Fig. 10.1
This chapter is devoted to the paradoxes of material constitution. They form an emerging field of puzzles about objects and people. The character of this development is conveyed by Fig. 10.1. Fortunately, these riddles have been recently organized with a paradox template. We shall use the template to connect past confrontations with the paradoxes with contemporary solutions.
Fig. 10.1
In the opening decades of the fifth century B.C., Epicharmus wrote a play with a philosophically precocious plot. A man is approached for payment of his portion of a fee for a forthcoming banquet. Lacking money, he resorts to a riddle: If you have a number of pebbles and add a pebble or subtract a pebble, do you have the same number of pebbles? No, replies the creditor. Or again, if you have a length of one cubit and add or subtract a bit, then would that length still exist? No, replies the creditor. The debtor then invites the creditor to think of men the same way. Men are always changing, some growing, some diminishing. Since this applies to both the creditor and the debtor, neither of them is the same as they were yesterday or the same as they will be in the future. The creditor acquiesces to this philosophical point. The debtor then triumphantly concludes that he owes nothing. After all, he is not the one who contracted to pay the fee. That man is gone. Nor will he be the one enjoying the banquet. That man is yet to be.
The creditor does not know what to say. Finally, he strikes the debtor. Reeling from the blow, the debtor angrily protests the assault. The creditor expresses sympathy but explains that he is not the man who struck him.
Which premise should the creditor deny? If he denies that the debtor is identical to the collection of parts that constitutes him, then the creditor would be saying that there are two things in the same place at the same time: the creditor and the collection of particles. This seems like double vision. What stops the collection of particles from being a person in its own right? The “mere collection” looks like a man, walks like a man, and talks like a man.
According to mereological essentialism, each part of an object is essential to it. The number of objects may grow but not the objects themselves. What appears to be a single individual is a rapid succession of individuals.
Epicharmus’s “growing argument” generalizes to a case in which the number of parts stays the same. Recall Heraclitus’s assertion that when one steps into a river twice, one steps into different bodies of water. The river stays the same even though all of its parts change. Can an artifact survive complete replacement of its parts?
The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrus Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question as to things that grow; one side holding that the ship remained the same, and the other contending it was not the same.
(Plutarch 1880, 7–8)
In the seventeenth century, Thomas Hobbes improved the riddle of the Ship of Theseus. He supposes that someone hoards the old planks and finally reassembles them into a ship. Is the hoarder’s ship the Ship of Theseus?
The hoarder compares the Ship of Theseus to an object that is dismantled and reassembled. Consider London Bridge, which was built in 1831. In 1962, the British government auctioned off the obsolete bridge to a land developer, Robert McCulloch, for $2,460,000. He reassembled the blocks in Lake Havasu City, Arizona. The process was completed on October 10, 1971, and the bridge was dedicated by the lord mayor of London. The local radio station KBBC continues to invite tourists to visit London Bridge in its new location.
Those who deny that the hoarder’s ship is the Ship of Theseus insist that the Ship of Theseus was in continuous existence while its old parts were being replaced. It did not pop out of existence when the hoarder reassembled all the old planks.
Suppose McCulloch used the blocks of London Bridge to make a castle in California, and preservationists subsequently complain that he destroyed London Bridge by reconfiguring its blocks into his California castle. McCulloch could not plausibly defend himself by claiming that London Bridge continues to exist; that it now just happens to share the exact location of his California castle. Further, suppose that a repentant McCulloch dismantles the California castle and assembles the blocks into a bridge at Lake Havasu City. Is this bridge identical to the old London Bridge? If so, is it also identical to his California castle?
The growing argument is mentioned by Plato and Aristotle. Neither gives it much attention. Paradoxes about parts and wholes only became intensively discussed after the skeptic Arcesilaus took over Plato’s Academy. Having undermined Platonism from within, Arcesilaus commenced a campaign against the Aristotelians and the Stoics across town.
Arcesilaus thought the Stoics were especially dogmatic. Instead of lowering expectations about what philosophy can achieve, the Stoics offered just what one naively hopes to secure from philosophical reflection: overall knowledge of the universe integrated with moral wisdom.
