Within the span of seven years, every cell of your body will die and be replaced—you literally are not the same person you once were. If this is the case, where lies our identity and psyche? Should we be held accountable for the actions of another body, or another mind? These questions, and many more, are contemplated in The Outer Limits of Reason (The MIT Press, 2013). Noson S. Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. In this excerpt from “Philosophical Conundrums,” Yanofsky references the Ship of Theseus before questioning the existence of personal identity.

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In ancient Greece, there was a legendary king named Theseus who supposedly founded the city of Athens. Since he fought many naval battles, the people of Athens dedicated a memorial in his honor by preserving his ship in the port. This “ship of Theseus” stayed there for hundreds of years. As time went on, some of the wooden planks of Theseus’ ship started rotting away. To keep the ship nice and complete, the rotting planks were replaced with new planks made of the same material. Here is the key question: If you replace one of the planks, is it still the same ship of Theseus? This question about a mythical ship is the poster child for one of the most interesting problems in all of philosophy, namely the problem of identity. What is a physical object? How do things stay the same even after they change? At what point does an object become different? When we talk about a certain object and say that “it changed,” what exactly is “it”?

What happens if you change two of the ship’s planks? Would that make it somehow less of the original ship than after one plank is changed? What if the ship consists of a hundred planks and forty-nine of the planks are changed? How about fifty-one changed planks? What about changing ninety-nine of the hundred planks? Is the single plank at the bottom of the ship enough to maintain the original lofty status of the ship? And what if all of the planks are changed? If the change is gradual, does the ship still maintain its status as the ship of Theseus? How gradual must the change be?

We are not answering these questions simply because there are no objective correct answers. Some maintain that changing one plank changes the ship and makes it no longer the ship of Theseus. Others claim that as long as there is at least one plank from the original, it is still the original. There are also those who maintain that the changed ship is always the same as the original ship because it has the form of the original. None of these different positions are wrong. However, there is no reason to say that any of them are correct either.

Let us continue asking more questions about our beleaguered boat. What happens if we switch the old wooden planks for more modern plastic planks? Then, as we change more and more of the planks, the ship will be made of a different material than the original. What happens if the people who replace the planks make mistakes in putting in the new planks and the ship has a slightly different form? Another question: Does it matter who is making all these changes to the ship—that is, whether one group of workers does it or another? If the ship is to be preserved for hundreds of years, then surely many different people will have to be making the changes. What if we make so many changes to the boat that it can no longer float out to sea? Can we still call it the ship of mighty Theseus if it cannot perform the same function as the original?

Such questions go on indefinitely. I will restrain myself and discuss just one more scenario. Imagine that every time a plank is changed, rather than consigning the old planks to the scrap heap, we store them in a warehouse. After some time, all the old planks are assembled into a ship. This new construction is made to look exactly like the old ship with the planks in their original position. Question: Which ship has the right to call itself the ship of Theseus, the ship with the replaced planks or the ship constructed out of the old planks?

A common answer to some of these questions is that the ship remains the same because the changes are gradual. However, it is not clear why that should make a difference. How gradual must the changes be in order for the original ship to maintain its status? Is there a minimum speed limit for changes? To put the question of what is “gradual” in perspective, consider the case of Washington’s ax. A certain museum wanted to preserve the ax of the founding father of the United States. The ax consists of two parts: a handle and a head. As time went on, the wooden handle would rot and the metal head would rust. When needed, each of these two parts was replaced. As the years passed, the head was changed four times and the handle was replaced three times. Is it still Washington’s ax? Notice that here there is no question of the change being gradual. Every time a change is made, half the parts of the ax are replaced.

Our discussion is not limited to ships and axes. A tree is lush and green in the summer and bare and brown during the winter. Mountains rise and fall. Cars and computers get refurbished. Any physical object changes over time. This is the content of Heraclitus’ famous dictum that you cannot step into the same river twice. For Heraclitus, the river changes at every instant.

Physical objects are not the only things that change. Businesses, institutions, and organizations are also dynamic entities that constantly change and evolve. Barings Bank was in existence from 1762 through 1995. In that time, the owners, workers, and customers all changed. The Brooklyn Dodgers have been around since 1883. Their players, managers, owners, and fans have definitely changed. What remains the same about a baseball team? After heartlessly betraying their city of birth, the Dodgers cannot even claim that they play in the same city as they originally did. In colleges, the students change every four years. Even the professors change over the years. The only real heart and soul of a college are the beloved secretaries. But, alas, even they change. Political parties are also not immune to change. The Democratic Party was founded in the 1790s to support states’ rights over federal rights, the opposite of their current platform. Everything changes!

