Moderate Realism and Its Logic

Moderate Realism and Its Logic

D. W. Mertz
Copyright Date: 1996
Published by: Yale University Press
Pages: 328
https://www.jstor.org/stable/j.ctt32btsq
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  • Book Info
    Moderate Realism and Its Logic
    Book Description:

    Instance ontology, or particularism-the doctrine that asserts the individuality of properties and relations-has been a persistent topic in Western philosophy, discussed in works by Plato and Aristotle, by Muslim and Christian scholastics, and by philosophers of both realist and nominalist positions. This book by D. W. Mertz is the first sustained analysis that applies the rules and systems of mathematics and logic to instance ontology in order to argue for its validity and for its problem-solving capacities and to associate it with a version of the realist position that Mertz calls "moderate realism."Mertz surveys the history of instance ontology in writings from Plato and Aristotle through Leibniz, followed by modern philosophers such as Bertrand Russell and D. M. Armstrong, among others. He also includes a thorough critique of the recent work of Keith Campbell and other contemporary nominalists. Building on the insights gained through this historical overview, he delves deeper into the logic of instance ontology and uncovers some of its extraordinary problem-solving features: distinguishing legitimate from illegitimate impredicative reasoning; uniformly diagnosing the self-referential paradoxes; being free from the limitation theorems of Gödel and Tarski; providing a basis for the derivation of arithmetic construed intensionally; and formally distinguishing identity and indiscernibility.

    eISBN: 978-0-300-14620-2
    Subjects: Philosophy

Table of Contents

  1. Front Matter
    (pp. i-viii)
  2. Table of Contents
    (pp. ix-xii)
  3. Preface
    (pp. xiii-xvi)
  4. part one the ontology of particularism
    • chapter one Instance Ontology
      (pp. 3-58)

      In traditional ontology there is an ancient but recurring doctrine which asserts that attributes are as individual and unrepeatable as the individuals that possess them. This doctrine, referred to asinstance ontology, orparticularism, is defined most succinctly in terms of the inclusive category of relations. Its claim is that relations, which include properties as the limiting case of monadic relations, exist as individuals among the individuals they relate. More precisely, relations are particularized to numerically distinct instances as they relate numerically distinct ordered sets of relata (n-tuples). For example, in the facts or states of affairs corresponding to the...

    • chapter two Traditional versus Instance Ontology
      (pp. 59-82)

      Given the broad contexts established in chapter 1, we are now in a position to examine in depth some of the telling weaknesses of rivals to instance immanent realism in responding to the fundamental ontological problems of individuation, universals, and predication and their answers to the thesis of predicable possession. By contrast, we shall observe how unit relations provides a solution to each of these problems. The effort will yield a clear conception of the nature of relation instances proposed here, for which detailed arguments will be offered in subsequent chapters.

      Relations are central to structure, and structure is ubiquitous....

    • chapter three Plato and Aristotle on Instance Ontology
      (pp. 83-117)

      In this and the next two chapters we shall examine some of the more historically prominent appeals to attribute instances. My intent is not only to provide further insights into fundamental ontological problems and to determine the role that unit attributes were given in their solutions, but also to examine the pattern of association one finds existing between unit properties and the concept ofrelation. It is generally overlooked that as a historical recurrence, the association between attribute instances and ontological analyses of relations, though spotty, has been persistent and continues into contemporary times. It is a primary thesis of...

    • chapter four Some Medieval and Early Modern Views
      (pp. 118-153)

      Both the doctrine of unit properties and the property reduction of relations were carried over into medieval philosophy primarily through translations and commentaries on Aristotle’s works. Of early importance are Simplicius’s (fl. 527–65)Commentary on the Categories of Aristotle, Porphyry’s (232–304)Isagoge, and Boethius’s (480–525) commentaries on theIsagoge, on Aristotle’sCategoriesandDe Interpretatione, and hisDe Trinitate. Starting from the middle of the twelfth century, the doctrine of unit properties became the majority view of European scholastics, common to both nominalism and moderate realism. The latter is in contrast to the Platonic realism that flourished...

