Aristotle’s logic and metaphysicsAlan CodePART 1: LOGICAL WORKSOVERVIEW OF ARISTOTLE’S LOGICThe Aristotelian logical works are referred to collectively using the Greekterm
‘Organon’. This is a reflection of the idea that logic is a tool orinstrument of, though not necessarily a proper part of, philosophy. In thetraditional ordering of these works the
Categories comes first. It deals,among other things, with the simple terms (subjects and predicates) thatwhen combined go together to form simple statements, and it characterizesprimary substances as the ultimate subjects for predication. It also containsa treatment of ten categories, with particular emphasis on the fourcategories of substance, quantity, relation and quality. The
DeInterpretatione, which is placed second, discusses the statements that resultfrom combining nouns and verbs, and includes a treatment of variousmodal relations between statements. The main topic of the two
Analytics isdemonstration
(epideixis), the type of valid deductive argument, orsyllogism,
(sullogismos) involved in scientific knowledge
(epistêmê). The
Prior Analytics, which contains a formal theory of syllogistic reasoning,shows how statements combine to form arguments, and in the
PosteriorAnalytics demonstrations are analyzed as explanatory syllogisms from firstprinciples. This work combines the notion of syllogistic inference with anaccount of the nature of scientific first principles in its analysis of thestructure of science. The
Topics is chiefly concerned with dialecticaldebate, and the work
On Sophistical Refutations contains a treatment ofvarious kinds of fallacies in dialectical argument. At the conclusion of thiswork Aristotle indicates that unlike his other inquiries, such as histreatment of rhetoric, that build upon the results of his predecessors, priorto his own efforts there simply was no general inquiry concerningsyllogistic reasoning.The
Rhetoric, not itself included in the
Organon, isconcerned with the use of rhetorical argumentation for the purpose ofpersuading an audience.
PREDICATION, AND SUBSTANCE AS SUBJECTPredicationIn the
Categories (using terminology not employed for this purpose outsidethat work) predication is characterized in terms of the two relations ‘saidof a subject’ and ‘present in a subject’. The relata are ‘things that are’
(onta), and this type of predication may be dubbed ‘ontological’. Althoughthe verb translated ‘to be predicated’
(katêgoreisthai) is used extensivelyoutside the
Categories, the way in which the phrases ‘said of’ and ‘presentin’ are used here is idiosyncratic to this work. Due to the way it isconnected with the notion of definition, it is convenient to describe therelation ‘being said of a subject’ as
essential predication. Essentialpredications say what a subject is intrinsically, or
per se.<sup>1</sup> By way ofcontrast, the relation ‘being present in a subject’, which in the
Categoriescovers all types of predication other than essential predication, is
accidental predication.<sup>2</sup>Although these two relations are taken as primitives in the
Categories,remarks there provide a partial characterization.<sup>3</sup> The ‘said of’ relation istransitive, and as will be seen below, is connected with definition in a waythat the ‘present in’ relation is not. Given that
man is predicable ofSocrates, anything predicable of man, for instance, is thereby predicable ofSocrates. The definition of the species man applies to him as well. The classof things ‘present in a subject’ are described as being present not in the waythat a part is present in a whole, and as incapable of existing separatelyfrom some subject that they are in. These two types of ontologicalpredicability help account for linguistic predicability (the application of alinguistic predicate to a subject). A simple subject-predicate sentence is usedto make a simple affirmative statement in which one item is predicated ofanother, usually distinct, item. The linguistic predicates ‘man’ and‘grammarian’ are applicable to some subject just in case the species manand grammatical knowledge, respectively, are ontologically predicable ofthat subject.The notion of predication is employed in
De Interpretatione 7 todistinguish particulars from universals. A ‘universal’
(katholou) is an itemof such a nature as to be predicable of a plurality of things; a ‘particular’
(kath’ hekaston) is an item that cannot be predicated, either essentially oraccidentally, of a plurality. Aristotle sometimes uses the term ‘individual’
(atomon) for items not essentially predicable of other things (thus leaving itopen whether an individual is accidentally predicable of something distinctfrom itself).The
Categories distinguishes between the simple linguistic expressions(things spoken of without combination) of which statements arecomposed, and the entities those expressions signify. The name ‘man’, forinstance, and the verb ‘runs’ are simple significant expressions thatcombine to form the declarative subject-predicate sentence ‘Man runs’.Although when used without combination, neither of these words has atruth-value, they may be combined to form a statement that is either trueor false. The word ‘man’ signifies man, the word ‘runs’ signifies the activityof running, and one uses the sentence ‘Man runs’ to truly affirm somepredicable (namely,
running) of some subject (namely,
man). The word‘man’, which may serve as either a subject or a predicate expression,signifies a substance,<sup>4</sup> for it signifies the species man, and that is asubstance. There are also particular substances, like Socrates, which are thesignification of names that function as grammatical subjects, but never asgrammatical predicates. The particular itself is always an ontologicalsubject, and never a predicable.According to
Categories 4 the ten kinds of things that are signified bysimple expressions are: substances, quantities, qualities, relatives, places,times, positions, states, doings and undergoings. Although Aristotle doesnot himself explain the rationale for this list, it is a classification of thekinds of things that could be said of something in response to a questionasked about it. When we say of some particular substance what it is, aswhen we say of Socrates that he is a man, the simple expression (here‘man’) signifies a substance. However, in addition to predicates offered inresponse to the question (1) ‘What is it?’ when asked of a particularsubstance, there are other kinds of linguistic terms that are given inresponse to other kinds of questions. For instance, we may ask ofsomething (2) ‘How large is it?’ and elicit a reply such as ‘six feet’. In a likemanner each of the other entries on this list classifies a kind of answer tosome other kind of question: (3) ‘What is it like?’ (to which we mightanswer ‘pale’); (4) ‘What is it in relation to something?’ (A double, a half);(5) ‘Where is it?’ (in the Lyceum); (6) ‘When was it?’ (yesterday, last year);(7) ‘What position is it in?’ (lying down, or sitting); (8) ‘What state is it in?’(armed); (9) ‘What is it doing?’ (cutting); or (10) ‘What is being done toit?’ (being cut). Just as questions such as ‘What is Socrates?’ and ‘What isBucephalus?’ collect predicate expressions such as ‘man’, ‘horse’ and‘animal’ that signify substances, these other nine questions collect predicateexpressions that signify other kinds of predicables.The ten kinds of things signified by these kinds of expressions arestandardly referred to as the Aristotelian categories. Aristotle frequentlyuses the Greek word
‘katêgoria’ to mean ‘predicate’, or ‘kind of predicate’.When the term is used in this sense, particular substances are notthemselves in the ‘category’ of substance (since they are always subjects andnever predicates). Elsewhere when Aristotle makes use of a classification of‘categories’, this full list of ten does not appear.<sup>5</sup> For instance,
MetaphysicsDelta 7 correlates the various
per se senses of ‘to be’ with an eight-foldcategorial schema of the sort suggested by this list.A subject’s essential predicates are those that signify
what it is. Thesubject is called what it is synonymously from such predicates. In the firstchapter of the
Categories, two things are
homonyms just in case, althoughthere is a term that applies to both, the definitions associated with the twoapplications are distinct; two things are
synonyms just in case the sameterm applies to both, and the associated definition is the same as well.Some universal X is said of some subject Y if, and only if, both the nameand the definition of X truly apply to Y. For this reason whenever auniversal is said of a subject, the universal and its subject are ‘synonyms’.The word ‘man’, for instance, is applicable to the particular man becausethe universal it signifies, the species man, is predicable of him. However,not only does the name of the species apply, its definition applies as well. Thedefinition of man is an account saying what man is, and the definition thatapplies to Socrates is the definition of the species man. Assuming forillustrative purposes that the account that defines man is ‘biped animal’, itis true that whatever is a man must be a biped animal. The definition of thespecies man applies to particular men, and the species is predicatedessentially of those particulars. The defining expression that signifies theessence of a particular just is the definition of its species.In the
Organon universals, not sensible particulars, are the objects ofdefinition. The definition appropriate for a particular is the definition ofthe species to which it belongs. In order for a particular to be a logicalsubject, or subject of predication at all, it must be something essentially.The species to which a particular belongs, although not identical with theparticular, is what the particular essentially is. It is the definable somethingthe particular must be essentially if it is to be anything at all.Not only substantial universals, but any object of definition whatsoeveris a subject for essential predication. The color white, for instance, is a color,and hence color is predicable of white. Substances and non-substances alikemay possess definitions, and hence be endowed with essential natures. Inaddition to the names of substantial universals, there are also names of theuniversals that are accidentally predicable of substances. Although, in somecases, the name of a non-substantial universal (the name ‘white’, forinstance) applies to the substances to which the universal is present, ingeneral not the name itself, but rather some linguistic predicate associatedwith the name, is applicable to all and only those things having theuniversal as an accidental property. Socrates is called ‘brave’, not ‘bravery’.Despite this, the definition of any universal X that is accidentallypredicable of a subject Y can never be truly applied to Y. Although thename ‘white’ applies to white particulars in virtue of the fact that they allhave the color white, the definition of that color is not linguisticallypredicable of any of them. They are not called white in virtue of what theyare.If a non-substantial property is present in a subject, then (in general) itsname does not apply to that subject, but there will be some associatedexpression that differs in ending, which is applicable to the subject. In suchcases the subject is called what it is called
paronymously from thatproperty. Although the noun ‘bravery’ cannot be truly predicated ofSocrates, the adjective ‘brave’ is applicable to Socrates because bravery ispresent to him. The brave thing is a paronym.
Substance as subjectTranslators of Aristotle’s Greek typically render the abstract substantive
‘ousia’ as ‘substance’,<sup>6</sup> suggesting the idea that substances are the subjectsof predication. In the
Categories all beings except for primary substancesare predicable (either essentially or accidentally) of primary substances. Onthe other hand, a primary substance is a primary substance because it is asubject
(hupukeimenon) for the other things, but is not itself predicable ofanything further. Each primary substance is an individual subject ofpredication that is not itself predicable of a substance, and as such is ‘somethis’
(tode ti).In this treatise all primary substances are particulars—the particular man,the particular horse, and so on. Aristotle here treats individual men,horses, and the like as primary substances. In the
Metaphysics he alsoconsiders the claims of their matter and form to be substance, but in thiswork the individual is not subjected to the hylomorphic analysis foundboth in his natural science and the
Metaphysics. There is no discussion inthe
Organon of matter, nor of the relations between the individual man,his body and his form (or soul).In the
Categories primary substances are particulars, and their naturalkinds (i.e., their species and genera) are universals. These natural kinds arecalled ‘secondary substances’, and are the only substances other than theprimary substances. The only universals in the
Categories are (1) secondarysubstances, (2) their differentiae, and (3) the various quantities, qualities,and other non-substantial items that are had by the substances.<sup>7</sup> Somelinguistic predicates, such as ‘man’, signify universals that are essentiallypredicable of all the substantial particulars of which they are predicable.These terms classify particulars according to their natural kinds.In addition to its distinction between primary and secondary substance,with the attendant designation of the primary substances as the subjects foreverything else, the
Categories also lists a number of the distinctivecharacteristics
(idia) of substances, quantities, relatives and qualities. Forinstance, substances do not have contraries, nor do they admit of degrees.Most importantly, anything that can persist through time as numericallyone and the same while receiving contrary properties must be a primarysubstance. One and the same individual man can be pale at one time, darkat another; hot at one time, cold at another; bad at one time, good atanother. In this way the ultimate subjects of predication are treated as thepersisting subjects for accidental change.
THE STRUCTURE OF SCIENTIFIC KNOWLEDGESyllogisticThe theory of syllogistic reasoning in the
Prior Analytics concerns therelation between the premises and the conclusion of a syllogism. Theconclusion
follows of necessity from the premises. In his account of thisrelation he appeals to characteristics of arguments that abstract from thecontent of the statements involved. He identifies a few obvious (perfect)cases of this relation, and then shows that all non-obvious (imperfect) casescan be reduced to the obvious.The notion of syllogistic inference is utilized both in Aristotle’s analysisof scientific reasoning and in his treatment of dialectical argument. Ascientific demonstration is a syllogism that proves its conclusion byshowing how it necessarily follows from its explanatory principles.Knowing scientifically requires this kind of argument from indemonstrablestarting points. Reasoning from necessarily true explanatory principles tonecessarily true scientific conclusions takes place in a variety of sciencesthat do not share a common genus or kind. This is why a general accountof this relation must abstract from the particular content of the statementsof any given science. In this sense his theory is sometimes described as‘formal’.In a similar manner, the logical expertise exemplified by a dialectician intwo person question-answer exchanges involves the production of validinferences, and this ability is not confined to a single domain. In the firstbook of the
Topics dialectical skill is characterized as the ability both toreason syllogistically from credible opinions
(endoxa) to conclusions thatnecessarily follow from them, and to avoid being refuted by one’s ownconcessions in argument. Dialectic is useful for intellectual training, forpersuading a general audience and for philosophical knowledge. It enablesone to develop and examine the arguments on both sides of philosophicalpuzzles
(aporiai), thereby facilitating the discernment of truth. Furthermore,the dialectical scrutiny of credible opinions provides a path thatleads to the first principles of the sciences. Unlike scientific argumentswhich argue from first principles and are concerned with items within asingle subject genus, dialectical argument is possible concerning any subjectmatter whatsoever, and in this sense is topic neutral. Hence a generalaccount of the way in which a dialectician shows that credible opinions andan interlocutor’s concessions necessitate further conclusions requiresabstraction from subject matter. In dialectical argument one asksquestions, and produces syllogisms using the answers as premises.However, since such arguments do not reason from explanatory premisesalready known by the respondent, they do not result in knowledge.Although credible opinions, which can include commonly accepted viewsas well as the opinions of the wise, must not be obvious falsehoods, theymay in fact be false, and certainly need not be explanatory first principles.Reasoning from them is in any case no guarantee that the conclusionsreached are true, and even where the premises are true, they (typically) donot explain the truth of the conclusion.<sup>8</sup>In the first chapter of the
Prior Analytics Aristotle informallycharacterizes a syllogism as an account9 in which certain things beingposited, something other than what has been posited follows of necessity invirtue of the former’s being the case. He further explains that ‘in virtue oftheir being the case’ means ‘resulting through them’, and that this involvesnot needing any term outside of those in the premises for the generation ofthe necessity. A syllogism is a case of a valid argument in which theconclusion follows of necessity from the premises, and does so in virtue ofthe way subject and predicate terms are combined. The heart of hissyllogistic is a general characterization of those valid arguments thatcontain a pair of simple statements as premises, have a simple statement asconclusion, and involve just three terms: major, middle, minor. In aid ofgenerality, actual Greek terms (like ‘animal’ or ‘pale’) are replaced byGreek letters (like ‘A’ and ‘B’) used as schematic letters. The forms of thefour basic types of statements (the ‘assertoric’ propositional forms) arecharacterized in terms of their quantity and quality, and his three syllogistic‘figures’ are characterized by reference to the order of the major, middleand minor terms of an argument.<sup>10</sup> In addition, Aristotle presents anumber of rules of conversion. He identifies within the three ‘figures’ thesyllogisms, or valid arguments, and believes that every scientificdemonstration and every syllogism in the informal sense can be capturedby a string of two premise syllogisms from these figures (and ultimatelyfrom the first figure).Although the
Prior Analytics does not explicitly refer to the
DeInterpretatione, its account of syllogistic inference builds upon ideas aboutstatements that can be found in the latter. There both designating termsand verbs are said to have a signification on their own (though not a truthvalue).They can, however, be combined to form simple sentences.<sup>11</sup> Astatement
(apophansis) is a sentence that is capable of either truth orfalsehood. The
Organon has no further discussion of sentences that lack atruth-value (such as prayers), and leaves them as a topic of discussion forrhetoric and poetics. Every simple statement is either an affirmation
(kataphasis) or a denial
(apophasis) An affirmation affirms some predicateof a subject, whereas a denial denies some predicate of a subject.Both particulars and universals may serve as the subjects of a statement,but the predicate of a statement is always universal. Where both thesubject and the predicate are universals, one may further specify whetherthe affirmation or denial is of the subject taken as a whole, or merely as apart. The statement that ‘every animal is pale’ affirms
pale of its subject,
animal, as a whole. Such a statement is called ‘universal’ in quantity. Byway of contrast, ‘some animal is pale’ affirms
pale of only a part of itssubject. Such a statement is called ‘particular’ in quantity.<sup>12</sup> One mayspecify in terms of their quantity (universal or particular) and quality(affirmative or negative) the four so-called assertoric categoricalpropositional forms employed in Aristotle’s syllogistic: universalaffirmative, or A propositions (for example, every man is mortal);universal negative, or E propositions (for example, no man is mortal);particular affirmative, or I propositions (for example, some man is mortal);and particular negative, or O propositions (for example, some man is notmortal).<sup>13</sup> Aristotle tried to show that all valid arguments could be put intosyllogisms constructed of premises and conclusions of these forms.However, his account does not give axioms or rules for the propositionalconnectives, or statements containing either nested quantification orrelational predicates. This drastically limits its scope of application. Anadditional problem results from the fact that use of a categorical statementin a syllogism presupposes that its terms have instances. (For instance, if itis true that all men are mortal, it is also true that some men are mortal.)There are logical relations that obtain between the different propositionalforms. Consider four propositions, or statements, sharing the same subjectand predicate but each exemplifying a different propositional form. The Aand O propositions are
contradictories,<sup>14</sup> as are the E and the I; the A andE are
contraries; <sup>15</sup> I is the
subalternate of A, and O the
subalternate of E.<sup>16</sup>The
Prior Analytics captures some further basic relations between thepropositional forms by means of the following three conversion rules:C1 if every S is P, some P is SC2 if some S is P, some P is SC3 if no S is P, no P is SThese are not themselves syllogisms, and function in effect as rules for validarguments having a single assertoric premise and a single assertoricconclusion.The syllogisms given formal treatment in this account consist of twopremises and a conclusion, and each has both a
figure and a
mood.Statements are composed of terms, and the notion of
figure is characterizedby specifying the relationships between the terms occurring in the premisesand the conclusions. The two
extreme terms are the subject and thepredicate of the conclusion, the
major term being the predicate of theconclusion, the
minor term being its subject. The
middle term is the onethat occurs in both premises, but not in the conclusion. The
major premiseis the premise containing the major term, and the
minor premise is thepremise containing the minor term. An argument is in the
first figure if themajor term is the predicate of the major premise, and the minor term is thesubject of the minor premise. In such cases the middle term is the subject ofthe major premise, and the predicate of the minor premise. An argument isin the
second figure when the middle term is the predicate of bothpremises, and in the
third figure when the middle term is the subject ofboth premises.The syllogisms, or valid arguments within the three figures may bespecified in terms of their
mood, where the mood of a syllogism can berepresented as a trio of propositional forms: the form of the major premise,the minor premise and the conclusion (in that order).
Prior Analytics A4–6states all the valid and invalid moods of the three figures. The valid moodsof the first figure are AAA, EAE, AII, EIO (plus the subaltern moods AAI,EAO).<sup>17</sup> Invalid moods are shown to be such by producingcounterexamples—that is, instances of a figure and mood combination inwhich the premises can be true, and the conclusion false.Having specified the syllogisms of the first three figures, Aristotlereduces the so-called ‘imperfect’ syllogisms of the second and third figure tothe ‘perfect’ syllogisms of the first figure. The perfect syllogisms of the firstfigure are basic cases in which nothing other than the premises themselvesare needed in order for it to be evident that the conclusion follows ofnecessity from the premises. Although in an imperfect syllogism theconclusion does necessarily follow, in order to make this evident one mustdo more than simply present the premises. The reduction shows that a validargument that uses second or third figure resources to derive a conclusioncan be replaced by valid reasoning that derives the same conclusion fromthe same premises relying upon only the obvious inferences of the firstfigure, together with the conversion rules.<sup>18</sup> In some cases a directreduction utilizing conversion is possible, but where this is not possible(second figure AOO and third figure OAO), he resorts to
reductio adabsurdum.<sup>19</sup> A
reductio argument shows that the premises have a certainsyllogistic consequence by producing a direct deduction of thecontradictory of one premise from the other premise taken together withthe contradictory of the conclusion.
