Aristotle’s logic and metaphysics

Aristotle’s logic and metaphysics
Aristotle’s logic and metaphysics Alan Code PART 1: LOGICAL WORKS OVERVIEW OF ARISTOTLE’S LOGIC The Aristotelian logical works are referred to collectively using the Greek term ‘Organon’. This is a reflection of the idea that logic is a tool or instrument of, though not necessarily a proper part of, philosophy. In the traditional ordering of these works the Categories comes first. It deals, among other things, with the simple terms (subjects and predicates) that when combined go together to form simple statements, and it characterizes primary substances as the ultimate subjects for predication. It also contains a treatment of ten categories, with particular emphasis on the four categories of substance, quantity, relation and quality. The De Interpretatione, which is placed second, discusses the statements that result from combining nouns and verbs, and includes a treatment of various modal relations between statements. The main topic of the two Analytics is demonstration (epideixis), the type of valid deductive argument, or syllogism, (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 Posterior Analytics demonstrations are analyzed as explanatory syllogisms from first principles. This work combines the notion of syllogistic inference with an account of the nature of scientific first principles in its analysis of the structure of science. The Topics is chiefly concerned with dialectical debate, and the work On Sophistical Refutations contains a treatment of various kinds of fallacies in dialectical argument. At the conclusion of this work Aristotle indicates that unlike his other inquiries, such as his treatment of rhetoric, that build upon the results of his predecessors, prior to his own efforts there simply was no general inquiry concerning syllogistic reasoning. The Rhetoric, not itself included in the Organon, is concerned with the use of rhetorical argumentation for the purpose of persuading an audience. PREDICATION, AND SUBSTANCE AS SUBJECT Predication In the Categories (using terminology not employed for this purpose outside that work) predication is characterized in terms of the two relations ‘said of a subject’ and ‘present in a subject’. The relata are ‘things that are’ (onta), and this type of predication may be dubbed ‘ontological’. Although the verb translated ‘to be predicated’ (katêgoreisthai) is used extensively outside the Categories, the way in which the phrases ‘said of’ and ‘present in’ are used here is idiosyncratic to this work. Due to the way it is connected with the notion of definition, it is convenient to describe the relation ‘being said of a subject’ as essential predication. Essential predications say what a subject is intrinsically, or per se.<sup>1</sup> By way of contrast, the relation ‘being present in a subject’, which in the Categories covers 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 is transitive, and as will be seen below, is connected with definition in a way that the ‘present in’ relation is not. Given that man is predicable of Socrates, anything predicable of man, for instance, is thereby predicable of Socrates. The definition of the species man applies to him as well. The class of things ‘present in a subject’ are described as being present not in the way that a part is present in a whole, and as incapable of existing separately from some subject that they are in. These two types of ontological predicability help account for linguistic predicability (the application of a linguistic predicate to a subject). A simple subject-predicate sentence is used to make a simple affirmative statement in which one item is predicated of another, usually distinct, item. The linguistic predicates ‘man’ and ‘grammarian’ are applicable to some subject just in case the species man and grammatical knowledge, respectively, are ontologically predicable of that subject. The notion of predication is employed in De Interpretatione 7 to distinguish particulars from universals. A ‘universal’ (katholou) is an item of 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 or accidentally, of a plurality. Aristotle sometimes uses the term ‘individual’ (atomon) for items not essentially predicable of other things (thus leaving it open whether an individual is accidentally predicable of something distinct from itself). The Categories distinguishes between the simple linguistic expressions (things spoken of without combination) of which statements are composed, and the entities those expressions signify. The name ‘man’, for instance, and the verb ‘runs’ are simple significant expressions that combine to form the declarative subject-predicate sentence ‘Man runs’. Although when used without combination, neither of these words has a truth-value, they may be combined to form a statement that is either true or false. The word ‘man’ signifies man, the word ‘runs’ signifies the activity of running, and one uses the sentence ‘Man runs’ to truly affirm some predicable (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 a substance. There are also particular substances, like Socrates, which are the signification of names that function as grammatical subjects, but never as grammatical predicates. The particular itself is always an ontological subject, and never a predicable. According to Categories 4 the ten kinds of things that are signified by simple expressions are: substances, quantities, qualities, relatives, places, times, positions, states, doings and undergoings. Although Aristotle does not himself explain the rationale for this list, it is a classification of the kinds of things that could be said of something in response to a question asked about it. When we say of some particular substance what it is, as when we say of Socrates that he is a man, the simple expression (here ‘man’) signifies a substance. However, in addition to predicates offered in response to the question (1) ‘What is it?’ when asked of a particular substance, there are other kinds of linguistic terms that are given in response to other kinds of questions. For instance, we may ask of something (2) ‘How large is it?’ and elicit a reply such as ‘six feet’. In a like manner each of the other entries on this list classifies a kind of answer to some other kind of question: (3) ‘What is it like?’ (to which we might answer ‘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 to it?’ (being cut). Just as questions such as ‘What is Socrates?’ and ‘What is Bucephalus?’ collect predicate expressions such as ‘man’, ‘horse’ and ‘animal’ that signify substances, these other nine questions collect predicate expressions that signify other kinds of predicables. The ten kinds of things signified by these kinds of expressions are standardly referred to as the Aristotelian categories. Aristotle frequently uses the Greek word ‘katêgoria’ to mean ‘predicate’, or ‘kind of predicate’. When the term is used in this sense, particular substances are not themselves in the ‘category’ of substance (since they are always subjects and never predicates). Elsewhere when Aristotle makes use of a classification of ‘categories’, this full list of ten does not appear.<sup>5</sup> For instance, Metaphysics Delta 7 correlates the various per se senses of ‘to be’ with an eight-fold categorial schema of the sort suggested by this list. A subject’s essential predicates are those that signify what it is. The subject is called what it is synonymously from such predicates. In the first chapter of the Categories, two things are homonyms just in case, although there is a term that applies to both, the definitions associated with the two applications are distinct; two things are synonyms just in case the same term 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 name and the definition of X truly apply to Y. For this reason whenever a universal is said of a subject, the universal and its subject are ‘synonyms’. The word ‘man’, for instance, is applicable to the particular man because the 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. The definition of man is an account saying what man is, and the definition that applies to Socrates is the definition of the species man. Assuming for illustrative purposes that the account that defines man is ‘biped animal’, it is true that whatever is a man must be a biped animal. The definition of the species man applies to particular men, and the species is predicated essentially of those particulars. The defining expression that signifies the essence of a particular just is the definition of its species. In the Organon universals, not sensible particulars, are the objects of definition. The definition appropriate for a particular is the definition of the species to which it belongs. In order for a particular to be a logical subject, or subject of predication at all, it must be something essentially. The species to which a particular belongs, although not identical with the particular, is what the particular essentially is. It is the definable something the particular must be essentially if it is to be anything at all. Not only substantial universals, but any object of definition whatsoever is a subject for essential predication. The color white, for instance, is a color, and hence color is predicable of white. Substances and non-substances alike may possess definitions, and hence be endowed with essential natures. In addition to the names of substantial universals, there are also names of the universals that are accidentally predicable of substances. Although, in some cases, the name of a non-substantial universal (the name ‘white’, for instance) applies to the substances to which the universal is present, in general not the name itself, but rather some linguistic predicate associated with the name, is applicable to all and only those things having the universal as an accidental property. Socrates is called ‘brave’, not ‘bravery’. Despite this, the definition of any universal X that is accidentally predicable of a subject Y can never be truly applied to Y. Although the name ‘white’ applies to white particulars in virtue of the fact that they all have the color white, the definition of that color is not linguistically predicable of any of them. They are not called white in virtue of what they are. If a non-substantial property is present in a subject, then (in general) its name does not apply to that subject, but there will be some associated expression that differs in ending, which is applicable to the subject. In such cases the subject is called what it is called paronymously from that property. Although the noun ‘bravery’ cannot be truly predicated of Socrates, the adjective ‘brave’ is applicable to Socrates because bravery is present to him. The brave thing is a paronym. Substance as subject Translators of Aristotle’s Greek typically render the abstract substantive ‘ousia’ as ‘substance’,<sup>6</sup> suggesting the idea that substances are the subjects of predication. In the Categories all beings except for primary substances are predicable (either essentially or accidentally) of primary substances. On the other hand, a primary substance is a primary substance because it is a subject (hupukeimenon) for the other things, but is not itself predicable of anything further. Each primary substance is an individual subject of predication that is not itself predicable of a substance, and as such is ‘some this’ (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 also considers the claims of their matter and form to be substance, but in this work the individual is not subjected to the hylomorphic analysis found both in his natural science and the Metaphysics. There is no discussion in the 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 natural kinds (i.e., their species and genera) are universals. These natural kinds are called ‘secondary substances’, and are the only substances other than the primary substances. The only universals in the Categories are (1) secondary substances, (2) their differentiae, and (3) the various quantities, qualities, and other non-substantial items that are had by the substances.