Having rejected the postulate of the necessity of causal links, Hume replaces it with the condition of regularity. Paraphrasing his words, if x is a cause of y, each event that is similar to x is followed by an event similar to y. Thus, the complete definition of causation can look like this: x is a cause of y iff x is spatiotemporally contiguous with y, x temporally precedes y, and for all x’, if x’ is similar to x, then there is a y’ such that y’ is similar to y and y’ follows x’. One of the main difficulties with this definition is the notorious vagueness of the notion of similarity between events. If we interpret similarity as being identical in some respect, then it is plausible that every object is similar to every other object, and as a consequence the condition of regularity can never be satisfied. On the other hand, similarity conceived as identity in all respects (qualitative identity) collapses into numerical identity (given the PII), and therefore the condition of regularity reduces to the previous two conditions (contiguity and temporal precedence). The main challenge to Hume’s analysis is to characterize the notion of a relevant aspect with respect to which the similarity between events is interpreted. But even if this can be done, Hume’s analysis is open to serious criticism. Critics point out that there are cases of regular successions of events without a causal link. Days regularly follow nights, and yet there is no causal relation between the two. Similarly, if according to the timetable after the departure of train A train B regularly arrives at the station, this does not indicate that one causes the other. Note that typically the regular but not causal correlations can be explained with the help of a common cause (the succession of day and night is explained by the rotation of the earth, and the timetable acts as the common cause of both the departure of train A and the arrival of train B). So it can be concluded that Hume’s regularity approach has difficulties with distinguishing between direct causal regularities and regularities arising from a common cause.
Another group of counterexamples to the Humean analysis contains cases of causal links where no regularity is present. It is sometimes argued that causal links between unique events (for instance the Big Bang) don’t satisfy the requirement of regularity. Actually, they satisfy it but trivially, making all spatiotemporally conjoined unique events causally connected with each other. But it is unquestionable that in real life we make numerous causal claims where there is no underlying regularity. We say that the failure of brakes was a cause of the car crash, although not every failure of that sort leads to a crash. This clearly shows that Hume’s analysis is in need of serious corrections.
Neo-Humean approaches to causation try to eliminate some of its weak points. One of them is the nomological conception. According to it, an event x of type A is a cause of an event y of type B iff x and y occur in conditions C and there is a law of nature according to which if an event of type A happens in conditions C, an event of type B occurs. There are two main differences between this approach and Hume’s regularity account: the presence of background conditions C and the reference to laws of nature. The role of laws of nature is to eliminate accidental regularities, while the presence of conditions C should take care of the problem of the apparent lack of regularity of some causal links (the failure of brakes leads to an accident only in certain specific circumstances). But these additions to the regularity approach bring new problems. What are laws? Hume himself insisted that laws are nothing over and above mere regularities, but if that’s the case the addition of laws to the definition of causation does not constitute an improvement with respect to the old, Humean version. The introduction of conditions C creates a different problem. By a crafty selection of appropriate “conditions” we can make virtually any succession of events a causal one. It may be claimed, for instance, that the snapping of my fingers causes the lights to go out if we include in the appropriate conditions that someone turns off the switch at the same moment. Yet another objection is that there are laws which are not causal. Pascal’s law states that a gas exerts equal pressure in all directions, but it is not correct to say that the fact that the pressure in one direction equals p is caused by the fact that the pressure in the opposite direction is also p. Finally, most laws of physics are symmetric in time, but from this it does not follow that backward causation is a common fact.
One of the most sophisticated versions of the regularity approach is the conception of causation proposed by J.L. Mackie. Mackie notes that the notion of a cause is closely related to sufficient and necessary conditions, but a cause of x cannot be simply defined as a necessary or a sufficient condition of x. Let us consider Mackie’s example with a fire of a house being caused by a short circuit. The short circuit by itself is not sufficient for the house to burn down; other conditions have to be present, such as the presence of inflammable materials, of oxygen, the absence of automatic sprinklers and smoke detectors, etc. Generally speaking the short circuit is not necessary for the fire either, for fires can start in many different ways, for instance after a strike of a lightning bolt. But in the actual conditions the short circuit was necessary, because without it the conditions themselves would not have created the fire. (Mackie speaks in this case about a necessary condition post factum.) The short circuit is an INUS condition for the occurrence of the fire, where the acronym INUS stands for an Insufficient but Necessary part of an Unnecessary but Sufficient condition. A more precise definition of an INUS condition is as follows: A is an INUS condition for B iff there are conditions X and Y such that (AX or Y) is a necessary and sufficient condition of B, but neither A nor X is a sufficient condition of B. In our example A is the short circuit, B is the fire, X refers to all the conditions which together with A were sufficient for the fire to occur, and Y stands for a disjunction of all alternatives ways of starting a fire. In most cases a cause of an occurrence B is an INUS condition of B such that it occurred, and no alternative conditions Y were present (however, Mackie admits the possibility that a cause itself may be sufficient for its effect, or even sufficient and necessary – he refers to all such cases jointly as “at least” INUS conditions of B).
