One approach is to say that the changes that a person undergoes are very gradual. As long as a certain proportion of a person stays the same, then identity is maintained. For example, if only five percent of a person’s mental and physical properties change, then personal numerical identity is maintained. This sort of notion conflicts with the transitive view of identity. Consider the following formulas that express identity, or equivalence:
Transitive Identity: if A = B and B = C, then A = C
Symmetry: if A = B then B= A
Reflexivity: A = A
Now, consider that we say that an organism can change just 5% in order to maintain numerical identity. A changes 5% to turn into B. So A = B. Say that this organism continues to change another 5%, from B to C. By the transitive identity equation, A = C. However, this violates our original condition that an organism can only change a net 5% in order to maintain numerical identity. Because identity is transitive, we cannot limit the amount of change that an organism can undergo in order to maintain personal identity.
Other Proposed Solutions to the Problem of Personal Identity.
The Body Criterion: Sammy the 5 year old and Sam the adult are the same person if and only if Sammy’s child body is the same as Sam’s adult body. There are obvious problems with this, given that our bodies change so much throughout our lives. Without going into detail, Sven indicates that philosophers are able to give us more complex versions of this that do not seem so silly. A benefit to this view is that we often do actually judge someone to be identical to himself or herself based on his or her body.
The Biological Criterion. Katie the infant is the same person as Katherine the adult if and only if the infant Katie has a biological organism that is continuous with the biological organism of Katherine the adult.
Narrative Identity Criterion. What makes an experience a person’s ( a part of that person’s identity) is that it is incorporated into the person’s self-told story of his or her life. For example, Max’s drunken rampage where he vandalized a police station is only part of his identity if he actually remembers it and it is part of the narrative that he tells about his own life.
Psychological Criterion. Ruthie the baby is the same person as Ruth the Supreme Court Justice is and only if Ruthie the baby is uniquely psychologically continuous with Ruth the Supreme Court Justice.
Memory Criterion. Toddler Stefani is the same person as Lady Gaga if and only if (a) Lady Gaga remembers being toddler Stefani, (b) Lady Gaga’s ability to remember that is based on actual recollection (not fabrication of memories) and (c), no other being satisfies conditions (a) and (b). This is a more refined version of the psychological criterion. Simply put, I am the same as myself ten years ago because I can remember myself ten years ago. An advantage to the memory criterion is that memories can withstand physical changes. Also, it seems to be how we identify ourselves.
Transplant Intuition. Locke imagines that the mind of a prince is put into the body of a cobbler when the cobbler dies. Locke says that the organism that is the cobbler’s body and the prince’s soul is the same person (is numerically identical to) the prince. This so-called “transplant intuition” is the main motivation behind the psychological approach to personal identity. Pop culture examples include the TV show Dollhouse or the movies Total Recall and Freaky Friday.
John Locke thinks that we identify ourselves as our consciousness. Because our consciousness can extend back in time, or because it is in principle possible that we can remember things that happened a long time ago, we can rightfully say that we are identical to our past selves. In other words, he thinks that the limits of our conscious memories are the limits of our personal identity. A result of this view is that things that we cannot, in principle, remember are not parts of our personal identity.
In short, in order for you to be the same person as you were on the weekend, you must remember in an autobiographical way what happened to you then. To remember something autobiographically is to remember not just what happened but also what context you were in when things happened. For example, it isn’t’ enough that I remember that I watched the Superbowl on Sunday in order for me to be the same person as I was on Sunday. Rather, I also have to remember where I was, what I did and what my experiences were like.