We are not only talking about change. Rather, we are discussing what it means for an object to be that object. What does it mean for a certain institution to be that institution? When we say that a certain object changes, we mean that it had a certain property beforehand and after the change it does not. In the beginning, the ship of Theseus had planks that Theseus himself touched. At the end, there were planks that he did not touch. That is a change in the properties of the ship. Our fundamental question is: What are the core properties of the ship of Theseus? We have shown that there are no clear answers to this question.

This discussion becomes far more interesting when we stop talking about ancient ships and start talking about human beings. Every person changes over time. We grow from infants to old people. What properties does a three-year-old have in common with their eighty-three-year-old self? These philosophical questions are called the problems of personal identity. What are the properties that make up a particular human being? We are not the same person we were several years ago. Nevertheless, we are still considered the same person.

Philosophers usually fall into one of several camps on this question. Some thinkers push the notion that a person is essentially their body. We each have different bodies and can say that every person is identified with their body. By postulating that a human being is their body, we are subject to the same insoluble questions that we faced with the ship of Theseus and other physical objects. Our bodies are in constant flux. Old cells die and new cells are constantly being born. In fact, most of the cells in our body are replaced every seven years. This leads to hundreds of questions that philosophers have posed over the centuries. Why should a person stay in jail after seven years? After all, “he” did not perform the crime. It was someone else. Should a person own anything after seven years? The old person bought it. In what sense is a person the same after having a limb amputated? Science fiction writers are adept at discussing challenging questions like cloning, mind transfers, identical twins, conjoined twins, and other interesting topics related to the notion that a person is the same as their body. When an ameba splits, which is the original and which is the daughter? When your body loses cells it loses atoms. These atoms can go on to belong to others. Similarly, other peoples’ atoms can become part of your body. What about death? We usually think in terms of the end of a person’s existence when they are dead even though the body is still there. Sometimes we use sentences like “She is buried there” as if “she” were still a person. And sometimes we use sentences like “His body is buried there” as if there is a difference between “him” and his body. In short, it is problematic to say that a human being is identified with their body.

Other thinkers favor the notion that a person is really their mental state or psyche. After all, human beings are not simply their bodies. A person is more than a physical object because there is thought. To such philosophers, a person is a continuous stream of consciousness—they are memories, intentions, thoughts, and desires. This leads us to ask other insoluble questions: What if a person has amnesia? Are they the same person? Doesn’t a person’s personality change over time? Who is the real you: the one who is madly in love with someone or the one who is bored with the same person two months later? Literally hundreds of questions can be posed about change in a person’s thoughts, memories, and desires. Again, philosophers and science fiction writers have become quite adept at describing interesting scenarios that challenge our notion of a human being as a continuous stream of mental states. These scenarios are concerned with Alzheimer’s disease, amnesia, personality changes, split-brain experiments, multiple personality disorders, computers as minds, and so on. There are also many questions along the lines of the mind-body problem. How much is the mind—that characterizes a human being— independent of the brain, which is a part of the body?

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One of the more interesting challenges to the position that continuity of mental states characterizes a human being is the question of transitivity of identity. My mental states are essentially the same as they were ten years ago. That means I am the same person I was ten years ago. Furthermore, ten years ago, my mental states were essentially the same as they were ten years earlier. Hence the person I was ten years ago is the same as the person I was twenty years ago. However, at present, I do not have similar mental states to those I had twenty years ago. So how can it be that I am the same person I was ten years ago, and that person is the same as I was twenty years ago, but I am not the same as I was twenty years ago?

Yet another option is that everyone has a unique soul that determines who they are. Avoiding the questions of the definition or existence of a soul, let us concentrate instead on how this answers our question of the essential nature of a human being. Assuming the existence of a soul, what is the relationship between the soul and the body? What is the relationship between a soul and a person’s actions, psyche, and personality? If there is no connection, then in what sense is one soul different from another soul?

How can you differentiate between souls—or identities, for that matter—if they have no influence over any part of you? What would the purpose of an identity be? If, on the other hand, a connection exists, then does the identity change when the body, actions, psyche, or personality changes? Is the soul in flux? If the identity does change, we are back to the same questions we had previously asked: Who is the real you? Are you the one with the soul prior to the change or are you the one with the changed soul?

