Stanford Encyclopedia of Philosophy article "Aristotle's Metaphysics"

• Title "metaphysics"
• from Greek meta "after" + physika "physics"
  
• option one: simply an omnium gatherum name for things that were placed "after the physics"
• option two: these treatises have a weak sort of unity: they were placed here because they fit into a curriculum of reading Aristotle in which it made sense to read about these topics after the Physics.
• option three: these treatises form a unified treatment of a coherent area of inquiry, called variously "first philosophy," "metaphysics," "science of being qua being"
• "Books" of the Metaphysics.
• referred to either with Roman numerals
• or with Greek letters: Α, α, Β, Γ, Δ , Ε, Η, Ζ, Θ, ...
• alpha 1 I
  little alpha 2 II
  beta 3 III
  gamma 4 IV
  delta 5 V
  epsilon 6 VI
  zeta 7 VII
  eta 8 VIII
  theta 9 IX
  iota 10 X
  kappa 11 XI
  lambda 12 XII
  mu 13 XIII
  nu 14 XIV
  

• Subject matter of the Metaphysics.
• Wisdom: 
• all suppose what is called wisdom (sophia) to deal with the first causes (aitia) and the principles (archai) of things  Metaphysics A.1 981b28
• First Philosophy
• "first" not in the sense that we should start with the Metaphysics, but rather in the sense that the subject treated here is most basic: it is at the highest level of generality.
• these things are "better known in themselves" although they are not "better known to us" (Posterior Analytics 71b32; Prior Analytics 68b35-7; Physics A.1, 184a16-20; Metaphysics Z.3, 1029b3-12; Topics Z.4, 141b2-142a12)
  
• the study of being qua being
  
• NOT a study that is concerned with one sort of being, "being qua being," that is different from other beings
  
• rather, a study of being that studies beings in so far as they are beings
• other sciences study the same beings, but qua other things (living beings, mathematical objects, etc.)
• theology
  
• a science that studies things that are eternal, not subject to change, and independent of matter is theology, and this is the “first” and “highest” science.
  
• metaphysical problems Aristotle addresses (list from Book Β):
• Are sensible substances the only ones that exist, or are there others besides them?
  
• Is it kinds or individuals that are the elements and principles of things?
  
• if it is kinds, which ones: the most generic or the most specific?
  
• Is there a cause apart from matter?
  
• Is there anything apart from material compounds?
  
• Are the principles limited, either in number or in kind?
  
• Are the principles of perishable things themselves perishable?
  
• Are the principles universal or particular, and do they exist potentially or actually?
  
• Are mathematical objects (numbers, lines, figures, points) substances?
  
• If they are, are they separate from or do they always belong to sensible things?
  
• And (“the hardest and most perplexing of all,” Aristotle says) are unity and being the substance of things, or are they attributes of some other subject?
  
• In the remainder of Book B, Aristotle presents arguments on both sides of each of these issues, and in subsequent books he takes up many of them again.

• some terminological clarification (this should be familiar by now, but it bears repeating)
• a universal is something that applies to or is present in or is said of many things
• dog is said of Rover and Spot and Lassie
• animal is said of mammals and reptiles
• every one of those many things is equally an example of that universal
  
• an individual is something that may be divisible in various ways, but once you divide it, each division no longer has all the things which are that individual
  
• animal can be divided: there are several natural kinds of animals: but once you divide it into mammals, reptiles, etc., they are still animals, but each division is only a subset of what animal is.
• in a sense, qua animal, it cannot be divided
• it is a unity
• an individual may or may not be determinate: genus and species are determinate (there is a specific set of differentiae for each, and they are determinate)
  
• a particular is an individual that is also one in number: it cannot be divided without ceasing to be what it is AND it is not a universal AND it has indeterminate accidents
  
• "Sally the Great Dane" is a particular: there is only one Sally and if you divide her, she ceases to be Sally.
• She is indeterminate: she has infinite accidents qua Sally
• you and I are particular and individual
  
• a substance is the most basic being on which other beings depend for their being: in Categories, it was clear that you and I are substances, primary substances to be exact.
  

