Aristotle’s Metaphysics has as its central theme an inquiry into how substance may be defined as a category of being. Aristotle defines substance as ultimate reality, in that substance does not belong to any other category of being, and in that substance is the category of being on which every other category of being is based. Aristotle also describes substance as an underlying reality, or as the substratum of all existing things. He describes substance as both formal and material reality, and discusses the relation between potentiality and actuality.

According to Aristotle, the being of any individual thing is primarily defined by what it is, i.e. by its substance. Substance is both essence (form) and substratum (matter), and may combine form and matter. Substance constitutes the reality of individual things. The substance of each individual thing is the particular nature of that thing. The substance of each individual thing is that which does not belong to other individual things, while the universal (principle or element) of an individual thing is that which belongs to many individual things.

Aristotle differentiates between three kinds of substances, according to whether or not change can occur in their actual or potential being. The first two kinds of substances are physical (or material), and are ‘movable’ or ‘changeable.’ These physical substances are capable of changing, or of being changed. They may be either: 1) perishable, or 2) imperishable (i.e. eternal). The third kind of substance is non-physical, non-material, eternal, ‘immovable,’ and 'unchangeable.' Non-material substances may include: 1) mathematical objects (such as numbers), and 2) Ideas.

The elements of a substance may be singular (one) or multiple (many). A simple substance may consist of only one element. A composite substance may consist of many elements. The same elements may be shared by many different kinds of things. However, Aristotle says that eternal substances do not consist of elements, because elements may not always be the same in a substance, and because elements may not exist eternally.

Aristotle discusses the causes, principles, and elements of substances. According to Aristotle, wisdom is knowledge of the causes and principles of things. Wisdom is a science of first principles, and all knowledge is of universals. Substances are particular things, while universal principles (elements, or attributes) are common to many things.

Aristotle explains that there are four kinds of causes of things: 1) the substance or essence of a thing (the formal cause), 2) the matter and subject of a thing (the material cause), 3) the source of 'motion' or change in a thing (the efficient cause), and 4) the purpose for which a thing has being (the final cause).

Aristotle maintains that to know the truth of a proposition is to know what causes that proposition to be true. The truth of a proposition may be caused by the truth of another proposition. The truest proposition may be the proposition which is always true. The truest proposition may also be the proposition which causes other propositions to be true, and which does not depend on the truth of other propositions.

To make a true statement is to say of what is, that it is, or to say of what is not, that it is not. To make a false statement is to say of what is not, that it is, or to say of what is, that it is not.

According to Aristotle, ‘that which is’ cannot simultaneously be ‘that which is not.’ Being and non-being (or existence and non-existence) cannot be predicated of the same subject at the same time in the same respect.

Although a proposition may potentially be either true or false, it cannot be both true and false at the same time in the same respect. A proposition may appear to be true, and yet may be false. A proposition may appear to be false, and yet may be true.

If a proposition is not necessarily false, then it may possibly be true. If a proposition is not necessarily true, than it may possibly be false. A proposition which is necessarily true cannot possibly be false. A proposition which is necessarily false cannot possibly be true.

The appearance of something may differ from the true reality of that thing. Moreover, the appearance of something may be relative to the position of an observer, and may depend on the opinions and attitudes of the observer. Things may not appear the same to everyone, and may have contradictory appearances.

Aristotle claims that the causes of things are not infinite, and that there must be a first cause, or a first principle of all things. All things may have the same first cause, or may have the same things as their first causes.

Causes may be potential or actual, necessary or accidental. Things may be classified as prior or posterior to other things, in terms of their potentiality and actuality.

According to Aristotle, a change must occur in something for its potentiality to become an actuality. The potentiality of something may include its capability to change, or its capability to be changed, or both. Potentiality may be innate or acquired, actual or non-actual. The potentiality of something may also be a capability to act or to be acted upon, to be active or passive.

The potentiality of a cause-and-effect relationship to occur between one thing and another thing may include the potentiality of an effect to be produced by a cause and the potentiality of a cause to produce an effect. Different effects may be produced by different causes, and different causes may produce different effects.

If something necessarily exists, then it cannot be other than it is, but must exist in the way that it does exist. Things which exist necessarily are not merely potentially existent, but must be actually existing things. The logically necessary existence of some things also provides a logical foundation for other (contingent) things to exist actually or potentially.

According to Aristotle, actuality is prior to potentiality, in that potentiality can only occur if there is some actually existing thing which is capable of becoming another thing. There must be an actual potentiality for an event to occur if its potentiality is to become an actuality.

Aristotle also says that eternal or imperishable things are prior in substance and in being to perishable things, because eternal things have no beginning or end. Non-eternal or perishable things have a beginning and an end.

Furthermore, essential causes and principles are prior to accidental causes and principles. Events cannot happen accidentally unless there are essential reasons or principles while allow them to happen that way.

Aristotle explains that while physics (or natural science) is concerned with things which are ‘movable’ or ‘changeable,’ metaphysics is concerned with things which are ‘immovable’ or ‘unchangeable.’ Metaphysics is a ‘first philosophy’ in that it is concerned with defining the nature of being, while the other branches of science and philosophy are concerned with defining the classes (genera and species) of being.

Aristotle. "Metaphysica," translated by W.D. Ross, in The Basic Works of Aristotle. Edited by Richard McKeon. New York: Random House, 1941.