<sup>7</sup> Some linguistic predicates, such as ‘man’, signify universals that are essentially predicable 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 for everything else, the Categories also lists a number of the distinctive characteristics (idia) of substances, quantities, relatives and qualities. For instance, substances do not have contraries, nor do they admit of degrees. Most importantly, anything that can persist through time as numerically one and the same while receiving contrary properties must be a primary substance. One and the same individual man can be pale at one time, dark at another; hot at one time, cold at another; bad at one time, good at another. In this way the ultimate subjects of predication are treated as the persisting subjects for accidental change. THE STRUCTURE OF SCIENTIFIC KNOWLEDGE Syllogistic The theory of syllogistic reasoning in the Prior Analytics concerns the relation between the premises and the conclusion of a syllogism. The conclusion follows of necessity from the premises. In his account of this relation he appeals to characteristics of arguments that abstract from the content of the statements involved. He identifies a few obvious (perfect) cases of this relation, and then shows that all non-obvious (imperfect) cases can be reduced to the obvious. The notion of syllogistic inference is utilized both in Aristotle’s analysis of scientific reasoning and in his treatment of dialectical argument. A scientific demonstration is a syllogism that proves its conclusion by showing how it necessarily follows from its explanatory principles. Knowing scientifically requires this kind of argument from indemonstrable starting points. Reasoning from necessarily true explanatory principles to necessarily true scientific conclusions takes place in a variety of sciences that do not share a common genus or kind. This is why a general account of this relation must abstract from the particular content of the statements of any given science. In this sense his theory is sometimes described as ‘formal’. In a similar manner, the logical expertise exemplified by a dialectician in two person question-answer exchanges involves the production of valid inferences, and this ability is not confined to a single domain. In the first book of the Topics dialectical skill is characterized as the ability both to reason syllogistically from credible opinions (endoxa) to conclusions that necessarily follow from them, and to avoid being refuted by one’s own concessions in argument. Dialectic is useful for intellectual training, for persuading a general audience and for philosophical knowledge. It enables one to develop and examine the arguments on both sides of philosophical puzzles (aporiai), thereby facilitating the discernment of truth. Furthermore, the dialectical scrutiny of credible opinions provides a path that leads to the first principles of the sciences. Unlike scientific arguments which argue from first principles and are concerned with items within a single subject genus, dialectical argument is possible concerning any subject matter whatsoever, and in this sense is topic neutral. Hence a general account of the way in which a dialectician shows that credible opinions and an interlocutor’s concessions necessitate further conclusions requires abstraction from subject matter. In dialectical argument one asks questions, and produces syllogisms using the answers as premises. However, since such arguments do not reason from explanatory premises already known by the respondent, they do not result in knowledge. Although credible opinions, which can include commonly accepted views as well as the opinions of the wise, must not be obvious falsehoods, they may in fact be false, and certainly need not be explanatory first principles. Reasoning from them is in any case no guarantee that the conclusions reached are true, and even where the premises are true, they (typically) do not explain the truth of the conclusion.<sup>8</sup> In the first chapter of the Prior Analytics Aristotle informally characterizes a syllogism as an account9 in which certain things being posited, something other than what has been posited follows of necessity in virtue of the former’s being the case. He further explains that ‘in virtue of their being the case’ means ‘resulting through them’, and that this involves not needing any term outside of those in the premises for the generation of the necessity. A syllogism is a case of a valid argument in which the conclusion follows of necessity from the premises, and does so in virtue of the way subject and predicate terms are combined. The heart of his syllogistic is a general characterization of those valid arguments that contain a pair of simple statements as premises, have a simple statement as conclusion, and involve just three terms: major, middle, minor. In aid of generality, actual Greek terms (like ‘animal’ or ‘pale’) are replaced by Greek letters (like ‘A’ and ‘B’) used as schematic letters. The forms of the four basic types of statements (the ‘assertoric’ propositional forms) are characterized in terms of their quantity and quality, and his three syllogistic ‘figures’ are characterized by reference to the order of the major, middle and minor terms of an argument.<sup>10</sup> In addition, Aristotle presents a number of rules of conversion. He identifies within the three ‘figures’ the syllogisms, or valid arguments, and believes that every scientific demonstration and every syllogism in the informal sense can be captured by a string of two premise syllogisms from these figures (and ultimately from the first figure). Although the Prior Analytics does not explicitly refer to the De Interpretatione, its account of syllogistic inference builds upon ideas about statements that can be found in the latter. There both designating terms and 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> A statement (apophansis) is a sentence that is capable of either truth or falsehood. The Organon has no further discussion of sentences that lack a truth-value (such as prayers), and leaves them as a topic of discussion for rhetoric and poetics. Every simple statement is either an affirmation (kataphasis) or a denial (apophasis) An affirmation affirms some predicate of 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 the subject and the predicate are universals, one may further specify whether the affirmation or denial is of the subject taken as a whole, or merely as a part. The statement that ‘every animal is pale’ affirms pale of its subject, animal, as a whole. Such a statement is called ‘universal’ in quantity. By way of contrast, ‘some animal is pale’ affirms pale of only a part of its subject. Such a statement is called ‘particular’ in quantity.