# Intolerant clones.

The "Tolerance Principle" noted in Crispin Wright (1975)
is that if two things are similar enough and one falls under the vague
predicate F, the other must fall under F too. Tolerance implies the
absence of a sharp boundary between F things and non-F things. Most
theories take the absence of a sharp boundary to be the mark of the
vague.

The epistemic theory disagrees, holding that what makes F vague is not that it doesn't have a sharp boundary, but that we can't discover where the boundary is. In support of the epistemic theory, Roy Sorensen (1994) offers an intriguing argument. If two clones both grow tall, the one that starts first grows tall first. If Mr Copy starts growing ever so shortly after Mr Original, he grows tall ever so shortly after him. So there is an (unknown) time when Original is tall and Copy is not tall, though the difference in their heights is as small as you please. So "tall" is not Tolerant. The boundary between tall and non-tall must be sharp.

But there is an ambiguity here. The sentence "Original grows tall before Copy" may be about the events, or it may be about the participants in the events. If it is about the events, it means that the growing tall of Original is before the growing tall of Copy. If it is about the participants, it means that Original is tall before Copy is tall. So supporters of unsharp boundaries can say that there are two senses of "grows tall first", and that Sorensen's argument equivocates between them. Original grows tall first in the sense of being first to undergo the process of becoming tall. It doesn't follow that he grows tall first in the sense that there is a time when he is tall and Copy is not tall. So it doesn't follow that Original is first past some supposed boundary post that divides the extension and antiextension of "tall".

Can Sorensen reply that there are not really two senses of "grows tall first" thus to be distinguished? It might seem that the supposed "event" sense is none too clear: certainly it is not always determinate which of two overlapping events is the earlier, especially if the endpoints of the events are vague. But Sorensen speaks of clones in his argument, and the event of any one clone growing tall is a qualitative duplicate of the event of any other clone growing tall. If two events are qualitative duplicates, then even if they are vague we can still order them unambiguously in time, however short the interval between them may be. For we can regard two duplicate events as a congruent pair, which could be exactly superimposed by spatial and temporal rigid motion. Then the event which needs to be translated forwards in time to achieve superposition is determinately the earlier event.

Perhaps there are theories of vagueness on which this argument would not be correct. But the epistemic theory is not one of them, so it seems Sorensen ought to recognize the two senses of "grows tall first". Then he needs to show that growing tall first in the event sense, the sense of being first to complete a growing process, entails growing tall first in the participant sense, the sense of being first past the boundary of tallness. But there cannot be a sound argument to show this, for it is not true.

Here is a counterexample. Suppose Copy starts growing after Original, but then undergoes a much accelerated growing process. Say he starts growing when Original is already borderline tall, and overtakes while Original is still borderline. Suppose he definitely stops growing before Original stops growing. Then we can compare the events of Copy growing tall and Original growing tall: Copy's growing was definitely completed first. It doesn't follow that we can compare Copy and Original, the participants in the events. It's indeterminate which of them grew tall first, in the sense of being first past the boundary for tallness. It depends whether Original was already tall when Copy overtook him, and the information about event order does not tell us that. So it seems there is a gap here in Sorensen's argument.

Perhaps Sorensen could say that the counterexample fails, because we should take "the growing tall of x" to mean not all of x's growing or increasing in height, but only that vaguely defined part of his growing which is his growing tall. On that understanding, in the counterexample it is not true that we know the temporal order of the growing tall of Original and the growing tall of Copy. The counterexample assumes we do know, and that is why it fails.

When we do know the temporal order, as we do in the cases where the clones grow at the same rate, it might seem we could fill the gap in Sorensen's argument as follows. If the growing tall of Original is earlier than the growing tall of Copy, then the growing tall of Original is over before the growing tall of Copy is over. When the growing tall of Original is over Original is tall. When the growing tall of Copy is not over Copy is not tall. So if Original's growing is over first, there is a time when Original's growing tall is over and Copy's growing tall is not over. At that time Original is tall, and Copy is not tall. So being first in the event sense does entail being first in the sense of first past the boundary.