It has to be noted that some further restrictions on the causal condition A have to be introduced, otherwise Mackie’s analysis will lead to obviously incorrect conclusions. To see this, let us use the letter C to abbreviate the complete sufficient condition of B that was actually present, and let us select any fact S irrelevant to the occurrence of B that happened simultaneously with C (for instance the fact that when the fire started somebody walked past the house whistling “Ode to joy”). The formula [(S or C) and (not-S or C)] is logically equivalent to C, and hence if there is a condition Y such that (C or Y) is a necessary and sufficient condition of B, then {[(S or C) and (not-S or C)] or Y} is a necessary and sufficient condition of B too. But now observe that the condition (S or C) satisfies the requirement for an INUS condition of B. (S or C) is not sufficient for B, nor is (not-S or C), and yet their conjunction is sufficient (as it is equivalent to C). But it is highly unintuitive to pick the disjunction S or C as a cause of B. To eliminate cases like this it may be suggested that causes should not have the form of disjunctions of simple events.
An interesting element of Mackie’s conception is that he admits that causal claims are always made in a context. In order to account for this fact, he introduces the notion of a causal field. Let us consider as an example the case of a person going down with flu. The answer to the question “What caused this man to contract the flu?” depends on the context. If we consider as the causal field the set of all moments in his life, and ask why he contracted the disease at this moment rather than any other, then the correct answer may be that he was infected by influenza viruses. But we can also select as the causal field the set of all people who came into contact with influenza viruses, and we may be interested in selecting the factor which is responsible for the fact that some of them contracted the disease, while the others did not. Mackie introduces the causal field to his definition of a cause, assuming that the conditions characterizing this field are present when the cause is present.
Reading:
M.J. Loux, Chapter 6 "Causation", pp. 187-203, Metaphysics: A Contemporary Introduction.
Wednesday, April 28, 2010
Causation and necessity
We can distinguish two types of causal statements: general causal statements and singular ones. General statements relate types of phenomena (for instance: smoking causes cancer), whereas singular causal statements connect individual occurrences (for example: the cause of the sinking of the Titanic was that it collided with an iceberg). While the two categories of causal claims are undoubtedly related, their relation is not straightforward. It may seem that general causal statements of the form “Phenomenon A causes phenomenon B” can be reduced to the following singular claim: “For all x, if x is of type A, then x causes some y of type B”. But this won’t work. From the fact that smoking causes cancer it does not follow that every smoker will suffer from cancer. General causal claims are very often statistical only, and their truth is typically hedged by the ceteris paribus condition. On the other hand, if we wanted to define singular causal claims of the type “x causes y” with the help of the general formula “The type of phenomena A to which x belongs causes the type of phenomena B containing y”, we would encounter an immediate problem connected with the fact that each individual event can be classified into many distinct types. In the following we will restrict our analysis to singular claims only, and therefore we will interpret causation as a relation between individual objects.
It may be useful to start an analysis of causation from the following questions:
(1) What are the relata of the causal relation?
(2) What are formal properties of the causal relation?
(3) What is the temporal relation between a cause and its effect?
(1) Typically three categories of objects are regarded as being capable of standing in the causal relation: things, events and facts. One natural way of speaking about causal links seems to identify causes as things. For instance, we can say that John smashed a window glass with a stone, and a car hit a pedestrian. This suggests that causes are things (John, car) while effects are events (shattering the window, hitting the pedestrian). But clearly this is an oversimplified way of speaking. If John is busy talking on the phone, there is no shattering, although the purported cause (John) is still present. If the car is parked in a garage, no pedestrian is in danger of being hit by it. Strictly speaking, it is not John but his throwing the stone that causes the breaking, and it is not the car but its particular movement that causes the hitting of the pedestrian. This observation leads to the most commonly accepted conception of causation, according to which both causes and effects are events (throwing the stone – shattering the glass, movement of the car – hitting the pedestrian).