<sup>12</sup> One may specify in terms of their quantity (universal or particular) and quality (affirmative or negative) the four so-called assertoric categorical propositional forms employed in Aristotle’s syllogistic: universal affirmative, 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 not mortal).<sup>13</sup> Aristotle tried to show that all valid arguments could be put into syllogisms constructed of premises and conclusions of these forms. However, his account does not give axioms or rules for the propositional connectives, or statements containing either nested quantification or relational predicates. This drastically limits its scope of application. An additional problem results from the fact that use of a categorical statement in a syllogism presupposes that its terms have instances. (For instance, if it is true that all men are mortal, it is also true that some men are mortal.) There are logical relations that obtain between the different propositional forms. Consider four propositions, or statements, sharing the same subject and predicate but each exemplifying a different propositional form. The A and O propositions are contradictories,<sup>14</sup> as are the E and the I; the A and E 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 the propositional forms by means of the following three conversion rules: C1 if every S is P, some P is S C2 if some S is P, some P is S C3 if no S is P, no P is S These are not themselves syllogisms, and function in effect as rules for valid arguments having a single assertoric premise and a single assertoric conclusion. The syllogisms given formal treatment in this account consist of two premises and a conclusion, and each has both a figure and a mood. Statements are composed of terms, and the notion of figure is characterized by specifying the relationships between the terms occurring in the premises and the conclusions. The two extreme terms are the subject and the predicate of the conclusion, the major term being the predicate of the conclusion, the minor term being its subject. The middle term is the one that occurs in both premises, but not in the conclusion. The major premise is the premise containing the major term, and the minor premise is the premise containing the minor term. An argument is in the first figure if the major term is the predicate of the major premise, and the minor term is the subject of the minor premise. In such cases the middle term is the subject of the major premise, and the predicate of the minor premise. An argument is in the second figure when the middle term is the predicate of both premises, and in the third figure when the middle term is the subject of both premises. The syllogisms, or valid arguments within the three figures may be specified in terms of their mood, where the mood of a syllogism can be represented as a trio of propositional forms: the form of the major premise, the minor premise and the conclusion (in that order). Prior Analytics A4–6 states all the valid and invalid moods of the three figures. The valid moods of 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 producing counterexamples—that is, instances of a figure and mood combination in which the premises can be true, and the conclusion false. Having specified the syllogisms of the first three figures, Aristotle reduces the so-called ‘imperfect’ syllogisms of the second and third figure to the ‘perfect’ syllogisms of the first figure. The perfect syllogisms of the first figure are basic cases in which nothing other than the premises themselves are needed in order for it to be evident that the conclusion follows of necessity from the premises. Although in an imperfect syllogism the conclusion does necessarily follow, in order to make this evident one must do more than simply present the premises. The reduction shows that a valid argument that uses second or third figure resources to derive a conclusion can be replaced by valid reasoning that derives the same conclusion from the same premises relying upon only the obvious inferences of the first figure, together with the conversion rules.<sup>18</sup> In some cases a direct reduction utilizing conversion is possible, but where this is not possible (second figure AOO and third figure OAO), he resorts to reductio ad absurdum.<sup>19</sup> A reductio argument shows that the premises have a certain syllogistic consequence by producing a direct deduction of the contradictory of one premise from the other premise taken together with the contradictory of the conclusion. Demonstration and first principles For Aristotle the universe can be rendered intelligible, or understood, by humans. Metaphysics Epsilon 1 divides all knowledge into the theoretical, the practical and the productive. Whereas the goal of a productive science is always some product distinct from the exercise of the science itself (such as a shoe, a statue or health), and the goal of practical knowledge consists of the activities of life, theoretical knowledge is an understanding of the truth merely for its own sake. Theoretical knowledge itself is divided into the mathematical sciences, the natural or physical sciences and theology. The practitioner of a theoretical science knows, or understands, something by grasping its ‘why’ or ‘cause’. Knowledge is attained when something is explained by means of starting points or principles (archai) that are even better known than what is explained. The account in the Posterior Analytics of the structure of a demonstrative science is both patterned after and inspired by the way in which the Ancient Greek mathematical sciences, especially geometry, had developed in the direction of axiomatization. Ideally, the premises of a