• Coming from Categories, we are set to expect "substance" to be front and center in the Metaphysics
  
• Book Ζ  takes up study of substance
• reiterates and refines some of what he said in Γ:
•  ‘being’ is said in many ways
• the primary sense of ‘being’ is the sense in which substances are beings
• the secondary senses of ‘being’  applies to the non-substance categories.
  
• "(The question ‘What is being?’) is just the question ‘What is substance?’” (1028b4)
• Z.3 begins with a list of four possible candidates for being the substance of some x (where x is something that all indications point to having/being a substance):
  
• the essence of x
• a universal predicated of x
• x is a human (for example)
• any universal that is predicated of x?
  
• a genus to which x belongs
• this human is an animal
  
• so the substance of any thing is the genus to which it belongs
  
• a subject of which x is predicated
• Smells like the Categories: substance is that which is neither said of nor in any thing
• But here, The substance of x is the subject of which x is predicated: so x is said of y, and thus y is the substance of x.
• example: this lump of flesh is Joe OR This lump of flesh + a soul is Joe OR this soul is Joe.
• of course, it could be taken other ways, but A is concerned with hylomorphic analysis here in Z3.
  
• Ζ.3 is devoted to an examination of the fourth candidate: the idea that the substance of something is a subject of which it is predicated.
• the subject that he here envisages, he says, is either matter or form or the compound of matter and form(1029a2-4)
• the theory of change Aristotle develops in the Physics requires a subject for substantial changes — a subject of which substance is predicated — and it identifies matter as the fundamental subject of change (192a31-32).
  
• matter is the thing that remains there when a new being comes into existence: before a plant grows, we've got a certain amount of matter that will become the plant, then the plant grows and that matter is the plant, then the plant dies, and that matter still exists.
  
• The subject criterion (substance is that which is not predicated of a subject but of which all else is predicated) by itself leads to the possible answer that the substance of x is the matter of which x is composed (1029a10).
  
• form is predicated of matter as subject:
  
• e.g. this flesh is a human
  
• one can always analyze a hylomorphic compound into its predicates and the subject of which they are predicated
• this flesh (+ whatever else makes up a human body) is this human
• this earth, fire, (and whatever else is in flesh) is this flesh.
• this earth is ...(prime matter?)
  
• when all predicates have been removed (in thought), the subject that remains is nothing at all in its own right — an entity all of whose properties are accidental to it (1029a12-27).
  
• it is called 'prime matter'
  
• The resulting subject is matter from which all form has been expunged
• it is unlikely that Aristotle thought such a thing could exist: it is pure potentiality with no actuality at all: it is quality-less matter
• if he thought it a concept worth using, it can only have been something possible in thought, not in existence
  
• But Aristotle rejects the idea that matter is substance as impossible (1029a28)
• substance must be “separate” (chôriston) and “some this” (tode ti, sometimes translated “this something”)
• WHY?
  
• a plausible interpretation:
• Being 'separate' has to do with being able to exist independently
  
• x is separate from y if x is capable of existing independently of y
• being "some this" means being a determinate individual.
  
• on Aristotle's account not every “this” is also “separate.”
  
• A particular color or shape might be considered a determinate individual, but it is not capable of existing on its own — it is always of some substance or other
• matter too fails to be simultaneously both chôriston and tode ti
• matter of which a substance is composed may exist independently of that substance, but it is not as such any definite individual — it is just a quantity of matter.
  
• this pile or this cubic centimeter of flesh is not a separable this? it is, but when it is in fact separated from the thing it is part of, it always instantaneously acquires another form (a cube, a pound, a lump): it does not exist separate from some form or other.
  
