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N o ; holes are hole-linings; but when I speak of them as holes, I find it convenient to use "same" meaning "co-perforated' wherever a man of your persuasion would use 'same' meaning 'identical'. You know my reason for this trickery: my sentences about sameness of holes will be true just when you wrongly suppose your like- sounding sentences to be.

The same goes for sentences about number o f holes, since we both analyse these in terms of sameness Bargle. You still haven't told me how you say there are as many holes in my cheese as crackers on my plate, without also saying how many there a r e. Here goes.

There exist three things X, Y, and Z. X is part of the sum of the crackers, Y is part of the cheese, and Z is part of Y. Every maximal connected part of Y is a hole, and every hole in the cheese is the Downloaded by [Yale University Library] at 04 June same hole as some maximal connected part o f Y.

X overlaps each of the crackers and Z overlaps each maximal connected part of Y. Everything which is either the intersection of X and a cracker or the intersection of Z and some maximal connected part of Y is the same size as any other such thing. X is the same size as Z. Your devices won't work because co-perforation is not an equiva- lence relation.

Any two overlapping parts of my cheese have a common part that is a hole-lining, though in most cases the hole-lining is entirely filled with cheese. T o be co-perforated is therefore nothing more than to overlap, and overlapping is n o equivalence relation.


The result is that although, as you say, you can find two hole-linings in this cheese that are not co-perforated, you can find another one that is co-perforated with both o f them. I f you were right that a hole made of cheese could be entirely filled with the same kind o f cheese, you could find far more than two non- co-perforated hole-linings; and there would be no such thing as cheese without holes in it.

But you are wrong. A hole is a hole not just by virtue of its own shape but also by virtue of the way it contrasts with the matter inside it and around it. The same is true of other shape-predicates; I wouldn't say that any part of the cheese is a dodecahedron, though I admit that there are p a r t s - - p a r t s that do not contrast with their surroundings--that are shaped like dodecahedra.

Consider the paper-towel roller. H o w many holes? Y o u know what I mean: many, but they're all the same. I think you must say there are at least two. The left half and the right half are not the same hole. They have no common part, so no c o m m o n part that is a hole.

They're not holes, they're two parts of a hole. Geach, 'Identity', Reviewof Metaphysics 21 : This translation adapts a device from Nelson Goodman and W. Why aren't they holes themselves?

Vol. 48, No. 2; August, 1970

They are singly-perforated and they are made of matter unlike the matter inside them. If I cut them apart you'd have to say they were holes?

You admit that a hole can be a proper part of a bigger--say, thicker-skinned--hole?

You admit that they are shaped like holes? Yes, but they aren't holes. I can't say why they aren't.

I know which things are holes, but I can't give you a definition. But why should I? You already know what hole-linings are.

I say the two halves Downloaded by [Yale University Library] at 04 June of the roller are only parts of a hole because I--like y o u - - w o u l d say they are only parts of a hole-lining.

What isn't a hole-lining isn't a hole.


In that case, I admit that co-perforation may be an equivalence relation at least a m o n g singly-perforated hole-linings. All holes are singly-perforated. A doubly-perforated thing has two holes in it that are not the same hole. Are you sure? Take the paper-towel roller and punch a little hole in its side. N o w you have a hole in a hole-lining.


You'd have to say you have a hole in a hole. You have a little hole which is part of a big hole; the big hole is not singly-perforated; and the little hole and the big hole are the same hole, since the little hole is a common part of each.

I think not. You speak of the big hole; but what we have are two big holes, not the same, laid end to end. There is also the little hole, not the same as either big hole, which overlaps them both.

Of course we sometimes call something a hole, in a derivative sense, if it is a connected sum of holes. Any decent cave consists of many holes that are not the same hole, so I must have been speaking in this derivative sense when I said that caves are holes.

What peculiar things you are driven to say when philosophy corrupts your mind I Tell me the truth: would you have dreamt for a m o m e n t of saying there were two big holes rather than one if you were not suffering under the influence of a philosophical theory? N o ; I fear I would have remained ignorant.


I see that I can never hope to refute you, since I no sooner reduce your position to absurdity than you embrace the absurdity. N o t absurdity; disagreement with common opinion. Very well. But I, for one, have more trust in common opinions than I do in any philosophical reasoning whatever. In so far as you dis- agree with them, you must p a y a great price in the plausibility of your theories.

We have been measuring that price. I have shown that it is not so great as you thought; I am prepared to pay it.

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The price is still too high. We agree in principle; we're only haggling.

We do. And the same is true of our other debates over ontic parsimony. Indeed, this argument has served us as an illustration-c-novel, simple, and self-contained--of the nature of our customary disputes. And yet the illustration has interest in its own right. Your holes, had I been less successful, would have punctured my nominalistic materialism with the greatest of ease.

Rehearsed and refreshed, let us return t o - - s a y - - t h e question Downloaded by [Yale University Library] at 04 June of classes. We thank Charles Chastain, who also is neither Argle nor Bargle, for many helpful comments.

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By using historical method, it can be revealed conditions and problems faced by the editor of Mangle in each period.There exist three things X, Y, and Z. Consider the paper-towel roller. Some include more of the cheese, some include less. Every maximal connected part of Y is a hole, and every hole in the cheese is the Downloaded by [Yale University Library] at 04 June same hole as some maximal connected part o f Y. You still haven't told me how you say there are as many holes in my cheese as crackers on my plate, without also saying how many there a r e.

Two crackers, to be sure, but how can you say there are two holes?

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