However, some philosophers insist that this account is too restrictive, as it does not make room for cases of negative causation. Sometimes it seems natural to single out absences of events rather than events themselves as causal factors contributing to a given effect. We say that the lack of attention of the driver was a cause of the crash, and that the absence of sprinklers contributed to the fire. But there are no negative events (in Kim’s conception, events are property attributions, but it is customary not to admit negative properties). In order to admit negative causation (sometimes also called causation by omission) it is proposed that causes and effects be facts, not events. Facts are just ontological counterparts of true statements, so there is no problem with the assumption that there are negative facts corresponding to negative statements. But critics point out that negative causation is really not necessary, and moreover that admitting it opens the door to many unintuitive cases of spurious causation. It may be claimed that underlying every case of apparent negative causation there is an instance of positive causation (for instance the driver’s lack of attention could have been actually his talking on the phone). And we tend to dismiss statements of the sort “The fact that I had not been struck by lightning caused me to survive” if there was no reason to expect that the lightning was imminent.
(2) It should be clear that the causal relation is not reflexive (there are events that don’t cause themselves). But is it irreflexive (no event is a cause of itself)? That depends. If we admit the possibility of causal loops (as in time travel), and we agree that causality is transitive, then there may be cases of self-causation (x causes y and y causes x, therefore x causes x). Similarly, causality is not symmetric, but it is open to debate whether it is asymmetric (if there are causal loops, clearly it is not asymmetric). The case for transitivity looks plausible enough, but recently this feature of causality came under attack. Some philosophers point out that there are cases which seem to violate the transitivity requirement, such as the following one. A bomb had been planted at the door of a politician’s house, but luckily it was spotted by the security and defused. It is natural to assume that the placing of the bomb was a cause of its defusing (if there hadn’t been a bomb, there wouldn’t have been the act of defusing), and the defusing of the bomb causes the politician to survive. But it is unnatural to say that the placing of the bomb was a cause of the politician’s survival (clearly the counterfactual “If the bomb had not been planted, the politician would not have survived” is false).
(3) It is typically assumed that a cause happens earlier (or, at least, not later) than its effect. But, again, if we want to admit that it is conceptually possible to have backward causation, we have to reject this requirement.
The main question we have to ask now is “What is causation?”. Answers to this question can be given in the form of a reductive analysis, explicating the causal relation in terms of some more fundamental concepts. We will start with the most famous reductive analysis of causation given by David Hume. Hume observes that it is an uncontroversial fact that causation displays the following two properties: the cause and the effect are contiguous in space and time (they “touch” each other), and the cause temporally precedes the effect. Actually, both claims can be questioned. The issue of temporal precedence has been already mentioned in point (3). As for the contiguity, at best it can be applied to direct causes only. Clearly there is a temporal and spatial gap between my act of hurling the stone and the smashing of the window. But it can be claimed that there has to be a chain of events contiguous in space and time leading from the throwing to the breaking. Still, this does not seem to be conceptually necessary. There is nothing inconsistent in considering causal links acting at a distance with no intermediate stages. Actually, this is how gravitational interaction between massive bodies can be assumed to work in Newtonian mechanics. So it looks like the two conditions proposed by Hume are not necessary for causation to occur. But we have to agree with Hume that they are not sufficient either, for there are plenty of events following one another which are not causally connected.
Hume then asks, what should be added in order to have a sufficient condition for the presence of a causal link. One typical response is that the cause has to be necessarily linked with its effect, or in other words, that if the cause occurs, the effect must occur. But Hume famously questions this. Firstly, he notices that the purported necessity cannot be of the logical kind, for no contradiction arises from the supposition that a given event does not produce its expected effect. I can imagine without contradiction the stone magically passing through the glass, or bouncing off it. But perhaps the necessity connecting causes and effects is of a different kind (nomological, or physical). Hume’s response is that no such necessity is given to us in sensory experience. We never perceive two events as connected, only as conjoined.
Clearly, Hume’s criticism of the necessary character of causation has its roots in his version of empiricism. Hume insists that every meaningful concept should be traced back to some sensory experience (‘impression’). But this requirement may be seen as overly restrictive. Hume’s radical empiricism does not square well with modern science which commonly postulates the existence of unobservable objects and properties. According to Hume’s criterion, along with the notion of necessity we should abandon such concepts as that of atoms, electrons, electromagnetic field, etc., as they cannot be supported by any direct sensory data either. On the other hand, more moderate versions of empiricism can in principle accommodate the notion of a necessary causal link, if it is treated as a theoretical concept used to make empirical predictions and explain observable facts.
