qua being, including in particular the different categories of being and how those categories are connected with the nexus of predication in language, thought and reality. The purpose of formal ontology is to bring together the clarity, precision and methodology of logical analyses on the one hand with the philosophical significance of ontological analyses on the other.
2. Time, Being and Existence
A criterion of adequacy for any formal ontology is that it should provide a logically perspicuous representation of our commonsense understanding of the world, and not just of our scientific understanding.
A second criterion of adequacy for a formal ontology is that it must explain and provide an ontological ground for the distinction between being and existence, or, if it rejects that distinction why it does so. Put simply, the problem is: Can there be things that do not exist? Or is being the same as existence? Different formal ontologies will answer these questions in different ways.
…the distinction between things that did exist, do exist, or will exist, or what in the proposed book we call realia, as opposed to existentia, which is restricted to the things that exist at the time we speak or think,…
3. Ontology and Modality
Another criterion of adequacy for a formal ontology is that it must explain the ontological grounds, or nature, of modality, i.e., of such modal notions as necessity and possibility.
The abstract intensional objects of conceptual realism, for example, do not exist as concrete objects, but, as we explain later, they also are not Platonic forms. They do not exist in an independent Platonic realm, in other words, but rather have a mode of being dependant upon the evolution of culture and consciousness.
4. Formal Theories of Predication
Comparative formal ontology is the preferable, if not also the proper, domain of many issues and disputes in metaphysics, epistemology, and the methodology of the deductive sciences. For just as the construction of a particular formal ontology lends clarity and precision to our informal categorical analyses and serves as a guide to our intuitions, so too comparative formal ontology can be developed so as to provide clear and precise criteria for constructing and comparing different formal ontologies so that ultimately we can make a rational decision about which such system we should ourselves adopt.
Different formal ontologies are primarily based on different formal theories of predication, which in turn are based on different theories of universals, the three most important being nominalism, conceptualism, and realism. A basic feature of a formal ontology, in other words, is a formal theory of predication based on a theory of universals. A key aspect of such a theory is how the categories of being, especially the category of objects and the category of universals, are related to one another, and how the unity of the nexus of predication is explained in terms of those categories. Such a categorial analysis indicates another basic feature of a formal ontology, namely, how it represents the categorial structure of the world, and in particular whether it can represent the categorial structure of our commonsense understanding of the world as well that of our scientific theories, without the two being in conflict. A formal ontology is not just a formal axiomatic development, in other words, but rather it is a system in which ontological categories are represented by logical categories, and ontological analyses by logical analyses.
Nominalism, which denies that there are any universals, whether real or conceptual, is logically the weakest formal ontology. From a logical point of view what is interesting about nominalism is the kind of constraint it imposes on a theory of predication. That constraint, however, has a more interesting counterpart in constructive conceptualism and represents an important stage of cognitive development, a stage that is an essential part of conceptualism and the more general framework of conceptual realism. The more general framework allows the constraint to be acknowledged and yet also transcended, whereas the similar constraint in nominalism leaves no room for such transcendence.
There is another reason as well, namely, that predication in language, which is the only form of predication acknowledged in nominalism, depends upon our cognitive capacity for language, including in particular our rule-following cognitive capacities underlying the use of referential and predicable expressions. A cognitive theory of predication is needed to explain predication in language, in other words, and that is precisely what the form of conceptualism we defend here is designed to do. In fact, the referential and predicable concepts of our form of conceptualism are none other than the rule-following cognitive capacities underlying the use of referential and predicable expressions, and the unity of the nexus of predication in conceptualism is what underlies and accounts for the unity of predication in language. Conceptualism is to be preferred over nominalism because, unlike the latter, which is based on an unexplained account of predication in language, it is framed in terms of a theory of predication, i.e., a theory of predication about the cognitive structure of our speech and mental acts, and therefore a theory of thought that underlies and explains predication in language.
