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Abstract Individuals
Published online by Cambridge University Press: 01 September 1966
Extract
The title of this paper may seem to involve a contradiction: my purpose is to show that it does not.
Individuals fall into two categories; those which depend for their existence upon the existence of other individuals, and those which do not. In the second category are found such things as shoes, ships, cabbages, kings, and discrete bits of sealing wax. These may be called individual substances, and the way in which the existence of a cabbage depends upon water and earth, or in which Descartes says the existence of all things depends upon God, will not be in point here. The individuals of the first category are characterized by a much more obvious kind of dependence. They include the sound of an individual shoe falling on the floor, the sinking of the Bismarck, the stupidity of George I, the centre of gravity of a bit of sealing wax. All these are individuals, though they are not individual substances. They are what I shall call abstract individuals, or abstract particulars.
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- Information
- Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 5 , Issue 2 , September 1966 , pp. 217 - 231
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- Copyright © Canadian Philosophical Association 1966
References
1 “For it is clear, when one considers the nature of time, that just the same power and agency is needed to preserve any object at the various moments of its duration, as would be needed to create it anew if it did not yet exist.” (Meditation III, translated by Anscombe and Geach)
2 The relevant section of the Categories is 1a20-2a34. The author was greatly helped by Ackrill's, J. L. translation and notes (Aristotle's ‘Categories’ and ‘De Interpretation’, Oxford 1963)Google Scholar, and by Miss Anscombe's commentary ( Three Philosophers, Oxford 1963).
3 This is not to say that there are not significant differences among the items of list one, as was pointed out to the author by Mr B. van Fraassen. For example, the death of Robespierre and the end of the affair are (concrete, not abstract) events, which can be dated, while the other items are not. But for the purposes of this paper these differences, compared with those between lists one and two, are unimportant.
4 Or alternatively (in logical systems richer than the theory of quantification alone) to Frege's theory. See for example Quine, , Mathematical Logic, Cambridge 1951, pp. 146–152Google Scholar.
5 See the appendix for fuller details. Note also that definition (9) facilitates a sharper distinction between such pairs of negations as ‘x is not trustworthy’ and ‘x is untrustworthy’ than is usually made in predicate logic. The former is translated as ∼ (∃y) y = t(x), while the latter is (∃y)y = u(x). A formal means of sanctioning the entailment of the first by the second lies beyond the scope of this paper.
6 Lambert, K., ‘Existential import revisited’, Notre Dame Journal of Formal Logic 4 (1963), pp. 288–292CrossRefGoogle Scholar. See also Lambert's paper “Explaining away singular non-existence statements’, Dialogue 1 (1963), pp. 381–389CrossRefGoogle Scholar.
7 The natural deduction rules used for deriving conclusions are those of Copi, I., Symbolic Logic, 2nd edition, New York 1965, pp. 102–114Google Scholar, modified for free logic as follows. First ‘E! x' is defined as ‘(∃,y)y = x' (note that only in free logic could ‘x exists’ be translated in this way, because of (10) above). Copi's rules, while retaining all their present restrictions, then become:
UI 
EG 
EI 
UG 
Id (same as in Copi)
8 Compare also: God is the Perfect Being
Existence is a perfection
Therefore, God exists.
9 Compare ‘Speech-situation S’ in Austin's, J. L. ‘How to talk’, reprinted in his Philosophical Papers, Oxford 1961Google Scholar. Austin's ‘Speech-situation S1’ is a combination of the complications (ii) and (iii) below.
10 For the axioms and rules of inference of free logic with identity, valid for every domain, see the first paper of Lambert's mentioned above.