Reading:
B. Garrett, "Causation", pp. 53-66, What is this thing called metaphysics?
It may be useful to start an analysis of causation from the following questions:
(1) What are the relata of the causal relation?
(2) What are formal properties of the causal relation?
(3) What is the temporal relation between a cause and its effect?
(1) Typically three categories of objects are regarded as being capable of standing in the causal relation: things, events and facts. One natural way of speaking about causal links seems to identify causes as things. For instance, we can say that John smashed a window glass with a stone, and a car hit a pedestrian. This suggests that causes are things (John, car) while effects are events (shattering the window, hitting the pedestrian). But clearly this is an oversimplified way of speaking. If John is busy talking on the phone, there is no shattering, although the purported cause (John) is still present. If the car is parked in a garage, no pedestrian is in danger of being hit by it. Strictly speaking, it is not John but his throwing the stone that causes the breaking, and it is not the car but its particular movement that causes the hitting of the pedestrian. This observation leads to the most commonly accepted conception of causation, according to which both causes and effects are events (throwing the stone – shattering the glass, movement of the car – hitting the pedestrian).
However, some philosophers insist that this account is too restrictive, as it does not make room for cases of negative causation. Sometimes it seems natural to single out absences of events rather than events themselves as causal factors contributing to a given effect. We say that the lack of attention of the driver was a cause of the crash, and that the absence of sprinklers contributed to the fire. But there are no negative events (in Kim’s conception, events are property attributions, but it is customary not to admit negative properties). In order to admit negative causation (sometimes also called causation by omission) it is proposed that causes and effects be facts, not events. Facts are just ontological counterparts of true statements, so there is no problem with the assumption that there are negative facts corresponding to negative statements. But critics point out that negative causation is really not necessary, and moreover that admitting it opens the door to many unintuitive cases of spurious causation. It may be claimed that underlying every case of apparent negative causation there is an instance of positive causation (for instance the driver’s lack of attention could have been actually his talking on the phone). And we tend to dismiss statements of the sort “The fact that I had not been struck by lightning caused me to survive” if there was no reason to expect that the lightning was imminent.
(2) It should be clear that the causal relation is not reflexive (there are events that don’t cause themselves). But is it irreflexive (no event is a cause of itself)? That depends. If we admit the possibility of causal loops (as in time travel), and we agree that causality is transitive, then there may be cases of self-causation (x causes y and y causes x, therefore x causes x). Similarly, causality is not symmetric, but it is open to debate whether it is asymmetric (if there are causal loops, clearly it is not asymmetric). The case for transitivity looks plausible enough, but recently this feature of causality came under attack. Some philosophers point out that there are cases which seem to violate the transitivity requirement, such as the following one. A bomb had been planted at the door of a politician’s house, but luckily it was spotted by the security and defused. It is natural to assume that the placing of the bomb was a cause of its defusing (if there hadn’t been a bomb, there wouldn’t have been the act of defusing), and the defusing of the bomb causes the politician to survive. But it is unnatural to say that the placing of the bomb was a cause of the politician’s survival (clearly the counterfactual “If the bomb had not been planted, the politician would not have survived” is false).
(3) It is typically assumed that a cause happens earlier (or, at least, not later) than its effect. But, again, if we want to admit that it is conceptually possible to have backward causation, we have to reject this requirement.
The main question we have to ask now is “What is causation?”. Answers to this question can be given in the form of a reductive analysis, explicating the causal relation in terms of some more fundamental concepts. We will start with the most famous reductive analysis of causation given by David Hume. Hume observes that it is an uncontroversial fact that causation displays the following two properties: the cause and the effect are contiguous in space and time (they “touch” each other), and the cause temporally precedes the effect. Actually, both claims can be questioned. The issue of temporal precedence has been already mentioned in point (3). As for the contiguity, at best it can be applied to direct causes only. Clearly there is a temporal and spatial gap between my act of hurling the stone and the smashing of the window. But it can be claimed that there has to be a chain of events contiguous in space and time leading from the throwing to the breaking. Still, this does not seem to be conceptually necessary. There is nothing inconsistent in considering causal links acting at a distance with no intermediate stages. Actually, this is how gravitational interaction between massive bodies can be assumed to work in Newtonian mechanics. So it looks like the two conditions proposed by Hume are not necessary for causation to occur. But we have to agree with Hume that they are not sufficient either, for there are plenty of events following one another which are not causally connected.