The Stoics believed that the universe was an organic whole. Their analogies have been inadvertently updated by the twentieth century’s James Lovelock. This biochemist defends the “Gaia hypothesis” that the earth is a living organism. (In Greek mythology, Gaia is the goddess who drew the living world forth from Chaos.) In the 1960s, the National Aeronautics and Space Administration (NASA) Jet Propulsion Laboratory asked Lovelock to design experiments to detect life on Mars. They wanted to send the Viking lander to Mars to check whether life existed there. Lovelock disappointed the rocketeers by claiming that atmospheric analysis already showed there is no life on Mars. Astronomers knew that the Martian atmosphere is static. In contrast, Earth’s atmosphere is dynamic. This indicates an underlying regulative process. Extra-terrestrials would not need to visit Earth to learn whether it has life. Lovelock further speculated that the hypothetical astronomers would be in a position to know that Earth itself is now alive: about one billion years after its formation, a nonliving Earth was occupied by a metalife form that transformed this planet into its own substance. Just as cell colonies develop into organs and bodies, organisms coevolve to promote the growth of the whole, Gaia.
The Stoics went further than Lovelock. They believed the whole universe is a rational animal. God is just the most creative aspect of nature. Rocks and other inanimate things have the least creative tension, plants more, animals yet more. At the top of this chain of being are rational animals. Since their rationality makes human beings mirror the universe as a whole, they are microcosms—miniature counterparts of nature. People are healthy and happy to the extent that their inner order corresponds to the outer order of nature. To learn how to live, learn about life.
In Stoic cosmology, growth is the most fundamental process of all living things. Arcesilaus used the growing argument to challenge the coherence of this organic theme. If the only change is a succession of momentary objects, then no individual can develop better harmony with the universe. From the conquered stronghold of Plato’s Academy, Arcesilaus was picking off students from the dwindling ranks of the Stoics.
This decay was reversed when Chrysippus became third head of the Stoa. He saved Stoicism by writing over 705 books in its defense. None of them survives as a whole. The fragments that subsist in quotation and paraphrase are often obscure. Given the fragmentary nature of the record, the historian is often in the position of knowing Chrysippus’s answer but not knowing the question. For instance, commentators have been puzzled by Chrysippus’s taxonomy of four levels of existence: substrate, qualified, disposed, and relatively disposed. What theory lies behind this jargon? David Sedley says these distinctions were drawn in response to Epicharmus’s growing argument:
There has been much recent debate about the nature and purpose of this theory, but I think that some of the mystery is dispelled once one sees that it originated at least partly in response to the Growing Argument. It is founded on the recognition that an ostensibly unitary object may under different descriptions have different and even incompatible things truly said of it. The insight was not in itself a new one, but Chrysippus’ scheme is the first attempt to derive from it a formal classification of the levels of description available.
(Sedley 1982, 259-60)
Sedley interprets Chrysippus as a relativist about identity: the debtor is identical to both a lump of matter and a man. As a specific lump of matter, the debtor does not persist through growth. But as a man, the debtor does persist. The relativist about identity believes that “Is x the same as y?” is meaningless; we can only ask “Is x the same F as y?” Under this view, many things can simultaneously exist in the same spot.
The relativist’s strategy presupposes that we can reidentify individuals in terms of their qualities. The debtor’s quality of being a man is not specific enough to do the job. We need a quality peculiar to the debtor. Yet the quality must be general enough to cover him for an entire lifetime. The debtor’s hair color, shape, and size change over time, so these cannot be the peculiar quality. One might try a psychological quality like having the same memories. But even if this solution worked for the debtor, it would not extend to inanimate things.
The debtor might be unique in being the only man to have four uncles who fought in Ionia. But this distinction cannot be the basis of the debtor’s identity. He would still exist if someone else had four uncles who had fought in Ionia. The property of having four uncles who fought in Ionia belongs to Chrysippus’s fourth level of existence, of being “relatively disposed.”
Chrysippus’s search for peculiar qualities is further complicated by a doctrine introduced by the founder of Stoicism. Zeno of Citium responded to skepticism by insisting that some truths are infallibly known. If your mother approaches you in broad daylight, you know she is your mother. Chrysippus took this to mean that your mother has an unchanging peculiar property that allows you to re-cognize her.
The skeptics denied that you can know that your mother is present simply by virtue of looking at her in good light. You cannot rule out the possibility that your mother has a duplicate. Perseus once refuted the Stoic Ariston by inducing one of a pair of twins to deposit money with Ariston and afterward having the other twin reclaim it.
One may doubt that any quality is necessarily peculiar to an individual. If one individual has a quality, what prevents another individual from having the same quality? Consider two planks that are exactly alike except one is painted green. The principle that distinct things must have distinct properties will not stop us from painting the other plank green!
