How to Start and Stop (draft for presentation)

1. The problem

Suppose I will die at a certain moment T. Before T I am alive.[2] After T I am dead. But at the very instance of T, am I alive or dead?

Intuitions do not seem to provide us with a single answer. The following two thought experiments seem to give us different answers.
Experiment 1: Suppose I am a shrinking genie.[3] My whole life is to run a certain race. I have a certain amount of energy which is just enough for me to finish the run, and I will die when all my energy is used up. Suppose the percentage of the energy consumed matches the percentage of the distance run, and suppose I shrink in the same rate as the rate my energy is used. In that scenario, I have the full height at the starting point, three quarters of the full height when I cover a quarter of the running distance, half of the original height when I am halfway through, and so forth.

Now, do I have a last moment of existence?

No! Clearly the last moment cannot be any moment before or after the very moment I reach the ending point of the race. But it cannot be the very moment I reach the ending point of the race either. Because as soon as I reach the ending point, I have zero height, and thus I don’t exist! Hence, the last moment does not exist. In other words, at the moment of my death, I am already dead.

Experiment 2: Suppose I am a transmigrating soul, rational and powerful. I can freely move in and out of bodies. To move out of the body that I am currently occupying, all it takes is to make a decision to leave. After I make a decision to leave, I will be out of the body immediately.[4] In this thought experiment, with respect to a particular body I occupy, do I have a last “living” moment, living in the sense of being an embodied soul?

The answer is yes, and the last moment is precisely the moment that I decide to leave. If, at the moment of my decision, I am already outside of the body, the decision becomes a confused, empty decision: how can I decide to leave the body, as a rational soul, if I am already outside of the body? Thus, in this case I do have a last moment of “existence.”

To generalize, the problem is whether an object is in the new state or in the old state at the moment of transition. Yet, the above two examples show us that our intuitions do not give us a single answer.

The failure of the intuitions may lead us to look at the problem more critically. A quick reaction is that the problem is not a genuine problem. First, the problem cannot be a meaningful, empirical problem, because we can never experience the moment. Moment, after all, is an abstraction or idealization. Second, the problem cannot be a meaningful, logical problem. From the modern logical or mathematical point of view, there is no determined solution to this problem; any solution can be made technically correct. Hence, this problem is not a pseudo one.

But being an empirical or logical problem does not exhaust all possibilities. Why cannot this problem be a metaphysical one? If time is a continuum and moments are real, and if things and their states are real, doesn’t it make good sense to inquire the state of things at the moments of transition?

However, given that empirical observations and logical investigations do not help in this context, how should we tackle the problem?

If we look at the history of philosophy, some of the best discussions of this problem are given in the Medieval period. Medieval logicians seemed to have a lot of interest in this problem, which they called the problem of start [incipit] and stop [desinit]. And they had determined preference for one solution to the others. Due to the scope of this paper, I will discuss the views by just one medieval logician, the 14th century philosopher Walter Burley.[6] By looking at and offering a new interpretation of how Walter Burley came up with the solution he had, I hope to zoom in some insights which may help us better understand the problem.

2. Walter Burley’s Solution

In the above I’ve given an informal presentation of the problem of transition. Now let’s present the problem more rigorously. First of all, in our discussions we shall presuppose three things all along: (1) the Law of Excluded Middle, (2) the Law of Non-Contradiction, and (3) the thesis that time is a continuum. Now, the problem is really these two questions:

1. At the moment of x’s beginning to be Y, is x Y?
2. At the moment of x’s ceasing to be Y, is x Y?

If the answer to the first question is yes, then we say that x has an intrinsic limit[5] for starting. If the answer to the first question is no, then we say that x has an extrinsic limit for starting. If the answer to the second question is yes, then we say that x has an intrinsic limit for stopping. If the answer to the second question is no, then we say that x has an extrinsic limit for stopping.

With these terms at hand, let’s present Walter Burley’s solution. According to Burley, entities can be divided into three kinds: the instantaneous permanent entities---entities that exist for only an instant (e.g., angels)---enduring permanent entities (e.g., ordinary, physical things), and successive entities (e.g., time intervals). For the purpose of this paper, we will be discussing only the permanent entities, entities such as tables, chairs, persons. Thus, we need to consider only Burley’s solution for permanent entities. According to Burley, a permanent entity has an intrinsic limit for starting and an extrinsic limit for stopping. In other words, at the moments of both starting and stopping, the entity is in the later states. For example, I have the first moment, but not the last moment, of my life.

