# Identity

Another fundamental ontological notion you need to grasp before you start modelling is the ontological notion of identity. To start the discussion, let’s take a look at the picture below:

As you might know, that is Aphrodite of Milos, better known as the Venus de Milo, an ancient Greek statue and one of the most famous works of ancient Greek sculpture (Wikipedia). On the left side, it’s the statue’s current state, and on the right, it’s how it was supposably built. My question for you is: Do these pictures portrait the same individuals or different ones?. Is it the same statue that went through some changes or these changes destroyed the first individual (the statue with arms) and created a new one (the statue without arms)? If you think like most people, your answer would be: “Yes, they are the same individual.”. Now, what if the statue was broken into very little pieces, like in the picture below:

Would you say that these marble debris are still the statue? Somehow our intuition says no, right? These debris cannot be Venus anymore. But why do we say “Yes” to the first question and “No” to the second one? Because of our common sense identity principle for statue. An identity principle is a sort of function we use to distinguish two individuals. Let’s use the simplest example of all: the identity principle of sets. Two sets, A and B, are the same if, and only if, they have the same elements. Therefore, if A = {1,2} and B = {2,3} then A != B. So the identity of a set is defined by its members. Changing a member of a set changes the identity of the set. Now, let’s think about a more complicated example. Let’s say, the identity principle we adopt for people. Could we say that someone’s identity depends on their name? Or some sort of identification code, like the American ‘social security’, the Brazilian ‘CPF’ or the Italian ‘codice fiscale’? The answer is NO! These can’t be used as our identification function. And I’ll tell you why…

Let’s start with a Person’s name. Did you ever meet two folks with the very same name? I have. If you don’t believe, just go on Facebook and experiment search for common names of your country. I just searched for “João Carlos da Silva”, a fairly common Brazilian name, and I found at least 5 guys with that exact name. If name was our identity function, we would not be able to distinguish between them. Another problem with using name as identity is that often, people change their names. Our function needs to be not only able to distinguish two individuals in the same moment in time, but also through time. How else would we be able to meet someone today and recognize that same person tomorrow? So, our function needs to always return the same individual for a given input. Now, let’s analyze the reason why the social security number (SSN), the codice fiscale and the CPF are not very good identity principles for people. The answer is quite simple, our function needs to apply to everybody. If you are not American or never worked in the USA, you probably don’t have a SSN, right? Even young children born in the USA might not have. The last important fact about identity principle is that every individual must have exactly one. So, what is the identity principle for a person? One’s fingerprint, iris pattern, DNA? Well, it is really hard to define it, even though we know it is there.

What we can “touch” are what’s called the identity conditions. These are “parts” of the identity function, necessary conditions for identity but not sufficient by themselves. In order for me to consider A and B as the same Person they need to have the same birth date. And the statue need to be made of the same material. Why identity principles and conditions are important for us? Because by thinking about them we are guided in the construction of our types hierarchy. They impose constraints on how we can combine the different OntoUML constructs to design our conceptual models. Will talk about these constraints when we present the stereotypes usage. For now, just keep in mind that: Some types have the characteristic of providing identity principles for their instances. They are stereotype as: «Kind», «Collective», «Quantity», «Relator», «Mode» and «Quantity». Here are some examples:

Some other types don’t provide identity principle for their instances, but they all share a common one. They are stereotyped as: «Subkind», «Role» and «Phase». Here are some examples:

Some other types don’t provide identity and their instances follow different identity principles. They are stereotyped as: «RoleMixin», «Mixin» and «Category». Here are some examples: