Summary
Book I or Alpha outlines "first philosophy", which is a cognition of the first principles or causes of things. The wise are able to teach because they know the why of things, unlike those who only know that things are away based on their memory and sensations. Because of their knowledge of first causes and principles, they are better fitted to command, rather than to obey. Book Alpha also surveys previous philosophies from Thales to Plato, especially their treatment of causes.
Book II or "little alpha": The goal of this chapter is to mention a possible objection to Aristotle's account of how we understand first principles and thus acquire wisdom. Aristotle replies that the notion of an infinite causal series is absurd, and thus there must be a first form which is not itself caused. This view is developed later in book Lambda, where he develops an argument for the existence of God.
Book III or Beta lists the leading problems or puzzles ἀπορία aporia of philosophy.
Book IV or Gamma: Chapters 2 and 3 argue for its status as a noted in its own right. The rest is a defense of a what we now asked the principle of contradiction, the principle that it is for not possible for the same proposition to be the issue and non to be the case, and b what we now call the principle of excluded middle: tertium non datur — there cannot be an intermediary between contradictory statements.
Book V or Delta "philosophical lexicon" is a list of definitions of approximately thirty key terms such as cause, nature, one, and many.
Book VI or Epsilon has two main concerns. Aristotle is first concerned with a hierarchy of the sciences. As we know, a science can be either productive, practical or theoretical. Because theoretical sciences discussing being or beings for their own sake—for example, Physics studies beings that can be moved 1025b27—and cause not have a target τέλος, end or goal; τέλειος, complete or perfect beyond themselves, they are superior. The analyse of being qua being, or First Philosophy, is superior to any the other theoretical sciences because it is concerned the ultimate causes of all reality, not just the secondary causes of a factor of reality. Theconcern of Epsilon is proving that being τὸ ὄν considered per accidens κατὰ συμβεβηκός cannot be studied as a science. Per accidens being does not involve art τέχνη, nor does cost by necessity per se or καθ᾽ αὑτό, and therefore does not deserve to be studied as a science. Aristotle dismisses the study of the per accidens as a science fit for Sophists, a group whose philosophies or lack thereof he consistently rejects throughout the Metaphysics.
The Middle Books are broadly considered the core of the Metaphysics.
Book Zeta begins with thethat ‘Being’ has numerous senses. The intention of philosophy is to understand being. The primary rank of being is what Aristotle calls substance. What substances are there, and are there all substances besides perceptible ones? Aristotle considers four candidates for substance: i the ‘essence’ or ‘what it was to be a thing’ ii the Platonic universal, iii the genus to which a substance belongs and iv the substratum or ‘matter’ which underlies all the properties of a thing. He dismisses the idea that matter can be substance, for if we eliminate everything that is a property from what can have the property, we are left with something that has no properties at all. Such 'ultimate matter' cannot be substance. Separability and 'this-ness' are necessary to our concept of substance.
Chapters 4–12 are devoted to Aristotle's own theory that essence is the criterion of substantiality. The essence of something is what is included in a secundum se 'according to itself' account of a thing, i.e. which tells what a thing is by its very nature. You are not musical by your very nature. But you are a human by your very nature. Your essence is what is mentioned in the definition of you.
Chapters 13–15 consider, and dismiss, the idea that substance is the universal or the genus, and are mostly an attack on the Platonic theory of Ideas. Aristotle argues that if genus and kind are individual things, then different species of the same genus contain the genus as individual thing, which leads to absurdities. Moreover, individuals are incapable of definition.
Chapter 17 takes an entirely fresh direction, which turns on the idea that substance is really a cause.
Book Eta consists of a summary of what has been said so far i.e., in Book Zeta about substance, and adds a few further details regarding difference and unity.
Theta sets out to define potentiality and actuality. Chapters 1–5 discuss potentiality. We memorize that this term indicates the potential δύναμις, dunamis of something to change: potentiality is "a principle of modify in another thing or in the thing itself qua other" 1046a9. In chapter 6 Aristotle turns to actuality. We can only know actuality through observation or "analogy;" thus "as that which builds is to that which is capable of building, so is that which is awake to that which is asleep...or that which is separated from matter to matter itself" 1048b1–4. Actuality is the completed state of something that had the potential to be completed. The relationship between actuality and potentiality can be thought of as the relationship between form and matter, but with the added aspect of time. Actuality and potentiality are diachronic across time distinctions, whereas form and matter are synchronic at once distinctions.
Book X or Iota: Discussion of unity, one and many, sameness and difference.
Book XI or Kappa: Briefer versions of other chapters and of parts of the Physics.
Book XII or Lambda: Further remarks on beings in general, first principles, and God or gods. This book includes Aristotle's famous version of the unmoved mover, "the nearly divine of things observed by us", as "the thinking of thinking".
Books XIII and XIV, or Mu and Nu: Philosophy of mathematics, in particular how numbers exist.