How did Burley reach his answer to the starting and stopping of permanent entities? Two prominent scholars on medieval philosophy, Norman Kretzmann[7] and Paul Spade, have worked on this issue, and they have developed two different interpretations. Let’s examine their accounts respectively.

3. Kretzmann’s foreknowledge account

Briefly put, Norman Kretzmann’s “foreknowledge” account runs as follows: Kretzmann claims that when x begins to be Y at t, x must already be Y at t. The reason is that if the change has not occurred at t, no one---not even God---can know at what moment the change takes place. Since God must have the foreknowledge of the change, the entity must be in the new state at the moments of transition.

Although this account is admirably simple, it is flawed. The problem is that there is an obscurity in the notion of change. Kretzmann presupposes that when a change of x occurs at the moment t, x is already in the new state. But is it really true?

Suppose upon my announcement a change---a new political entity---will come into being. At the moment of the change, which is the moment I make the announcement, I can certainly say that this is the first moment of the new political entity, but there is nothing wrong if I say that this is the last moment of the old political entity.[8] Why does x have to be in the new state at t when it changes at t?

Thus, there is a gap between the claim that God knows that x changes at t and the claim that God knows that x is already in the new state at t. In other words, even if we grant that God knows that x changes at t, we can still deny that God knows the first moment of x’s being in the new state, simple because there is no first moment. Would the latter impose a limitation on God’s foreknowledge? No. Without the claim, God’s foreknowledge is still limited: God cannot know both the first moment of the new state and the last moment of the old state, because knowing both entails a contradiction to the thesis that time is a continuum. So, why should we prefer God’s knowing the first moment of the new state to God’s knowing the last moment of the old state?

4. Spade’s causal account

To explain why enduring permanent entities have an intrinsic limit for starting and an extrinsic limit for stopping, Paul Spade suggests that we consider two causal principles:[9] 1. Every effect requires a cause simultaneous with it; 2. To cause something to begin to be Y is to cause it to be Y. If we adopt these two principles, we can have a neat explanation for Burley’s account of the enduring permanent entities:[10] When x begins to be Y, it requires a cause which is simultaneous with it. But when x is caused to begin to be Y, it is caused to be Y which is to say, it is already Y.[11] Hence, x must have an intrinsic limit for starting. The similar thing can be said to justify the claim that x has an extrinsic limit for stopping.

At first sight, Spade’s causal account seems plausible and novel. But does it really work? Let’s look at it more closely.

One immediate but crucial implication of Spade’s account is that an instantaneous entity does not exist.[12] Nevertheless, Burley claims that instantaneous entities, such as time instants, are real. Thus, a substantial price the causal account has to pay is that it has to reject Burley’s claim about instantaneous entities.

But this is not the only problem of the causal theory. As I will argue in the following, Spade’s second causal principle, that to cause x to begin to be Y is to cause x to be Y is not easy to defend.

First of all, let’s point out that there might be exceptional cases to that principle. Suppose I participate in a running race, and I have made all preparations for a start behind the running line. Now I hear the gun-shot. Upon hearing the gun-shot, I form an indexical belief that it is time for me to run now, which causes me to begin to run.[13] Suppose that my shoes are glued down to the ground. When I begin to run, I in fact fall down and end up with not running. In this situation, clearly I do begin to run, because if I don’t begin to run, why do I fall down? Also, I end up with not running, because my feet are not moving. Hence, it makes sense to say that the indexical belief causes me to begin to run, but it does not cause me to run.

Suppose we can get around the above counter-example, by claiming that when x begins to be Y, it must successfully end up with being Y And suppose we have vindicated the causal principle, that to cause to begin to be Y is to cause x to be Y. There is still a deeper problem. Suppose x begins to be Y at instant t. Why should we say that x must have a cause at t, which is different from causes of the preceding moments? How do we justify that? Let us look closely at it.