Chrysippus’s reaction to the growing argument was not limited to the defensive task of finding a solution. He realized that if he could formulate a variation of the paradox that did not involve growth, then the skeptics would have no grounds to blame the paradox on growth. The growing argument would no longer be a special embarrassment for Stoicism. Here is how Philo of Alexandria reports Chrysippus’s paradox:
Chrysippus, the most distinguished member of their school, in his work On the Growing (Argument), creates a freak of the following kind. Having first established that it is impossible for two peculiarly qualified individuals to occupy the same substance jointly, he says: “For the sake of argument, let one man be thought of as whole-limbed, the other as minus one foot. Let the whole-limbed one be called Dion, the defective one Theon. Then let one of Dion’s feet be amputated.” The question arises which one of them has perished, and his claim is that Theon is the stronger candidate. These are the words of a paradox-monger rather than of a speaker of truth. For how can it be that Theon, who has had no part chopped off, has been snatched away, while Dion, whose foot has been amputated, has not perished? “Necessarily,” says Chrysippus. “For Dion, the one whose foot has been cut off, has collapsed into the defective substance of Theon, and two peculiarly qualified individuals cannot occupy the same substrate. Therefore it is necessary that Dion remains while Theon has perished.”
(Long and Sedley 1987, 171–72)
Philo makes it seem as if Chrysippus conceded that there were two men already in the pre-amputated body and that the amputation crowds one of them out. The question given this interpretation is “Who goes and who stays?” But Chrysippus could not accept this interpretation because of his allegiance to the principle that two men cannot occupy the same body at the same time. Relativists about identity generally require that the colocated objects be of distinct sorts.
Michael Burke (1994) has recently advanced an argument for Chrysippus’s surprising conclusion. He does not claim to be using the same reasoning as Chrysippus. Burke’s reasoning is certainly different from the relativism about identity that Sedley attributes to Chrysippus. Burke thinks it is absurd that two things could be in the same place at the same time. Burke is not placated by the qualification that the sorts must be distinct. If x and y share all the same parts, then how could they fail to be of the same sort? Any property of x would be shared by y.
Following Aristotle, Burke thinks there is a hierarchy of substances. Once a mere collection of bricks is arranged into a patio, the mere collection no longer exists. The bricks that now compose the patio can no longer fall under the lower sort “mere collection of bricks” because it would be qualitatively identical with a patio. Since nothing would stop the collection of bricks from being a patio, it would be a patio rather than anything less than a patio. Higher substances dominate lower substances in the sense that their “persistence conditions” prevail. (Persistence conditions are rules for deciding whether an object survives a given change. A patio survives replacement of a brick but a set of bricks does not.) Burke thinks Theon is a lower substance than Dion because Theon has been defined as Dion’s body minus exactly one foot. Given the stipulated meaning, Theon would perish if another foot were removed.
The practice of applying the personal name Theon to a body part exacerbates our puzzlement; we tend to assume Theon names a man. But “Theon” only labels a large body part. Before the amputation, Theon can exist because it is the dominant substance in that region of space. But after the amputation, Theon would be colocated with Dion. Since Dion is a higher substance than Theon, the persistence conditions of the object are those of Dion rather than of Theon. Theon therefore collapses out of existence under the weight of Dion’s higher status.
As Burke sees it, the puzzles all turn on the premise that the same parts can constitute different sorts of things at the same time. These sorts have conflicting persistence conditions. Burke preempts this conflict by saying that there will always be a highest sort that dominates the others. Since an object is an instance of a sort only if it has the persistence conditions of that sort, the dominant sort forces the subordinate sort to pass out of existence when they would otherwise be exactly colocated.
Burke’s strategy also applies to a recent variation of the paradox that makes the rival substances exactly coincide spatially and historically. Allan Gibbard (1975) has us imagine that Goliath is a statue and Lumpl is a piece of clay that constitutes Goliath. A sculptor first fashions the top half of Goliath, then the bottom half. When he joins them, Goliath comes into existence and Lumpl comes into existence. After the clay dries, the sculptor becomes dissatisfied and smashes the sculpture—thereby simultaneously destroying Lumpl and Goliath. Burke’s solution is that only Goliath existed. The sort statue dominates the sort lump of clay.
Many philosophers regard Burke’s talk of dominant substances as a lapse back into Aristotelian metaphysics. They are egalitarian about sorts. This leaves them with a conflict when one thing falls under two sorts that have conflicting persistence conditions.