Demonstration and first principlesFor Aristotle the universe can be rendered intelligible, or understood, byhumans.
Metaphysics Epsilon 1 divides all knowledge into the theoretical,the practical and the productive. Whereas the goal of a productive scienceis always some product distinct from the exercise of the science itself (suchas a shoe, a statue or health), and the goal of practical knowledge consistsof the activities of life, theoretical knowledge is an understanding of the truthmerely for its own sake. Theoretical knowledge itself is divided into themathematical sciences, the natural or physical sciences and theology. Thepractitioner of a theoretical science knows, or understands, something bygrasping its ‘why’ or ‘cause’. Knowledge is attained when something isexplained by means of starting points or principles
(archai) that are evenbetter known than what is explained.The account in the
Posterior Analytics of the structure of ademonstrative science is both patterned after and inspired by the way inwhich the Ancient Greek mathematical sciences, especially geometry, haddeveloped in the direction of axiomatization. Ideally, the premises of amathematical proof both
necessitate the conclusion, and
explain why it istrue. It is with this ideal in mind that he says in
Posterior Analytics A2 thatwe think that we have knowledge or understanding (in the unqualifiedsense) whenever we suppose both (1) that we know its ‘cause’ (the reason itis the case), and (2) that it could not possibly be otherwise. The word‘cause’ is used here to translate the Greek term
‘aitia’, but it should bestressed that the range of applicability of the Greek term overlaps with, butis not coextensive with that of our word ‘cause’. Anything that can beexplained has an
aitia, regardless of whether it is the type of thing that wewould ordinarily describe as ‘caused’. For instance, the premises of amathematical proof, although not causes, nonetheless explain the truth ofthe conclusion, and may reasonably be said to be responsible for it. The
aitia of something is what is responsible for its being a certain way, and assuch is an explanatory factor the grasp of which constitutes knowing whysomething is the case. What is known in the unqualified sense of that termmust be a necessary truth.Building on his key insight that knowledge requires both anunderstanding of ‘causes’ and the necessity of what is known, the treatisegoes on to discuss the different kinds of first principles, and how they arerelated to theorems. The necessary truths that constitute the body of ademonstrative science are exhaustively partitioned into indemonstrablefirst principles, and their demonstrable consequences. The former areunderstood through themselves. Their consequences, the theorems, areknown or understood only through their ‘causes’ and principles. Ourknowledge of the latter is demonstrative in that such knowledge involvesdeducing them from first principles that explain why they are the case.
Posterior Analytics A2 states that the principles must be true, primary,immediate, better known than, prior to and explanatory of those things ofwhich they are the principles. Since a first principle is known throughitself, and not through other things, there is no explanation as to why theprinciple is true. It is not explained or ‘caused’ by anything, and hence itcannot be known by tracing it back to causes. A first principle isindemonstrable, for it is both primary and immediate. To be immediate, itmust be primary in the sense that there is nothing prior to it in terms ofwhich it is understood or known. If it is a statement (such as a definition)with both a subject and a predicate, there is no middle term that explainsor mediates the connection between its subject and its predicate. A firstprinciple cannot itself be explained by deducing it from prior principles orcauses, and in this way is indemonstrable.<sup>20</sup> The other necessary truths of ascience are explained or ‘caused’ by something other than themselves. Theyare known by tracing them back to principles, and ‘causes’ that are knownthrough themselves. Such theorems are known only when one understandswhy they must be true. Theorems are known by deducing them fromnecessarily true first principles that are their ‘causes’, and the firstprinciples must themselves be known independently of, and prior todemonstration. Demonstration itself is a scientific syllogism, a syllogism byvirtue of which we know.Aristotle thinks that all knowledge comes from pre-existing knowledge.In the case of knowledge of theorems, the pre-existing knowledge is theknowledge of the principles. However, since the first principles are betterknown than the conclusions of any demonstrative argument, althoughknowledge of them also comes from pre-existing knowledge, they mustcome to be known in some way other than demonstration. In connectionwith this topic Aristotle draws a distinction between what is known to usand what is known without qualification. What is known to us, prior toknowing first principles, is what we know through sense perception. This isnot scientific knowledge, or knowledge without qualification. Our task isto move from what is known to us to knowledge of what is most knowablewithout qualification. These are the intelligible principles that will in turnexplain and account for the original sensible phenomena from which westarted. In the last chapter of the
Posterior Analytics, B19, Aristotleexplains that we come to know first principles through induction
(epagogê), an argumentative procedure that proceeds to a generalizationfrom some group of its instances. Aristotle is aware that such inferences arenot deductively valid, and unfortunately does not develop a set of rulesgoverning such inferences. Consequently, details of his views about thisprocedure cannot be described with confidence. What he does say indicatesthat induction is supposed to be the means by which an inquirer advancesfrom what is initially knowable (to that individual) to what is knowablewithout qualification. In B19 it is said that
knowledge of first principles isbased on
experience, that experience in turn is based on numerous
memories, and finally that memories themselves result from numerous andrepeated
perceptions, All animals, ourselves included, have naturaldiscriminative perceptual capacities. Perception provides the ultimateinductive basis for knowledge of first principles. The epistemic state theexercise of which constitutes knowledge of principles is called
‘nous’, orintelligence. Very little is said about it here, and when it is discussedelsewhere, in
De Anima Gamma 4 and 5, the text is highly controversialand notoriously difficult.Each demonstrative science has both a kind term that demarcates itssubject matter and a set of attributes that it studies.
Posterior Analytics A7and A10 show that a demonstrative science makes use of first principlesin order to prove its conclusions about those objects that are encompassedby the general kind that it studies. Such demonstrated conclusions ascribeto these objects those properties that pertain to them
intrinsically. A sciencestudies items mentioned in the definitions of those things falling within thescope of its subject genus, as well as those definable things themselves, andtheir demonstrable attributes. These additional items are properties, or‘modifications’
(pathê) either of the things within the scope of the genus, orof the genus itself. They are not included in the definitions of the subjectsthat possess them, and consequently demonstrations must be given to showthat they belong to their subjects intrinsically. Geometry studies figures,and seeks causes and principles that govern each kind of figure
qua thatkind of figure. An example would be the proof of the theorem that theangles of a triangle equal two right angles. In general, the geometer appealsto first principles to explain what belongs to various kinds of figures insofaras, and because, they are figures.Aristotle put forward his account of scientific knowledge in oppositionto the Platonic conception of a general dialectical science of being. WhereasPlatonic dialectic purported to yield scientific understanding of theprinciples of the departmental sciences, Aristotle’s rival account wasdesigned to uphold the independence or autonomy of the departmentalsciences. The statements within such a science include propositional firstprinciples as well as the theorems in which the ‘modifications’ of varioustypes of figures are demonstrated.<sup>21</sup> Aristotle divided the first principles ofa science into axioms and theses, and divided the latter into hypotheses anddefinitions. Whereas the definition of X is an account signifying what X is,a hypothesis is an existence postulate that states of what is defined
that itis. The definitions and hypotheses of a science are employed only in thatbranch of knowledge, and being first principles are not demonstrated bysome other science. A definition is immediate in the sense that the predicateof a definition signifies just what the subject is, and hence the connectionbetween subject and predicate is not explicable by reference to a middleterm.By way of contrast with theses, the axioms are common to all sciences.Aristotle describes axioms as the principles from which reasoning arises,and as such they must be known in order to learn or scientificallyunderstand anything at all. The two most important examples of axiomsare the law of non-contradiction, and the law of the excluded middle (theprinciple that there cannot be an intermediate between contradictories).The axioms are common to all of the sciences, and knowledge of the axiomsis common to all scientific understanders. This is relevant to Aristotle’sconception of metaphysics as general ontology, a science which amongother things investigates the axioms (for which see pp. 60–1).A science does not study just any attribute that might happen to belongto its subject matter, for there is no science of the accidental. In order todetermine which statements, terms and first principles are appropriate for agiven science with a given subject matter, one must specify the
respect inwhich the science in question studies the application of the various terms tothe subject it studies. For instance, the biologist does not study all theproperties of living things, but only those that apply to them in respect ofbeing living beings. Biology studies both the definitions of each species ofliving things and the properties that belong to each species
per se, orintrinsically.A science studies what must belong to a subject in some respect, and inso doing investigates what belongs to it intrinsically, or
per se.<sup>22</sup>
PosteriorAnalytics A4 distinguishes the following three distinct ways in whichsomething can belong to a subject
per se. First, if something is in theaccount saying what some subject is (i.e., in the definition of the subject) itbelongs to that thing
per se. It is in this way that both biped and animalbelong to the species man intrinsically1. In a second way something belongsto a subject intrinsically if that item is such that the subject in question is inits definition. It is in this way that ‘male’ and ‘female’ hold good of animalintrinsically2. Finally, in still another way, an item is said to belong to asubject in respect of itself if that item belongs to the subject because of, oron account of the subject. In this third way, ‘being-receptive-of-grammar’belongs to man intrinsically3; ‘having-interior-angles-equal-to-two-rightangles’belongs to triangle intrinsically3. What does not belong to a subjectintrinsically, or intrinsically2 is sometimes called by Aristotle ‘accidental’.Consequently, items that intrinsically belong to something in this third wayare sometimes called
per se, or intrinsic accidents. He also distinguishesthings that are beings intrinsically from things that are beings accidentally.Something is a being intrinsically, or
per se, just in case it is not called whatit is called through being something else that happens to be that. By way ofcontrast, a pale thing, or a cultured thing, is a being accidentally since it iscalled what it is called (namely ‘pale’ or ‘cultured’) through beingsomething else, a man, that happens to be called ‘pale’ or ‘cultured’.The first sense of ‘intrinsic’, or
per se, is the most basic of all, andbecause of its connection with definition can be used to characterize thenotion of essence. The essence of each thing is what it is said to beintrinsically1, and it is essentially predicable of that of which it is theessence.