The cause of x at t, if there is any, is either exactly the same as the cause of x’s being Y or different from the cause of x’s being Y. The latter means that the cause of x’s beginning to be Y is a peculiar one. Let us discuss the two respectively.

Suppose we say that the cause x has at t, if there is any, is just the cause of x’s being Y? Then the claim that x has cause at t simply restates the thesis x is Y at t, which clearly begs the question.

Suppose the cause x has at t (if there is any) is different from the cause of x’s being Y? Clearly that cause does not exist at any time before t. But does it exist after t? If it does, since after t x is Y after t the cause must have the effect that x is Y. But to say that x has a cause at t is just another way to say that x is Y at t, because the cause has the effect that x is Y despite we distinguishing it from the cause of x’s being Y. If so, don’t we beg the question? If it does not, then the cause of x’s beginning to be Y is instantaneous, which contradicts the earlier thesis that an instantaneous entity does not exist.

To avoid this contradiction, we might say that all causes are enduring entities, whether they are permanent or successive. Suppose the cause[14] for x at times before t is A, and the cause for x after t is B. Then we may say that the “instantaneous” cause for x at t is just a metaphorical way to talk about the intersection of A and B at t. And at t, the “instantaneous” cause is the vector sum of A and B, which sum is different from A (the cause at the preceding moments), and different from B (the cause at the succeeding moments). Hence, in this sense the very cause at t is “instantaneous,” not in the metaphysical sense that an instantaneous cause exists at t, but in the sense that at t it differs from both the preceding cause and the succeeding cause. If this is right, it seems that we can legitimately say that x has a peculiar cause at t, which is a cause of x’s beginning to be Y, different from the cause of x’s being Y.

Nevertheless, in this way of construction, in order for x to have a cause at t which is different from A and B, we presuppose and A and B both have an intrinsic limit at t! But how do we justify that? Moreover, if B is the cause of x’s being Y and B has an intrinsic limit at t, then x is Y at t, and why do we still need causal principle 2?

If my foregoing analysis is right, then to show that x has a cause at t amounts to showing that x is Y at t. Note what this implies. The causal principles 1 and 2 give us what we want only if x has a cause at t, otherwise even if we accept the second principle, the principle is useless (since it is only trivially true---its subject, the cause for x at t, does not exist). But to show that x has a cause at t amounts to showing that x is Y at t. The causal elaborations are thus redundant; we don’t need them to derive what we want.[15]

So much for the criticisms. Now here comes the real thing.

5. My phenomenological account

Although Kretzmann’s and Spade’s accounts do not work, they have considerable merit. Kretzmann’s account links the problem to the conscious act of God. And Spade’s explanation approaches the problem in the context of cause and effect. In the following let me propose a phenomenological account, which combines certain features in Kretzmann’s and Spade’s accounts.

Like Spade, I also place Burley’s solution in the context of the causal framework. But unlike Spade, who didn’t limit the scope of cause, I take cause as being limited to the intentional willing of God, which is modeled after our own phenomenology and intentional willing.

Like Kretzmann, I also justify Burley’s solution by appealing to the conscious act of God. But unlike Kretzmann, I don’t think that the relevant conscious act is God’s fore-knowledge; I think it is rather God’s intentional willing.

In order to unfold this account, I need to discuss the notion of “moment.” The question I would like to address is this: Is the notion of “moment” experientially based? Or to put it in a simple way, do we have experience of moments? (A quick note: hereinafter I am doing phenomenology, so I don’t use argument.)

Let’s first run a quick search on our experience. Our experience seems to be continuous. When I focus on my experience of toothache right now, the toothache is continuous, since it always involves retentions, that is to say, it manifests itself as having already existed before. There is no first moment or last moment of the toothache that I experience. A so-called sudden or abrupt feeling or thought is not instantaneous either, strictly speaking. It just lasts for a short period of time; it still takes time. The momentary experience is not the experience of the moment. “Momentary” is just a loose way to talk about a very short period of time. In other words, in the experience of sudden feelings, there is still retention, and there are no starting point and ending point that we can identify. The difference between a short period of time and a long period of time is a quantitative difference, and this quantitative difference cannot be used to account for the qualitative difference between moment and interval.