• I am flesh and bones, but my substance is not flesh and bones: my flesh and bone can exist separately from me (when I die), but then it instantaneously on death becomes something only homonymously flesh and boneL it is not a determinate thing in and of itself (some other form must supervene on it: "dead flesh" "meat" "food for worms"?)
  
• Z.4 claims that substance is essence
• ‘Essence’ is the standard English translation of  to ti ên einai, literally “the what it was to be” for a thing, which Roman translators translated by making up the new word "essentia," which became English "essence."
  
• Aristotle also sometimes uses the shorter phrase to ti esti, literally “the what it is,” for approximately the same idea
• in the Organon, Aristotle links essence to  definition (horismos)
• Aristotle defines things, not words.
  
• The definition of tiger tells us what it is to be a tiger— the “what it is to be” of a tiger, what is predicated of the tiger per se.
• a definition is an account (logos) that signifies an essence Topics 102a3
  
• he links both of these notions to a certain kind of per se predication (kath’ hauto, “in respect of itself”) — what belongs to a thing in respect of itself belongs to it in its essence (en tôi ti esti) for we refer to it in the account that states the essence Posterior Analytics, 73a34-5
• there is an essence of just those things whose logos is a definition 1030a6
• the essence of a thing is what it is said to be in respect of itself 1029b14
  
• there are important qualifications to the claim that substance is essence
  
• definition (horismos), like ‘what it is’ (ti esti), is said in many ways 1030a19
•  items in all the categories are definable, so items in all the categories have essences
  
• So which essences?
  
• definition and essence are primarily (protôs) and without qualification (haplôs) of substances 1030b4-6
  
• (seems question-begging if it is meant to be more than just explaining: we are trying to figure out what substance is and why, and here we are told that essence might be substance, but only essence that is of a substance?)
  
• Ζ.6 argues that if something is “primary” and spoken of in respect of itself (kath’ hauto legomenon) it is one and the same as its essence
• the word ‘eidos’, which meant ‘species’ in the logical works, has acquired a new meaning in a hylomorphic context, where it means ‘form’ (contrasted with ‘matter’) rather than ‘species’ (contrasted with ‘genus’)
• In Metaphysics Ζ, a universal such as man or horse — which was called a species and a secondary substance in the Categories — is “not a substance, but a compound of a certain formula and a certain matter, taken universally” (Z.10, 1035b29-30)
• "matter taken universally" what is that?
  
• The eidos of Book Ζ is not the species that an individual substance belongs to but the form that is predicated of the matter of which it is composed
• Ζ.7-9 discusses form's role in hylomorphism
• Ζ.7-9 is an addition to book Zeta, because it is not included in the summary given in chapter 1 of Zeta. That is evidence that Aristotle revised.
• in a form-matter composite, such as an artifact or tool:
• we do not produce the matter
• we do not produce the form (what could we make it out of?)
• we put the form into the matter, which produces the compound (1033a30-b9)
  
• form and matter both pre-exist the compound (1034b12)
• the efficient cause is the form (in the soul of the artisan)
• in the case of animals and plants, all of the above holds too, except that we don't put the form into the matter, the parent does
• we don't call what comes to be after its matter, but after it's form:
• a ring, a human, a dog, or a tree came to be, not gold, bodies, or wood
• the form makes it the kind of thing it is and so it is what satisfies the condition for being the substance of a thing: it makes it what it is.
• Ζ.10 and 11: form, essence, and definition
• a big problem: does the definition include reference to the matter?
• if so, form and matter are not so clearly separate or separable from each other.
• because matter would be part of the definition, which is an account of the essence, so matter would be part of the essence
• remember above where mention was made of "matter taken universally": can Aristotle dodge this problem via that concept?
  