Topics A5 states that a definition (
horos or
horismos) is an account
(logos) signifying the essence of that thing. (Rather than using a singleword to mean essence here, he employs a phrase that corresponds to theEnglish ‘what it is (for it) to be’
(to ti ên einai). The essence of something isthe entity signified by the entire account saying what it is. Although heargues that the Platonic method of collection and division cannotdemonstrate a definition, the influence of that method can be seen inAristotle’s own conception of definition as a complex expression thatmentions both the
genus to which the item belongs and the
differentiaethat distinguish it from other coordinate members of that genus.A definition is an account signifying an essence. An account signifyingwhat something is signifies its essence, and the definition of something isthe account that says what it is.<sup>23</sup> If the definition of man is ‘biped animal’,then biped animal is the essence of man. Just as the word ‘man’ signifiesthe species man, the definition of man signifies the essence of man. Topredicate an essence of that of which it is the essence one may linguisticallypredicate the appropriate associated defining expression, thereby sayingwhat that thing is. A definable item is one and the same as the essencesignified by its definition. Whenever some universal is defined, the subjectof the definition is the same as the essence signified by the definiens. Thusif man is correctly defined as ‘biped animal’, then the species man and theessence signified by the phrase ‘biped animal’ are the same thing.For this reason definitions are immediate principles. The statement ofessence says what a thing is intrinsically1, and is even better known thanany theorem, but its truth is not demonstrated by any argumentativeprocedure. His account of the nature of a deductive science is built aroundthis idea of indemonstrable statements of essence. Scientists know things byknowing their essences. The essences signified by real definitions function asmiddle terms in scientific demonstrations. They are the ‘causes’ that explainthe intrinsic connection between subject and predicate in a scientifictheorem.
PART 2:METAPHYSICSOVERVIEW OF ARISTOTLE’S METAPHYSICSThere is disagreement as to how much of the collection of fourteentreatises called the
Metaphysics was originally intended to be part of asingle work, but it is generally agreed that their final organization is notdue to Aristotle. By the first century BC an Aristotelian corpus wasorganized following the Stoic division of philosophy into logic, naturalscience and ethics. The topics investigated in the
Metaphysics do notreadily fall under these headings, and it is possible that the title was meantto indicate a supra-sensible subject matter, or perhaps the fact that it is tobe studied after natural science. However, this label may mean no morethan ‘the things after physics’, and hence indicate no more than a decisionto place it in the corpus after the treatises on natural science. The title isnot Aristotle’s own, and he himself described the science it investigatesusing the labels ‘wisdom’, ‘first philosophy’ and ‘the science of “that whichis”
qua “thing that is”’. Different books of the
Metaphysics give differentcharacterizations of this science, and the treatise as a whole does notcontain a completed overall project.Many scholars have thought that at least Books A-elatton, Delta and Kwere added later by editors. A-elatton, the brief second book, deals withphilosophy as the knowledge of truth, as well as the connection betweenthe finitude of causes and the possibility of knowledge. It has theappearance of an introduction, and according to one tradition consists ofnotes taken by Pasicles, the nephew of Eudemus of Rhodes, on lecturesdelivered by Aristotle. Delta, which may have circulated independently inantiquity, is a lexicon of philosophical terms, many of which play a crucialrole in the
Metaphysics. It includes entries on ‘principle’, ‘cause’,‘substance’, ‘being’, ‘prior’ and ‘posterior’. However, it lacks entries onmany key metaphysical terms (for example, ‘essence’, ‘subject’, ‘matter’,‘form’, ‘some this’ and ‘separate’). Book K contains alternative versions ofparts of B, Gamma and Epsilon, as well as some excerpts from the
Physicson such topics as luck, change, infinity and continuity.Book A begins with the famous dictum that all humans by nature desireto know. After a description of a progression starting from ‘perception’,and going through ‘memory’, ‘experience’ and ‘skill’ to ‘theoreticalknowledge’, it describes the goal of the investigation as wisdom
(sophia), akind of knowledge of the causes and principles of things. Such a sciencewould involve a general account of the causes and principles of all things,and would involve an understanding of the highest good. In the course ofarguing that it is pursued for its own sake, he explains that philosophybegins in wonder, and above all we engage in it when we are puzzled, andcannot explain why things are the way they are. Next, A3–9 presents alengthy survey of the views of his predecessors on the causes of things.Having discussed, among others, Thales, Anaximenes, Anaxagoras,Empedocles, Democritus, Leucippus, Parmenides, the Pythagoreans andPlato, he concludes in A10 that nobody has employed a type of cause otherthan those he named in the second book of his
Physics: the material,formal, final and efficient.The organization of material in the treatise as a whole is in part areflection of Aristotle’s belief that investigation involves a methodologyaccording to which one starts with what is familiar to us initially, andmoves towards an understanding of first principles that are knowable bynature. He starts with a review of the previously held opinions. In ageneral way this is accomplished by the survey in Book A, but whererelevant there are other references to what has been thought by others.Second, there should be a statement of the puzzles<sup>24</sup> that these views giverise to. Prior to arriving at explanatory starting points, an inquirer is in astate of ignorance and puzzlement-thought is tied up in knots. Concerningthe nature, scope and subject matter of wisdom, the most general science ofthe causes, there are opposing views, each supported by considerationshaving at least some degree of credibility. Book B contains a collection ofbrief sketches of puzzles about the causes of things. Some are morethoroughly investigated and answered elsewhere in the
Metaphysics. Thislist both initiates and structures metaphysical investigation, the goal ofwhich is the understanding that results from the resolution of such puzzles.It includes both puzzles about the unity of what later turn out to be thevarious parts of metaphysics, as well as probing questions about the propercharacterization of the highest explanatory entities. Insofar as thesearguments arise from
endoxa, this part of philosophical investigationinvolves an exercise of dialectical skill. The final stage consists of apresentation of solutions, ideally making use of starting points or principlesthat are both natural and explanatory. Although sometimes there are clearindications that a solution is being offered, often it is not easy to determinewhether a passage is presenting his own view rather than developing apuzzle to be solved.Book Gamma asserts the existence of a general science that studies ‘thatwhich is’
qua, ‘thing which is’. By virtue of its generality it is contrastedwith those sciences that study only some part of what there is. It also solvessome of the puzzles of Book B by arguing, among other things, first thatgeneral ontology is also the science of substance, and subsequently that itstudies those concepts, such as unity and plurality, that apply to thingsquite generally. General ontology also studies such basic logical principlesas the law of non-contradiction and the law of excluded middle. In thecourse of pursuing the latter there is a lengthy examination and putativerefutation of the Protagorean doctrine of truth.Book Epsilon divides theoretical knowledge into mathematics, naturalscience and theology. Most parts of mathematics deal with things that areunchanging but do not exist separately; the physical sciences deal withrealities that do exist separately (although their forms cannot exist exceptin matter), and are subject to change; finally, theology studies separate andunchanging substance. First philosophy will be theology if such substancesexist (otherwise it will be natural science), and it is here claimed that firstphilosophy will also be the universal science that studies ‘that which is’
qua‘thing that is’. This book also reiterates a four-fold distinction found inDelta 7 according to which the word ‘being’
(on) can be used for (1) ‘thatwhich is’ so and so
per accidens (where the predicate does not belongintrinsically or
per se<sup>25</sup> to its subject; for example, a human is cultured, butnot in its own right), (2) ‘that which is’ so and so intrinsically or
per se (wherethe predicate does belong
per se, and typically the subject and predicate arein the same category of ‘that which is’), (3) ‘that which is’ so and so eitherpotentially or in actuality (i.e., the predicate belongs either actually orpotentially to the subject) and (4) ‘that which is’ in the sense of that whichis true. General ontology is not concerned with either the first or fourth.There simply is no science of the accidental (this happening neither alwaysnor for the most part), and since truth depends upon the combination andseparation of things in the mind, it is simply a modification of thought.Accordingly, the following three books begin with a discussion of ‘thatwhich is’ in connection with categories, and later move to a discussion ofthe further division of ‘that which is’ into potential and actual.<sup>26</sup>The so-called middle books, Zeta, Eta and Theta (as well as Lambda 1–5)are concerned with sensible substance, and draw on some of the basicprinciples employed in Aristotle’s hylomorphic physics. Zeta presents acomplex set of arguments that eventually leads to the view that the formof a sensible substance, rather than its matter or the sensible compositeitself, is a primary substance. It is argued that definition and essence belongprimarily to substances, and that no universals are substances. Additionallythere are arguments against the existence of Platonic Forms, and againstthe claim that particulars are definable.In addition to the concepts of matter and form, the middle books bringin from his natural science a distinction between actuality (or activity) andpotentiality. Books Eta and Theta make use of these concepts in an attemptto clarify further the relationship between the matter and form of a sensiblecomposite, and the sense in which the form is an activity or actuality. Eta 6treats the form of a composite and its matter as one and the same thing inthe sense that the form is in actuality what the matter is potentially. Thusmaterial composites are unities in their own right, and not merely one
peraccidens. The matter is not itself another actual substantial individual, andis ‘some this’ only in potentiality, not in actuality. A living thing isultimately composed of inanimate materials (ultimately, of earth, air, fireand water), but its proximate matter is its organic body, and this is notseparate from the substance of which it is the matter.Book Iota is close in topic to other concerns of general ontology asconstrued in Gamma 2. It discusses the various kinds of unity andplurality, and in connection with the latter distinguishes the four forms ofopposition: contraries, contradictories, privations and relative terms.The discussion in Lambda 1–5 of the principles and causes of sensiblethings partially overlaps with the middle books. Lambda 1 dividessubstances into sensible and non-sensible, and further divides the formerinto the perishable (sublunary substances) and the eternal (the heavenlybodies). Non-sensible substances are both eternal and immutable, and it ispointed out that some have divided this group into (Platonic) Forms andmathematical objects.Next, Lambda 6–10 present some of Aristotle’s own positive theologicalviews about non-sensible substance, and present arguments for theexistence of an eternally actual unmoved mover of the outermost sphere ofthe cosmos. This is the god of his metaphysical system, and is identifiedwith thought thinking itself.Books M and N are concerned with rival views concerning whether thereare, besides the sensible substances, any eternal, immutable substances.They contain an exposition and criticism of Platonist accounts both of theexistence and nature of Forms and of the objects of the mathematicalsciences (for instance, numbers, lines and planes). There are argumentschallenging the explanatory role that Pythagoreans on the one hand, andvarious Platonists on the other, envisaged for numbers, as well asarguments against the existence of the Forms. Against the Platonist viewthat mathematical objects are separate substances it is argued that themathematician studies physical objects
qua indivisible units, or
qua lines,or
qua planes, etc., and that such things as lines, numbers and planes do nothave separate being. As for the Forms, alternative versions of the attacks onthe existence and putative explanatory power of separate, Platonic Formsin chapters A6 and 9 are to be found in M4 and 5, together with somematerial not in the earlier book.<sup>27</sup>
METAPHYSICS AS GENERAL ONTOLOGYThe general science of causes is general ontologyGamma 1 begins with the assertion that there is a science that studies ‘thatwhich is’