Next, let’s consider the experiential base of starting and stopping---perhaps there is something special about them that we can use to account for moment? What makes starting different from the subsequent undertaking? Well, it is the presence of the experience of change. We experience change at starting (or stopping), but this experience is no longer there in maintaining or enduring a course of action. But the experience of change is not instantaneous; it is continuous like any other experience. How, then, can we know that starting (or stopping) is a starting POINT rather than a starting PERIOD? We can certainly stipulate that starting is a starting point as we in fact do in ordinary language, but it is based on the experiential characteristics of starting (viz., the experience of change); it is rather derived from an application of the notion of “moment” (which I will discuss later).

Now, if the notion of “moment” is not experientially based, what is it based on? How do we construct this notion? A search for answers to these questions will lead us to our interpretation of Burley’s account. In the following let me show that we use the notion of “simultaneity” to construct the notion of “moment.”

My first observation is that the notion of “simultaneity” is experientially based (I am not talking about simultaneity in the physical sense, but in the phenomenological sense). To work out the experiential base of “simultaneity,” I need to introduce several terms.

First, let me introduce the term “co-presence.” Experience X are co-present with Y if and only if when I experience Y, I also experience X. Simultaneity is a special kind of co-presence, but not any co-presence is simultaneity. While I am reading the paper, I am also having a headache. The experience of the headache is co-present with the experience of moving the lips. But this mere co-presence is not good enough to enable us to say that they are simultaneous, unless we sense a connection, a type of correlation between them.

Second, let me introduce “causality-based co-presence” (abbreviated as CB co-presence). Here Humeans would dislike my view. Humeans believe that causality is the no more than the result of the habitual association of ideas. But I think that there is a subjective experience of certain causality, causality between my willing and my acting, that is not based on the habitual association of ideas. Suppose I will to raise my left arm, and as a result, my left arm moves upward. Here we don’t just have a co-presence of the experience of my willing and the experience of the movement of my muscle. I feel something else besides those. There is an anticipation of the experience of the movement of my muscle that comes along with the experience of my willing. And the anticipation is fulfilled in our having the experience of the movement of my muscle. The totality of anticipating/fulfilled anticipation constitute a relation between willing  and acting, so that willing or acting by itself (without having the other) is considered to be incomplete. Willing without acting is unsaturated willing; and acting without willing is blind acting, acting un-accounted-for. Note that the anticipation here is not an experience we have alongside the experiences of willing and acting; it is rather a movement that links two experiences (experience of willing and experience of acting). In maintaining the action, the anticipation is no longer there, but we still can sense another connection between willing and acting, the acting is grasped as being correlated with willing (which I will discuss in the next paragraph). Here I call co-presence that has these connections causality-based co-presence (CB co-presence).

Third, let me introduce the distinction between “initiation CB co-presence” and “holding-on CB co-presence.” If the relation in CB co-presence is the relation of anticipating/fulfilled anticipation (as I discussed earlier), the CB co-presence is the initiation CB co-presence. When we hold on to our willing and acting, the anticipation/fulfilled anticipation relation is no longer there. But we do feel the willing and the acting being correlated, in the sense that the acting is the result of willing and the acting is under our control. This correlation is continuous, as our willing is continuous and our acting is continuous. If the relation is CB co-presence is this correlation, the CB co-presence is the holding-on CB co-presence.

Having introduced these terms, I claim that the original phenomenological understanding of “simultaneity” is the initiation CB co-presence. And we use this notion to construct the notion of “moment.” Since simultaneity is a relation, moments are just the relata of this relation (the objects that the relation relates). The starting point of project A is what simultaneity picks out at the polar ends for our willing and acting on A, and the ending point of A is what simultaneity picks out at the polar ends for our willing and acting on non-A. Once starting and ending points are defined, we can extend the notion of simultaneity. We can say that two experiences, A and B, are simultaneous if and only if (1) the starting point and the ending point of A are simultaneous with the starting point of the ending point of B, and (2) A are B have the holding-on CB co-presence.