What is wrong with this argument is its first step. It relies on the principle that the earlier event is over first: if P is earlier than Q, then P is over before Q is over, so that there is a time t that is not a moment of P but is a moment of Q. Call this principle the "Earlier First" principle. Clearly it is a correct principle for events whose temporal order is defined by the order of their endpoints. So it is correct for events with sharp endpoints, and for events with vague endpoints provided the order of the endpoints is definite. But without a further argument we have no right to assume it is correct for events whose temporal order is defined without reference to their endpoints.

As we noted above, the events that are the growings tall of clones are ordered without reference to their endpoints. These events are qualitative duplicates, and the criterion we use to order them is to imagine moving one in time and space until it coincides exactly with the other. The event that needs to move forward in time is the earlier event. No appeal is made to endpoint order here, and we have therefore no reason to suppose that the Earlier First principle is a correct principle for events ordered by the movement criterion.

The Earlier First principle applied to events ordered by the movement criterion entails sharp boundaries. For let P and Q be duplicate vague events. Suppose P is earlier than Q according to the movement criterion. Then there is a fixed difference d, such that if t is the time of any moment P(t) of P, then t+d is the time of the matching moment Q(t+d) of Q. Nothing follows yet about sharp boundaries. But now assume the Earlier First principle. Then P is over before Q is over, and there is a time t+d in Q but not in P. So Q(t+d) is a moment of Q, P(t) is the corresponding moment of P, t is in P and t+d is not in P. By interpolation of 1000 clones, d can be as small as we please, yet there is always a t such that t is in P but t+d is not in P. So there is a sharp if unknown boundary between those times that are moments of P and those that are not.

Defenders of unsharp boundaries will reply that as we have been given no reason to suppose that the Earlier First principle is a correct principle in this context, its use here simply begs the question. They will say the same about other clone cases that might be proposed.

For example, suppose Original and Copy start growing at exactly the same time, but Original grows faster. Won't we say that Original grows tall first, however small the difference in the rate of growth may be? And since we clearly won't be relying on the movement criterion for duplicate events, won't the Earlier First principle now apply, so that the argument can be completed after all? And what about still more complex cases, where the growth rates of the growth rates may differ?

It may seem vague, or at least obscure, what we are to say about these cases. It does seem plausible that such events have a definite order, but defenders of unsharp boundaries should not concede that the order is defined by definite order of endpoints. Instead, they can point to the fact that although these events are not duplicates, they are isomorphic. Just as we order duplicate events by the movement criterion, we can order isomorphic events by an analogous criterion. We imagine making duplicate events coincide by temporal motion, and we imagine making isomorphic events coincide by temporal stretching and compression to produce a perfect match. Because the isomorphic events started at the same moment, we say that the one that needs to be stretched more is the earlier. Again we are relying on a criterion that makes no appeal to endpoint order, so we have no reason to suppose that the Earlier First principle is a correct principle in this context either. So it seems there is no straightforward way to fill the gap in Sorensen's argument.

The moral of Sorensen (1992) is that events that have vague descriptions can nevertheless stand in sharp temporal relations. Despite Sorensen (1994), however, the sharpness of an event's temporal relations does not entail sharp boundaries for predicates used in describing it. We must distinguish properties of events from properties of participants in events. Mr Original can become tall first without there being a time when he first becomes tall.

(1)I am very grateful to Mark Sainsbury for instructive discussion and comments. I also thank Gabe Segal, Scott Sturgeon, and two anonymous referees.

REFERENCES

Sorensen, R. 1992: "The Egg Came Before the Chicken", Mind, 101, pp 541-2.

_____1994: "A Thousand Clones", Mind, 103, pp 47-54.

Wright, C. 1975: "On the Coherence of Vague Predicates", Synthese, 30, pp 325-365.

