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«AN INVESTIGATION OF THE LUMPS OF THOUGHT CONTENTS 0. What this paper is about 1. What lumps of thought are 2. How lumps of thought can be ...»

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ANGELIKA KRATZER

AN INVESTIGATION OF THE LUMPS OF THOUGHT

CONTENTS

0. What this paper is about

1. What lumps of thought are

2. How lumps of thought can be characterized in terms of situations

3. A semantics based on situations

4. Counterfaetual reasoning and lumps of thought

5. Non-accidental generalizations: The nature of geneficity

6. Negation

7. Conclusion

0. WHAT THIS P A P E R IS A B O U T

This paper is about situation semantics and about the meaning of counter- factuals. It argues that there is a close connection between the laws of counterfactual reasoning and a relation between propositions that I want to call 'lumping'. Capturing this relation seems to require a component of semantic interpretation which recognizes parts of possible worlds (situ- ations) as primitives and implies a new approach to genericity and ne- gation.

* Research for this paper was supported by the National Science Foundation under grant BNS 87-19999. Different parts of the paper were presented in talks at the University of Massachusetts at Amherst in February and August, 1985, at Yale University in January, 1986, at the University of Texas at Austin~in April, 1987, at the sixth Amsterdam colloquium in April, 1987 (in absentia), at MIT in April, 1988, and at CSLI in Stanford in September,

1988.1 would like to thank the audiences of these talks for their comments and suggestions.

A number of improvements in an intermediate version of the paper are the result of discussions with Emmon Bach and Barbara Partee while co-teaching a course on events. I am grateful for Edmund Gettier's efforts to find counterexamples. In particular, I would like to thank Arnim yon Steehow for presenting the paper in Amsterdam and giving me helpful comments. Elisabeth Selkirk, Barbara Partee, Irene HeLm, Fred Landman, Steve Berman, Nirit Kadmon, Karina Wilkinson, Alice ter Meulen, Max Cresswell, Jon Barwise, John Bigelow, Gennaro Chierchia, Peter Staudaeher, and Roger Sehwarzschild all read some version of the paper and gave me much appreciated feedback. Two anonymous reviewers for Linguistics and Philosophy helped to improve the final version. Elisabeth Selkirk was always generous in providing me with semantic intuitions. Her concern for focus inspired the proposed semantics for negation. The paper owes an obvious debt to the work of David Lewis.

Linguistics and Philosophy 12: 607-653, 1989.

© 1989 Kluwer Academic Publishers. Printed in the Netherlands.

608 ANGELIKA KRATZER

1. WHAT LUMPS OF THOUGHT ARE

Imagine the following situation: One evening in 1905, Paula painted a still life with apples and bananas. She spent most of the evening painting and left the easel only to make herself a cup of tea, eat a piece of bread, discard a banana or look for an apple displaying a particular shade of red. Against the background of this situation, consider the following two

dialogues that might have taken place the following day:

Dialogue with a pedant Pedant: What did you do yesterday evening?

Paula: The only thing I did yesterday evening was paint this still life over there.

Pedant: This cannot be true. You must have done something else like eat, drink, look out of the window.

Paula: Yes, strictly speaking, I did other things besides paint this still life. I made myself a cup of tea, ate a piece of bread, discarded a banana, and went to the kitchen to look for an apple.

Dialogue with a lunatic Lunatic: What did you do yesterday evening?

Paula: The only thing I did yesterday evening was paint this still life over there.

Lunatic: This is not true. You also painted these apples and you also painted these bananas. Hence painting this still life was not the only thing you did yesterday evening.

In both dialogues, Paula exaggerated in claiming that painting a still life was the only thing she had done that evening. She had done other things, and the pedant correctly noticed this. Being a captive of his unfortunate character, he could not help insisting on the truth, and this is really all we can blame him for.