mathematical proof both necessitate the conclusion, and explain why it is true. It is with this ideal in mind that he says in Posterior Analytics A2 that we think that we have knowledge or understanding (in the unqualified sense) whenever we suppose both (1) that we know its ‘cause’ (the reason it is 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 be stressed that the range of applicability of the Greek term overlaps with, but is not coextensive with that of our word ‘cause’. Anything that can be explained has an aitia, regardless of whether it is the type of thing that we would ordinarily describe as ‘caused’. For instance, the premises of a mathematical proof, although not causes, nonetheless explain the truth of the 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 as such is an explanatory factor the grasp of which constitutes knowing why something is the case. What is known in the unqualified sense of that term must be a necessary truth. Building on his key insight that knowledge requires both an understanding of ‘causes’ and the necessity of what is known, the treatise goes on to discuss the different kinds of first principles, and how they are related to theorems. The necessary truths that constitute the body of a demonstrative science are exhaustively partitioned into indemonstrable first principles, and their demonstrable consequences. The former are understood through themselves. Their consequences, the theorems, are known or understood only through their ‘causes’ and principles. Our knowledge of the latter is demonstrative in that such knowledge involves deducing 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 of which they are the principles. Since a first principle is known through itself, and not through other things, there is no explanation as to why the principle is true. It is not explained or ‘caused’ by anything, and hence it cannot be known by tracing it back to causes. A first principle is indemonstrable, for it is both primary and immediate. To be immediate, it must be primary in the sense that there is nothing prior to it in terms of which 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 explains or mediates the connection between its subject and its predicate. A first principle cannot itself be explained by deducing it from prior principles or causes, and in this way is indemonstrable.<sup>20</sup> The other necessary truths of a science are explained or ‘caused’ by something other than themselves. They are known by tracing them back to principles, and ‘causes’ that are known through themselves. Such theorems are known only when one understands why they must be true. Theorems are known by deducing them from necessarily true first principles that are their ‘causes’, and the first principles must themselves be known independently of, and prior to demonstration. Demonstration itself is a scientific syllogism, a syllogism by virtue 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 the knowledge of the principles. However, since the first principles are better known than the conclusions of any demonstrative argument, although knowledge of them also comes from pre-existing knowledge, they must come to be known in some way other than demonstration. In connection with this topic Aristotle draws a distinction between what is known to us and what is known without qualification. What is known to us, prior to knowing first principles, is what we know through sense perception. This is not scientific knowledge, or knowledge without qualification. Our task is to move from what is known to us to knowledge of what is most knowable without qualification. These are the intelligible principles that will in turn explain and account for the original sensible phenomena from which we started. In the last chapter of the Posterior Analytics, B19, Aristotle explains that we come to know first principles through induction (epagogê), an argumentative procedure that proceeds to a generalization from some group of its instances. Aristotle is aware that such inferences are not deductively valid, and unfortunately does not develop a set of rules governing such inferences. Consequently, details of his views about this procedure cannot be described with confidence. What he does say indicates that induction is supposed to be the means by which an inquirer advances from what is initially knowable (to that individual) to what is knowable without qualification. In B19 it is said that knowledge of first principles is based on experience, that experience in turn is based on numerous memories, and finally that memories themselves result from numerous and repeated perceptions, All animals, ourselves included, have natural discriminative perceptual capacities. Perception provides the ultimate inductive basis for knowledge of first principles. The epistemic state the exercise of which constitutes knowledge of principles is called ‘nous’, or intelligence. Very little is said about it here, and when it is discussed elsewhere, in De Anima Gamma 4 and 5, the text is highly controversial and notoriously difficult. Each demonstrative science has both a kind term that demarcates its subject matter and a set of attributes that it studies. Posterior Analytics A7 and A10 show that a demonstrative science makes use of first principles in order to prove its conclusions about those objects that are encompassed by the general kind that it studies. Such demonstrated conclusions ascribe to these objects those properties that pertain to them intrinsically. A science studies items mentioned in the definitions of those things falling within the scope of its subject genus, as well as those definable things themselves, and their demonstrable attributes. These additional items are properties, or ‘modifications’ (pathê) either of the things within the scope of the genus, or of the genus itself. They are not included in the definitions of the subjects that possess them, and consequently demonstrations must be given to show that they belong to their subjects intrinsically. Geometry studies figures, and seeks causes and principles that govern each kind of figure qua that kind of figure. An example would be the proof of the theorem that the angles of a triangle equal two right angles. In general, the geometer appeals to first principles to explain what belongs to various kinds of figures insofar as, and because, they are figures. Aristotle put forward his account of scientific knowledge in opposition to the Platonic conception of a general dialectical science of being. Whereas Platonic dialectic purported to yield scientific understanding of the principles of the departmental sciences, Aristotle’s rival account was designed to uphold the independence or autonomy of the departmental sciences. The statements within such a science include propositional first principles as well as the theorems in which the ‘modifications’ of various types of figures are demonstrated.