The epistemic theory disagrees, holding that what makes F vague is not that it doesn't have a sharp boundary, but that we can't discover where the boundary is. In support of the epistemic theory, Roy Sorensen (1994) offers an intriguing argument. If two clones both grow tall, the one that starts first grows tall first. If Mr Copy starts growing ever so shortly after Mr Original, he grows tall ever so shortly after him. So there is an (unknown) time when Original is tall and Copy is not tall, though the difference in their heights is as small as you please. So "tall" is not Tolerant. The boundary between tall and non-tall must be sharp.

But there is an ambiguity here. The sentence "Original grows tall before Copy" may be about the events, or it may be about the participants in the events. If it is about the events, it means that the growing tall of Original is before the growing tall of Copy. If it is about the participants, it means that Original is tall before Copy is tall. So supporters of unsharp boundaries can say that there are two senses of "grows tall first", and that Sorensen's argument equivocates between them. Original grows tall first in the sense of being first to undergo the process of becoming tall. It doesn't follow that he grows tall first in the sense that there is a time when he is tall and Copy is not tall. So it doesn't follow that Original is first past some supposed boundary post that divides the extension and antiextension of "tall".

Can Sorensen reply that there are not really two senses of "grows tall first" thus to be distinguished? It might seem that the supposed "event" sense is none too clear: certainly it is not always determinate which of two overlapping events is the earlier, especially if the endpoints of the events are vague. But Sorensen speaks of clones in his argument, and the event of any one clone growing tall is a qualitative duplicate of the event of any other clone growing tall. If two events are qualitative duplicates, then even if they are vague we can still order them unambiguously in time, however short the interval between them may be. For we can regard two duplicate events as a congruent pair, which could be exactly superimposed by spatial and temporal rigid motion. Then the event which needs to be translated forwards in time to achieve superposition is determinately the earlier event.

Perhaps there are theories of vagueness on which this argument would not be correct. But the epistemic theory is not one of them, so it seems Sorensen ought to recognize the two senses of "grows tall first". Then he needs to show that growing tall first in the event sense, the sense of being first to complete a growing process, entails growing tall first in the participant sense, the sense of being first past the boundary of tallness. But there cannot be a sound argument to show this, for it is not true.

Here is a counterexample. Suppose Copy starts growing after Original, but then undergoes a much accelerated growing process. Say he starts growing when Original is already borderline tall, and overtakes while Original is still borderline. Suppose he definitely stops growing before Original stops growing. Then we can compare the events of Copy growing tall and Original growing tall: Copy's growing was definitely completed first. It doesn't follow that we can compare Copy and Original, the participants in the events. It's indeterminate which of them grew tall first, in the sense of being first past the boundary for tallness. It depends whether Original was already tall when Copy overtook him, and the information about event order does not tell us that. So it seems there is a gap here in Sorensen's argument.

Perhaps Sorensen could say that the counterexample fails, because we should take "the growing tall of x" to mean not all of x's growing or increasing in height, but only that vaguely defined part of his growing which is his growing tall. On that understanding, in the counterexample it is not true that we know the temporal order of the growing tall of Original and the growing tall of Copy. The counterexample assumes we do know, and that is why it fails.

When we do know the temporal order, as we do in the cases where the clones grow at the same rate, it might seem we could fill the gap in Sorensen's argument as follows. If the growing tall of Original is earlier than the growing tall of Copy, then the growing tall of Original is over before the growing tall of Copy is over. When the growing tall of Original is over Original is tall. When the growing tall of Copy is not over Copy is not tall. So if Original's growing is over first, there is a time when Original's growing tall is over and Copy's growing tall is not over. At that time Original is tall, and Copy is not tall. So being first in the event sense does entail being first in the sense of first past the boundary.