The lunatic case is very different. I don't think that Paula has to accept this person's criticism. She didn't paint apples and bananas apart from painting a still life. Painting apples and painting bananas was part of her painting a still life, like my arms and legs are part of me. Wherever I go, my arms and legs will come along. Is it true, then, that I can never be alone? I think not. Somehow, when I talk about myself, my parts have no independent existence, their presence doesn't count. Likewise, on that memorable evening, a very special relationship between three propositions

AN I N V E S T I G A T I O N OF THE LUMPS OF T H O U G H T 609

was established: It was true that Paula painted a still life. And it was also true that she painted apples and that she painted bananas. But once we consider the first proposition a fact of this world (at the time in question), we are not entitled any longer to consider the latter two propositions as separate facts. If you count the entities in this room and you count me as one of them, you'd better forget about my ears. And if you count the facts of our world and you count Paula's painting a still life as one of them, you'd better overlook her painting apples. Quite generally, whenever we start counting, we have to make sure that the entities in our domain are truly distinct. Consider the following example (inspired by Carlson (1977, p. 346ff.) which illustrates the lunatic's fallacy in a different domain.





Noah's ark How many kinds of animals did Noah take into the ark? He took a pair of dogs. That's one kind. He also took a pair of cats. That's another kind.

Hence he took at least two kinds of animals. He also took a pair of doves.

Now we have three kinds. He also took mammals. That's certainly a kind we haven't had before. That makes four kinds of animals. And he took birds, which gives us five kinds....

We like to think about the facts of a world in terms of the set of propositions which are true in it. And we are used to construe propositions as sets of possible worlds. The proposition that Paula painted a still life is the set of possible worlds in which Paula painted a still life. And the proposition that Paula painted apples is the set of possible worlds in which she painted apples (at the time under consideration). Both of these propositions happen to be true in our world. Possible worlds semantics captures this property in that the corresponding sets of possible worlds contain our world as a member. As far as our world is concerned, the two propositions are even more closely related, though: they are not distinct facts of our world. There is an aspect of the actual world that makes the proposition that Paula painted a still life true. And that very same aspect of our world also makes the proposition that she painted apples true. It will be useful to have a technical term for the relationship we are after. Let us say that the proposition that Paula painted a still life lumps the proposition that she painted apples in the actual world. 1 Note that whatever aspect of the actual world makes the proposition that Paula 1 A proposition lumps another proposition in a world w in virtue of certain part-whole relationships holding between situations of w. The two propositions don't stand in a partwhole relationship themselves.

610 ANGELIKA KRATZER painted apples true is presumably not sufficient to make the proposition that she painted a still life true. The proposition that Paula painted apples, then, does not lump t h e proposition that she painted a still life in the actual world. If Paula's still life had contained only apples and no bananas, the case would be different. Whatever aspect of the actual world would make the proposition that Paula painted apples true would also make the proposition that Paula painted a still life true. Hence the two propositions would lump each other in the actual world.

Like many interesting semantic relationships, the lumping relation is affected by vagueness. Consider the following example: My neighbor's house burnt down. His kitchen burnt down as part of it. The proposition that his house burnt down, then, lumps the proposition that his kitchen burnt down in the actual world. My neighbor's barn was destroyed by the same fire. Was the barn part of the house? Does the proposition that his house burnt down lump the proposition that his barn burnt down in the actual world? We may or may not be able to settle on an answer to this question. We don't have to. There will be cases where the lumping relationship clearly holds. There will be other cases which are not so clear. If the lumping relationship plays a role in the semantics of certain constructions, we expect that its vagueness will contribute to the vagueness of these constructions in a systematic and detectable way.

We have seen that traditional possible worlds semantics construes propositions as sets of possible worlds. On this approach, it is not obvious how we can formally capture the lumping relationship. It seems, then, that we may be missing something in possible worlds semantics. We may be missing something, but it may not be very important. Or is it? I am going to argue in this paper that once we pay close attention to the lumping relationship, we will gain some new insights into the labyrinth of counterfactual reasoning, an area which has puzzled semanticists for a long time.