5. Conceptual Realism
Conceptual realism, the system we think is best and have adopted, contains, in addition to a conceptualist theory of predication, an intensional realism that is based on a logic of nominalized predicates, and a natural realism that is based on a logic of natural kinds.
Unlike the a priori approach of the transcendental method, which claims to be independent of the laws of nature and our evolutionary history, i.e., of our status as biological beings with a culture and history that shapes our language and much of our thought, conceptual realism is framed within the context of a naturalistic epistemology and a naturalistic approach to the relation between language and thought, thought and reality, and our scientific knowledge of the world.
The realism part of conceptual realism, we have said, contains both a natural realism and an intensional realism, each of which can be developed as separate subsystems, and both of which are not only consistent in themselves but compatible with each other within the larger framework. We call these two subsystems conceptual natural realism and conceptual intensional realism. Conceptual natural realism represents a modal form of moderate realism, which, by being extended to include a logic of natural kinds, can be developed into a modern form of Aristotelian essentialism. Conceptual intensional realism, on the other hand, represents a modern counterpart of Platonism based on the intensional contents of our referential and predicable concepts. These two subsystems capture the more important ontological features of both logical realism and natural realism as theories of universals while also explaining our epistemic access to the abstract intensional objects of logical realism on the one hand and the natural kinds and natural properties and relations of natural realism on the other. The two subsystems are compatible in the larger framework of conceptual realism, as we have said, because each is constructed on the basis of a different logical aspect of that framework.
Conceptual intensional realism, for example, is based on a logical analysis of nominalized predicates and propositional forms as abstract singular terms, i.e., a logical analysis of the abstract nouns and nominal phrases that we use in describing the intensional contents of our speech and mental acts. The intensional objects that are denoted by these abstract singular terms serve the same purposes in conceptual intensional realism that abstract objects serve in logical realism as a modern form of Platonism. The difference is that, unlike Platonic Forms, the intensional objects of conceptual realism do not exist independently of mind and the natural world, the way they do in logical realism, but are products of the evolution of culture and language, and especially of the institutionalized linguistic practice of nominalization. In this way our epistemic grasp of abstract intensional objects is explained in terms of the concepts that underlie our rule-following cognitive capacities in the use of language.
The natural kinds and natural properties and relations of conceptual natural realism, on the other hand, are not intensional objects; and in fact they are not objects at all but are rather unsaturated causal structures that are complementary to the structures of natural kinds of things. Unlike conceptual intensional realism, which is based on the logic of nominalized predicates, and hence is directed upon an “object”-ification of predicable concepts, conceptual natural realism is directed upon the structure of reality and depends upon empirical assumptions as to whether or not there are natural properties or relations corresponding to particular predicable concepts, and similarly whether or not there are natural kinds corresponding to particular sortal common-name concepts.
6. Predication in Conceptual Realism
Conceptual realism, we have noted, is based upon a cognitive theory of predication, and referential and predicable concepts are in fact the rule-following cognitive capacities that underlie our use of referential and predicable expressions…. the nexus of predication in conceptual realism is the result of jointly exercising a referential and predicable concept as complementary cognitive structures, and as such it is what accounts for both predication in language and the unity of thought.
The theory also provides an account of complex predicate expressions that contain abstract noun phrases, such as infinitives and gerunds, and also complex predicate expressions with quantifier phrases occurring as direct-object expressions of transitive verbs. Conceptually,… the content of such a quantifier phrase and the referential concept it stands for is “object”-ified through a doubly reflexive abstraction that by deactivation and “nominalization” of the quantifier phrase first generates a predicable concept and then the intensional content of that predicable concept. All direct objects of speech and thought are intensionalized in this way so that a parallel analysis is given for both ‘Sofia finds a unicorn’ and for ‘Sofia seeks a unicorn’. And yet, relations, such as Finds, that are extensional in their second argument positions can still be distinguished from those that are not, such as Seeks, by appropriate meaning postulates.
