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Classical physics: *
Aristotle refers to the 4 causes in his Physics.
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Material cause: an object's motion will behave in different ways depending on the substance from which it is made (eg clay, steel)
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Formal cause: an object's motion will behave in different ways depending on its material arrangement or shape (eg a clay sphere, a clay block)
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Efficient cause: that which caused the object to come into being; an "agent of change" or an "agent of movement".
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Final cause: the reason that caused the object to be brought into existence.
Of these only the 3rd, the efficient cause, may sometimes, but not always, be described in terms of quantitative force. The action of an artist on a block of clay, for instance, can be described in terms of how many pounds of pressure per square inch is exerted on it. The efficient causality of the teacher in directing the activity of the artist, however, cannot be so described. The final cause acts on the agent to influence or induce her to act. So if the artist works "to make money," making money is the cause of her action, but this cannot be described as a quantitative force. The causality of the final cause cannot be reduced to efficient causality, much less to the mode of efficient causality we call "force."