• he thinks that definitions include the parts of what is being defined
• thus his definition of human is "rational animal"
• "rational" and "animal" are universals
• if "rational" or "animal" are definable, then the definition of human should include their definitions.
• if terms within the definitions of "rational" and "animal" can be defined, then the definition of human should include those definitions
• and thus we proceed until we come to simple terms that cannot be defined.
• is there a point at which matter somehow enters the definition via this principle that the definitions of all things in a given thing's definition should be considered as included in the original definition of that thing?
• so what do we do with hylomorphic compounds?
• matter seems to be a part of them
• so it must be included in the definition of the compound!
• and if the matter is something like "flesh," then the definitions of its parts must be included in the definition of the compound.
• but this seems wrong to Aristotle.
• Why?
• take a circle: it has two halves, which are parts of it
• must we include the halves in the definition?
• NO: a semicircle is only definable in terms of a circle, not the other way around.
• if that were not so, we could never define circle, because semicircles are composed of ever smaller parts, and there would be an infinite regress much like Zeno's paradox of motion about getting 1/2 way there, then 1/2 of that, etc.
• the point here is that there is no principle that all parts of a thing must be included in its definition: the example is meant to be a clear case of that: don't try to argue with the example so much as the principle
  
• after considering trying to tinker with the notion of parts, Aristotle takes a different path:
• he tries to specify more carefully the whole of which matter is supposedly a part
• The bronze is part of the compound statue, but not of the statue spoken of as form 1035a6
  
• the line when divided passes away into its halves, and the man into bones and muscle and flesh, but it does not follow that they are composed of these as parts of their essence 1035a17-20
• Rather, it is not the substance but the compound that is divided into the body and its parts as into matter 1035b21-2
• yet more clearly (1035b4) ... the soul of animals (for this is the substance of living things) is their substance 1035b15
• the solution to the problem of whether matter is a part of the definition is only partially successful
• a statue's definition need not mention any particular kind of matter (e.g. bronze), but what about the definition of human? even if it needn't mention this particular flesh, mustn't it mention flesh, bones, etc.? Could there be a human without them? Perhaps they are not essential, but merely propria?
  
• But: The form of man is always found in flesh and bones and parts of this kind as Aristotle himself writes 1036b4
  
• Some things surely are a particular form in a particular matter  1036b23
• it is not possible to define them without reference to their material parts 1036b28
  
• Perhaps his point is that whenever it is essential to a substance that it be made of a certain kind of matter (e.g., that man be made of flesh and bones), this is in some sense a formal or structural requirement, so we are referring to the matter not qua matter, but qua form: "taken universally"?
  
• remember that "flesh," for instance is a hylomorphic compound itself
• so perhaps we can merely refer to the formal "part" of flesh and bones...
• the problem is that we can then ask "what about the matter that makes up flesh: doesn't it have to be mentioned in the account of flesh?"
  
• but if we go all the way down the ladder of forms from nonuniform (arm, leg, liver, femur) to uniform parts (flesh, bone, blood, molecule, atom, quark), don't we eventually get to prime matter?
• and if we must include the formal part of each "material" component of a substance in the definition of that substance, don't we really have to include most everything but prime matter?
• if by ‘matter’ one has in mind the ultimate subject alluded to in Ζ.3 (so-called ‘prime matter’), there will be no reference to it in any definition, “for this is indefinite” (1037a27).
• anything indefinite has no definition, because the very definition of "indefinite" includes lack of a definition.
  
• another problem: what unifies a definition
• if man is rational animal, why is this one and not many--rational and animal? (1037b13-14)
• why is it different from an accidental unity like "pale human"?
• A. doesn't think it's just that we have a single word for "rational animal" (namely "human") while we don't happen to have one for "pale human"
• in Z 12, A tries to solve the problem by saying that the division should be by the differentia of the differentia 1038a9
  
• What does that mean? in the following, each subsequent answer after the first offers a differentia of the previous differentia
  
• what is that?
  