<sup>21</sup> Aristotle divided the first principles of a science into axioms and theses, and divided the latter into hypotheses and definitions. 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 it is. The definitions and hypotheses of a science are employed only in that branch of knowledge, and being first principles are not demonstrated by some other science. A definition is immediate in the sense that the predicate of a definition signifies just what the subject is, and hence the connection between subject and predicate is not explicable by reference to a middle term. 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 scientifically understand anything at all. The two most important examples of axioms are the law of non-contradiction, and the law of the excluded middle (the principle that there cannot be an intermediate between contradictories). The axioms are common to all of the sciences, and knowledge of the axioms is common to all scientific understanders. This is relevant to Aristotle’s conception of metaphysics as general ontology, a science which among other things investigates the axioms (for which see pp. 60–1). A science does not study just any attribute that might happen to belong to its subject matter, for there is no science of the accidental. In order to determine which statements, terms and first principles are appropriate for a given science with a given subject matter, one must specify the respect in which the science in question studies the application of the various terms to the subject it studies. For instance, the biologist does not study all the properties of living things, but only those that apply to them in respect of being living beings. Biology studies both the definitions of each species of living things and the properties that belong to each species per se, or intrinsically. A science studies what must belong to a subject in some respect, and in so doing investigates what belongs to it intrinsically, or per se.<sup>22</sup> Posterior Analytics A4 distinguishes the following three distinct ways in which something can belong to a subject per se. First, if something is in the account saying what some subject is (i.e., in the definition of the subject) it belongs to that thing per se. It is in this way that both biped and animal belong to the species man intrinsically1. In a second way something belongs to a subject intrinsically if that item is such that the subject in question is in its definition. It is in this way that ‘male’ and ‘female’ hold good of animal intrinsically2. Finally, in still another way, an item is said to belong to a subject in respect of itself if that item belongs to the subject because of, or on 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 subject intrinsically, or intrinsically2 is sometimes called by Aristotle ‘accidental’. Consequently, items that intrinsically belong to something in this third way are sometimes called per se, or intrinsic accidents. He also distinguishes things 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 what it is called through being something else that happens to be that. By way of contrast, a pale thing, or a cultured thing, is a being accidentally since it is called what it is called (namely ‘pale’ or ‘cultured’) through being something 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, and because of its connection with definition can be used to characterize the notion of essence. The essence of each thing is what it is said to be intrinsically1, and it is essentially predicable of that of which it is the essence. Topics A5 states that a definition (horos or horismos) is an account (logos) signifying the essence of that thing. (Rather than using a single word to mean essence here, he employs a phrase that corresponds to the English ‘what it is (for it) to be’ (to ti ên einai). The essence of something is the entity signified by the entire account saying what it is. Although he argues that the Platonic method of collection and division cannot demonstrate a definition, the influence of that method can be seen in Aristotle’s own conception of definition as a complex expression that mentions both the genus to which the item belongs and the differentiae that distinguish it from other coordinate members of that genus. A definition is an account signifying an essence. An account signifying what something is signifies its essence, and the definition of something is the 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’ signifies the species man, the definition of man signifies the essence of man. To predicate an essence of that of which it is the essence one may linguistically predicate the appropriate associated defining expression, thereby saying what that thing is. A definable item is one and the same as the essence signified by its definition. Whenever some universal is defined, the subject of the definition is the same as the essence signified by the definiens. Thus if man is correctly defined as ‘biped animal’, then the species man and the essence signified by the phrase ‘biped animal’ are the same thing. For this reason definitions are immediate principles. The statement of essence says what a thing is intrinsically1, and is even better known than any theorem, but its truth is not demonstrated by any argumentative procedure. His account of the nature of a deductive science is built around this idea