qua ‘thing which is’ and what belongs to ‘that which is’intrinsically, or
per se.<sup>28</sup> By virtue of its generality this science is contrastedwith the departmental sciences that cut off merely some part of ‘that whichis’ and study the properties that are unique to that part. To study ‘thatwhich is’
qua ‘thing that is’ is not to study some special object called ‘thatwhich is
qua thing that is’. The
‘qua’ locution is here used to indicate therespect in which this science studies its subject matter, and indicates that itdeals with those ubiquitous truths that apply to each ‘thing that is’. Themetaphysician must
both state the general (propositional) principles thatapply to ‘that which is’ as such
and treat of their properties or features. Anexample of a metaphysical principle that belongs to beings as such is theprinciple of non-contradiction (PNC). To study what belongs to ‘thatwhich is’
per se also involves a study of the terms that apply to ‘things thatare’ as such (for instance, ‘same’ and ‘one’), and to investigate truths aboutthem.This concept of general ontology is further clarified by the way in whichAristotle proceeds to deal with issues raised by four puzzles stated in B1about the nature of the metaphysical enterprise itself. These are four of thefirst five items on the list, and they concern the characterization of theuniversal science that deals in the most general way possible with thecauses and starting points of all things. The second puzzle (995b6–10), forinstance, assumes that this science will at the very least deal with theprinciples of substance, and inquires whether it will also deal with thecommon axioms—those principles ‘from which everybody makes proofs’.Does it, for instance, study the PNC? Gamma 3 solves this puzzle byshowing that the science of substance is the science that studies thecommon axioms. Gamma also provides answers to at least portions of theother puzzles, though without explicitly referring back to them. Forinstance, after Book B has queried whether the science of substance alsostudies the
per se accidents of substances, it goes on to ask whether it willstudy in addition to these accidents such terms as ‘same’, ‘other’, ‘similar’,‘dissimilar’, ‘contrariety’, ‘prior’ and ‘posterior’, and then concludes byasking whether it will also study even the
per se accidents of these lastmentioned items. This is to ask whether in addition to investigating thedefinitions of the
per se accidents of substance, it will also study such issuesas whether each contrary has a single contrary. Gamma 2 is in part devotedto answering these last two questions in the affirmative.In some respects, general ontology exhibits the kind of structure that isanalyzed in the
Posterior Analytics. It involves both a certain subjectmatter, and a set of items, both propositions and terms, that belong to itssubject matter in respect of itself. However, the various kinds of ‘things thatare’ are not themselves species of a single genus, and ‘that which is’ is not ageneric kind predicable in common of all the ‘things that are’.<sup>29</sup> Substance,quality, quantity and so on are different categories of being, but thesecategories cannot be subsumed under a single genus. Nonetheless, there canbe a single science of ‘that which is’. Such a science studies what belongs toa ‘thing that is‘in respect of its being a ‘thing that is’—the things thatpertain to it simply insofar as and because it is one of the ‘things that are’.
General ontology as the science of substanceAristotle uses his term
‘ousia’ (‘substance’) for the fundamentalexplanatory principles of his general ontology. Strictly speaking, eachscience is the science of that primary thing by reference to which the otheritems within the scope of that science are called what they are called.<sup>30</sup>This strategy, when applied to the expression ‘thing that is’ allows him toconclude that the science of general ontology is in fact the science ofsubstance.As the first sentence of Gamma 2 declares, ‘that which is’, althoughspoken of in a plurality of ways, is nonetheless always spoken of in relationto a single thing, i.e., some single nature, and that single starting point is
ousia, or substance. Although there is no single condition in virtue of whichall ‘things that are’ are properly called ‘things that are’, some things are socalled in a primary way, others in a derivative way, and a single sciencestudies them all. The subject matter of ontology is not in the ordinary sensea generic kind, but this does not distinguish it from
all special sciences. Forinstance, there is a single departmental science that studies everything thatis healthy, despite the fact that the different kinds of healthy things do notcome together under a single generic kind. A single science taking for itssubject healthy things is possible because everything that is healthy is socalled with reference to a single item, namely health. A diet is healthybecause it maintains health, medicine because it produces health, acomplexion because it signifies health, and a body because it receiveshealth. In general, everything that is healthy is so called because it stands insome relation to a single thing, health. The relation of course varies for thedifferent kinds of healthy things, but that with reference to which they arecalled ‘healthy’ is the same in all cases.It is in this way that there is a sort of subject for general ontology aswell. The term ‘thing that is’ is not ambiguous in its application tosubstances, qualities, quantities, and so on, and yet it applies primarily tosubstances, and derivatively to all else. Substances are ‘things that are’simply because they are substances. The applications of this label to thingsother than substances must be explained by relating them in appropriateways to substances, the primary ‘things that are’. Every non-substantialkind of ‘thing that is’ is a kind of ‘thing that is’ by virtue of bearing theright kind of relation to the primary kind, to substance. However, just as inthe case of health, the relation varies from one kind of non-substantial‘thing that is’ to another. There is no single explanation for the applicationof the term ‘thing that is’ to non-substances. Qualities, for example, are‘things that are’ because for a quality to
be just is for it to
qualify a substance;quantities, of course, do not stand in this relation to substance, but ratherare ‘things that are’ by virtue of being the magnitudes of substances.
How and why general ontology studies ubiquitous termsIn addition to its concern with principles that apply to all ‘things that are’solely in virtue of being ‘things that are’, general ontology also deals withcertain principles that do not apply to absolutely everything. Havingasserted that there is a single, unified science that studies ‘that which is’
qua ‘thing that is’, and having explained that such a science studies thecauses and principles of substance, the remainder of Gamma 2 shows thatgeneral ontology also studies the ubiquitous terms that apply to ‘that whichis’ as such.Gamma 2 argues that ‘one’, ‘many’, ‘same’, ‘other’, ‘similar’, ‘dissimilar’,‘equal’, ‘unequal’, ‘different’ and ‘contrary’ are all examples of
per seattributes of ‘that which is’.<sup>31</sup> These are
per se modifications, or
idia of‘that which is’
qua ‘thing that is’. To study them, one both states theirdefinitions and proves theorems about them. This is one respect in whichgeneral ontology conforms to the model for knowledge found in
PosteriorAnalytics. For instance, one might define contraries as things differingmaximally within the same kind, and then demonstrate a
per se accident ofcontrariety by proving as a theorem that each contrary has exactly onecontrary.General ontology must study unity (the signification of the ubiquitousterm ‘one’) for the following reason. There is a single science thatinvestigates all of the types of ‘things that are’
qua. ‘things that are’, as wellas their various sub-types. Since each ‘thing that is’ is in its own right, or
per se, one thing that is, and there are just as many types of the ‘that whichis’ as there are of ‘that which is one’, general ontology must study unityand its varieties. The three types of unity are sameness, similarity andequality, and so general ontology treats of the definitions of each of these.Furthermore, there is always a single science for opposites, and sinceplurality is the opposite of unity, general ontology must also study pluralityand its forms. The three types of plurality are otherness, dissimilarity andinequality, and so general ontology also studies these and their various sub-types. One type of otherness is difference, and contrariety is a type ofdifference. Contrariety, then, is one type of difference; difference is onetype of otherness; otherness is one type of plurality; plurality is theopposite of unity; and finally, unity belongs
per se to ‘that which is’. Hencecontrariety itself must be dealt with by the general ontology.
How general ontology studies basic logical principlesGeneral ontology is not only the science that studies what it is for terms tobe contradictories, but also studies truths about the subjects to which suchterms can be applied. In this spirit Gamma 3 claims, alluding to one of thepuzzles of Book B, that we must state whether the science of substance justdescribed also investigates the things that are called axioms in themathematical sciences. This question is answered in the affirmative becausethe science of substance is the general science of ‘that which is’
qua ‘thingthat is’, and this studies what belongs
per se to all ‘things that are’. Eachcommon axiom applies to all ‘things that are’
qua ‘things that are’, anddoes not have an application merely in one particular kind apart from therest of what there is.These common principles are indemonstrable, and metaphysicalargument does not demonstrate their truth. However, this science canprove things
about these axioms. Gamma 3, for instance, attempts to provethat the principle of non-contradiction (PNC) is the firmest of all principles.The PNC is the principle that it is impossible for the same thing (predicate)to belong and not belong to the same thing (subject) at the same time, inthe same respect. This is equivalent to saying that it is impossible for bothmembers of a contradiction to be true (at the same time, in the samerespect, etc.).According to the account given in
De Interpretatione 6 a contradiction
(antiphasis) is a pair of opposed
(antikeimena) statements, one of which isan affirmation
(kataphasis), the other of which is a denial
(apophasis). Theaffirmation and the denial are statements about the same subject, but whatis affirmed of the subject in the former is precisely what is denied of it inthe other. In
Metaphysics Iota 7 a ‘contradiction’ is characterized as an
antithesis such that for anything whatsoever, one part or the other of theantithesis is present, there being nothing between the two members of theantithesis.<sup>32</sup> Iota 4 classifies contradiction as the primary type ofopposition, the other three types being contrarieties, privations and relativeterms (pairs such as master/slave).Book B cites the PNC as an example of the common beliefs that allemploy in proof, and Gamma argues that it is the firmest of all suchprinciples in that one could never be in error with respect to it (since itis impossible to believe a contradiction). Being the firmest of all principles,it is the most knowable, and must be grasped and understood by anybodywho is able to understand anything at all, and can never be employedmerely as a hypothesis.To show the impossibility of believing a contradiction he argues asfollows. He starts by asserting that it is impossible for contraries tosimultaneously belong to the same subject. This is a consequence of thePNC. The notion of contrariety involved is that mentioned above andcharacterized in Delta 10. Contraries are those things belonging to thesame kind that differ as widely as possible within that kind. Assuming thatbeliefs are attributes of believers, we are told that a belief that contradictsanother is the contrary of that belief. Consequently, it is impossible for abeliever to believe both members of a contradiction at the same time; forwere somebody to have both beliefs, that person would be in contrarystates—but that is impossible.Gamma 4 claims that it has been proven by means of the principle itselfthat the PNC is the firmest principle. It then goes on to state that althoughthe PNC cannot be demonstrated, it can be given a demonstrationelenctically. In
Prior Analytics 620 an
elenchus, or refutation, is a syllogism,the conclusion of which is the contradictory of some propositionmaintained by the opponent, and the premises of which are conceded bythe interlocutor. The premises need not be, and typically are not, prior toand explanatory of the conclusion, and hence typically an elencticdemonstration does not yield knowledge of its conclusion.The elenctic demonstration outlined in Gamma 4 begins by having anopponent signify something both to himself and to another. The elencticproof that follows is intended to refute an interlocutor who denies the PNC,and to do so by showing that certain commonly known things that theopponent believes actually entail the PNC (or at least particular instances ofit). As such this argument is not a scientific demonstration, but rather an
elenchus. The
elenchus shows that the principle is already known byanybody who knows anything. However, being a first principle nopremises could possibly show why it is true, and a valid deduction of thePNC is not a demonstration, for nothing is prior to and explanatory of the PNC.