Hume then asks, what should be added in order to have a sufficient condition for the presence of a causal link. One typical response is that the cause has to be necessarily linked with its effect, or in other words, that if the cause occurs, the effect must occur. But Hume famously questions this. Firstly, he notices that the purported necessity cannot be of the logical kind, for no contradiction arises from the supposition that a given event does not produce its expected effect. I can imagine without contradiction the stone magically passing through the glass, or bouncing off it. But perhaps the necessity connecting causes and effects is of a different kind (nomological, or physical). Hume’s response is that no such necessity is given to us in sensory experience. We never perceive two events as connected, only as conjoined.
Clearly, Hume’s criticism of the necessary character of causation has its roots in his version of empiricism. Hume insists that every meaningful concept should be traced back to some sensory experience (‘impression’). But this requirement may be seen as overly restrictive. Hume’s radical empiricism does not square well with modern science which commonly postulates the existence of unobservable objects and properties. According to Hume’s criterion, along with the notion of necessity we should abandon such concepts as that of atoms, electrons, electromagnetic field, etc., as they cannot be supported by any direct sensory data either. On the other hand, more moderate versions of empiricism can in principle accommodate the notion of a necessary causal link, if it is treated as a theoretical concept used to make empirical predictions and explain observable facts.
Reading:
B. Garrett, "Causation", pp. 53-66, What is this thing called metaphysics?
Tuesday, April 27, 2010
How things persist
Things exist in time. More specifically, they persist. A thing, such as a tree, remains the same object throughout its existence, although it changes some of its properties, loses some of its parts and acquires new ones. The relation that holds between the same object at different times is called ‘diachronic identity’. But the question is: What is this new type of identity? How does it relate to numerical identity? Is diachronic identity reducible to numerical identity, or perhaps to qualitative identity? These questions are answered differently by two major conceptions of how things persist in time: endurantism and perdurantism. Endurantism can be characterised broadly as the position according to which things persist in time by being wholly and completely present at every single moment of their existence. On the other hand, perdurantism assumes that at a given moment only a small part of a thing is present. The whole thing is an object which extends in time as well as in space.
Let us look more closely at both views. Endurantism seems to be in agreement with our pre-philosophical intuitions regarding persistence. When I look at a table in front of me, I believe that no part of it is missing from my view. Things have only spatial parts and spatial dimensions, but no temporal ones. According to endurantists, the expressions “Napoleon at the time of the battle of Austerlitz” and “Napoleon at the time of the battle of Waterloo” refer to one and the same individual: Napoleon. Hence diachronic identity reduces to numerical identity. Things are three-dimensional objects taking up various spatial regions at different times.
Perdurantism, on the other hand, claims that things are four-dimensional objects taking up regions of space-time. The expressions “Napoleon at the time of the battle of Austerlitz” and “Napoleon at the time of the battle of Waterloo” refer to numerically different objects: temporal parts of the four-dimensional entity that we call “Napoleon” and whose temporal dimension stretches from the moment of Napoleon’s birth to his death. Consequently, the relation of diachronic identity is not defined as numerical identity, but instead can be explicated as the relation that holds between any two temporal parts of the same thing: x is diachronically identical with y iff x and y are different temporal parts of individual z. (An alternative interpretation of diachronic identity under perdurantism is that it is reducible to numerical identity after all, when we say that “Napoleon at t1 is identical with Napoleon at t2” means “The four-dimensional object whose temporal part at t1 is Napoleon at t1 is numerically the same as the four-dimensional object whose temporal part at t2 is Napoleon at t2”.) Temporal parts of an object can be divided into stages and slices. A stage of a thing x is a part of x that occupies a non-zero interval (it has a non-zero temporal “width”), whereas a slice of x is a part of x taken in a zero-length moment of time, and thus it has no temporal dimension. Slices are three-dimensional, and they represent what we would usually refer to as objects of our perception. It is noteworthy that the way things persist according to the perdurantist is analogous to the temporal existence of events. An event, such as the battle of Waterloo, is never fully present in an interval that is shorter than its entire duration.
