< p > Identity is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from entities of a different type (effectively, whatever makes something the same or different). Thus, according to Leibniz, if some object x is identical to some object y, then any property that x has, y will have as well, and vice versa (otherwise, by definition, they would not be identical).

< p > Aristotle's Law of Identity (or the Axiom of Identity) states that to exist, an existent (i.e. an entity that exists) must have a particular identity. A thing cannot exist without existing as something, otherwise it would be nothing and it would not exist. Also, to have an identity means to have a single identity: an object cannot have two identities at the same time or in the same respect. The concept of identity is important because it makes explicit that reality has a definite nature, which makes it knowable and, since it exists in a particular way, it has no contradictions (when two ideas each make the other impossible).

< p > Change is the alteration of identities, whether it be a stone falling to earth or a log burning to ash. For something to change (which is an effect), it needs to be acted on (caused) by a previous action. Causality is the law that states that each cause has a specific effect, and that this effect is dependent on the initial identities of the agents involved.

< p > We are intuitively aware of change occurring over time (e.g. a tree loses a leaf). The Ancient Greeks took some extreme positions on the nature of change: Parmenides denied that change occurs at all, while Heraclitus thought change was ubiquitous.

< p > Currently there are three main theories which deal with the problem of change:

< p > Mereological Essentialism assumes that an object's parts are essential to it, and therefore that an object cannot persist through any change of its parts.
Perdurantism holds that objects are effectively 4-dimensional entities made up of a series of temporal parts like the frames of a movie (it treats the tree, then, as a series of tree-stages).
Endurantism, on the other hand, holds that a whole object - and the same object - exists at each moment of its history, (so that the same tree persists regardless of how many leaves it loses).