• that is a being
• what kind
• a living being
• what kind
• an animal living being
  
• what kind
• a mammalian animal living being
  
• what kind
• a rational mammalian animal living being
  
• clearly the last (or completing, teleutaia) differentia will be the substance of the thing and its definition 1038a19
• this only shows how a long string of differentiae in a definition can be reduced to one differentia (rational mammalian animal living) but does not solve the problem of the unity of definition
• the above example string of differentiae should not be taken as A's actual definition of human: it is merely there to be an example: any such example would do the trick. So don't argue with the specific example: argue with the principle here.
  
• Aristotle returns to the problem at H.6 and offers a different solution (explored below).
• in spite of these two problems, we seem to have a clear idea about the nature of A.'s 'substantial form' : namely, a substantial form ...
  
• is the essence of a substance
• 'corresponds' to a species
• is what is denoted by the definiens of a definition
• Terminological aside: a definition consists of two parts, the definiendum and the definiens
• think of a definition as formable into a sentence of the form "X is defined as P."
  
• X is the definiendum, the subject of the definition.
• P is the definiens, what we often refer to simply as the 'definition.'
  
• since only universals are definable, substantial forms are universals
• confirmed by “Socrates and Callias are different because of their matter … but they are the same in form” 1034a6-8
  
• if you take this passage as Aristotle's considered opinion
  
• one and the same substantial form is predicated of two different clumps of matter. And being “predicated of many” is what makes something a universal (De Interpretatione 17a37)
• Ζ.13, however, consists of arguments to the conclusion that universals are not substances.
• this is a fundamental tension in Aristotle's metaphysics. He seems committed to all three of the following propositions:
• (i)    Substance is form
• (ii)    Form is universal
• (iii)    No universal is a substance
• two main, opposed, lines of interpretation
• there are forms of particular individuals
  
• Aristotle's substantial forms are not universals after all, but each belongs exclusively to the particular whose form it is, and there are therefore as many substantial forms of a given kind as there are particulars of that kind.
  
• that substantial forms are particulars is supported by Aristotle's claims:
  
• that a substance is “separate and some this” (chôriston kai tode ti, Ζ.3): separate may mean separable
  
• that there are no universals apart from their particulars (Z.13)
• that universals are not substances (Z.13).
• OR
• there is only one substantial form for all particulars of the same species
  
• that substantial forms are universals is supported by Aristotle's claims:
• that substances are, par excellence, the definable entities (Z.4),
  
• that definition is of the universal (Z.11)
  
• that it is impossible to define particulars (Z.15).
• if there were a substantial form unique to some sensible particular, Callias for example, then the definition corresponding to that Callias form, or essence, would apply uniquely to Callias — it would define him, which is precisely what Aristotle says cannot be done
• Consider the following:
• an individual (tode ti) can be a universal (katholou).
  
• universals are contrasted with particulars (kath’ hekasta), not individuals
  
• but Aristotle sometimes ignores the distinction
  
• an individual tode ti is fully determinate, and it is not further differentiable
• a kath’ hekaston is a particular thing, unrepeatable, and not predicated of anything else
• thus a universal tode ti is a fully determinate universal not further divisible into lower-level universals, but predicated of numerous particulars.
  
• The claim that there are no universals apart from particulars needs to be understood in context. 
  
• “there is no animal apart from the particulars (ta tina)” (1038b33) may refer to the 'particular' kinds of animals, not particular individual animals
• his point may be that a generic kind, such as animal, is ontologically dependent on its species, and hence on the substantial forms that are the essences of those species
• The arguments of Ζ.13 against the substantiality of universals are still part of the puzzles, the aporiae (remember, he discusses phainomena and endoxa, then proceeds to raise aporiae (puzzles), then offers considered opinions), not yet his considered opinion, so they may be qualified in some way
  
• For example, 1038b11-15 includes the premise that the substance of x is peculiar (idion) to x. It then draws the conclusion that a universal cannot be the substance of all of its instances (for it could not be idion to all of them), and concludes that it must be the substance “of none.”
  