The main motivation for perdurantism comes from the problem of change which threatens the endurantist approach. Things change their properties in time: for some moments t1 and t2 and a property P it is the case that x has P at t1 and x does not have P at t2. But according to endurantism x at t1 is numerically identical with x at t2. If we apply Leibniz’s law, which states that if x = y and Px, then Py, then we have to conclude that an object has P and doesn’t have P, which is obviously a contradiction. Perdurantism avoids this problem by assuming that the properties P and not-P are attributed to numerically different individuals: different temporal slices. But the endurantist is not without options with respect to the problem of property change. One solution is to relativise properties to time. Let us consider a poker which is cold at t1 and hot at t2. We may say that the poker possesses the property of being-cold-at-t1 and being-hot-at-t2, and these properties are not mutually exclusive as long as t1 is different from t2. But an objection can be raised that this approach treats properties as if they were relations between objects and moments, and consequently no property can be intrinsic. And, besides, isn’t it legitimate to speak about properties simpliciter, without any temporal relativisation? Another solution, available to the endurantist, is to relativise the relation of possession between the object and its properties. Objects don’t just possess properties, but they always possess them at certain moments. This position is known as adverbialism, as it amounts to the adverbial modification of the verb “be” (the poker is-at-t1 cold and the poker is-at-t2 hot). One consequence of this approach is that there is no single relation of exemplification between particulars and universals, but an infinite (even uncountable) number of different relations of exemplification. Finally, let us notice that all the above endurantist solutions seem to assume that moments exist independently, and therefore commit themselves to the substantivalist view.
We will now consider an argument against endurantists which employs the notion of change of parts. The argument is due to Peter van Inwagen, with some corrections added by Mark Heller. Suppose that a person X underwent an amputation of his left hand. Let t1 denote a moment before, and t2 after the amputation. Let us also denote by ‘X-minus’ the whole consisting of X’s body without the left hand (regardless of whether the hand is attached to it or not). The endurantist should accept the following identity statements:
(1) X at t1 = X at t2
(2) X-minus at t1 = X-minus at t2
(3) X-minus at t2 = X at t2
But from these three premises we can derive, using the assumption of the transitivity of identity, that
(4) X at t1 = X-minus at t1
This conclusion is clearly unacceptable. My body is not identical at this moment with my body minus my left hand. Now we will have to look closely at the justification of all the premises (1)-(3), to see which one should be rejected. Premise (1) follows from endurantism and the assumption that an object can lose its part without losing its identity. Premise (2) is a simple consequence of endurantism. Premise (3) is implied by the principle according to which two numerically distinct objects cannot occupy the same spatial region at the same time. Now it should be clear that rejecting endurantism and accepting perdurantism solves the problem. If we agree that the expressions “X (X-minus) at t1 (t2)” refer to temporal slices of appropriate four-dimensional objects, then premises (1) and (2) are evidently false, although (3) is unquestionably true. Another possible interpretation of (1)-(3) under perdurantism is that actually these identities are between appropriate four-dimensional objects, identified by their three-dimensional slices. In that case (1) and (2) are true, but (3) becomes false (two distinct four-dimensional objects can nevertheless share their three-dimensional slices).
But the endurantist has some viable strategies of defence. Firstly, he can claim that a thing cannot lose any of its parts without losing its numerical identity. But this is a highly unintuitive supposition, and if it’s true, then with each passing second our bodies are turned into new things, because they are constantly losing old parts and acquiring new ones. Secondly, the existence of X-minus can be called into question. For instance Van Inwagen rejects the doctrine which he calls “the doctrine of arbitrary and undetached parts”. X-minus before the amputation is not a separate, autonomous object, but an undetached part of X, and its existence is questionable. Thirdly, the assumption that two distinct things cannot occupy the same space at the same time can be rejected. It is argued that a sculpture, for instance “The Thinker” by Rodin, is numerically distinct from the lump of material it is made of (bronze) and yet throughout some period of time the two things occupy the same space. Finally, some authors question the transitivity of identity. According to Peter T. Geach, identity is a relative and contextual notion. We can say that X at t1 is the same person as X at t2, and that X-minus at t1 is the same body as X-minus at t2, but from this it doesn’t follow that X at t1 is the same body as X-minus at t1, nor that X at t1 is the same person as X-minus at t2.
One problem for perdurantism is that it does not offer clear criterions of how to distinguish four-dimensional wholes which are genuine things from arbitrary regions filled with matter. A given temporary slice of a four-dimensional object has an infinite numbers of future continuations. Which one is selected as the right one, and why? Yet another difficulty was noticed by van Inwagen. Four dimensional objects are often presented as collections of stages (slices). But a collection of objects possesses its elements necessarily. From this it follows that Napoleon could not have different stages from the ones he really had (for instance, he could not have been born earlier or later).
