INTRODUCTION TO ARISTOTLE'S METAPHYSICS

Z (Book VII)

We are seeking wisdom, the science of the highest causes and principles.  Aristotle has identified a subject matter of the science, being qua being, and we shall be considering its causes.  G (i.e., Metaphysics IV) had identified a core of that science, substance, and said that the core was the reason why all other things are parts of that subject matter.  Now Z.1 opens with a repetition of the many meanings of being discussed in G 1-2, and then turns to ask what substance is, since we still do not have any definite idea.  So Aristotle starts with an idea he used in the Categories, that substance is different from non-substantial being, not just in the empty sense used in G that a quality, for example, is the quality of a substance, but because substance is always the subject of predication.  In the Categories, Aristotle had noted that in 'x is y' statements the substances always take the x position, because they are the ultimate subjects of predicates.  For example, Socrates is a substance, because he is the subject of predicates like man and snub-nosed.   
            The way substance and non-substance behave in statements effectively defines them, and tells us that to be being, that is, to be real, implies being either a subject or a predicate.  Moreover, the fact that substance is the subject is the cause or reason for certain other facts - and therefore part of wisdom we are seeking.  That is, substance is independent of non-substance, and it is prior in knowledge, definition and time to non-substance.  Socrates is snub-nosed, and Socrates can exist without being snub-nosed, but snub-nosedness does not exist apart Socrates
The fact that substance is a subject leads the way to Z.3.  Since substance is the subject of predication, and is prior in being to non-substance, it looks like substance underlies or is the substrate for non-substance.
Another dividend of Z.1 is that since substance is the cause of the existence of non-substance in some way, we can ignore for now non-substance because it is secondary and derivative, and just focus our attention on substance.
Since we are now on the trail of substance, Z.2 lists briefly what sort of things people call substances.  The chapter follows the basic division of A.3-7, the history of the causes, - the material sort of substances are mentioned first, and they are what most people agree are substances.   The second, more abstract, group are suggested by Plato and his associates, Speusippus and Xenocrates, and include the Forms and mathematicals.  Aristotle's method aims to preserve rather than overthrow the common opinion, and so Plato is bound to lose out to the first group.  But substance is also not as straightforward as the materialists suggests. 
Since we are seeking causes, it is not enough to say that certain things are substances.  We have to say why they are substances, and that in turn will allow us to say more precisely what things are substances.  After all, if we find out that substances are substances because they are made of fire, earth, air and water, then we'll know that mathematicals are not substances, because the material elements are not causes of mathematicals in any way.  In Z.3 Aristotle proposes four possible causes and opens up a new level of investigation - essence, universal, genus, which all seem abstract, and substrate, which seems material.  He starts with substrate for a couple of reasons.  First, it is where we had ended up in Z.1; second, just as in A.1-2 Aristotle had started his discussion with what was obvious to the senses and moved to what was more universal and causative, and again in A.3-7 he started with the material cause and moved to the formal and final, so here the substrate seems a more obvious cause for something's being a substance.  Aristotle expressly mentions this second reason as he moves on to the more abstract causes at the beginning of Z.4.
If substance is a substrate, then it stands to reason that the primary substrate will be substance in the truest sense.  Now without any warning, Aristotle introduces the most important innovation of the Metaphysics, the distinction between form and matter, using statue as one of his more-obvious-to-the-senses-but-less-clear-to-the-intellect examples intended to lead us to a truer understanding.  A statue is a substrate for certain attributes, like dusty, since it physically as well as metaphysically underlies the dust.  But the statue is itself a composite of the shape and the material, say, bronze, it is made of, and we are more likely to say that the bronze underlies the shape, than that the shape underlies the bronze.  If substrate is to be substance, then it looks as if the matter is going to be the substance, and the shape just another attribute.  This is bad enough since it eliminates most of the 'what is it's' which seemed so substantial in Z.1.  But worse is to come - since the primary substrate is the truest substance, we should next look for the substrate of the bronze, that which underlies all its attributes, all the qualities, even the quantities, its three-dimensionality.  What underlies all the attributes cannot have any attributes itself, and so is really nothing.  This substrate is so lacking in being that not even PNC can apply to it.  Again, most people think that substances are separable and individual, and it was on this basis that Aristotle had ranked beings in E.1.  This ultimate substrate has no character by which we could separate or individuate it.  Matter as substrate, then, cannot be substance, and we need to seek something more abstract and form-like.