• this conclusion does not say that no universal can be a substance, but only that no universal can be the substance of any of its instances
• Aristotle's point may be that since form is predicated of matter, a substantial form is predicated of various clumps of matter. But it is not the substance of those clumps of matter, for it is predicated accidentally of them.
  
• The thing with which it is uniquely correlated, and of which it is the substance, is not one of its instances but the substantial form itself.
  
• This conclusion should not be surprising in light of Aristotle's claim in Ζ.6 that “each substance is one and the same as its essence.” A universal substantial form just is that essence.
• In Ζ.17 says that a substance is a “principle and a cause” (archê kai aitia, 1041a9) of being.
  
• four causes: material, formal, efficient, and final
• things may be causes of one another — hard work of fitness, and fitness of hard work — although not in the same sense: fitness is what hard work is for, whereas hard work is a principle of motion 195a10 
• one and the same thing can be a cause in more than one sense: form, mover, and telos often coincide 198a25
  
• the soul, the form or essence of a living thing, is a cause in three of the ways we have distinguished 415b10, namely efficient, formal, and final
• the job of a cause or principle of being is to explain why one thing belongs to another (1041a11): why this is a man, or that is a house: why a man is a man, or why a house is a house
• Why are these things, i.e., bricks and stones, a house?1041a26
• Aristotle proposes that the cause of being of a substance (e.g., of a house) is the form or essence that is predicated of the matter (e.g., of the bricks and stones) that constitute that substance
• “why is this a man?” or “why is that a house?”
  
• involves a species predication (“Callias is a man,” “Fallingwater is a house”)
• that answer invokes hylomorphic analysis:
• Callias is a human because the form or essence of human is present in the flesh and bones that constitute the body of Callias;
  
• Fallingwater is a house because the form of house is present in the materials of which Fallingwater is made.
  
• species predication ("Callias is a human") is explained in terms of an underlying form predication whose subject is not the particular compound but its matter  ("Callias is a human because the form 'human' is present in that flesh").
  
• Form predications are thus more basic than their corresponding species predications.
  
• A substantial form, as a primary definable, is its own substance, for it is essentially predicated of itself alone (a human form is human in virtue of itself).
• the substantial form of a material compound, because it is predicated (accidentally) of the matter of the compound, is the cause of the compound's being the kind of thing that it is. The form is therefore, in a derivative way, the substance of the compound, as well.
• Substance and Actuality and Potentiality
• Metaphysics Ζ by and large talks about things at a given time: an individual substance at a particular time
• Metaphysics Book Θ introduces a discussion of substances over time: let's move on to theta:
  
• another key Aristotelian distinction, that between potentiality (dunamis) and actuality (entelecheia or energeia)
• two different senses of dunamis:
  
• in the strictest sense, dunamis = the power that a thing has to produce a change
• a thing has a dunamis in this sense when it has within it a source of change in something else (or in itself qua other) Θ.1, 1046a12
• exercise of such a power is a kinêsis — a movement or process
  
• the housebuilder's craft is a power whose exercise is the process of housebuilding
• a second sense of dunamis--translated as ‘potentiality’= a thing's capacity to be in a different and more completed state.
  
• this sense of dunamis is related not to movement (kinêsis) but to actuality (energeia)Θ.6, 1048a25
• potentiality so understood is indefinable (1048a37)
• Actuality is to potentiality, Aristotle tells us, as someone waking is to someone sleeping, as someone seeing is to a sighted person with his eyes closed, as that which has been shaped out of some matter is to the matter from which it has been shaped (1048b1-3).
• a piece of wood, which can be carved or shaped into a table or into a bowl, has (at least) more than one different potentiality (it is potentially a table and also potentially a bowl and also potentially ...)
• matter (in this case, wood) is linked with potentialty
•  substance (in this case, the table or the bowl) is linked with actuality
• it might seem that once it is carved the wood is actually a table, but it is possible that he does not wish to consider the wood to be a table
• perhaps the wood composing the completed table is also, in a sense, still a potential table
• it is not the wood qua wood that is actually a table, but the wood qua table
• as matter, it remains only potentially the thing that it is the matter of
• the wood only constitutes the table and is not identical to the table it constitutes
• Just as Aristotle gives form priority over matter so he gives actuality priority over potentiality Θ.8, 1049b4-5 :
  
