Pre-Socratic, Plato and Aristotle Metaphysics

Plato's four cardinal virtues

In Plato's Republic, the four cardinal virtues are wisdom (sophia), courage (andreia), moderation (sophrosyne) and justice (dikaiosyne). Each virtue is tied to a part of the soul or a class of the city. Wisdom belongs to the rational part and to the guardians, courage to the spirited part and to the auxiliaries, and moderation is the agreement of the parts about who should rule. Justice is the virtue by which each part performs its own proper function without interfering with the others. Autonomy, the idea of self-legislation associated with Kant, is a modern concept and does not appear in Plato's list.

Moderation requires special attention because it is easy to confuse with courage or self-restraint alone. For Plato, moderation is harmony and agreement among the parts of the city on who should rule, so that each class accepts its proper place. Because this agreement is a property of the whole community, moderation is found throughout the republic, among guardians, auxiliaries and producers alike, and not in one class only.

• cardinal virtue — a principal virtue on which the other virtues depend. Example: Justice is treated by Plato as the cardinal virtue that holds the others in order.
• sophrosyne — moderation or self-control, understood as harmony and agreement among parts. Example: A city in which all classes agree on who rules shows sophrosyne as a whole.

Heraclitus and Parmenides on change and being

Heraclitus holds that the world is in constant flux, so that nothing remains the same across time. Beneath this plurality of changing things, however, he posits a unifying principle, the logos, which is often associated with fire. The unity he affirms is therefore a unity that underlies the many, not a denial of the many.

Parmenides takes the opposite route. He argues that what is must be one, whole, unchanging and eternal, because what is cannot come into being or pass away. Change and plurality are therefore treated as illusory appearances, and non-being cannot be thought or spoken of. The contrast with Heraclitus is that one affirms unity beneath change, while the other denies the reality of change and plurality altogether.

In Parmenides, the verb 'is' designates being in its totality, which is a unique, perfect and complete whole. It does not designate something infinite and ever changing, nor something transformative or dynamic, since these are attributes of becoming, which Parmenides rejects.

• logos (Heraclitus) — the unifying principle or measure that governs the flux of things.
• to eon (Parmenides) — what is, being as one, whole, unchanging and eternal.

Aristotle's categories

Aristotle's categories are the most general kinds of predicates that can be said of things. Substance (ousia) is the primary category and is the most basic kind of being. A primary substance is an individual that is neither said of a subject nor present in a subject, such as a particular person or horse. A secondary substance is a species or genus, which is said of primary substances and tells us what kind of thing they are. The other categories, including quantity, quality and relation, describe attributes of a substance and do not express its kind.

A sentence of the form 'X is a Y' places an individual under a kind, so it is an assertion about substance. For example, 'Plato is a philosopher' tells us the kind to which Plato belongs. By contrast, a predicate such as 'greater than' expresses relation, a predicate such as a colour expresses quality, and a predicate of amount expresses quantity.

When a demonstrative picks out an individual, as in 'this is a horse', the word 'this' refers to a particular, which is a primary substance. The word 'horse' is a universal, and it functions as a secondary substance that classifies the particular without being the particular itself.

• primary substance — an individual thing, such as 'this horse'. Example: 'This tree is tall' predicates height of a primary substance.
• secondary substance — a species or genus predicated of individuals. Example: 'Tree' is a secondary substance.

Plato's divided line

In Book VI of the Republic, Plato divides reality and knowledge into a line with two main sections, the visible and the intelligible, and each section is divided again. The visible realm contains eikasia (imagination), which grasps shadows and reflections, and pistis (belief), which grasps physical objects. The intelligible realm contains dianoia (thought or reasoning) and noesis (understanding).

Mathematical objects such as figures and numbers are placed in dianoia. In this lower division of the intelligible realm, the mind reasons from hypotheses and uses visible diagrams as images, so it does not yet reach the first principle. Noesis, the highest level, is reached through dialectic, in which the mind grasps the Forms themselves and proceeds to an unhypothetical first principle.

• dianoia — discursive reasoning from hypotheses, typical of mathematics.
• noesis — direct intellectual grasp of the Forms.
• pistis — belief about visible physical things.

Democritus atomism

Democritus holds that reality consists of only two things, atoms and void. Atoms are solid, full, indivisible and indestructible, and they have shape, size, arrangement and position. All compound things arise from the combination, separation and rearrangement of atoms in the void. Because atoms differ in shape and arrangement, the variety of things is explained without any additional principle.

Atoms are never at rest. They move perpetually through the void, and their collisions and aggregations produce the things we perceive. Since the cosmos arises from this atomic motion governed by necessity, the cosmos possesses an underlying lawful order. Atomic motion is therefore neither random nor without pattern.

• atom (atomos, 'uncuttable') — the smallest indivisible unit of matter. Example: A stone and a drop of water differ only in the shapes and arrangements of their atoms.
• void — the empty space in which atoms move.

Aristotle's four causes

In Physics II, Aristotle distinguishes four ways of answering the question 'why' about a thing. The material cause is that out of which a thing comes to be, the efficient cause is the source of the change or making, the formal cause is the form or definition of the thing, and the final cause is that for the sake of which it is made. A single thing can therefore have several causes, each answering a different kind of why-question.

Take a wooden table as an example. The wood is the material cause, the carpenter is the efficient cause, the shape and design of a table is the formal cause, and its use for eating is the final cause. The plan to install a thing for a purpose belongs to the final cause, since it states the end.