of indemonstrable statements of essence. Scientists know things by knowing their essences. The essences signified by real definitions function as middle terms in scientific demonstrations. They are the ‘causes’ that explain the intrinsic connection between subject and predicate in a scientific theorem. PART 2: METAPHYSICS OVERVIEW OF ARISTOTLE’S METAPHYSICS There is disagreement as to how much of the collection of fourteen treatises called the Metaphysics was originally intended to be part of a single work, but it is generally agreed that their final organization is not due to Aristotle. By the first century BC an Aristotelian corpus was organized following the Stoic division of philosophy into logic, natural science and ethics. The topics investigated in the Metaphysics do not readily fall under these headings, and it is possible that the title was meant to indicate a supra-sensible subject matter, or perhaps the fact that it is to be studied after natural science. However, this label may mean no more than ‘the things after physics’, and hence indicate no more than a decision to place it in the corpus after the treatises on natural science. The title is not Aristotle’s own, and he himself described the science it investigates using the labels ‘wisdom’, ‘first philosophy’ and ‘the science of “that which is” qua “thing that is”’. Different books of the Metaphysics give different characterizations of this science, and the treatise as a whole does not contain a completed overall project. Many scholars have thought that at least Books A-elatton, Delta and K were added later by editors. A-elatton, the brief second book, deals with philosophy as the knowledge of truth, as well as the connection between the finitude of causes and the possibility of knowledge. It has the appearance of an introduction, and according to one tradition consists of notes taken by Pasicles, the nephew of Eudemus of Rhodes, on lectures delivered by Aristotle. Delta, which may have circulated independently in antiquity, is a lexicon of philosophical terms, many of which play a crucial role in the Metaphysics. It includes entries on ‘principle’, ‘cause’, ‘substance’, ‘being’, ‘prior’ and ‘posterior’. However, it lacks entries on many key metaphysical terms (for example, ‘essence’, ‘subject’, ‘matter’, ‘form’, ‘some this’ and ‘separate’). Book K contains alternative versions of parts of B, Gamma and Epsilon, as well as some excerpts from the Physics on such topics as luck, change, infinity and continuity. Book A begins with the famous dictum that all humans by nature desire to know. After a description of a progression starting from ‘perception’, and going through ‘memory’, ‘experience’ and ‘skill’ to ‘theoretical knowledge’, it describes the goal of the investigation as wisdom (sophia), a kind of knowledge of the causes and principles of things. Such a science would involve a general account of the causes and principles of all things, and would involve an understanding of the highest good. In the course of arguing that it is pursued for its own sake, he explains that philosophy begins in wonder, and above all we engage in it when we are puzzled, and cannot explain why things are the way they are. Next, A3–9 presents a lengthy 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 and Plato, he concludes in A10 that nobody has employed a type of cause other than 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 a reflection of Aristotle’s belief that investigation involves a methodology according to which one starts with what is familiar to us initially, and moves towards an understanding of first principles that are knowable by nature. He starts with a review of the previously held opinions. In a general way this is accomplished by the survey in Book A, but where relevant 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 give rise to. Prior to arriving at explanatory starting points, an inquirer is in a state of ignorance and puzzlement-thought is tied up in knots. Concerning the nature, scope and subject matter of wisdom, the most general science of the causes, there are opposing views, each supported by considerations having at least some degree of credibility. Book B contains a collection of brief sketches of puzzles about the causes of things. Some are more thoroughly investigated and answered elsewhere in the Metaphysics. This list both initiates and structures metaphysical investigation, the goal of which 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 the various parts of metaphysics, as well as probing questions about the proper characterization of the highest explanatory entities. Insofar as these arguments arise from endoxa, this part of philosophical investigation involves an exercise of dialectical skill. The final stage consists of a presentation of solutions, ideally making use of starting points or principles that are both natural and explanatory. Although sometimes there are clear indications that a solution is being offered, often it is not easy to determine whether a passage is presenting his own view rather than developing a puzzle to be solved. Book Gamma asserts the existence of a general science that studies ‘that which is’ qua, ‘thing which is’. By virtue of its generality it is contrasted with those sciences that study only some part of what there is. It also solves some of the puzzles of Book B by arguing, among other things, first that general ontology is also the science of substance, and subsequently that it studies those concepts, such as unity and plurality, that apply to things quite generally. General ontology also studies such basic logical principles as the law of non-contradiction and the law of excluded middle. In the course of pursuing the latter there is a lengthy examination and putative refutation of the Protagorean doctrine of truth. Book Epsilon divides theoretical knowledge into mathematics, natural science and theology. Most parts of mathematics deal with things that are unchanging but do not exist separately; the physical sciences deal with realities that do exist separately (although their forms cannot exist except in matter), and are subject to