Most people probably have an opinion representing some hybrid version of all three ideologies: a person is a composite of body, mind, and soul. Nevertheless, all schools of thought are somewhat problematic.

Rather than answering all the questions posed in this section, let us try to resolve the issues by meditating on why none of the questions have clearcut answers. Why is it that when we pose these questions to different people, we get so many different answers?

Examine the way people learn to recognize different objects, make definitions, and create distinctions. In the beginning, babies are bombarded with many different sensations and stimuli. As toddlers grow, they learn to recognize objects in the world. For example, when they see a shiny silver thing covered with brown gooey stuff coming toward them, they have to learn that it is applesauce on a spoon and that they should open their mouth. By learning to recognize that the physical stimulus of silver covered with brown gooey stuff is applesauce, they are able to handle life better. Human beings need to classify objects. We learn how to tell things apart and determine when they are the same. We learn that an object still exists even when it is out of sight (“object permanence”). Children learn after a while to recognize their mother. A few months later, they learn that even though she is wearing makeup—that is, even when she looks different— she is still the same person. Children have to learn that their mother is the same even when she is wearing perfume and smells totally different. Here toddlers are acting as philosophers and learning how to deal with different questions of personal identity. With all these skills, children are imposing order and structure on the complicated world they have entered. Before these skills are mastered, they are showered with an incomprehensible stream of stimuli and sensations. With these classification abilities the children can comprehend and start to control their environment. If they fail to learn the classification skills, they will be overburdened with external stimuli and unable to deal with their surroundings.

With enough sophistication, children also learn to classify abstract entities. For example, they might learn what it means to be a family. Their mother is a family member. Their father and siblings are also part of the family. What about first cousins? Second cousins? These are a little vague. Sometimes they are part of the family, and sometimes not. Children must learn what is a family and what is not. As they grow, they learn to classify even more abstract entities like numbers and political parties.

Not only do children learn to classify objects and people, they also learn to name them. They realize that they live in a society of other classifiers, and in order to communicate with these compulsive classifiers, they follow their example of giving names to objects. They first give the external stimuli their own names. As their communication skills progress, they learn to forgo their names and start to use other people’s nomenclature for objects. They call brown gooey stuff “applesauce.” They learn to call the woman who takes care of them “mom,” regardless of her wearing makeup or not. By using the same names as others, children are showing society that they are conforming to the prevailing classification system and that their mental processes are similar to those of others. Society then rewards them by showering them with love and providing the protection they need.

The point is that classifying and naming are learned skills. Children do not learn exact definitions of things because they are never exposed to exact definitions. They learn to classify and name physical stimuli. Some notions are exact and unchanging. The concept of the number 4 is exact and has a clear definition. In contrast, many other notions lack sharp definitions. The first part of this section shows that even physical objects do not have sharp definitions.

With this in mind, we can discuss the many questions posed at the beginning of the section. Is the ship of Theseus the same after changing one plank? The proper response is that the definition we have for the ship is not clear enough to provide an answer to that question. There is no exact definition of the ship of Theseus. We only have what we learned—that is, the stimuli we were taught to associate with the ship.

The ship of Theseus does not really exist as the ship of Theseus. There is no exact definition of what is meant by the ship of Theseus. It exists as a collection of sensations but not as an object. Yes, if you kick it you will feel pain in your toes. When you look at it, you will see brown wood. If you lick it, you will taste stale wood and salt water. But these are all just sensations that one learns to associate with something we call the “ship of Theseus.” Human beings combine these sensations and form the ship of Theseus. Of course, the ship exists as atoms. But it is made of atoms as atoms. The atoms are not tagged as the ship’s atoms. Rather, it is we who make those atoms into a whole entity called a ship. It is we who further demarcate this ship as somehow belonging to the mythical general Theseus. The first part of this section cited many examples demonstrating how the ship can lose and change atoms and still be the same ship. It’s all in our mind. We are fortunate to live among other people who learned to give the same names to commonly occurring external stimuli. Each of us calls these similar stimuli the “ship of Theseus.” Since we all agree with this naming convention, we do not commit each other to insane asylums. Nevertheless, the existence of the ship of Theseus is an illusion.

Reprinted with permission from The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us by Noson S. Yanofsky and published by The MIT Press, 2013.