What is wrong with this argument is its first step. It relies on the principle that the earlier event is over first: if P is earlier than Q, then P is over before Q is over, so that there is a time t that is not a moment of P but is a moment of Q. Call this principle the "Earlier First" principle. Clearly it is a correct principle for events whose temporal order is defined by the order of their endpoints. So it is correct for events with sharp endpoints, and for events with vague endpoints provided the order of the endpoints is definite. But without a further argument we have no right to assume it is correct for events whose temporal order is defined without reference to their endpoints.

As we noted above, the events that are the growings tall of clones are ordered without reference to their endpoints. These events are qualitative duplicates, and the criterion we use to order them is to imagine moving one in time and space until it coincides exactly with the other. The event that needs to move forward in time is the earlier event. No appeal is made to endpoint order here, and we have therefore no reason to suppose that the Earlier First principle is a correct principle for events ordered by the movement criterion.

The Earlier First principle applied to events ordered by the movement criterion entails sharp boundaries. For let P and Q be duplicate vague events. Suppose P is earlier than Q according to the movement criterion. Then there is a fixed difference d, such that if t is the time of any moment P(t) of P, then t+d is the time of the matching moment Q(t+d) of Q. Nothing follows yet about sharp boundaries. But now assume the Earlier First principle. Then P is over before Q is over, and there is a time t+d in Q but not in P. So Q(t+d) is a moment of Q, P(t) is the corresponding moment of P, t is in P and t+d is not in P. By interpolation of 1000 clones, d can be as small as we please, yet there is always a t such that t is in P but t+d is not in P. So there is a sharp if unknown boundary between those times that are moments of P and those that are not.

Defenders of unsharp boundaries will reply that as we have been given no reason to suppose that the Earlier First principle is a correct principle in this context, its use here simply begs the question. They will say the same about other clone cases that might be proposed.

For example, suppose Original and Copy start growing at exactly the same time, but Original grows faster. Won't we say that Original grows tall first, however small the difference in the rate of growth may be? And since we clearly won't be relying on the movement criterion for duplicate events, won't the Earlier First principle now apply, so that the argument can be completed after all? And what about still more complex cases, where the growth rates of the growth rates may differ?

It may seem vague, or at least obscure, what we are to say about these cases. It does seem plausible that such events have a definite order, but defenders of unsharp boundaries should not concede that the order is defined by definite order of endpoints. Instead, they can point to the fact that although these events are not duplicates, they are isomorphic. Just as we order duplicate events by the movement criterion, we can order isomorphic events by an analogous criterion. We imagine making duplicate events coincide by temporal motion, and we imagine making isomorphic events coincide by temporal stretching and compression to produce a perfect match. Because the isomorphic events started at the same moment, we say that the one that needs to be stretched more is the earlier. Again we are relying on a criterion that makes no appeal to endpoint order, so we have no reason to suppose that the Earlier First principle is a correct principle in this context either. So it seems there is no straightforward way to fill the gap in Sorensen's argument.

The moral of Sorensen (1992) is that events that have vague descriptions can nevertheless stand in sharp temporal relations. Despite Sorensen (1994), however, the sharpness of an event's temporal relations does not entail sharp boundaries for predicates used in describing it. We must distinguish properties of events from properties of participants in events. Mr Original can become tall first without there being a time when he first becomes tall.

(1)I am very grateful to Mark Sainsbury for instructive discussion and comments. I also thank Gabe Segal, Scott Sturgeon, and two anonymous referees.

REFERENCES

Sorensen, R. 1992: "The Egg Came Before the Chicken", Mind, 101, pp 541-2.

_____1994: "A Thousand Clones", Mind, 103, pp 47-54.

Wright, C. 1975: "On the Coherence of Vague Predicates", Synthese, 30, pp 325-365.

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Title Annotation: | Symposium: Vagueness and Sharp Boundaries |
---|---|

Author: | Hossack, Keith |

Publication: | Mind |

Date: | Jan 1, 1994 |

Words: | 1776 |

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