Endurantism is typically associated with presentism, and perdurantism with eternalism. But other combinations are also possible. Perdurantism can logically coexist with the theory of the growing (shrinking) universe. In such a case things would be four-dimensional wholes that grow or shrink as time passes. It is also possible to have both endurantism and eternalism. It seems that the only combination which is logically impossible is that of perdurantism and presentism (although some authors disagree with that). Perdurantism assumes that things have different temporal parts, so it is essential to admit that moments other than the present one exist. Also, presentism implies that the universe is three-dimensional (as time is not a dimension, because it is reduced to a point). But perdurantism identifies things with four-dimensional objects, and four-dimensional objects cannot exist in a three-dimensional world.
Readings:
E.J. Lowe, Chapter 3 "Qualitative change and the doctrine of temporal parts", pp. 41-58, A Survey of Metaphysics.
M.J. Loux, Chapter 8 "Concrete particulars II: persistence through time", pp. 230-256, Metaphysics: A Contemporary Introduction.
Let us look more closely at both views. Endurantism seems to be in agreement with our pre-philosophical intuitions regarding persistence. When I look at a table in front of me, I believe that no part of it is missing from my view. Things have only spatial parts and spatial dimensions, but no temporal ones. According to endurantists, the expressions “Napoleon at the time of the battle of Austerlitz” and “Napoleon at the time of the battle of Waterloo” refer to one and the same individual: Napoleon. Hence diachronic identity reduces to numerical identity. Things are three-dimensional objects taking up various spatial regions at different times.
Perdurantism, on the other hand, claims that things are four-dimensional objects taking up regions of space-time. The expressions “Napoleon at the time of the battle of Austerlitz” and “Napoleon at the time of the battle of Waterloo” refer to numerically different objects: temporal parts of the four-dimensional entity that we call “Napoleon” and whose temporal dimension stretches from the moment of Napoleon’s birth to his death. Consequently, the relation of diachronic identity is not defined as numerical identity, but instead can be explicated as the relation that holds between any two temporal parts of the same thing: x is diachronically identical with y iff x and y are different temporal parts of individual z. (An alternative interpretation of diachronic identity under perdurantism is that it is reducible to numerical identity after all, when we say that “Napoleon at t1 is identical with Napoleon at t2” means “The four-dimensional object whose temporal part at t1 is Napoleon at t1 is numerically the same as the four-dimensional object whose temporal part at t2 is Napoleon at t2”.) Temporal parts of an object can be divided into stages and slices. A stage of a thing x is a part of x that occupies a non-zero interval (it has a non-zero temporal “width”), whereas a slice of x is a part of x taken in a zero-length moment of time, and thus it has no temporal dimension. Slices are three-dimensional, and they represent what we would usually refer to as objects of our perception. It is noteworthy that the way things persist according to the perdurantist is analogous to the temporal existence of events. An event, such as the battle of Waterloo, is never fully present in an interval that is shorter than its entire duration.
The main motivation for perdurantism comes from the problem of change which threatens the endurantist approach. Things change their properties in time: for some moments t1 and t2 and a property P it is the case that x has P at t1 and x does not have P at t2. But according to endurantism x at t1 is numerically identical with x at t2. If we apply Leibniz’s law, which states that if x = y and Px, then Py, then we have to conclude that an object has P and doesn’t have P, which is obviously a contradiction. Perdurantism avoids this problem by assuming that the properties P and not-P are attributed to numerically different individuals: different temporal slices. But the endurantist is not without options with respect to the problem of property change. One solution is to relativise properties to time. Let us consider a poker which is cold at t1 and hot at t2. We may say that the poker possesses the property of being-cold-at-t1 and being-hot-at-t2, and these properties are not mutually exclusive as long as t1 is different from t2. But an objection can be raised that this approach treats properties as if they were relations between objects and moments, and consequently no property can be intrinsic. And, besides, isn’t it legitimate to speak about properties simpliciter, without any temporal relativisation? Another solution, available to the endurantist, is to relativise the relation of possession between the object and its properties. Objects don’t just possess properties, but they always possess them at certain moments. This position is known as adverbialism, as it amounts to the adverbial modification of the verb “be” (the poker is-at-t1 cold and the poker is-at-t2 hot). One consequence of this approach is that there is no single relation of exemplification between particulars and universals, but an infinite (even uncountable) number of different relations of exemplification. Finally, let us notice that all the above endurantist solutions seem to assume that moments exist independently, and therefore commit themselves to the substantivalist view.