METAPHYSICS AS THE THEORY OF SUBSTANCESensible substance: being as a definable ‘this something’Although
Metaphysics Zeta and Eta may originally have formed anindependent treatise on substance, they nonetheless do carry out animportant part of the task of general ontology. As Z1 explains, its mainquestion, ‘What is substance?’ is in fact the fundamental ontologicalquestion ‘What is “that which is”?’, a question over which both Aristotleand his predecessors have repeatedly puzzled. Accordingly, the inquiry intosubstance is pursued within the context of his program for generalontology. The opening lines of Zeta begin this inquiry with the assertionthat ‘that which is’
(to on) is spoken of in many ways, and then elaborateupon this claim by listing some of its significations in connection with thecategories. On the one hand being, or ‘that which is’, signifies both ‘what Xis’
(ti esti) and ‘some this’
(tode ti); additionally (now turning to othercategories) it signifies either a quality (‘what X is like’) or quantity (‘howmuch X’ is), or each of the other things predicable in the way these latterthings are. He takes it as clear that of the various significations of thephrase ‘that which is’, the primary signification is the ‘what X is’ whichsignifies a substance. That is, the most basic kind of being is the beingexpressed by a definition that answers the ‘What is it?’ question whenasked of a substance. All other things are beings, or ‘things that are’,derivatively. Anything that is a ‘thing that is’, but not in the primary way,is properly called a ‘thing that is’ by virtue of standing in some appropriaterelation of ontological dependence to something that is a ‘thing that is’ inthe primary way. Some things are beings because they are qualities ofsubstances; others because they are quantities of substances; and so on. Asrequired by the account of ‘being’ (or ‘that which is’) given in Gamma 2,the term
‘on’ applies primarily and without qualification to substances, andderivatively to all else. General ontology is indeed the science of substance.Although Gamma proclaimed the ontological priority of substance, it didnot explain what it is to be a substance. To advance the project of generalontology Zeta now initiates an investigation designed to arrive at anaccount of substance. For this general project to succeed, it mustcharacterize substance in such a way that every type of ‘thing that is’ willbe accounted for by reference to what substances are. In order forsubstances to play this role, their being (i.e., what they are) cannot in turnbe explained by appeal to any causes or explanatory factors external tothem. A substance cannot be a ‘thing that is’ by virtue of standing in somerelation to something other than itself. Substances are ‘things that are’simply because they are substances. Hence each substance is what it isintrinsically, or
per se. A substance is
both ‘some this’ and a ‘what X is’.Being intrinsically a particular subject, it is ‘some this’; being somethingessentially, it will also be a ‘what X is’.<sup>33</sup>Furthermore, Z1 states that substances are primary in all of the ways inwhich something can be primary. This is because: (1) only substances areseparate, (2) the account of the being of each non-substantial item mustcontain an account of the being of some substantial item (from which thatnon-substantial item cannot be separated, and upon which its beingdepends), and (3) understanding, or knowledge, of each thing proceedsfrom an understanding of the substances signified by definitions. Thesubsequent investigation in the middle books aims at a general account ofperceptible substance that meets these conditions on the primacy ofsubstance. The last three conditions imposed upon the analysis ofsubstance stem not from some particular theory of substance, but from thesingle idea that strictly speaking the subject matter of general ontology issubstance.Here, as elsewhere, investigation must begin with what is known, orfamiliar, to the inquirer. Since Aristotle takes it that there is widespreadagreement that at least some perceptible bodies are substances, his inquiryinto substance must begin with them. The eventual goal is to have movedfrom these to an understanding of what is most knowable by nature.Aristotle investigates perceptible substances in order to consider later suchquestions as whether there is, in addition to the matter of sensiblesubstances, another kind of matter, and whether we need to inquire intosome other kind of substance (for instance, numbers, or something of thatsort). Z17 says that the new starting point that it offers might help us toget clear about that substance that exists separated from perceptiblesubstance.Accordingly, in Z2 he starts by listing various types of things that havebeen thought to be substances. The items thought to be the clearestexamples of substance are bodies. This includes not only the four basicelements (earth, water, air and fire), but also living things, both plants andanimals, as well as their parts, and anything that is either a part of orcomposed of bodies. The entry on substance in Delta 8 explains whybodies are called substances. It is because they are not predicable of asubject, but the other things are predicable of them. This is the conditionuniquely satisfied by primary substances in
Categories 5. What makessomething a primary substance in the
Categories is that it satisfies this verycondition. Z2 neither endorses nor rejects this or any other view aboutwhat things are in fact substances, or what makes them so. Z16subsequently reveals that the parts of animals are not actual substances,but rather things that exist in potentiality in that they fail to be separate,and that the four elements are not substances in that they are like heapsrather than unities. In general, most of the things thought to be clearexamples of substance (including items treated in the
Categories as primarysubstances), turn out to be potential beings, and not substances inactuality.Next, after also touching on various Platonist views that treat (separate)Forms and/or mathematical objects as substances, Aristotle says that whatis needed is a consideration of such questions as whether there are anysubstances besides the sensible ones, and what is the manner of being forboth the sensible substances and for whatever non-sensible substances theremay be. Later he will argue that there are no (separate) Forms,<sup>34</sup> andBooks M and N defend his view that there are no non-sensiblemathematicals that enjoy the status of separate substances. However,before answering the question ‘What things are substances?’, Z2 advisesthat we first sketch out an answer to the question ‘What is substance?’ Thisinvolves determining what explains what makes it the case that somesubstance is a substance. The explanatory entity E that explains why somesubstance X is a substance may be called ‘the substance of X’. The task athand is to say what it is for something to perform that explanatory role,and then to say in a general way which of X’s causes is the entity E thatperforms it.Z3 begins this search by listing as possible candidates for the substance ofX four items that are familiar from Aristotelian logic:<sup>35</sup> its
essence, a
universal it instantiates, a
genus to which it belongs or some
subjectassociated with it. The first three correspond to the predicate position of astatement, and are items that a dialectician might invoke as an answer tothe question ‘What is X?’ The fourth candidate for substance is a
subject ofwhich other items are predicable. The ‘subject’ is thought most of all to besubstance, and Z3 explains that the ‘subject’ is that of which all otherthings are said, but is not itself said of anything further. Consequently, thesubstance of X would be something that is not said of a subject, but ratheris that of which the other things are said.This characterization of the substance of X as the subject for predicationshould be compared with the claim in
Categories 5 that the primarysubstances are those things of which all else is predicable, they themselvesbeing predicable of nothing further. Whatever its merits as acharacterization of the class of substances, in Z3 it is found inadequate as aspecification of the substance of some substantial being X. Within ahylomorphic context, the matter, the form and the composite may each becalled a ‘subject’, and the logical subject condition for substance by itselfdoes not provide an adequate account of what it is about a substance thatmakes it the case that it is a substance. Aristotle argues that on its own itleads to the materialist view that the substance of a material object (i.e.,what it really is) is some matter that is the ultimate subject of all itspredicates. By stripping off in thought all predicables, one arrives at anultimate subject of predication that is nothing in its own right, and haswhatever predicates it does only accidentally. However, such matter isneither separate nor ‘some this’,<sup>36</sup> and hence cannot be the substance forwhich we are searching. Although recent scholarship has raised seriousproblems for taking this to commit Aristotle to the existence of anindeterminate ultimate subject of predication, traditionally this chapter hasbeen read as introducing Aristotle’s own concept of prime matter. Primematter has also been thought of both as a principle of individuation fornumerically distinct material objects, and as the persisting substratum forthe basic elemental transformations in his natural science.The hylomorphic analysis of perceptible substance is invoked in Z3without explanation as something already familiar. It is not entailed by thegeneral characterization of the science of ‘that which is’
qua ‘thing that is’,nor is it involved in his logic. Rather it is taken over from Aristotle’snatural science, and depends upon some of the basic constitutive principlesof the science that treats of the general principles that govern naturalbodies insofar as they are subject to change. Although the substances of the
Organon are persisting subjects for non-substantial changes, in the logicalworks there is no treatment of the causes of change, and substances are notanalyzed as compounds of matter and form. The technical concept ofmatter is never employed in the logical works, nor is the correlative notionof form. In these works the word
‘eidos’ is used not for the hylomorphicconception of form, but rather for a secondary substance, the species (andsometimes for the Platonic Form). The notion of form introduced in Z3must be understood within the context of this kind of hylomorphicanalysis. It is the formal component of a particular hylomorphiccompound.He turns next to a discussion of another candidate for substance: theessence. In connection with his inquiry into substance, Z4, 5 and 6 dealwith the logical concepts of definition and essence. In the logical works anessence is simply the ontological correlate of a definition (an answer to a‘What is X?’ question). Z4 and Z5 argue that only substances havedefinitions in the primary sense, and consequently there are essences (in anunqualified sense) only for substances. Nonetheless, in a derivative way,items from other categories are also definable and endowed with essences.Z6 attempts to establish the principle that all things that are primary, andcalled what they are called intrinsically, are one and the same as theiressence. This thesis ‘expresses the view that the definiens and thedefiniendum must, in a correct definition of a substance, signify one andthe same entity. A substantial form is identical with its essence. However,neither accidental unities (such as a pale man) nor hylomorphic compositesare identical with an essence.On Aristotle’s view the requirement that a substance be ‘what X is’ leadsto the view that a primary substance is identical with a definable form.This form is not the species, for later<sup>37</sup> the species is analyzed as auniversal composite of matter and form, and as such is not a primarysubstance. There is currently considerable scholarly controversy as towhether Aristotle considered substantial forms to be particulars, universalsor neither particulars nor universals. One reason for holding that they areuniversals is that substances are first in the order of definition andknowledge, and definition is thought to be of the universal.