• 3 forms of priority are invoked here:
  
• priority in logos (account or definition)
• we must cite the actuality when we give an account of its corresponding potentiality
• ‘visible’ means ‘capable of being seen’; ‘buildable’ means ‘capable of being built’1049b14-16
• but we needn't cite the potentiality when we give an account of a corresponding actuality?
• does the account of "being seen" require us to cite the potentiality ("visible")?
• the answer seems to be 'no'
  
• in time
• potentiality seems to be prior to actuality in time
• the wood precedes the table
  
• the acorn precedes the oak
  
• but the actual which is identical in species though not in number with a potentially existing thing is prior to it 1049b18-19
• the seed (potential substance) must have been preceded by an adult (actual substance)
• so, chickens come before eggs
  
• in substance (being prior in substance means that the prior thing can exist without the thing to which it is prior, but that that posterior thing cannot exist without the prior thing)
  
• two arguments:
• First argument:
  
• things that come to be move toward an end (telos)
  
• the actuality is the end, and it is for the sake of this that the potentiality is acquired ... animals do not see in order that they may have sight, but they have sight that they may see ... matter exists in a potential state, just because it may come to its form; and when it exists actually, then it is in its form 1050a9-17
• Form or actuality is the end toward which natural processes are directed
• one and the same thing may be the final, formal, and efficient cause of another
• when an acorn realizes its potential to become an oak tree, the efficient cause is the actual oak tree that produced the acorn; the formal cause is the logos of "oak tree" defining that actuality; the final cause is the telos toward which the acorn develops — an actual (mature) oak tree.
• so the oak tree is prior to the acorn
  
• Second argument: 1050b6-1051a2
  
• a potentiality is for either of a pair of opposites:
• anything that is capable of being is also capable of not being
  
• what is capable of not being might possibly not be, and what might possibly not be is perishable
• hence anything with the mere potentiality to be is perishable
  
• what is eternal is imperishable
• so nothing that is eternal can exist only potentially
  
• what is eternal must be fully actual
• the eternal is prior in substance to the perishable
• for the eternal can exist without the perishable, but not conversely, and that is what priority in substance amounts to (cf. Δ.11, 1019a2)
• so what is actual is prior in substance to what is potential
• The unity of definition problem revisited
• the problem was raised above in Ζ.17: if man is rational animal, why is this one and not many--rational and animal (1037b13-14)
• Η.6 offers a solution based on potentiality and actuality
• he is trying to explain the unity of things which have several parts and in which the totality is not, as it were, a mere heap, but the whole is something besides the parts 1045a8-10
• one element is matter and another is form, and one is potentially and the other is actually ... and so ... the question will no longer be thought a difficulty 1045a20-25
• it is no longer a difficulty because the potential/actual relation is what glues such things together: they are not mere heaps, which would be simply a set of things put in the same place, so to speak, a heap.
  
• the round bronze example of 1045a26-35: explaining unity of "bronze" + "roundness" >> bronze sphere
  
• take a bronze sphere: if someone were to ask “what makes it one thing, a unity?” the answer would be obvious.
  
• The cause of the unity is just the cause of bronze being made spherical
• there is no cause of its unity other than that the form was put into the matter
• bronze (the matter) is a potential sphere, and the bronze sphere is an actual sphere
• round bronze is equally the essence of both the actual sphere and the potential one
• the bronze and the roundness are not two separate things
• the bronze is potentially a sphere, and when it is made round it constitutes an actual one — a single sphere of bronze
• applying it to a definition:
• explain “the unity of the thing whose account we call a definition” Z.12, 1037b11
• proper definables are universals
• universals are not material objects, and so it is not clear how they can be viewed as hylomorphic compounds
• Aristotle has at his disposal a concept that can fill this bill perfectly, viz., the concept of intelligible matter (hulê noêtê)
• The main purpose of intelligible matter is to provide something quasi-material for pure geometrical objects that are not realized in bronze or stone, for example, to be made of
  
• the triangle in a geometry problem is made of "intelligible matter"
  
• So the Stanford author surmises that it is for this reason that Aristotle goes on (1045a33) to introduce matter into the current context.
  
