Combinatorial predication and the ontology of unit attributes

Modern Schoolman

Volumn 79, Issue 2-3, 2002, Pages 163-196

  Mertz, D W ^a  

^a NONE

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EID: 38549174426     PISSN: 00268402     EISSN: None     Source Type: Journal    
DOI: 10.5840/schoolman2002792/310     Document Type: Article

References (89)

1. j, 3,., and is referred to in substantival number sentences such as 'Three is a prime number.'The advantages of this view are given in Mertz, Moderale Realism and its Logic (New Haven: Yale University Press, 1996), pp. 259ff.
2. D. M. Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997), pp. 68, 109;
3. James P. Moreland, 'Theories of individuation: A Reconsideration of Bare Particulars,' Pacific Philosophical Quarterly 79 (1998), pp. 251-63,
4. and Universals, Qualities, and Quality-Instances: A Defense of Realism (Lanham, MD; University Press of America, 1985);
5. Gustav Bergmann, Logic and Reality (Madison: University of Wisconsin Press, 1964), pp. 133-34, 277.
6. In regard to Armstrong, he refers to bare particulars as 'thin particulars.' By this designation he seeks to emphasize his thesis that in extra-conceptual reality there are no particulars without some property attached as an ontic predicate, i.e., there are only states-of-affairs or facts. A thin (bare) particular is a conceptual abstraction from a state-of-affairs, as is the property or relation universal, the only other constituent of a state-of-affairs. Also see Armstrong's Nominalism & Realism: Universals & Scientific Realism, Vol. I (Cambridge: Cambridge University Press, 1978), pp. 113ff.
7. Michael Loux, Substance and Attribute (Dordrecht: Reidel, 1978), pp. 163ff.
8. Also, Loux, Metaphysics: A Contemporary Introduction (New York: Routledge, 1998), pp. 117ff.
9. E. J. Lowe, The Possibility of Metaphysics (Oxford: Clarendon Press, 1998), pp. 180-83, 197.
10. Paul Spade, Five Texts on the Mediaeval Problem of Universals (Indianapolis: Hackett Publishing Co., 1994), p. 172.
11. Keith Campbell takes this line in Abstract Particulars (Oxford: Basil Blackwell, 1990), p. 69.
12. Adopted here is the relationist over the substantivist view of space. For a justification of this view see Moderate Realism, pp. 39-42. There it is argued that the substantivist view that space(-time) is composed of points(-instances) fails because the latter reduce upon analysis to what would be bare particulars reserved as relata for spatial(-temporal) relations. Apparently these bare point-instances would be the same discrete space-time minima essential to the geometrodynamics conception of real space-time Campbell has advocated, e.g., in 'Unit Properties, Relations, and Spatio-Temporal Naturalism,' this issue. Further, it is instructive to note that Campbell holds space to be real as demonstrated by its property of right-& left-handedness (enantiomorphism) and hence concludes that a Leibnizian relationist conception of space is false, since the latter includes a characteristic foundationism (a view advocated by Campbell himself) claiming the eliminative reduction of relations to properties of their relata. The point I would make is that relationism need not be Leibnizian. The counter-theses advocated here are that foundationism is false, that relations and their instances are fully real and unreducible, and that space(-time) is constituted by instances of space(-time) relations.
13. Armstrong, Slates of Affairs, pp. 5-6, 41-43.
14. Campbell, Abstract Particulars, D. C. Williams, Review of Metaphysics 7 (1953), pp. 3-18, 171-92;
15. John Bacon, Universals and Property Instances: The Alphabet of Being (Oxford: Blackwell, 1995);
16. Peter Simons, 'Particulars in Particular Clothing: Three Trope Theories of Substance,' Philosophy and Phenomenological Research 54 (1994), pp. 553-74,
17. and 'Farewell to Substance: A Differentiated Leave-Taking,' Ratio 11 (1998), pp. 235-52.