Why isn’t simultaneity a relation between two intervals rather than a relation between two points? The reason is that simultaneity is “initiation CB co-presence” rather than “holding-on CB co-presence.” Given that there is a qualitative difference between “initiation CB co-presence” and “holding-on CB co-presence,” if the relatum of simultaneity is taken to be an interval, there is no way to find a parallel qualitative difference when we shift to the plane of relata. (Explain)

This said, we are ready to make sense of Walter Burley’s account. Willing and acting are simultaneous at the beginning point. If we limit the scope of x and Y in Spade’s causal principle 2 (that to cause x to begin to be Y is to cause x to be Y) in such a way that x is myself, and that Y is my action), then this causal principle is true. Now, it is reasonable to suppose that God’s intentional willing is of the same phenomenological nature as ours. Of course, God’s intentional willing is infinitely more powerful; it can cause all sorts of thing to happen in the world. Now since the effect is simultaneous with the cause (from the phenomenological point of view), and since the cause---God’s willing---has an intrinsic limit for starting (the beginning point picked out by the original simultaneity relation), the effect (e.g., permanent entities) also has an intrinsic limit for starting. For stopping, we need to understand it as the initiation of a new intentional willing project rather than that the old intentional project dies out. To fall into asleep, we need to understand it as the result of a willing to sleep rather than our conscious act fades out. Certainly we cannot do it, but God can because of the infinite power it has.

NOTES

[1] I am grateful to Paul Spade, Michael Dunn, Hans Kim, Yong Huang for helpful comments on earlier drafts of the paper.
[2] Assume that we are talking about the moments after my birth.
[3] I borrowed this example from Paul Benacerraf’s “Tasks, Super-tasks, and the Modern Eleatic,?Journal of Philosophy 59 (1962). Whereas Benacerraf used it in the discussion of Zeno’s paradox, I use it in a different context.
[4] To enter a body, I just need to make a decision to enter, provided that (1) the body I want to enter hasn’t had any soul before and (2) I am not inside any body when I make the decision.
[5] I borrowed the terminologies “intrinsic limit” and “extrinsic limit” from Paul Spade’s “How to Start and Stop.” These seem to be originate from similar terms in calculus. See Paul Spade, "How to Start and Stop: Walter Burley on the Instant of Transition," Journal of Philosophical Research 19 (1994), 193-221.
[6] Walter Burley, On the Purity of the Art of Logic, trans. by Paul Spade (Yale Library of Medieval Philosophy Series, 2001).
[8] Recall Aristotle’s ball example. A ball is thrown upwards, and it changes its course at the apex. At the moment of change, should we say that it is already moving downward, or that it is at rest, or that it is at the last point of ascending? I don’t think our intuition would help us decide on this issue.
[9] Spade, “How to Start and Stop, 207.
[10] This explanation can also be extended to successive entities if we wish to do so.
[11] This is because cause and effect are simultaneous.
[12] The proof is as follows: Suppose an instantaneous entity exists. Let’s say that it exists at instant a. Consider the cause for the non-being of that entity. When does that cause take place? It cannot happen at a, for it did, then the entity would not exist at a, according to the causal account. But it cannot happen at any other instant either, because if it did, then from a to that instant the instantaneous entity would have to exist all along, which contradicts the very nature of the entity being instantaneous. Hence, the cause does not exist at any moment. And yet, we know that the cause is real. Thus, we get a contradiction. As a result, we conclude that an instantaneous entity does not exist (if we do not abandon the causal account).
[13] Suppose we are working within the Fregean framework---the cause of actions are indexical beliefs.
[14] Here I take a cause for an entity at a moment as the vector sum of all efficient causes for that entity at that moment.
[15] What are the consequences of the causal account? Certainly it says nothing about whether the cause of x’s beginning to be Y (if there is any) is identical to the cause of x’s being Y and it says nothing about whether x has a cause (different from the cause of preceding time) at the moment when x begins to be Y But it does say that any cause, since it is real, has to be an enduring entity, whether it is permanent or successive. Certainly in the duration of x’s being Y there is an enduring cause. Instead of associating an instantaneous cause with an instantaneous effect, we now associate an enduring cause with an enduring state. But then the decision problem of the extrinsic and intrinsic limits reappears at the level of causes. If in the cases of effect we can appeal to cause to determine whether the effect has an extrinsic or intrinsic limit, what can we appeal to in determining whether the cause has an extrinsic or intrinsic limit? Thus, Spade’s causal account begs the question at another level.