Michael Rea (1995) characterizes the growing argument, the Ship of Theseus, Dion and Theon, and Lumpl and Goliath as instances of a more general problem of material constitution. The problem is a conflict between five individually plausible but jointly inconsistent principles:
1.Existence Assumption. There is a whole F, and there are parts that compose it.
2.Essentialist Assumption. If the parts compose F, then the parts must have composed that F. Those parts are necessary and sufficient for that F to exist.
3.Principle of Alternative Compositional Possibilities. If the parts compose F, then F could have been composed of some different parts.
4.Identity Assumption. If x and y share all the same parts at the same time, then x = y.
5.The Necessity Assumption. If x = y, then it is a necessary truth that x = y.
Since the problem is composed of fill-in-the-blank sentences rather than complete propositions, the set of sentence schemas is a template for paradoxes rather than a paradox. If we substitute “man” for F and let x be Dion and y be Theon, then we get a paradox very similar to Chrysippus’s paradox. The propositions that conform to the schema are individually plausible but jointly inconsistent. Rea believes that the resulting paradoxes tend to be stronger than natural specimens: any solution to the paradoxes conforming to Rea’s scheme is a solution to the historical paradoxes but not vice versa.
Just as there is a common form to the paradoxes, there is a common form to their solution. To solve the paradox, one must refute at least one member of the set.
The nihilist rejects the existence assumption. Peter van Inwagen (1981) denies that Theon exists prior to the amputation on the grounds that arbitrary undetached body parts do not exist.
Actually van Inwagen goes much further. He denies that there are any nonliving complex things. He believes that there are only organisms and simple, indivisible things. There are babies but there are no baby carriages. Carriages are nonliving complex things. If they existed, we would fall into absurdities. Suppose Plato and Socrates each have a carriage and systematically swap each component. Does Socrates wind up with Plato’s carriage and Plato with Socrates’? Van Inwagen regards our tendency to give conflicting answers as evidence that complex material things are incoherent.
Van Inwagen does not go around correcting mothers who say that there are carriages. Just as astronomers see little harm in talking of sunrise (even though they believe the sun does not rise), van Inwagen sees little harm in talking of carriages (even though he thinks they are impossible).
Nihilists make no exception for organisms. Peter Unger (1980) argues that there are no men; there are only particles arranged in a manly way. Unger enforces this point with the “problem of the many.” From microphysics, we know that each object is a cloud of particles. Each cloud lacks a determinate boundary between the particles that are part of the cloud and the particles that are part of the cloud’s environment. Since there are many equally good candidates for being “the cloud,” either they are all clouds or none are clouds. Unger thinks it is more absurd that there are many clouds (as opposed to one cloud) and so concludes that there are no clouds.
Parmenides and Zeno are even more severe than Unger. They deny the possibility that there could be a plurality of simple things. According to Parmenides, there is exactly one simple thing.
The second assumption, essentialism, says that if a bunch of things manage to compose something, then they do it on their own. The feat of composition does not depend on anything external. Thus, one can figure out whether the parts constitute the F just by concentrating on them and ignoring everything else. Burke denies this principle. He says that the parts that constituted Theon stop making Theon when the amputation occurs. For although the subtraction of the foot leaves all of Theon’s parts intact, it does force Dion to occupy that exact region. Since man trumps body part, Theon is pushed out of existence.
The third assumption, the principle of alternative compositional possibilities, says that the same thing can be composed of different parts. We have already seen the debtor reject the third member of the set. This denial is known as mereological essentialism and has been espoused by Roderick Chisholm (1979, ch. 3). He thinks only Theon survives. Each part is essential, so Dion ceases to exist when he loses his foot. Practical interests are served by ignoring minor changes and talking as if Dion survives. But strictly speaking, the loss of even a molecule would end Dion. Notice that this theory does not help with cases of complete coincidence such as Lumpl and Goliath.
The fourth assumption, the identity principle, says that whatever has the same parts is the same thing. This principle is acceptable to four-dimensionalists only if temporal parts are included. According to four-dimensionalism, Theon-plus (Dion’s intact body) and Theon are space-time worms that completely overlap until the amputation. Theon-plus ceases at the amputation while Theon continues (since he does not require a foot). Dion himself is a larger space-time worm who converges with Theon after the amputation.
Four-dimensionalists do not have a complete solution to the problem of material constitution. They cannot find any difference between Lumpl and Goliath because they perfectly coincide. Sort-relativists are more comprehensive. They say Lumpl and Goliath peacefully coexist. They differ in whether they would continue to exist if they lost a little matter (Goliath would, Lumpl would not) and if their matter were drastically rearranged (Lumpl would, Goliath would not).