18. Bertrand Russell, Inquiry into Meaning and Truth (London: Allen and Unwin, 1940), p. 98,
19. and Human Knowledge, its Scope and Limits (New York: Simon and Schuster, 1948), pp. 292-308.
20. A. J. Ayer, 'The Identity of Indiscernibles' (1954), in Michael Loux, Universals & Particulars, 2d. ed. (Notre Dame, IN: Notre Dame University Press, 1976), pp. 263-70.
21. Brand Blanshard, Reason and Analysis (LaSalle, IL: Open Court, 1962), pp. 399-401.
22. The problem for bundles-of-universals theories is simple: a bundle of universals is itself repeat-able, i.e., universal, and so a bundle theory that admits only universals and bundles thereof cannot account for individuation. Cf. Campbell, Abstract Particulars, p. 19.
23. Loux, Metaphysics, pp. 113-17;
24. Mertz, 'Individuation and Instance Ontology,' Australasian Journal of Philosophy 79 (2001), pp. 45-61.
25. These theories do not give an account of individuation, they simply posit a category of entities, substance universals, and assign to them the duty of individuation without explanation how this is possible. How is it that a property numerically identical across a plurality of individuals can, contrary to its repeatable nature, render these instantiating entities unrepeatable? See Alica Rothstein and Nathan Oaklander, 'Loux on Particulars: Bare and Concrete,' The Modern Schoolman, 78 (2000), pp. 97-102.
26. Peter Simons, 'Particulars in Particular Clothing' and 'Farewell to Substance.' See Edmund Husserl, Logical Investigations (London: Routledge & Kegan Paul, 1970), p. 478.
27. Arda Denkel, 'On the Compresence of Tropes,' Philosophy and Phenomenological Research 57 (1997), pp. 599-606.
28. Keith Campbell, Abstract Particulars, pp. 98-99.
29. Armstrong, States of Affairs, pp. 38, 99, 267.
30. Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London: Routledge & Kegan Paul, 1961), p. 7, Prop. 1.1; p. 13, Prop. 2.05.
31. Wittgenstein, Tractatus, p. 13, Props. 2.061, 2.062;
32. Armstrong, Stales of Affairs, pp. 139-147.
33. For a critique of Armstrong's independence thesis see my review of his States of Affairs in The Modern Schoolman 75 (1998), pp. 227-31.
34. Alfred North Whitehead, Process and Reality (New York: The Free Press, 1978), p. 20, also see pp. 27, 73.
35. Kenneth Olson, An Essay on Facts (Stanford, CA: Center for the Study of Language and Information, 1987), pp. 60-1.
36. WilIiam Vallicella, 'Three Conceptions of States of Affairs,' Nous 34 (2000), pp. 237-259.
37. See Mertz, 'Individuation and Instance Ontology.'
38. Armstrong, 'In Defense of Structural Universals,' Australasian Journal of Philosophy 64 (1986), pp. 85-91;
39. Universals: An Opinionated Introduction (Boulder, CO: Westview Press, 1989), pp. 90, 111;
40. Vallicella, "Three Conceptions of States of Affairs,' p. 248.
41. David Lewis, 'Comments on Armstrong and Forrest,' Australasian Journal of Philosophy 64 (1986), pp. 92-93.
42. Also see his Parts of Classes (Oxford: Blackwell, 1991), pp. 56-57.
43. E.g., as found in Armstrong, Nominalism and Realism, and Reinhardt Grossmann, The Categorical Structure of the World (Bloomington, IN: Indiana University Press, 1983).
44. Gottlob Frege, Translations from the Philosophical Writings of Gottlob Frege, ed. P. Geach and M. Black (Oxford: Blackwell, 1970), pp. 46-47, 54-55, 152.
45. Also see Frege, 'On the Foundations of Geometry' in Essays on Frege, ed. E. Klemke (Chicago: University of Chicago Press, 1968), pp. 569-71.
46. Moreland, Universals, Qualities, and Quality-Instances, pp. 170, 194.
47. Also see his 'Issues and Options in Exemplification, American Philosophical Quarterly 33 (1996), pp. 133-47.
48. Gustav Bergmann, Realism (Madison: University of Wisconsin Press, 1967), pp. 9, 42ff.
49. Herbert Hochberg, 'A Refutation of Moderate Nominalism,' Australasian Journal of Philosophy 66 (1988), 188-207.
50. P. F. Strawson, Individuals (London: Methuen, 1971), pp. 168ff.
51. See Mary Gill, Aristotle on Substance (Princeton: Princeton University Press, 1989), pp. 19ff.