• we may conclude that the material component in the definition of a species is intelligible matter
• elsewhere, he explicitly describes genus as matter: “the genus is the matter of that of which it is called the genus” (I.8, 1058a23)
• a species, then, although it is not itself a material object, can be considered a hylomorphic compound:
• Its matter is its genus, which is only potentially the species defined
• its differentia is the form that actualizes the matter
• The genus does not actually exist independently of its species any more than bronze exists apart from all form.
  
• The genus animal, for example, is just that which is potentially some specific kind of animal or other. Aristotle concludes (1045b17-21) that “the proximate matter and the form are one and the same thing, the one potentially, and the other actually ... the potential and the actual are somehow one.”
• his solution, of course, applies only to hylomorphic compounds.
  
• But that is all it needs to do
• he ends the chapter by claiming that the problem of unity does not arise for other kinds of compounds. All things which have no matter are without qualification essentially unities 1045b23
  

14. Glossary of Aristotelian Terminology

accident: sumbebêkos
accidental: kata sumbebêkos
account: logos
actuality: energeia, entelecheia
alteration: alloiôsis
affirmative: kataphatikos
assertion: apophansis (sentence with a truth value, declarative sentence)
assumption: hupothesis
attribute: pathos
axiom: axioma
be: einai
being(s): on, onta
belong: huparchein
category: katêgoria
cause: aition, aitia
change: kinêsis, metabolê
come to be: gignesthai
coming to be: genesis
contradict: antiphanai
contradiction: antiphasis (in the sense “contradictory pair of propositions” and also in the sense “denial of a proposition”)
contrary: enantion
definition: horos, horismos
demonstration: apodeixis
denial (of a proposition): apophasis
dialectic: dialektikê
differentia: diaphora; specific difference, eidopoios diaphora
distinctive: idios, idion
end: telos
essence: to ti ên einai, to ti esti
essential: en tôi ti esti, en tôi ti ên einai (of predications); kath’ hauto (of attributes)
exist: einai
explanation: aition, aitia
final cause: hou heneka (literally, “what something is for”)
form: eidos, morphê
formula: logos
function: ergon
genus: genos
homonymous: homônumon
immediate: amesos
impossible: adunaton
in respect of itself: kath’ hauto
individual: atomon, tode ti
induction: epagôgê
infinite: apeiron
kind: genos, eidos
knowledge: epistêmê
matter: hulê
movement: kinêsis
nature: phusis
negation (of a term): apophasis
particular: en merei, epi meros (of a proposition); kath'hekaston (of individuals)
peculiar: idios, idion
per se: kath’ hauto
perception: aisthêsis
perplexity: aporia
possible: dunaton, endechomenon; endechesthai (verb: “be possible”)
potentially: dunamei
potentiality: dunamis
predicate: katêgorein (verb); katêegoroumenon(“what is predicated”)
predication: katêgoria (act or instance of predicating, type of predication)
principle: archê (starting point of a demonstration)
qua: hêi
quality: poion
quantity: poson
refute: elenchein; refutation, elenchos
separate: chôriston
said in many ways: pollachôs legetai
science: epistêmê
soul: psuchê
species: eidos
specific: eidopoios (of a differentia that “makes a species”, eidopoios diaphora)
subject: hupokeimenon
substance: ousia
term: horos
this: tode ti
universal: katholou (both of propositions and of individuals)
wisdom: sophia