Z.4 introduces essence.  Aristotle defines essence by a special predicational relation called per se or “in virtue of itself.”  But of the two kinds of per se predication he distinguishes, only the first describes essence.  According to the first, the definition or a part of the definition of a thing is predicated of that thing per se, e.g., Socrates is man per se.  Man is the essence of Socrates.  According to the second - a surface is white per se, because in the definition of the predicate, white, is found the subject, surface - white cannot be defined without the notion of surface in which it inheres.  But white is not part of the essence of surface.   Now, Aristotle thinks that the first kind of per se predicate might be a good cause for substance, since it identifies what a thing is, just as in Z.1.  However, the introduction of the per se predicate goes a step beyond Z.1 and muddies the tidy distinctions we found there.  In Z.1 we pointed to an object and asked, 'what is it', 'how big is it' etc.  These questions presupposed nothing more than a pointing of the finger.  The answers were simple terms, like a man, six feet tall, etc.  'What is it' questions asked for substances and subjects, 'how big is it' questions asked for quantity and predicates.  In Z.4, by contrast, the question, 'what is it per se' presupposes that the object has already been identified by answering the original Z.1 questions.  Now the question, 'what is it per se,' can be asked whether the object was first identified by 'what is it' or by 'how big is it.'  The result is that there are essences of non-substances as well as of substances.  But we knew this already - PNC held good for everything definite, that is, anything that had an essence; PNC did not just hold good for substances.  Moreover, it is part of the basic inheritance of Platonism - essences are like Platonic Forms, as Z.6 makes clear, and there are Forms for every common definable term, including Aristotelian non-substances.  So whereas Z.1 seemed to make our task simpler by eliminating non-substance as derivative beings, essence seems to let them back in.  This problem is apparent the moment Aristotle says that your essence is not the essence of cultured.  For he is implying that 'cultured' has an essence.  Accordingly, Z.4-5 work to make the world safe for substance again by beating non-substantial essence back into a subordinate place consistent with Z.1.  His solution is already suggested by the second form of per se predication - and that is why he mentioned it in the first place.  In its definition white contains surface, that is to say, the essence of white includes being in a surface.  This observation is generalized in Z.4 to cases in which accidents are predicated of substances, in which case, the essence of the accident contains its substance in its definition, and therefore depends upon the substance it is predicated of.  This solution is an application of the 'medical scalpel' solution of G.2 - non-substance can have essence only because it is the essence of an accident of a substance. In this way Aristotle guarantees the primacy of substance even when essence is considered as its cause.
By the end of Z.4 Aristotle has hit upon the idea that essences, and therefore definitions, can properly belong only to self-subsistent and independent things, i.e. substances. Non-substantial terms, since they depend on substance for their existence and even for their logos - Aristotle's term for a defective definition - can only have definitions or essences in the medical scalpel sense.   This observation leads in Z.5 to per se 2 terms.  Since snub cannot be defined separately from nose, and male cannot be defined separately from animal, these terms are dependent upon their subjects for their essence.  Moreover, combined per se 2 terms, like snub nose, will involve infinite regress preventing their being defined - since snub is a concave nose, and snub is concave, a snub nose will be a concave nose nose......  For these reasons, there is essence and definition of substance alone.
