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Predication in Conceptual Realism

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Abstract

Conceptual realism begins with a conceptualist theory of the nexus of predication in our speech and mental acts, a theory that explains the unity of those acts in terms of their referential and predicable aspects. This theory also contains as an integral part an intensional realism based on predicate nominalization and a reflexive abstraction in which the intensional contents of our concepts are “object”-ified, and by which an analysis of predication with intensional verbs can be given. Through a second nominalization of the common names that are part of conceptual realism’s theory of reference (via quantifier phrases), the theory also accounts for both plural reference and predication and mass noun reference and predication. Finally, a separate nexus of predication based on natural kinds and the natural properties and relations nomologically related to those natural kinds, is also an integral part of the framework of conceptual realism.

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Notes

  1. See Cocchiarella (1996, 2001, 2007).

  2. By logical realism we mean the type of framework that was part of the logicism developed by Gottlob Frege and Bertrand Russell. (See Cocchiarella (1986) for a reconstruction of Frege’s and Russell’s early frameworks.) By natural realism we mean the types of frameworks developed in Cocchiarella (1976, 2007), which is really a conceptual natural realism, and in Armstrong (1978), which does not involve any connection with conceptualism.

  3. See, e.g., Cocchiarella (1985), or (1987), chapter 4. For proof of the equivalence of HST *λ (which is one part of the framework of conceptual realism) with weak Zermelo set theory, Z, the simple theory of types, ST, and NFU (Quine’s New Foundations with Urelements), anyone of which can be taken as a foundation for mathematics, see Cocchiarella (1985).

  4. See Cocchiarella (1987, chapter 3), Cocchiarella (1996, § 7), and Cocchiarella (2007, chapter 7).

  5. There is another important difference regarding certain theses about intensional possible worlds that are provable on the basis of a principle of rigidity. This principle can be validated in logical realism but not in conceptual realism, mainly because of certain limitations on our human capacity for concept formation. For more on this see Cocchiarella (2007, § 6.2).

  6. For a similar view on this issue see Russell (1903, § 55), and Frege (1979, p. 177).

  7. This in fact is how I understand Peter Abelard, whom some philosophers call a nominalist and others call a conceptualist.

  8. For an account of the imagist theory, see Price (1953, Chapter 8).

  9. Of course our communication with one another is not always perfect, which is partly a result of differences in our rule-following abilities in the use of language. Nevertheless, for the most part our cognitive capacities in the use of language are in sufficient agreement that we are able to communicate our thoughts to one another. This is what we mean in speaking of them as intersubjectively realizable capacities.

  10. See chapter 9 of Cocchiarella (2007).

  11. For an example of a presupposition-free use of a definite description, consider the teacher who says to her class that the student who writes the best essay will win an award. She is not asserting in this example that there will be one and only one student who writes an essay better than all of the other students and that that student will win an award, but only that if there is one and only such student, then that student will win an award. There might be several students who, except for each other, write essays better than the other students.

  12. See chapter 8 of Cocchiarella (2007) for a representation of the suppositio theory in conceptual realism.

  13. Leśniewski’s system of ontology, which is also called a logic of names, is reducible to the logic of names, proper and common, and simple and complex, that is part of conceptual realism and only very briefly described here. See Cocchiarella (2007, chapter 10), for details.

  14. Where A is a common name and \(\varphi (x)\) is an open formula with x free, then \(A/\varphi (x)\) is a complex common name read as A that is \(\varphi \). (We use A as a name variable for proper as well as common names, both of which occur as parts of quantifier phrases in the logic for conceptual realism.) For more details see Cocchiarella (2007). But both can also be nominalized, as we note below, and occur as objectual terms.

  15. This type of analysis of the direct object of a relational expression is similar to, but also different from, the analysis given by Montague in (1970).

  16. For convenience, we ignore the issue of representing tense throughout. A fuller representation would involve the use of the operators of tense logic.

  17. The representation of ‘kiss’ as an extensional predicate is given though the following meaning postulate (where A is a variable for names, whether proper or common):

    $$ \left[\lambda xKiss(x,\left[\exists yA\right])\right]=\left[\lambda x(\exists yA)Kiss(x,y)\right]. $$
  18. Combined with our account below of plural reference and predication, the same type of analysis applies to Armstrong’s example ‘The Apostles expected the Second Coming’. See Armstrong (1978, p. 77).

  19. Something like this kind of analysis was part of the identity theory of the copula in the medieval terminist logic of Ockham and others. For more on this see Cocchiarella (2007, chapter 8).