52. Moreland, 'Theories of Individuation: A Reconsideration of Bare Particulars.'
53. Francisco Suarez, On the Various Kinds of Distinctions (Disputationes Metaphysicae. Disputatio VII, de variis distinctionum gener-ibus), trans. Cyril Votiert, S.J., (Milwaukee: Marquette University Press, 1947), I, 17-29, pp. 28-38.
54. See John Malcolm, 'A Reconsideration of the Identity and Inherence Theories of the Copula,' Journal of the History' of Philosophy 17 (1979), pp. 383-400.
55. For a particular example of the inherence theory in Aquinas see Keith Buersmeyer, 'Predication and Participation,' The New Scholasticism 55 (1981), pp. 35-51.
56. Gottfried W. Leibniz, Philosophical Papers and Letters, 2d. ed., ed. Leroy Loemker (Dordrecht: Reidel, 1969), pp. 264, 334, 337.
57. F. H Bradley, Appearance and Reality, 2d ed. (Oxford: Clarendon Press, 1897; reprt. ed. 1966), pp. 144-45, 147-49.
58. Michael LaBossiere, 'Substances and Substrata,' Australasian Journal of Philosophy 72, 3 (1994), pp. 360-70.
59. Bradley, Appearance and Reality, pp. 154, 404, 509-10.
60. F. H. Bradley, 'Relations,' in Collected Essays, Vol. 2 (Westport, CT: Greenwood Press, 1970), p. 638.
61. Mark Henninger, Relations: Medieval Theories, 1250-1325 (Oxford: Clarendon Press, 1989).
62. Gottfried Leibniz, Philosophical Papers and Letters, p. 704.
63. David Hume, A Treatise on Human Nature, I. ii. 4; ed. T. H. Green and T. H. Grose (1886; rpt. ed., Germany: Scientia Verlag Aalen, 1964), pp. 352, 559.
64. There were explicit attempts in the sixteenth and seventeenth centuries to demonstrate that proofs in Euclid's Elements are reducible to syllogistic form. See Neal Gilbert, Renaissance Concepts of Method (New York: Columbia University Press, 1960), pp. 89-90.
65. Ian Mueller has shown that not even the first proposition of the Elements is reducible to syllogistic form. Ian Mueller, 'Greek Mathematics and Greek Logic,' in Ancient Logic and Its Modern Interpretation, ed. John Corcoran (Dordrecht: Reidel, 1974), pp. 35-70.
66. Bertrand Russell, The Principles of Mathematics, 2d ed. (1903: reprt. ed., New York: Norton, 1938), pp. 221ff.
67. Herbert Hochberg, 'The Wiener-Kuratowski Procedure and the Analysis of Order,' Analysis 41 (1981), pp. 161-3.
68. Bertrand Russell, My Philosophical Development (London: Allen & Unwin, 1959), p. 67.
69. Mertz, Moderate Realism, pp. 163-71.
70. Also see Campbell's "The Place of Relations in a Trope Philosophy' in Proceedings of the Colloque International de Philosophie de Grenoble: La Structure due Monde; Objets, Proprietes, etals de choses, forthcoming;
71. Also globally, the non-eliminability of relations provides the ontic underpinning for the analytic methodology that holds that to discover the relations an entity a has with other interrelated entities, i.e., to find a's 'position' in the context of a complex, is to have an explanation of a. As a slogan, 'To explicate is to interrelate.' This contrasts with the once common methodology that 'To explicate is to eliminate.' See Peter Strawson, Subject and Predicate in Logic and Grammar (London: Methuen, 1974), p. 37, 54-55.
72. Also see Jerrold Katz, The Metaphysics of Meaning (Cambridge, MA.; MIT Press, 1990), p. 186.
73. Frege, Translations, pp. 54-55.
74. Francisco Suarez, On the Various Kinds of Distinctions, I. 20, p. 31.
75. John Buridan, Questiones in metaphysicam aristoteles, V, Q. 8, fols. 31, 33.
76. Portions translated by Calvin Normore, 'Buridan's Ontology,' in How Things Are, ed., J. Bogen and J. McGuire (Dordrecht: Reidel, 1985), p. 198.
77. Bradley, Collected Essays, pp. 628-76.
78. William of Ockham, Ockham's Theory of Terms, trans. Michael Loux (Notre Dame, IN: University of Notre Dame Press, 1974), p. 170.
79. It is worth noting here that reinforcing this insight into the linking nature of relations is its power in providing a viable 'absence theory' for solving the difficult problem of true negative propositions. The intractability of this problem under standard ontology is highlighted by George Molnar, 'Truthmakers for Negative Truths,' Australasian Journal of Philosophy 78 (2000), pp. 72-86.