Z.4 had suggested substance might be essence, and essence makes a good answer to the 'what is it' question, but it is hard to see how an essence can be an individual, and if it isn't, we can hardly allow it to be substance.  Accordingly Z.6 asks whether the essence of a thing is identical with that thing.  The answer certainly seems to be 'yes,' when we consider Aristotle's first example in Z.4, 'what are you per se?'  How could your essence be different from you?  However, if essence is what is expressed in definition, and definitions can only apply to many things of the same kind and not to individuals as such, how can essence be the same as the individual?  But if essence is not the same as the individual and yet essence is substance, then we have created a Platonic Form.  [Specifically, Aristotle considers accidental combinations and then per se expressions.  A per se term is the same as its essence, of course, since a per se term is that which has an essence in the primary sense.  This will certainly be the case with Platonic Forms in that they are identical with their essence.  By the way, for the Platonist Forms, substance is not substrate.  And since knowledge of each thing is knowledge of its essence, each thing must be identical with its essence.  If a thing and its essence are different, there will be an infinite regress, x, essence of x, essence of essence of x....]
So much then for substrate and essence.  Each has advantages and drawbacks.  Both now begin to undergo major reinterpretation, so that when we get to Z.13 essence is practically identified with form and substrate with matter, and these will be the principles and causes of a new conception of substance.
Nothing in Z so far could lead us to expect Z.7-9, since it does not continue the discussion of essence of the last three chapters, nor take up genus or universal.  It intrudes without even the barest transition markers.  Nevertheless, there is some justification for its being placed here.  Z.6 ended with the statement that the discussion of essence was complete and that in different ways essence is and is not the same as the individual thing.  The fact that what we call substance in the highest degree, animals and plants, comes to be through generation argues for including this discussion in metaphysics and not relegating it to physics, the special science of change.  Indeed, G.2 had mentioned generations of substances as part of the science of being qua being, and so Aristotle is at least consistent here in his inclusion of this passage.  In all cases of generation, form comes from form, and essence preexists.  Z.8 goes on to explain that the maker of the bronze sphere does not make the bronze or the sphere but makes the composite.  This is a solution to the 10th aporia concerning whether changing things have changing principles, since form and matter as such are not generable; essence is not generated.  As a result too a principle of physics is itself not physical, and so has a good claim to be treated in metaphysics.  Now will this non-generated form be something apart from the informed things?  Aristotle answers Plato in the negative, and in doing so denies the relevance of the Platonic forms to explanations of change.  Z.9 in raising the issue of spontaneous generation, discusses the active role of matter in change, and as such sets up the discussion of Z.10 concerning the role of the parts of the logos of matter in the logos of a thing.  [The preexistence and non-generation of principles of composites holds good not just for substance and its matter, but also for composites of matter and non-substance, like the bronze sphere which is bronze quantified.  The only difference in these cases is that the quantity need not be preexistent except potentially.]