2. H o w LUMPS OF THOUGHT CAN BE CHARACTERIZED IN TERMS

OF SITUATIONS

As a result of our previous considerations, we are faced with the following task: We have to characterize the special relationship holding (in our world on some evening in 1905) between the proposition that Paula painted a still life and the propositions that she painted apples and that she painted bananas. Obviously, this relationship is not logical implication.

Paula's painting a still life doesn't logically imply her painting apples and bananas. Material implication isn't a better candidate. In the actual world, 611

AN INVESTIGATION OF THE LUMPS OF THOUGHT

at the time considered, Paula's painting a still life materially implies her making herself a cup of tea, for example. (Assuming that our scenario is true, both of these propositions were true at the time). But the proposition that Paula is making herself a cup of tea is not part of the 'lump of facts' whose properties we are trying to capture.

I suggested above that the proposition that Paula painted a still life and the proposition that she painted apples are not distinct facts of our world, since whatever aspect of our world makes the first proposition true will also make the second proposition true. On the other hand, not every aspect of our world in which "Paula painted a still life" is true, is also an aspect of our world in which any of the following is true: "Paula made herself a cup of tea", "Paulh ate a piece of bread", "Paula discarded a banana", "Pallia went to the kitchen". It seems, then, that we might be able to characterize the lumping relationship as soon as we grant that 'aspects' or 'parts' of possible worlds can make propositions true. What is an 'aspect' or a 'part' of a possible world? It seems that an 'aspect' or a 'part' of a possible world is nothing else but a possible situation, w h a t I want to suggest, then, is that the lumping relationship be characterized in terms of the notion 'truth in a possible situation'. If propositions are sets of possible situations rather than simply sets of possible worlds we will be able to actually define the lumping relationship rather than taking it as a primitive notion.

Assume that we are given a set of possible worlds. Strictly speaking, we will mainly consider worlds without much of a history, slices of worlds, worlds at a time. Yet I will continue talking about 'worlds'. (Time is not a concern in this paper. Let us put it aside whenever we can.) Along with the worlds, we are given their parts. The parts of a world are its situations.

Since worlds are parts of themselves, they are also situations. They are maximal situations, situations that are not part of other situations. Given all of this, consider the following definition of the lumping relationship

–  –  –

not very common in possible worlds semantics (in spite of Kripke (1965)), but it is popular elsewhere. Recent advocates are Barwise and Perry (1983), Veltman (1985), and Landman (1986). The idea seems simple enough, but is not easy to execute. There is the danger of losing classical two-valued logic, and there are insecurities concerning negation and quantification. While being indebted to all of my predecessors, my proposals will differ from theirs in significant detail. The motivation for these deviations will come from a close look at natural language semantics, and quite surprisingly - from an in-depth investigation of counterfactual reasoning.

–  –  –

3.1. The Metaphysics of Situations 2 What are situations? I suggested above that situations may help us define the lumping relation. In this section, I will in turn use intuitions about the lumping relation to sharpen our understanding of the nature of situations.

Section 4 will then use facts about counterfactual reasoning to further clarify the intuitions relied on here.

Situations cannot be identified with space-time chunks. The following example shows why" As a matter of fact, I am hungry and tired right now.

Let us consider that slice of our world history which comprises just this present moment. Is every part of this slice in which I am htlngry a part in which I am tired? And likewise, is every part in which I am tired a part in which I am hungry? If situations were simply space-time chunks, the answer would probably be 'yes'. The minimal space-time chunk in which I am hungry now would be the space-time chunk presently occupied by me. But this would also be the minimal space-time chunk in which I am tired now. We would have to conclude, then, that the proposition that I am hungry now and the proposition that I am tired now lump each other in the actual world. They would be one and the same fact. But they are not.



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