We will now consider an argument against endurantists which employs the notion of change of parts. The argument is due to Peter van Inwagen, with some corrections added by Mark Heller. Suppose that a person X underwent an amputation of his left hand. Let t1 denote a moment before, and t2 after the amputation. Let us also denote by ‘X-minus’ the whole consisting of X’s body without the left hand (regardless of whether the hand is attached to it or not). The endurantist should accept the following identity statements:
(1) X at t1 = X at t2
(2) X-minus at t1 = X-minus at t2
(3) X-minus at t2 = X at t2
But from these three premises we can derive, using the assumption of the transitivity of identity, that
(4) X at t1 = X-minus at t1
This conclusion is clearly unacceptable. My body is not identical at this moment with my body minus my left hand. Now we will have to look closely at the justification of all the premises (1)-(3), to see which one should be rejected. Premise (1) follows from endurantism and the assumption that an object can lose its part without losing its identity. Premise (2) is a simple consequence of endurantism. Premise (3) is implied by the principle according to which two numerically distinct objects cannot occupy the same spatial region at the same time. Now it should be clear that rejecting endurantism and accepting perdurantism solves the problem. If we agree that the expressions “X (X-minus) at t1 (t2)” refer to temporal slices of appropriate four-dimensional objects, then premises (1) and (2) are evidently false, although (3) is unquestionably true. Another possible interpretation of (1)-(3) under perdurantism is that actually these identities are between appropriate four-dimensional objects, identified by their three-dimensional slices. In that case (1) and (2) are true, but (3) becomes false (two distinct four-dimensional objects can nevertheless share their three-dimensional slices).
But the endurantist has some viable strategies of defence. Firstly, he can claim that a thing cannot lose any of its parts without losing its numerical identity. But this is a highly unintuitive supposition, and if it’s true, then with each passing second our bodies are turned into new things, because they are constantly losing old parts and acquiring new ones. Secondly, the existence of X-minus can be called into question. For instance Van Inwagen rejects the doctrine which he calls “the doctrine of arbitrary and undetached parts”. X-minus before the amputation is not a separate, autonomous object, but an undetached part of X, and its existence is questionable. Thirdly, the assumption that two distinct things cannot occupy the same space at the same time can be rejected. It is argued that a sculpture, for instance “The Thinker” by Rodin, is numerically distinct from the lump of material it is made of (bronze) and yet throughout some period of time the two things occupy the same space. Finally, some authors question the transitivity of identity. According to Peter T. Geach, identity is a relative and contextual notion. We can say that X at t1 is the same person as X at t2, and that X-minus at t1 is the same body as X-minus at t2, but from this it doesn’t follow that X at t1 is the same body as X-minus at t1, nor that X at t1 is the same person as X-minus at t2.
One problem for perdurantism is that it does not offer clear criterions of how to distinguish four-dimensional wholes which are genuine things from arbitrary regions filled with matter. A given temporary slice of a four-dimensional object has an infinite numbers of future continuations. Which one is selected as the right one, and why? Yet another difficulty was noticed by van Inwagen. Four dimensional objects are often presented as collections of stages (slices). But a collection of objects possesses its elements necessarily. From this it follows that Napoleon could not have different stages from the ones he really had (for instance, he could not have been born earlier or later).
Endurantism is typically associated with presentism, and perdurantism with eternalism. But other combinations are also possible. Perdurantism can logically coexist with the theory of the growing (shrinking) universe. In such a case things would be four-dimensional wholes that grow or shrink as time passes. It is also possible to have both endurantism and eternalism. It seems that the only combination which is logically impossible is that of perdurantism and presentism (although some authors disagree with that). Perdurantism assumes that things have different temporal parts, so it is essential to admit that moments other than the present one exist. Also, presentism implies that the universe is three-dimensional (as time is not a dimension, because it is reduced to a point). But perdurantism identifies things with four-dimensional objects, and four-dimensional objects cannot exist in a three-dimensional world.
Readings:
E.J. Lowe, Chapter 3 "Qualitative change and the doctrine of temporal parts", pp. 41-58, A Survey of Metaphysics.
M.J. Loux, Chapter 8 "Concrete particulars II: persistence through time", pp. 230-256, Metaphysics: A Contemporary Introduction.
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