Even those who have no theoretical position on personal identity can have doubts about the identity principle. The slogan “Same parts, same object” will be rejected by anyone who thinks that an object can be permanently destroyed by being temporarily disassembled.
There are religious implications. Catholics believe that they will be resurrected on Judgment Day. Although our bodies will have disintergrated, God will gather up our scattered remains and reassemble us. Doubters have asked why a man who is assembled from Lazarus’s parts is Lazarus rather than a duplicate of Lazarus.
Incidentally, Thomas Aquinas showed that Catholics need to take the further step of not requiring God to use the very same parts in the reassembly process. If a cannibal baby grows up on a pure diet of human remains, then how is God to resurrect the pure cannibal on Judgment Day? There are not enough parts to go around. Aquinas’s solution permits the resurrector to use different particles than those originally composing the individual—just as long as the same kind of matter is employed.
Aquinas’s liberalism is also required by Star Trek fans who want character continuity. Most of the crew contentedly use the transporter. It disassembles you and almost instantly reassembles you at another location. Or does it just kill you and make a duplicate? Suppose the teletransporter malfunctions: you learn that the machine successfully created an exact copy of you at the destination but failed to disassemble the original. You are asked to push the override button to remedy the omission. Should you push?
Some readers may comfort themselves with the thought that these paradoxes only arise for science fiction scenarios and in the fever of religious speculation. We are not surprised when common sense falters in strange circumstances.
However, this view of common sense needs to be qualified. For common sense is sometimes confounded by familiar situations that are of practical significance. The Ship of Theseus shows that common sense is sometimes embarrassed by completely ordinary transitions.
And let’s be fair: common sense also performs well in some strange circumstances (holding still for dental surgery, flying in a plane, etc.). The nature of common sense is not itself common sense. We should be braced for surprises about how well it performs.
Common sense has undesigned strengths for the same reason our eyes do. Although our eyes evolved for terrestrial viewing, they work well on the moon and for seeing distant stars. This is because simple solutions tend to be general solutions. Our eyes can see far more than they were designed to see and our common sense can accurately judge far more than it was designed to judge.
The fifth and final assumption of the puzzle of material constitution, the necessity of identity (if x = y, then necessarily x = y), is rejected by those who believe that identity can be contingent or even temporary. Gibbard solves his Lumpland Goliath problem by saying that Lumpl and Goliath happen to be identical. This answer seems refuted by the fact that Lumpl and Goliath have different hypothetical properties. Goliath could survive the loss of a finger and Lumpl could survive flattening. By the principle that identical things have identical properties, Goliath and Lumpl are distinct. Gibbard retorts that Lumpl and Goliath are contingently identical. He thinks necessity is by linguistic convention and that makes it a matter of psychological perspective. Goliath and Lumpl are the same thing that can be looked at in different ways. When viewing it as a statue, we allow that it could survive the loss of a finger but not flattening. When viewing it as a specific piece of clay, we allow that it could survive flattening but not the loss of a finger. Goliath would have been distinct from Lumpl if it had been formed from different clay.
For many years, philosophers believed that the contingency of some identity statements followed from the fact that scientists have empirically discovered “Water is H2O” and “Lightning is an electrical discharge in the atmosphere.” If it is merely a matter of an empirical fact that these identity statements are true, then couldn’t they have been false?
The contingency of identity was important for philosophers who believed that the mind is identical to the brain. They were familiar with an old argument against contingent identity: If a = b, then b has all the properties that a has. Individual a has the property of being necessarily identical to a. Therefore, if a = b, then it is a necessary truth that a = b. They dismissed the argument as a sophism. After all, were there not empirical demonstrations of contingent identities such as “Water is H2O”?
InNaming and Necessity, Saul Kripke defended the little sophism as a decisive demonstration. He does not attempt to shore up the proof with extra premises. Kripke merely disinhibits our inferential mechanism by removing confusions and distractions. Nowadays, most philosophers agree with Kripke. Despite the enormous popularity of contingent identity in the 1950s, few philosophers would now accept Gibbard’s solution to the paradoxes of material constitution. His solution is too late!
Whether or not Chrysippus’s solution to the growing argument is correct, he did effectively thwart the attack on Stoicism launched by the Academy’s Skeptics. However, as we shall see in the next chapter, a leaner skeptical threat matured after Chrysippus’s death.