    • chapter five Some Modern Views of Unit Attributes
      (pp. 154-162)

      Like their medieval precursors, modern theories of unit properties and relations divide into realist and nominalist versions. Turning first to realist theories, in more or less detail this doctrine has been advocated by John Cook Wilson, P. F. Strawson, N. Wolterstorff, and the early Bertrand Russell.

      The instance realism of both Cook Wilson and Strawson is advanced, at least in part, on the basis of apparent irreducible reference to unit attributes in ordinary language, as reviewed in chapter 1.1 note in passing that Cook Wilson also offers the argument encountered previously that the matter/form analysis of entities leads to an...

    • chapter six The Irreducibility of Relations
      (pp. 163-173)

      Historically, arguments against admitting relations as a fundamental ontic category are of two types. It is argued either that (a) the very concept of a relation is suspect or, indeed, incoherent—the often claimed moral of Bradley’s regress; or that (b) relations are reducible without loss to properties, so are ontically superfluous. As observed previously, perhaps the argument most frequently invoked, interpreted by some as for, by others as against, the coherence of the concept of relations, has been Bradley’s regress. Because of both the importance of its conclusion and the ambiguity that has existed historically in interpreting the direction...

    • chapter seven Specious Arguments against Relation Instances
      (pp. 174-183)

      Influential critics of the doctrine of relation instances include Bertrand Russell, D. W. Armstrong, and Reinhardt Grossmann. According to Armstrong and Grossmann,¹ despite its long history, the few developed arguments for particularism are inconclusive. Moreover, particularism leaves the problem of universals unsolved; and to solve it requires admitting relation universals in addition to their instances. But once universals are admitted, it is doubtful whether the intermediary instances have any explanatory power over and above that of universals alone. Finally, even if instances are admitted, according to Armstrong, no coherent account can be given of the link between relation instances and...

    • chapter eight Bradley’s Regress and Further Arguments for Relation Instances
      (pp. 184-196)

      In the previous two chapters it was argued that relations are not reducible to properties and that certain influential arguments against relation instances are specious. The first point completes an indirect argument against nominalism from chapter 2, where it was seen how nominalism implies the property reduction of relations. We also observed arguments for the doctrine in the work of Avicenna (chapter 4) and from the apparent uneliminable reference to unit attributes in natural language (chapter 1). In this chapter I shall increase the warrant for the thesis of unit relations by offering additional arguments based upon the intrinsic nature...

  5. part two the logic of particularism and some applications
    • chapter nine Formalization of a Particularized Predicate Logic
      (pp. 199-258)

      In the previous chapters an extended case was made for a realist ontology that includes, in addition to property and relation universals, corresponding unrepeatable instances of each. This ontology, which as such is equally a theory of predication, follows directly from our ontic analysis of relations, including properties as monadic predicates. Insofar as relations relate—that is, are predicative of or among entities as relata—they are unrepeatable; and insofar as they are universal, they are half-truth, nonpredicative abstractions from unrepeatable instances. That is, it was argued that to the extent that a relation fulfills its ontically defining role and...

    • chapter ten Instance Ontology and Logic Applied to the Foundations of Arithmetic and the Theory of Identity
      (pp. 259-284)

      In this final chapter I shall discuss two powerful examples of the problem-solving potential of instance ontology: one in the foundations of mathematics, the other in the theory of identity. The analytical fertility that gives rise to long sought-after results in these areas is offered as further inductive warrant for the truth of instance ontology and, in particular, the realist ‘intensional’ version partially formalized in PPL.

      Themost difficultproblem confronting contemporary studies in the foundations of mathematics is this: How can we develop logic, if, on the one hand, we are to avoid the danger of the meaninglessness of...

  6. Notes
    (pp. 285-306)
  7. Index
    (pp. 307-310)