﻿ Lowe (E.J.) - The Paradox of the 1,001 Cats (Theo Todman's Book Collection - Paper Abstracts)
The Paradox of the 1,001 Cats
Lowe (E.J.)
Source: Analysis, Vol. 42, No. 1 (Jan., 1982), pp. 27-30
Paper - Abstract

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Author’s Introduction

• In Section 110 of his book Reference and Generality1 (Third Edition; Comell University Press, 1980), Peter Geach presents the following puzzle or paradox. We are to suppose that a certain cat, Tibbles2, is sitting on a mat; moreover, Tibbles3 is the only cat sitting on the mat. Since Tibbles4 is, we suppose, a normal cat, it has at least one thousand hairs. Geach continues:
Now let c be the largest continuous mass of feline tissue on the mat. Then for any of our 1,000 cat-hairs, say hn, there is a proper part cn of c which contains precisely all of c except the hair hn; and every such part cn differs in a describable way both from any other such part, say cm, and from c as a whole. Moreover, fuzzy as the concept cat may be, it is clear that not only is c a cat, but also any part cn is a cat: cn would clearly be a cat were the hair hn plucked out, and we cannot reasonably suppose that plucking out a hair generates a cat, so cn must already have been a cat. So, contrary to our story, there was not just one cat called 'Tibbles5' sitting on the mat; there were at least 1,001 sitting there! (p. 215)
• Geach concedes, of course, that this conclusion is absurd, but it is interesting to observe wherein he professes to detect the fallacy. He explains:
Everything falls into place if we realize that the number of cats on the mat is the number of different cats on the mat; and c13, c279 and c are not three different cats, they are one and the same cat. Though none of these 1,001 lumps of feline tissue is the same lump of feline tissue as another, each is the same cat as any other: each of them, then, is a cat, but there is only one cat on the mat, and our original story stands. (p. 216)
• Now I concede that this manoeuvre of Geach's saves the truth of the original story; but, as he says, there is a price to pay. 'The price to pay is that we must regard - - - is the same cat as - - -" as expressing only a certain equivalence relation, not an absolute identity restricted to cats' (p. 216).
• Geach, however, is happy to pay this price, since he considers that it 'must be paid anyhow, for there is no such absolute identity as logicians have assumed' (ibid.), and in defence of this contention he refers us to earlier arguments in his book.
• I shall not consider those arguments here, though I do not as a matter of fact find them convincing. What I shall do, however, is to explain why I think that the truth of the original story can be saved far more plausibly without having to pay this price; and at the same time I shall try to show that Geach's resolution of the puzzle is in fact untenable.

In-Page Footnotes

Footnote 1: I don’t have this book, but see:-
"Geach (Peter) - Reference and Generality (Selections)"and
"Geach (Peter) - Reference and Generality: Prefaces and Analytical TOC".

Text Colour Conventions (see disclaimer)

1. Blue: Text by me; © Theo Todman, 2019
2. Mauve: Text by correspondent(s) or other author(s); © the author(s)