Examples of Various Middle Terms in Posterior Analytics II, 11

Formal Cause

Not illustrated by Aristotle; presumed as evident from previous chapters. Recall the eclipse syllogism:

All B is A What has light blocked by the earth cannot cast shadows.
All C is B. The moon has its light blocked by the earth.
All C is A. The moon has a failure to cast shadows.

Material Cause

All B is A Angle in semicircle is one half of two right angles.
All C is B Being one half of two right angles is being a right angle.
All C is A Angle in semicircle is right angle.
B (being one half of two right angles) is the material cause of A's (the angle in the semicircle) being C (a right angle). (The middle term is the essence of one or the other of the two terms A or C, but Barnes thinks the text leaves it unclear which.)

Efficient Cause

C is B. The aggressor is warred upon
B is A. The Athenians are the aggressor.
C is A. The Athenians are warred upon.
Here, B (being an aggressor) is the efficient cause of C's being A (of why Athens is warred upon). There was an efficient cause for this--Athens' attack on Persia. Problem: Not a real demonstration (contingent, singular). Barnes' example:
All ducks have webbed feet. C is B
All things with webbed feet are good swimmers and waders. B is A
All ducks are good swimmers and waders. C is A.
Here, Barnes says, "having webbed feet explains why ducks are good swimmers; and the webbing is (ppart of) the efficient expplanation of their swimming prowess." (pp. 229) But is having webbed feet a necessary fact about ducks?

Final Cause

(Barnes calls this section "miserably obscure", p. 229). Aristotle's first example is very sketchy but suggests we are trying to give a final cause of why C is A where this means "He walks," and the middle term should be "health". So we would get:
C is B He is healthy (i.e. he aims at health).
B is A. Healthy is walking. (i.e. health is produced by walking)
C is A. He is walking.
This seems to be Aristotle's later example:
C is B. Walking about means foodstuffs' not remaining on the surface.
B is A. Foodstuffs' not remaining on the surface is healthy.
C is A. Walking about after dinner is healthy.
The idea is supposed to be that the middle term (foodstuffs' not remaining on the surface) is the final cause of C's (walking) having A (being healthy). But this seems wrong: the foodstuffs' behavior CAUSES health in an efficient sense, and health is the final cause of walking. The house example, in Barnes' extrapolation (p. 231):
C is B. Shelters for belongings are roofed.
B is A. Houses are shelters for belonging.
C is B. Houses are roofed.

Multiple Explanations

Example 1.
Why does the light shine from the lantern?

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