The problem of Z.6, the identity of a thing with its essence, was generated because essence was at once what a thing is per se - so identical with that thing - as well as what is expressed in a definition - and so more like a species or universal.  Z.10 seems willing to accept this tension, and proceeds to consider the structure of the definition, so as to get us closer to substance.  This discussion seems to combine the three strands of 3, 4-6 and 7-9 by joining the notion of essence with that of form and the notion of substrate with that of matter.  Here the question is how an essence, and therefore a definition, which has parts, can be an individual, a tode ti.  Notice that we have come a long way from Z.1, where the unity of substance consisted in its being an individual subject.  The major stumbling-block for essence being substance lies with its lack of unity and individuality, since as we saw in Z.4-5 even accidents of substance can have an essence.  Moreover, even the essence of substance itself is far from totally unified.  There are parts of essences and definitions, and if the definition is given in terms of form and matter, then we have at least these two parts, plus the parts of those parts.  The formula of the parts of the form must be included in the formula of the whole, but the formula of the parts of the matter must not.  And to some degree Aristotle even considers here whether matter should be included in the account of essence at all.  If the formula of the parts must be contained in the formula of a thing, then will we will get a great cascade of irrelevant material into the definition, especially if we allow in the matter of the matter and the genus of the genus; and thereby the problems of substrate and essence are repeated.  This chapter also introduces the issue of priority, for the parts of the form are prior, but the parts of the matter are posterior, to the definition of the whole
Z.11 asks what parts of the definition belong to the form, and what to the concrete object.  It is important to be able to make the distinction, though difficult in cases where the same matter is associated with the same form, for one cannot be sure where the line is to be drawn, as for example, if all spheres were bronze, one might think that bronze was part of the form of bronze sphere.  All the same one cannot eliminate the matter altogether from the essence of material things, since man, for example, does not exist without a material body, and is essentially enmattered
Z.12 continues the theme that has been developing since Z.4, namely, wherein lies the unity of the essence or definition? Why, for example, should the parts of the definition of man, animal and two-footed, make up one thing?  It is important that the definition of substance at least be unified, since substance is supposed to denote one thing and the tode ti.  The answer is that two-footed is a per se 2 predicate of animal.  Divisionary definitions - which are quite different from form-matter definitions - contain unity through the implication of the genus in the differentia.  The genus exists either as matter or not at all, and the final differentia will be the substance of the thing.  For this  reason there will be essences and definitions only of species of a genus.

H (Book VIII)

Having left off Z.17 with a fresh start, we expect Aristotle to take up the notion of cause in H.  To some small degree he does so in H.4, but his main concern in this book is the relationship of matter and form, and especially how far matter can get us on the road to substance.  We first focus on the substrate function.  There must be a substrate for changes, local  (e.g. from here to there), of quantity (from small to large), quality (e.g., from black to white), and especially of substantial change (e.g., the generation of a human being).  In many cases this substrate may be matter, though substances too can undergo quality changes.   In H.2 this substrate is considered as a general unformed stuff, which may be differentiated in various ways.  Stones may be placed in different positions, and so become different things, e.g. a threshold or a lintel; meals can be served in the morning or evening, and so become breakfast and dinner.  Similarly, by changing the size or shape different things can be made.  Perhaps, then, substance can be explained as a modification or differentia of matter.  Aristotle rejects this idea - the differentiae cannot individually or collectively be substance.  Nevertheless, all matter comes somehow preformed by these differentiae, as will be shown more clearly in I.  He claims at the conclusion of H.2 that sensible substance is now clear; in fact, it is far from clear, since he has only been dealing with artifacts and accidents of simple bodies.  H.3 goes on to distinguish form from matter linguistically and ontologically.  First we must be careful of what our language means, since some words signify the form, e.g., curved, others the matter and the form together, e.g. snub.  Again, the form is not just something else alongside the matter, like another material element; it is eternal and does not come into being.  H.4 continues the discussion of the preformed nature of matter.  If every characteristic of a thing is a feature of its form, then its matter will be entirely characterless, prime matter.  In fact, however, different things have different matter, e.g. a saw cannot be made from wood.  Indeed, there can be multiple layers of material enformedness - the sweet is the matter for the viscous, which in turn is the matter for mucus.  In some cases, however, different things can be made of the same matter, e.g. a chest and a bed from wood.  Because matter constrains but does not dictate the form it admits, it is important to make a complete account of the relevant causes, both formal and material, and where the matter is stated, it must be the proximate matter, and not the matter of the matter.  In many cases, some of the four causes will not be relevant.   H.5 studies matter as the capacity for opposites.  Matter is necessary for there to be generation from opposites, since the opposites themselves are not generated.  Aristotle also takes up the question concerning opposites like wine and vinegar, life and death, which cannot be explained straightforwardly as actualizations of the same potentiality.  So also wine is not the matter for vinegar, since vinegar can hardly be considered an attainment of form. H.6 returns to the question of the unity of definition, which had been treated in Z.12 and gives a different answer.  Wherever there are parts that make up a whole, there must be some cause of the whole.  We will get nowhere if we ask what is the unity of animal and two-footed, Aristotle strangely says, unless we understand one part as the matter and the other as the form.  In that case, it will be obvious how they are unified.  Things without matter are just unified and need no further cause of their unity.  Definitions in terms of participation or communion are just attempts to achieve this unity.

