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Source: The Four Causes by Univ. of Washington Prof S. Marc Cohen PhD in Philosophy (Cornell).

I Import from Ancient Greek aition (plural aitia), to avoid the polysemous noun 'cause'.

The picture is Aristotle’s, but the names of the causes are not.
Quotations from Physics II.3, 194b24 ff:

1. Material cause: “that from which, present in it, a thing comes to be … e.g., the bronze and silver, and their genera, are causes of the statue and the bowl.”
2. Formal cause: “the form, i.e., the pattern … the form is the account of the essence … and the parts of the account.”

Please aid me to distinguish 1 and 2. The following examples fail, because their attempted distinctions can be eliminated by my rewriting them below to exemplify the other aition.

Aristotle’s point may be put this way: if we ask “what makes something so-and-so?” we can give four very different sorts of answer - each appropriate to a different sense of “makes.” Consider the following sentences: ...

✓ 1b. [Material Aition:] Wood is what the table is made out of.

✘ 1c. [Now Formal:] four legs and a flat top are what the table is made out of

✓ 2b. [Formal Aition:] Having four legs and a flat top is what it is to be a table.

✘ 1c. [Now Material:] Four legs and a flat top are what the table is made out of

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    FYI, Perseus Project entry on aitia ... If there's a Greek term and you want more context for it, the Perseus Project is usually a good bet. – James Kingsbery Apr 15 '15 at 19:44
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    The wood is the material causes : the table is "made of" wood; the formal cause is the "shape" imposed to the wood (the same piece of wood can receive the shape of a table or the shape of a chair); the efficient cause is the sculptor; the final cause is its "function" : to be used as a support for eat or write. – Mauro ALLEGRANZA Apr 15 '15 at 19:57
  • @JamesKingsbery: αἴτιος is where we get the English word "etiology" – Geremia Apr 17 '15 at 3:58
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Aristotle discovered hylemorphism to reconcile the reality of change with the stability of being. Previously, the Parmenideans, on one hand, held that (a) nothing changes and that change is an illusion, but (b) that the principle of non-contradiction is true—in accordance with the Latinized dictum ex nihilo nihil fit ("out of nothing nothing can be [made]"), i.e., that being cannot come from non-being. On the other hand, the Heraclitians denied (a) the existence of stable beings, thinking everything changes, but (b) affirmed the multiplicity of beings against the monist Parmenideans.

St. Thomas Aquinas, in his opusculum (short work) De Principiis Naturæ (cf. Joseph Kenny, O.P.'s Philosophy of Nautre: Let Thomas Aquinas Teach It for a good introduction / background), states:

[T]hat which is in potency to substantial existence and that which is in potency to accidental existence can be called matter: for example sperm is the matter of man [since sperm is potentially the substance of a man] and man is the matter of whiteness [since man is potentially white].

and

[J]ust as everything which is in potency can be called matter, so also everything from which something has existence whether that existence be substantial or accidental, can be called form; for example man, since he is white in potency, becomes actually white through whiteness, and sperm, since it is man in potency, becomes actually man through the soul.

So, matter is to form as essence is to existence.

Cf. another opusculum by St. Thomas, his famous De Ente et Essentia (On Being and Essence). He discusses the higher order of essence and existence with respect to that of matter and form; to give a foretaste:

essence includes matter and form.

and

neither can it be said that essence signifies some relation between matter and form or something added to them, because this would of necessity be an accident or something extraneous to the real thing, and the real thing would not be known through it. And these are traits of essence. For through the form, which is the actuality of matter, matter becomes something actual and something individual. Whence what supervenes does not confer on matter actual existence simply, but such an actual existence; as accidents in fact do. Whiteness, for example, makes something actually white. Whence the acquisition of such a form is not called generation simply, but generation in a certain respect. It remains, therefore, that the word “essence” in composed substances signifies that which is composed of matter and form.

Since the real distinction between potentiality and actuality is a foundational thesis of Thomism (cf. Thesis #1 of the 24 Thomistic Theses), you'll find Thomists explaining formal vs. material causes very well:

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There is this related in Metaphysics:

It is clear that we must obtain knowledge of the primary causes, because it is when we think that we understand its primary cause that we claim to know each particular thing. Now there are four recognized kinds of cause. Of these we hold that one is the essence or essential nature of the thing (since the "reason why" of a thing is ultimately reducible to its formula, and the ultimate "reason why" is a cause and principle); another is the matter or substrate; the third is the source of motion; and the fourth is the cause which is opposite to this, namely the purpose or "good";for this is the end of every generative or motive process. We have investigated these sufficiently in the Physics4;

This is a paraphrase, and I think a more useful one than the one you cited above. In particular, we have the material cause is what the thing is made out of (this seems pretty straightforward), but the formal cause is the "essential nature of the thing."

An analogy would be the difference between a builder's building materials and the blue-print. Both are needed to create a building, but the materials are (obviously) the material cause, whereas the blue-print provides the form that the building will take (and is the formal cause).

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