<sup>38</sup> A chiefreason for taking them to be particulars is that a substance must be aseparately existing ‘this something’, but universals are ontologicallydependent upon particulars.<sup>39</sup>This initial discussion of definition and essence is followed in Z7, 8 and9 by a treatment of the material, formal and efficient causes of natural,artistic and spontaneous generation. These three chapters argue that allgenerated objects are composites of matter and form, and that the formalcomponent of a substance is its essence. This ‘physical’ conception of anessence is different from but related to the ‘logical’ notion of an essence(i.e., the signification of the definition of a thing). Z10 and Z11 resume theinquiry into definition and essence within a hylomorphic context, and Z12subsequently takes on the problem of the unity of definition.Z3 listed the universal as a candidate for substance, and Z13, 14, 15 and16 discuss various topics connected with the claim that universals aresubstances. The genus being one type of universal, these chapters also dealwith its credentials for being substance. Since the objects of definition arethought to be universals, these issues naturally follow an exploration ofdefinition and its objects. The claim of universals to be substances stemsfrom the fact that to the Platonist they seem to satisfy best the requirementthat a substance be ‘what X is’. However, Z13 argues that since thesubstance of something is unique to that of which it is the substance, nouniversal is a substance. This would suggest that if the ‘what X is’requirement is to be met at all, it is the essence that will meet it. However,in order to count as a substance, an essence would also have to be ‘somethis’. The essence, an item originally introduced as a predicable, should alsosatisfy the subject condition for substance. It is the essence that is identicalwith hylomorphic form that plays this role. If the ‘what X is’ requirementis to be met by one of the first three candidates listed in Z3, it is the essencethat will meet it.In order to count as a substance, an essence would have to be aparticular, determinate subject, and not a universal. Aristotle thinks thatthe Platonic view that what is predicable in common of particulars isseparate and a ‘this something’ leads to an infinite regress that he refers toas the ‘third man’.<sup>40</sup> Although the reconstruction of this argument isdifficult, it seems to have involved the idea that if the particulars have aForm in common, and this Form is a separately existing ‘this something’,then there must be an additional Form that both the particulars and thefirst Form have in common, and so on
ad infinitum. According toAristotle, however, the form of a perceptible substance does not existseparately, but always requires perceptible matter.Although it is clear that Z13 presents arguments against the claim thatuniversals are substances, these arguments are presented as part of anaporematic investigation, and as such are linked up with the results ofearlier chapters in order to formulate a problem
(aporia). The problem isthat no substance is composed of universals or of actual substances, and sosubstances must be incomposite, and hence indefinable; yet it was argued inthe earlier treatment of definition in Z4 and Z5 that strictly speaking onlysubstances are definable. However, if substances are not definable, thennothing is.This problem is not directly solved in Z13–16, but Z17 makes a freshstart in the attempt to answer the question ‘What is substance?’ From itsnew perspective, the primary cause of being for a material composite is theessence that is responsible for the fact that the matter constitutes thatcomposite. The substance of X is neither one of the material elements ofwhich X is composed nor an element present in its essence, and is itselfboth simple and definable. This cause is in turn identified with the form.The form of X is its substance, and is the primary cause of its being. Asubstantial form is separate in definition, and hence prior in both the orderof definition and knowledge. Nonetheless, it cannot exist without matter,and in the case of perceptible things it is only the composite that is separatewithout qualification.
Sensible substance: actuality and potentialityThe substance of a living thing is its soul. It is because a soul is present to abody that the body constitutes a living, functioning organism. The body isthe matter, and is the thing in potentiality, whereas the form is the activityor actuality that must be present if that body is to be actually alive.According to a hylomorphic theory of this sort, a person lives a human lifein virtue of having the capacities assigned to the various parts of humansoul, the principle of human life. Soul is that by virtue of which (in theprimary sense) we live, think, perceive, etc. The form (or substance of) thespecies man is that form (i.e., human soul) that makes a human body alivein virtue of the fact that the body has it. The word ‘man’ is applicable toSocrates in virtue of his matter (his body) having a substantial form. Thesubstantial form or essence is strictly speaking a ‘this something’, andSocrates is a ‘this something’ because of the form that his body has.Book Theta initiates a more extended treatment of the distinctionbetween ‘that which is’ in actuality, and ‘that which is’ potentially. Tounderstand what an actuality
(energeia) is, Aristotle begins by consideringthe kind of potentiality
(dunamis) that is correlated with change, becausethis is the most basic and most familiar kind of potentiality. Change, unlikesubstantial form, is a kind of incomplete activity or actuality, but anunderstanding of the relation between change and the potential for changeenables one to comprehend the way in which substantial form is anactuality (or activity). Theta 6 explains the concept of an
energeia bymeans of a set of analogies. An actuality is something that stands tosomething else in the way that a change stands to its correlatedpotentiality. Both a substantial form and a change can be called ‘actuality’(although the form is a more perfect actuality), for as a change stands to itspotentiality, so the substance (i.e., the form) stands to its matter.Substantial form is an actuality that is the fulfillment of the potentiality thematter has for being ‘this something’. As a goal and fulfillment, it is theprimary cause of the composite’s being what it is.
METAPHYSICS AS THEOLOGYAristotle has argued that in the sensible world there are substances, andwhat makes them such is their form. These forms are internal principles, ornatures, and as such cannot exist without matter. The next major step inthe general ontological program is to investigate supra-sensible reality.There is reason to think that there are non-perceptible substances that existseparately, and perhaps they are the things entirely knowable by nature.The last three books of the
Metaphysics are concerned with the variousnon-sensible items that have been thought to be substances. Although adiscussion of this sort is needed to complete the general inquiry into ‘thatwhich is’, these books may not have been written as a part of the largerwork. They are not explicitly coordinated with the treatment of sensiblesubstance in the middle books, nor do they attempt to put their topicswithin the framework of the general ontology of Gamma.Books M and N argue that (1) although mathematical objects exist, theyare not substances, and (2) Platonic Forms do not even exist. Nonetheless,there are on his view supra-sensible beings of a different kind, and at leastone of these is the unmoved mover, or god of his metaphysics. Lambda 6–10 contains an account of this unmoved mover. Although itselfunchangeable, it is an eternal source of the motion of the outermostcelestial sphere, and being the final cause of that motion, it moves as anobject of love. God is incapable of being other than it is, and as such has nomatter, but rather is a being the substance of which is actuality
(energeia).<sup>41</sup> This actuality is activity of the best sort: intelligent activity
(nous). Being eternally engaged in the best kind of thinking, god is a livingbeing. God’s intelligence is not a thinking of us or of the universe, butrather is a thinking of thinking or intelligence itself (1074b34). He arguesboth that this activity is the good, and that it is the source of the order andgoodness of the universe.Although perceptible substances are the substances that are initially mostfamiliar to us, metaphysical inquiry is ultimately for the sake of coming toan understanding of this first principle. One moves towards anunderstanding of divine substance by starting with the causes of the thingsthat are most familiar to us and proceeding towards an understanding ofthe highest causes. Lambda 4 states that the causes and principles ofdifferent things are in one sense different, but in another sense, speakinggenerally and by analogy, they are the same for all things (1070a31–33).The unmoved mover is a cause analogous to those causes and principles ofperceptible substances studied by the special sciences. God is the final causeof motion in the outermost sphere, and this is analogous to the way inwhich the nature of an animal of some type is the final cause of the comingto-be of animals of that type. The eternal, continuous activity that is god’snature is analogous to the actuality of a perceptible substance. Tounderstand actuality, we start with an understanding of the manner inwhich a change is an actuality, and then move to an understanding of thesubstance of a perceptible body as an actuality. However, the highest causeis grasped when we attain an understanding of the best and most perfectactuality, and this is an understanding of god.
NOTES1 See p. 52 for the use of this phrase.2 Aristotle sometimes employs other conceptions of the accidental, includingone according to which the accidental is the contingent.3 See
Categories 2, 3, 5.4
(ousia): see p. 000.5 With the possible exception of the ten-fold list of predicables in
Topics A9.This list begins with ‘what x is’ (instead of ‘substance’), suggesting aclassification of predicates answering to the various kinds of questions thatcan be asked about any subject at all, substance or otherwise.Another way of classifying predicates is represented by the four-folddistinction in
Topics A5 between genus, definition,
proprium and accident.This classification is useful for his analysis of a science in terms of a subjectgenus, definitions of the items investigated, and theorems relating
propria tothe defined kinds it studies. The accidental is that which falls outside thescope of a science. See 51–52 below.6 The translation is not ideal since it, unlike the Greek, has no connection withthe verb ‘to be’.7 There is at present still debate as to whether the non-substantial individuals of
Categories 2 are particulars or universals.8
On Sophistical Refutations 2 classifies arguments used in discussion into fourclasses: didactic, dialectical, peirastic and eristic. Didactic arguments use aspremises truths from some science that are not yet the beliefs of the learner,and such arguments are in effect demonstrations. Dialectical argumentsdeduce the contradictory of an opponent’s thesis from
endoxa (which may ormay not represent the opponent’s own beliefs), and peirastic argumentsconstitute that subset of dialectical arguments in which the premises are bothbelieved by the respondent and must be known by anybody purporting tohave knowledge. Eristic arguments are not dialectical, and produce eitherreal or apparent syllogisms not from
endoxa, but from apparent
endoxa.9
Logos: this Greek term is used in this context to mean something like‘argument’. The term has many uses for Aristotle, including its application todefinition (for which see p. 52 below).10 Here only the theory of the assertoric syllogism (i.e. one composed ofstatements) is discussed. Since scientific knowledge of a theorem involvesknowing that it is necessary, an analysis of demonstration would seem torequire a modal syllogistic dealing with statements of necessity andpossibility.
