We change and evolve throughout our lives, physically and mentally. We grow larger and then wrinkly. We grow smarter and then lose some of our intelligence in old age. In spite of all these changes, how is it that we still can talk about the life of a single person? How is it that someone maintains personal identity over many different kinds of changes?
First, let’s clarify what we mean when we say “identity”. On the one hand, someone might use the term to talk about qualitative identity, meaning that two things share all the same properties or qualities. For example, two newly minted coins may have the same weight, color and designs. On the other hand, someone might use this term to talk about numerical identity, which means that two things really are just one in the same thing. In qualitative identity, we can have several individual objects that share the same properties. Numerical identity, however, requires that there is only one actual thing. For example, Batman is numerically identical with Bruce Wayne. Clark Kent is numerically identical to Superman. Lady Gaga is numerically identical to Stefani Germanotta.
Numerical identity is the kind of identity that we talk about when we discuss personal identity. When discussing numerical identity (also known as strict identity), we can talk about something being identical to itself either at the same time (synchronically) or across time (diachronically). For example, we can talk about me being the same person as myself right now and we can also talk about me being the same person as who I was when I was six years old in Minnesota.
The problem of personal identity is the question of what criteria someone has to share across time in order to stay the same person. In other words, what must stay the same about a person in order for him or her to be numerically identical with his or her former self? In fancy philosopher talk: What are the necessary and sufficient conditions of diachronic personal identity?