Q (Theta: Book IX)

Aristotle begins by turning aside from predicative or categorial being, that of substance, quality, quantity, etc., and takes up being as potentiality and actuality.  The notion of potentiality or capacity that he introduces, the capacity to be affected by another thing, is reminiscent of a definition of being Plato provides in the Sophist.  As a definition of being, it is seriously flawed as far as far Aristotle is concerned, because it makes being dependent upon other things for their existence, and therefore destroys separability altogether.  It is, however, a starting point, though itself not the conception of potentiality that will be most useful in the end for understanding substance.   Aristotle starts Q.1 with a distinction between active and passive capacity.  They are logically related to one another.  A passive capacity of water to be heated implies an active capacity of a fire to heat it.   In order to explain how they operate, Aristotle introduces in Q.2 a further distinction between rational and irrational capacities.  A rational capacity is a power, usually of practical knowledge, like medicine, that an agent can choose to exercise or not in a certain circumstance.  Socrates, Plato and Aristotle all thought that knowledge is of contraries, that, e.g. the doctor had the power to heal and make sick, and must choose which to do.  An irrational capacity, by contrast, cannot fail to be actualized when that which has the passive capacity is brought into appropriate relation with it, e.g. a fire cannot fail to heat a pot of water when the fire is set under the water.  The identification of rational capacities is helpful in Q.3, where Aristotle addresses the Parmenides-inspired Megarians who deny potentiality and claim that a thing cannot be what it is not.  Aristotle's responds with arguments based on the rational capacities, for the Megarians destroy choice.  Q.4 take the same problem from the other side, and argues that if something is possible, one cannot say that it will not come about.

In Q.6 Aristotle turns to the kind of potentiality and actuality that do not depend on motion and change.  Actuality is defined by a set of analogies with potentiality which are intended to move us from a material sense of potentiality to a sense of a capacity for an activity.  Action is distinction from change.  For change is a change from something to something different, and the change is a means to that end.  An action, by contrast, contains its end in it, as for example, seeing, understanding , being healthy or happy.  These actions have no natural end, whereas changes are incomplete.  Q.7 asks when a thing in the process of development exist potentially.  When nothing else hindering it will come to pass.  The semen is not potentially a man without katamenia.  In a series of development it is the penultimate which is potentially the ultimate, e.g. earth, wood, box - it is the wood, not the earth which is potentially box.  The primary matter of a thing is that which is not the material potentiality of anything else.  Q. 8 Now actuality is prior to potentiality in definition, in time - at least in the sense that the actual form must preexist in the seed or the mind of the artist and in substantiality, because that which is posterior in generation is prior in substantiality or form and because everything moves towards its principle.  In building the result of the activity resides in the thing built, but where there is no other result it resides in the active thing.  Also the potential cannot be eternal, since it is also the potential for the opposite; all imperishable things must be actual; and there cannot be any potentiality in them.  Thus the star cannot be cease in their motions.  The perishable things imitate the imperishable in their cycle of generation and corruption.  Q.9 argues that the good actuality is better than the good potentiality, since a bird in the hand is better than the bird in the bush.  Geometrical construction proceeds by a kind of actualization of the potential in the elements.  Finally Q.10 turns away from potentiality back to the topic of E.4, truth, as one of the meanings of being alongside the types of predication, and potentiality and actuality.  The facts are the cause of the statements about them being true and false, and these facts and the corresponding statements are composites.  But for simples, truth is like touching the things mentally; ignorance is non-contact.  There is no being mistaken