Prior Analytics A8–22 attempts to develop a theory of syllogisticinferences that involve modal categorical statements. It is unsuccessful in thatits treatment of modality is inconsistent, and apparently conflates sententialand adverbial readings of the modal operators.11 Since a sentence is a linguistic item, the terms of which it is composed shouldalso be linguistic. However, I will follow Aristotle’s usage in sometimescalling the objects picked out by its linguistic terms the ‘terms’ of astatement. Thus Socrates and the species man are sometimes referred to asthe ‘terms’ of the statement that Socrates is a man.12 Using this terminology in translations is potentially confusing since in callinga proposition ‘particular’ one is not thereby saying that its subject is aparticular. Although occasionally Aristotle will use singular premises insyllogistic inferences, the theory he develops in fact applies solely toarguments composed of statements of A, E, I or O form.13 The technical vocabulary of the
Prior Analytics typically reverses the order ofsubject and predicate, and picks out the four forms corresponding to thesekinds of schemata, labeled respectively ‘A’, ‘E’, ‘I’, and ‘O’: P
belongs toevery S; P
belongs to no S; P
belongs to some S; P
does not belong to some S.The letters ‘A’, ‘E’, ‘I’, and ‘O’ are mnemonic devices taken from the first twovowels in the Latin words ‘affirmo’ and ‘nego’.14 Both cannot be true together, and both cannot be false together. For theapplication of this concept to singular statements, see p. 60.15 They cannot both be true, but both can be false.16 A entails I, and E entails O.17 Following Aristotle, the major premise is listed first. These argument formshave come to be called Barbara, Celarent, Darii, Ferio (Barbari andCelaront), respectively, the vowels indicating the propositional forms. Thevalid moods of the second figure are EAE, AEE, EIO and AOO, plus thesubaltern moods EAO, AEO (Cesare, Camestres, Festino, Baroco, plusCesaro and Camestrop). Those of the third figure are AAI, EAO, AII, IAI,OAO, EIO (Darapti, Felapton, Datisi, Disamis, Bocardo and Ferison). Afourth figure (in which the major term is the subject of major premise, and theminor term is the predicate of minor premise) exists. The fourth figure is notdiscussed as such by Aristotle, although the
Prior Analytics shows awarenessof its valid moods AAI, AEE, IAI, EAO, EIO. (There is a subaltern mood AEO as well.)18 He also shows that Darii and Ferio can be derived using Celarent.19 He also shows how a third figure OAO (as well as AAI and IAI) can beestablished by a method of
ekthesis.20 Furthermore, Aristotle argues that demonstration of principles cannotproceed in a circular fashion, nor can there be an infinite series of principleswhich would enable each principle to be demonstrated by a prior principle(see
Posterior Analytics A3).21 This topic is pursued further below on pp. 59–60.22
Kath’ hauto; also translated as ‘in itself’ or ‘in its own right’.23 These remarks apply only to so-called ‘real’ definitions.
Posterior AnalyticsB10 distinguishes various ways in which the term ‘definition’ is used,including so-called ‘nominal’ definitions (accounts of what a term signifies)and ‘real’ definitions (accounts that make evident why something is). At leastsome of the former are of non-existent things, whereas the latter never are.24
Aporiai. When applied to a journey, the word
‘aporia’ indicates a conditionof difficulty (being without a way of passage) that prevents further progresstowards one’s destination. B1 applies this term both to the condition of theintellect when faced with credible, but opposing arguments, and to thearguments themselves.25 In either of the first two senses explicated in
Posterior Analytics A4. See p.25.26 See Z1, 1028a11–13 and Theta 1, 1045b27–1046a2.27 See also M9.28 ‘That which is
qua thing that is’ translates
‘to on hêi on’, an expression oftenrendered as ‘being
qua being’.29 See
Posterior Analytics B7, and
Metaphysics B3.30 Gamma 2, 1003b16–17.31 Later the chapter adds without further argument: ‘complete’, ‘prior’,‘posterior’, ‘genus’, ‘species’, ‘whole’ and ‘part’.32 It is an opposition to which the Law of Excluded Middle applies.33 Despite the fact that the question ‘What is it?’ is answered by reference to adefinable universal, it is nonetheless proper to apply the label ‘what X is’ toparticulars as well. The phrase ‘what X is’ may be used as a place-holder forterms such as ‘man’ or ‘horse.’ For instance, ‘what Socrates is’ is a man. Sincehe is a man, it is correct to say that Socrates is ‘what he is’ (i.e., the definablespecies man).34 In Z8, 14 and 16; see also M4, 5, 9 and A6 and 9.35 See pp. 41, 44, 50–53.36 Z3, 1029a26–28.37 Z10, 1035b27–31.38 Z11, 1036a28–29 with B6, 1003a5–17.39 Z13, 1039a1–2 with note 38.40 Z13, 1038b35–1039a3; also see passages in note 34.41 1071b20.
SELECT BIBLIOGRAPHY ON ARISTOTLE’S LOGIC AND METAPHYSICSGENERALFor Greek texts, English translations and commentaries, generalbibliographies, general introductions to Aristotle and collections of essays,see [1.1] to [1.59].
Further texts and commentaries relevant to Aristotle’slogic2.1 Burnyeat, M. and others (eds),
Notes on Book Zeta of Aristotle’s Metaphysics,Study Aids Monograph No. 1 (Sub-faculty of Philosophy, Oxford University,1979).2.2 —–(eds),
Notes on Books Eta and Theta of Aristotle’s Metaphysics, StudyAids Monograph No. 4 (Sub-faculty of Philosophy, Oxford University,1984).2.3 Frede, M. and Patzig, G.,
Aristoteles ‘Metaphysik Z’: Text, Übersetzung undKommentar, 2 vols (Munich, C.H.Beck, 1988). [Includes Aristotle’s
Metaphysics in Greek with a German translation.]2.4 Montgomery, M.,
Aristotle: Metaphysics Books VII–X, Zeta, Eta, Theta,Iota (Hackett, 1985).2.5 Smith, R.,
Aristotle: Prior Analytics (Indianapolis, Hackett, 1989).
Books containing introductions to Aristotle’s logic2.6 Bochenski, J.M.,
Ancient Formal Logic (Amsterdam, 1951).2.7 Kneale, W.C. and Kneale, M.,
The Development of Logic (Oxford, 1962).
BOOKS AND ARTICLES ON LOGIC AND METAPHYSICS2.8 Ackrill, J.L., ‘Aristotle’s theory of definition: some questions on
PosteriorAnalytics II.8–10’, in Berti [1.48], 359–84.2.9 Albritton, R., ‘Forms of particular substances in Aristotle’s
Metaphysics’,
Journal of Philosophy 54 (1957) 699–708.2.10 Aubenque, P.,
Le Problème de l'être chez Aristote (Paris, 1962).2.11 Bambrough, R., ed.,
New Essays on Plato and Aristotle (London, 1965).2.12 Barnes, J., ‘Aristotle’s theory of demonstration’, in Barnes, Schofield andSorabji [1.53], vol.1, 65–87. [Revised version of paper published in
Phronesis14 (1969) 123–52.]2.13 ——‘Proof and the syllogism’, in Berti [1.48] 17–59.2.14 Bogen, J. and McGuire, J.E., eds,
How Things Are (Dordrecht, 1985).2.15 Bolton, R., ‘Definition and scientific method in Aristotle’s
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Aristotle’s Criticism of Plato and the Academy, vol. I(Baltimore, 1944).2.20 Code, Alan, ‘The aporematic approach to primary being in
Metaphysics Z’,in Pelletier, F.J. and King-Farlow, A.,
New Essays on Aristotle, CanadianJournal of Philosophy, supplement10 (Edmonton, 1984), 1–20.2.21 ——‘Aristotle’s investigation of a basic logical principle’,
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Metaphysics Z13,1038b8–15’,
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Studies inAristotle (Washington, 1981), 1–24; reprinted in Frede [2.34], 29–48.2.33 ——‘The definition of sensible substances in
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nous in the cognition of first principles in
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Real-Encyclopädie der classischen Altertumswissenschaft,vol. IVA, cols. 1046–1067 (1931).2.53 Kosman, L.A., ‘Substance, being and
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Oxford Studies in AncientPhilosophy 2, 1984, 121–49.2.54 ——‘Understanding, explanation and insight in Aristotle’s
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Exegesis and Argument(Assen, 1973).2.59 Le Blond, J.M., ‘Aristotle on definition’, in ([1.53], vol.3), 63–79; originallypublished as ‘La Definition chez Aristote’,
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Logique et méthode chez Aristote (Paris, 1939; 2nd edn 1970).2.61 Lesher, J.H., ‘Aristotle on form, substance and universals: a dilemma’,
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Ousia: a prolegomenon to
Metaphysics Z and H’,
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Primary Ousia: An essay on Aristotle’s Metaphysics Z and H (Ithaca,NY, 1991).2.67 Lukasiewicz, J.,
Aristotle’s Syllogistic from the Standpoint of Modern FormalLogic (Oxford, 1951; 2nd edn 1957).2.68 McCall, S.,
Aristotle’s Modal Syllogisms (Amsterdam, 1963).2.69 McKirahan, R.D.,
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Le Jugement d’existence chez Aristote (Louvain, 1946; 2nd edn1976).2.72 Matthen, M., see [1.57].2.73 Merlan, P., see [1.85].2.74 ——‘On the terms “metaphysics” and “being-qua-being”’,
Monist 52 (1968)174–94.2.75 Moravcsik, J.M.E., ed.,
Aristotle: A collection of critical essays (Garden City,NY, 1967).2.76 Morrison, D.R., ‘Separation in Aristotle’s metaphysics’,
Oxford Studies inAncient Philosophy, vol.3, 1985, 125–57.2.77 Mueller, L, ‘Aristotle on geometrical objects’,
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