The same doubly reflexive abstraction explains the three different types of expressions that represent the natural number concepts, namely first, as numerical quantifier phrases, such as ‘three dogs’, ‘two cats, ‘five chairs’, etc., then, second, as the cardinal number predicates ‘has n instances’, or ‘has n members’, and the third as the numerals ‘1’, ‘2’, ‘3’, etc., i.e., as objectual terms that purport to name the natural numbers as abstract objects.
Finally, the deactivation of referential expressions that is a part of this cognitive theory of predication is also involved in fictional discourse and in stories in general. The objects of fiction, on this account, are none other than the intensional objects that deactivated referential expressions denote as abstract objectual terms. This account of the ontology of fictional objects explains their “incompleteness” as well as their status as intensional content.
8…
Names, whether proper or common, occur as parts of quantifier phrases in the simple logic of names of our cognitive theory. In the broader theory of reference of conceptual realism, however, names, whether proper or common, can also be “nominalized”, i.e., transformed into objectual terms that can occur as arguments of predicates.
Semantically, such a logic is needed to account for irreducible forms of plural reference and predication. The well-known Geach sentence ‘Some critics admire only each other’, for example, which semantically says that there is a group of critics who admire only other members of the group, cannot be analyzed in first-order logic alone; and it would be both semantically and ontologically misleading to analyze it in terms of set theory. Unlike a set, a group in the sense intended here is a plurality of individuals and not an abstract object.
A logic of plurals is needed not just as a semantical framework for plural reference and predication in natural language and our commonsense framework, but, and perhaps more importantly, also for an ontological account of the properties of groups of objects in our scientific theories. The temperature and pressure of a volume of gas, for example, are really properties of the group of atoms or molecules in that volume rather than properties of the individual atoms or molecules that make it up. The visual, auditory, and other sensory properties of different modules of the brain are properties of the groups of neurons that make up those modules rather than of the individual neurons in the group. Similarly, the dispersion and redistribution of different populations of species of plants and animals are statistical properties of the groups of plants and animals and not of the individuals in those groups. Groups, which are classes as many of two or more objects, are plural objects, and as such they are values of the objectual variables in this ontology.
9…
Conceptualism and natural realism have a clear affinity for each other, even though they do not have the same overall logical structure. Conceptualism, for example, presupposes some form of natural realism as the causal ground of our capacity for language and thought, and natural realism presupposes conceptualism as a framework by which it can be articulated as a formal ontology. Historically, in fact, the two ontologies have often been confused with one another, so that sometimes it was said that a universal “exists” in a double way, one being in the mind and the other in things in the world. Abelard, for example, held that a universal “exists” first as a common likeness in things, and then as a concept that exists in the human intellect through the mind’s power to abstract from our perception of things by attending to the likeness in them. Aristotle is sometimes also said to have held such a view. Aquinas, however, was clear about the distinction and maintained that a concept and a natural property or natural kind are not really the same universal, and that in fact they do not even have the same mode of being.
10. Criteria of Adequacy
Criteria of adequacy for a formal ontology that we have indicated so far can be summarized as follows.
• A formal ontology must provide a logically perspicuous representation of our commonsense understanding of the world as well as our scientific understanding.
• A formal ontology must explain the distinction between being and existence, i.e., give an ontological grounding of that distinction, or if it denies the distinction then explain why it does so and why the result is an adequate ontological framework.
• A formal ontology should provide an ontological, and not just a set theoretical, account of modality.
• A formal ontology must explain the nature of predication in thought as well as in language and indicate what theory of universals is part of that explanation.
It is because conceptual realism fulfills these criteria of adequacy, as well as others indicated throughout this book, that it is the best formal ontology to adopt.
Nino B. Cocchiarella - SYNTHESE LIBRARY 339 Formal Ontology and Conceptual Realism - Springer - 2007