80. Atomic affirmative propositions, e.g., P(a), are held to be true because they correspond to a 'truth-maker' - fact :P(a). Some have held that, by simple analogy, there must be for true negative propositions, e.g., ∼P(a), corresponding 'negative facts.' But this tack, in addition to positing dubious entities, does not account for the fundamental syntactical fact that subjects cannot be negated, but only linguistic predicates, e.g.; whereas one can say 'The ball is not red,' it is nonsensical to say 'The not ball is red.' On the theory of predication defended herein for a negative proposition what is asserted is the absence among the referent(s) of the grammatical subject term(s) (e.g., the ball) of a combi-natorial/predicable state controlled by the intension (e.g., Red) of the referent of the grammatical predicate. Here a predicable nexus is absent, i.e., non-existent, whereas the controlling intension is 'not absent' in the sense that it exists as an abstraction or construction independent of any possible instantiation within a predicable instance. The fact that it is ontic predicates that have this linking aspect explains why only the corresponding linguistic predicates can be negated. Recently Hochberg has attempted to eliminate the need to posit negative facts by proposing that the truth-maker for a negative proposition ∼P(a) is the set of all atomic facts corresponding to the true propositions of the form 'P(a)'. In addition to other problems, this construction commits an epis-temic fallacy of presumed omniscience, a flaw that often infects the substitution of formal models for ontic entities. The set of atomic positive facts is to be the ground for the truth of the negative proposition ∼P(a). Hence, to know that the negative proposition is true we would have to survey the entire infinite set of facts in order to determine that the would-be fact :P(a) is hot in it. Since this is an impossible task for finite minds, we would never be able to determine the truth of negative propositions. See Herbert Hochberg, 'Facts and Classes as Complexes and as Truth Makers,' The Monist 77 (1994), pp. 170-91.
81. Suarez, On the Various Kinds of Distinctions, I. 18-19, pp. 29-31.
82. D. M. Armstrong, A Theory of Universals: Universals & Scientific Realism, Vol. II (Cambridge: Cambridge University Press, 1978), p. 3.
83. Also his 'Keith Campbell and the Trope View of Predication,' Australasian Journal of Philosphy 67 (1989), pp. 386-7;
84. The problem solving power of this analysis of individuated predicates with universal intensions is further magnified when the logic inherent in it is formalized. The result is a 'formal ontology' in the sense of Nino Cocchiarella, 'Ontology II: Formal Ontology' in Handbook of Metaphysics and Ontology, eds. H. Burkhardt & B. Smith (Munich: Philosophia Verlag, 1991), pp. 640-47.
85. The logic inherent in realist instance ontology, what I have called 'PPL,' has a number of powerful results, e.g., distinguishing legitimate from illegitimate self-referential predication, distinguishing identity from indiscernibility, and providing an ontology for arithmetic. PPL is developed in Moderate Realism, with an improved version in 'The Logic of Instance Ontology,' Journal of Philosophical Logic 28 (1999), pp. 81-111.
86. Peter Simons, Paris: A Study in Ontology (Oxford: Clarendon Press, 1987), p. 327.
87. On the need for emergent properties in science see Michael Silberstein and John McGeever, 'The Search for Ontological Emergence,' Philosophical Quarterly 49 (1999), pp. 182-200.
88. Simons, 'Particulars in Particular Clothing.'
89. David Lewis has in his Parts of Classes advocated the view that mereology provides a general theory of composition. Against this view Simons has pointed out the limitations of mereology in explicating integrated wholes. See Simons' Parts: A Study in Ontology, pp. 324ff.