  20. Some predicates, such as those that lead to Russell’s paradox, must as a matter of logic fail to denote the intensional content as an object even though their nominalization purports to do so. That is why our logic is free of existential presuppositions for objectual terms. So even though a nominalized predicate purports (as an abstract singular term) to denote, it may, as a matter of logic, fail to do so.

  21. This is also why what is predicated of an object is sometimes spoken of as inhering in that object. Thus, from ‘Socrates is wise’ we may infer the inverse form ‘Wisdom inheres in Socrates’ as well ‘Wisdom is exemplified by Socrates’.

  22. Some realist philosophers, such as Gustav Bergmann, insist on a difference in logical type between concrete first-order objects and real properties and relations as second-order objects. The point is that, notwithstanding the difference in type, these philosophers take the latter to be the objects denoted in natural language by nominalized predicates and do not distinguish those objects from what predicates stand for in their role as predicates. Some, like Bergmann, also insist that exemplification is not a relation but a “tie” between concrete and abstract objects. See, e.g., Bergmann (1960).

  23. The relational forms of exemplification are defined similarly:

    $$ \varepsilon _{n}(x_{1}, \ldots ,x_{n+1})=_{df}(\exists R)\left[x_{n+1}=R\wedge R(x_{1}, \ldots,x_{n})\right]. $$

    With λ-abstracts for complex predicates, both the monadic and the relational forms can be given as a straight definition by identity. For example, the monadic form can be defined as follows:

    $$ \varepsilon =\left[\lambda xy(\exists F)(y=F\wedge F(x))\right]. $$
  24. Here we are using ‘falls under’ only as a convenient informal way of speaking. The logical form in question does not represent this so-called “falling under” as a relation, but as predication.

  25. See Popper and Eccles (1977, chapter P2), for a similar view. We should note, however, that although our view of abstract objects supports the Popper–Eccles interactionist theory of mind, it does not also depend on that theory.

  26. It is the inveterate human habit through reflexive abstraction of treating as an object what is not object, an abstraction that in this case has become institutionalized in the process of nominalization.

  27. For more on this issue see Cocchiarella (2007, chapter 7).

  28. When a proper name is “nominalized,” it functions exactly the way a name does as a singular term in free logic. That is because what it denotes is a class as many with at most one object, which, given that the name does denote, is just that one object.

  29. See Russell (1903, §§ 69–70). The plural ‘men’ also denotes the class as many of men.

  30. Our use of ‘it’ and the word ‘object’ in the phrase ‘plural object’ should be taken only as an informal, heuristic way of speaking in ordinary language analogous to Frege’s way of speaking about concepts as unsaturated functions, as when he says of the object expression ‘the concept horse’ that it does not denote an object. Some things, in other words, cannot be said but can only be shown (in our logic); or as Wittgenstein put it in the Tractatus “What can be shown, cannot be said” (4.1212).

  31. For details on the logic of classes as many, see Cocchiarella (2002 or 2007, chapter 11).

  32. This analysis is slightly different from that given in Cocchiarella (2002, 2007) where plural reference was always to groups, i.e., classes as many of two or more objects. This was corrected in Cocchiarella (2009).

  33. Logical forms that represent our speech and mental acts are not the same as those that figure into the deductive machinery of framework of conceptual realism except via meaning postulates. For more details on this see chapter 11, §§ 7–8, of Cocchiarella (2007).

  34. See Cocchiarella (2009) for details.

  35. For details on how this can be so see Cocchiarella (2007).

  36. Our theory of mass nouns is realistic in that it assumes the atomicity thesis. In other words, in accordance with quantum mechanics, there is no infinite descent involved in the semantics of mass nouns. See Cocchiarella (2009) for more on this issue.

  37. For more details about the logic of mass nouns in conceptual realism, See Cocchiarella (2009).

  38. Many, if not most, physical objects do not themselves belong to a natural kind but rather are complexes made up of natural kinds of things. It is only a description of events and a conceptual mode of predication that applies to those objects, even though the concepts we predicate of them, such as, e.g., color, might in theory be based on the natural properties of kinds of things (e.g., photons and the atoms and molecules) that make up those objects.

  39. Armstrong (1978, p. 3). A similar view of natural kinds as special properties was described in Cocchiarella (1976). But that view was later replaced by the present account in several articles as well as in chapter 12 of Cocchiarella (2007).

