Abstract
In this paper, I offer an examination of the two existing criteria of change, one indicated, implicitly, by Aristotle and the other proposed, quite formally, by Russell. Both criteria engender problems. While the Aristotelian criterion is both too narrow and too broad, as it includes bogus changes and excludes subjectless changes, the Russellian criterion avoids the distinction between genuine changes and bogus changes completely. The aim of the paper is to address these problems and to show how these two existing criteria of change can be made to deal with the problems through revision and integration.
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Notes
The Aristotelian criterion of change as discussed here is formulated based on Aristotle's account of change mainly in the Categories (15a14–15b32) and the Physics (200b33, 260a26–260b7). Aristotle himself did not provide any formulation of such a criterion.
I subscribe to the view that the incidence of matter (e.g., the tea in a cup or the bronze that constitutes a bronze statue) is fundamentally different from an object (e.g., a horse, Socrates). It is the view which I believe is also shared by Aristotle, although he does not anywhere explicitly make the distinction between the two. For a forceful argument on the difference, see Henry Laycock (2006), Words without Objects, esp. 1.2.
The version proposed by Lombard is even narrower, as it assumes that objects are the only subjects of change. Cf. Lombard, Events, 81.
The example is taken from Geach, who coins the name of “mere Cambridge changes” to describe bogus changes. Lombard claims that Geach's criticism of the “Cambridge criterion of change” actually applies to the Aristotelian criterion (which he calls the “Ancient criterion of change”), not to the criterion espoused by the Cambridge philosophers. Cf. Lombard, Events, 81. It is certainly true that, contrary to what Geach thinks, it is the Aristotelian criterion, not the Cambridge criterion, that generates the problem of such bogus changes as the one in the case of Socrates' becoming shorter as a result of Theaetetus' growth. But, other bogus changes are clearly not entailed by the Aristotelian criterion, changes such as those described by Geach in the following passage, “Socrates would change posthumously (even if he had no immortal soul) every time a fresh schoolboy came to admire him; and numbers would undergo change whenever, e.g., five ceased to be the number of somebody's children.” (P. T. Geach, God and the Soul, 71–72.) By the Aristotelian criterion, Socrates cannot change if he exists no more, as for anything to change it must persist (the x in the formula is necessarily assumed existence import), and by the same criterion, numbers cannot change just because they are neither objects (substances) nor incidences of matter.
When discussing the subject of change a few chapters earlier, he enumerates the kinds of change which includes ones in the categories of relation and time: “For when a thing comes to be of such a quantity or quality or in such a relation, time, or place, a subject is always presupposed, ...” (Physics, 190a34–35).
McTaggart (1921–1927) proposes a different version of the criterion which I will not consider here.
This fact is simply ignored when the criterion is interpreted and schematized by Geach and others.
Smith makes a corresponding distinction between nonrelational predicates and relational predicates. Terence Paul Smith (1973), “On the Applicability of a Criterion of Change,” 325–333.
This is used by Smith. But it is derived from Geach, God and the Soul, 71–72.
This does not mean that a change with subject does not occur in any place. It only means that it need not occur in the same place. That an arrow flies from one place to another is a change that occurs in different places.
References
Geach, P. T. (1969) God and the Soul. Routledge and Kegan Paul, London.
Laycock, Henry (2006) Words without Objects: Semantics, Ontology, and Logic for Non-Singularity. Oxford: Oxford University Press.
Lombard, Lawrence Brian (1986) Events, A Metaphysical Study. Routledge and Kegan Paul, London, Boston and Henley
McTaggart, John McTaggart Ellis (1921-1927) The Nature of Existence. The University Press, Cambridge, England.
Miller, Barry (1973) Logically Simple Propositions. Analysis 34: 123-128.
Le Poidevin, Robin (1998) Change. Routledge Encyclopedia of Philosophy. Ed. E. Craig. Routledge, London.
Russell, Bertrand (1937) The Principles of Mathematics. Allen & Unwin, London.
Smith, Terence Paul (1973) On the Applicability of a Criterion of Change. Ratio 15: 325-333.
Weberman, David (1999) Cambridge Changes Revisited: Why Certain Relational Changes Are Indispensable. Dialectica 53: 139-149.
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Han, X. The Criterion or Criteria of Change. Int Ontology Metaphysics 10, 149–156 (2009). https://doi.org/10.1007/s12133-009-0046-2
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DOI: https://doi.org/10.1007/s12133-009-0046-2