1170a14-b19. Since some of the pro-syllogisms are only implied, one Professor Burnet wrote out the argument in explicit syllogism form. Here I present a similar analysis by Sir David Ross, which he credits to Burnet but with minor variations. Credit goes to Ross' translation of the Ethica, in a footnote to pages 241-243:
Pro-Syllogism A:
Capacity is defined by reference to activity.
Human life is defined by the capacity of perception or thought.
Therefore, human life is defined by the activity of perception or thought.
Pro-Syllogism B:
The determinate is good by nature.
Life is determinate.
Therefore, life is good by nature.
Pro-Syllogism C (implied):
What is good by nature is good and pleasant for the good man.
Life is good by nature (conclusion of pro-syllogism B).
Therefore, life is good and pleasant for the good man.
Pro-Syllogism D (implied):
Life is good and pleasant for the good man (conclusion of C).
Perception and thought are life (conclusion of A).
Therefore, perception and thought are good and pleasant for the good man.
Pro-Syllogism E:
What is desired by all men and particularly by the good and supremely happy man is good in itself.
Life is so desired.
Therefore, life is good in itself.
Lemma:
Perception and thought are accompanied by consciousness of themselves.
Argument F:
Perception and thought are life (conclusion of A).
Therefore consciousness of perception and thought is consciousness of life.
Argument G:
Consciousness of having something good is pleasant.
Life is good in itself (conclusion of both B and E).
Therefore, consciousness of life is pleasant.
Argument H (implied):
Consciousness of life is pleasant (conclusion of G).
Consciousness of perception and thought is consciousness of life (conclusion of F).
Therefore, consciousness of perception and thought is pleasant.
Lemma:
The existence of the good man is specially desirable because the activities of which he is conscious are good.
Argument I:
The good man is related to his friend as he is to himself (conclusion of chapter 4 from the Ethica, previously).
His own existence is desirable to him (conclusion of C).
Therefore, that of his friend is desirable to him.
Argument K:
His own existence is desirable because of his consciousness of his good activities (a premise drawn from a previous statement in the Ethica).
Therefore, consciousness of his friend's good activities is also desirable to him.
Argument L:
If a man is to be happy, he must have all that is desirable to him.
Friends are desirable for a man (conclusion of I).
Therefore, if a man is to be happy, he must have friends.
There seem to be two weak chains in the argument, though I do not dispute the conclusion. The first weak chain seems to be the minor premise of A, that the capacity for perception or thought is what defines human life (note that both terms here are distributed, so the chain of syllogisms is logically valid). Though this goes into proving a conclusion I would not want to deny - the conclusion of D - it seems a simplistic reduction of the richness of human life to reduce it to thinking, especially the way the term is used in E (is the activity of perception and thinking desired by all men?). The second weak chain is the minor premise of argument L, that if a man is to be happy, he must have all that is desirable for him. There are many things desirable for me. I will not have all of them in my life, nor do I expect to.
I'd chalk this up to a good demonstration of the effort that goes into proving philosophical conclusions (twelve syllogisms), and to the imperfection often inherent in philosophical reasoning for uncontroversial conclusions.
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