  40. Ibid., p. 62.

  41. Ibid.

  42. See Cocchiarella (2007, § 12.4).

  43. Armstrong (1978, p. 3).

  44. Ibid., p. 3. Like Scotus’ haecceity (thisness), a bare particular has no distinctive nature of its own, which is the polar opposite of a natural kind. This seems to be what Armstrong means by a “thin” particular.

  45. Of course in science we sometimes conjecture that a natural property or relation is needed to explain certain phenomena, e.g., a certain charge or interaction between particles, and we then introduce a predicate that stands for the property or relation in question. But a predicable concept still underlies the correct use of that predicate in the appropriate theoretical context even if that concept is not familiar to most people. The same is also true of natural kinds and the introduction of common names such as ‘electron’, ‘up quark’, ‘down quark’, ‘muon’, etc. Of course, sometimes our scientific conjectures are wrong, as was the case with the so-called natural kind phlogiston. The common name ‘phlogiston’, as it turned out, denotes nothing.

  46. By an existent we mean a concrete object, and not, e.g., an intensional object.

  47. Armstrong (1978, p. 10).

  48. For obvious reasons. this thesis can be stated more simply as

    $$ (\forall ^{k}A)\diamondsuit^{c}(\exists ^{e}xA)(x=x). $$

    With nominalized common names (denoting classes as many), it can also be stated as

    $$ (\forall ^{k}A)\diamondsuit^{c}(\exists ^{e}x)(x\in A). $$
  49. See Cocchiarella (1976, 2007, chapter 12).

  50. For convenience, we state the principle here only for properties.

  51. It is not clear that Armstrrong would say that a “thick particular” is always of some natural kind. But probably (?) that is how he understands the conjunction of all of the natural properties of such a particular.

References

  • Armstrong DM (1978) Universals and scientific realism vol. II, a theory of universals. Cambridge University Press, Cambridge

    Google Scholar 

  • Bergmann G (1960) Ineffability, ontology, and method. Philos Rev 69:18–40

    Article  Google Scholar 

  • Cocchiarella NB (1976) On the logic of natural kinds. Philos Sci 43:202–222

    Article  Google Scholar 

  • Cocchiarella NB (1985) Frege’s double correlation thesis and Quine’s set theories NF and ML. J Philos Logic 14(4):1–39

    Article  Google Scholar 

  • Cocchiarella NB (1986) Frege, Russell and logicism: a logical reconstruction. In: Leila H, Jaakko H (eds) Frege synthesized: essays on the philosophical and foundational work of Gottlob Frege. D. Reidel Pub. Co., Dordrecht, pp 197–252

    Chapter  Google Scholar 

  • Cocchiarella NB (1987) Logical studies in early analytic philosophy. Ohio State University Press, Columbus

    Google Scholar 

  • Cocchiarella NB (1996) Conceptual realism as a formal ontology. In: Poli R, Simons P (eds) Formal ontology. Kluwer, Dordrecht, pp 27–60

    Chapter  Google Scholar 

  • Cocchiarella NB (2001) Logic and ontology. Axiomathes 12:117–150

    Article  Google Scholar 

  • Cocchiarella NB (2002) On the logic of classes as many. Stud Logica 70:303–338

    Article  Google Scholar 

  • Cocchiarella NB (2007) Formal ontology and conceptual realism. Synthese library, vol. 339. Springer, Dordrecht

    Google Scholar 

  • Cocchiarella NB (2009) Mass nouns in a logic of classes as many. J Philos Logic 38:343–361

    Article  Google Scholar 

  • Eberle RA (1970) Nominalistic systems. Synthese Library. D. Reidel Pub. Co., Dordrecht

    Book  Google Scholar 

  • Frege G (1979) Posthumous writings. In: Hermes H, Kambartel F, Kaulbach F (eds). University of Chicago Press, Chicago

  • Montague RM (1970) The proper treatment of quantification in ordinary English (reprinted in Formal Philosophy)

  • Montague RM (1974) Formal philosophy: selected papers of Richard Montague. In: Thomason R (ed). Yale University Press, New Haven

  • Popper K, Eccles J (1977) The self and its brain. Routledge and Kegan Paul, London

    Book  Google Scholar 

  • Price HH (1953) Thinking and experience. Harvard University Press, Cambridge

    Google Scholar 

  • Russell B (1903) The principles of mathematics, 2nd edn. Norton & Co., NY (1938)

    Google Scholar 

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Cocchiarella, N.B. Predication in Conceptual Realism. Axiomathes 23, 301–321 (2013). https://doi.org/10.1007/s10516-010-9140-x

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