change; finally, theology studies separate and unchanging substance. First philosophy will be theology if such substances exist (otherwise it will be natural science), and it is here claimed that first philosophy will also be the universal science that studies ‘that which is’ qua ‘thing that is’. This book also reiterates a four-fold distinction found in Delta 7 according to which the word ‘being’ (on) can be used for (1) ‘that which is’ so and so per accidens (where the predicate does not belong intrinsically or per se<sup>25</sup> to its subject; for example, a human is cultured, but not in its own right), (2) ‘that which is’ so and so intrinsically or per se (where the predicate does belong per se, and typically the subject and predicate are in the same category of ‘that which is’), (3) ‘that which is’ so and so either potentially or in actuality (i.e., the predicate belongs either actually or potentially to the subject) and (4) ‘that which is’ in the sense of that which is true. General ontology is not concerned with either the first or fourth. There simply is no science of the accidental (this happening neither always nor for the most part), and since truth depends upon the combination and separation of things in the mind, it is simply a modification of thought. Accordingly, the following three books begin with a discussion of ‘that which is’ in connection with categories, and later move to a discussion of the 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 basic principles employed in Aristotle’s hylomorphic physics. Zeta presents a complex set of arguments that eventually leads to the view that the form of a sensible substance, rather than its matter or the sensible composite itself, is a primary substance. It is argued that definition and essence belong primarily to substances, and that no universals are substances. Additionally there are arguments against the existence of Platonic Forms, and against the claim that particulars are definable. In addition to the concepts of matter and form, the middle books bring in from his natural science a distinction between actuality (or activity) and potentiality. Books Eta and Theta make use of these concepts in an attempt to clarify further the relationship between the matter and form of a sensible composite, and the sense in which the form is an activity or actuality. Eta 6 treats the form of a composite and its matter as one and the same thing in the sense that the form is in actuality what the matter is potentially. Thus material composites are unities in their own right, and not merely one per accidens. The matter is not itself another actual substantial individual, and is ‘some this’ only in potentiality, not in actuality. A living thing is ultimately composed of inanimate materials (ultimately, of earth, air, fire and water), but its proximate matter is its organic body, and this is not separate from the substance of which it is the matter. Book Iota is close in topic to other concerns of general ontology as construed in Gamma 2. It discusses the various kinds of unity and plurality, and in connection with the latter distinguishes the four forms of opposition: contraries, contradictories, privations and relative terms. The discussion in Lambda 1–5 of the principles and causes of sensible things partially overlaps with the middle books. Lambda 1 divides substances into sensible and non-sensible, and further divides the former into the perishable (sublunary substances) and the eternal (the heavenly bodies). Non-sensible substances are both eternal and immutable, and it is pointed out that some have divided this group into (Platonic) Forms and mathematical objects. Next, Lambda 6–10 present some of Aristotle’s own positive theological views about non-sensible substance, and present arguments for the existence of an eternally actual unmoved mover of the outermost sphere of the cosmos. This is the god of his metaphysical system, and is identified with thought thinking itself. Books M and N are concerned with rival views concerning whether there are, besides the sensible substances, any eternal, immutable substances. They contain an exposition and criticism of Platonist accounts both of the existence and nature of Forms and of the objects of the mathematical sciences (for instance, numbers, lines and planes). There are arguments challenging the explanatory role that Pythagoreans on the one hand, and various Platonists on the other, envisaged for numbers, as well as arguments against the existence of the Forms. Against the Platonist view that mathematical objects are separate substances it is argued that the mathematician studies physical objects qua indivisible units, or qua lines, or qua planes, etc., and that such things as lines, numbers and planes do not have separate being. As for the Forms, alternative versions of the attacks on the existence and putative explanatory power of separate, Platonic Forms in chapters A6 and 9 are to be found in M4 and 5, together with some material not in the earlier book.<sup>27</sup> METAPHYSICS AS GENERAL ONTOLOGY The general science of causes is general ontology Gamma 1 begins with the assertion that there is a science that studies ‘that which 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 contrasted with the departmental sciences that cut off merely some part of ‘that which is’ and study the properties that are unique to that part. To study ‘that which is’ qua ‘thing that is’ is not to study some special object called ‘that which is qua thing that is’. The ‘qua’ locution is here used to indicate the respect in which this science studies its subject matter, and indicates that it deals with those ubiquitous truths that apply to each ‘thing that is’. The metaphysician must both state the general (propositional) principles that apply to ‘that which is’ as such and treat of their properties or features. An example of a metaphysical principle that belongs to beings as such is the principle of non-contradiction (PNC). To study what belongs to ‘that which is’ per se also involves a study of the terms that apply to ‘things that are’ as such (for instance, ‘same’ and ‘one’), and to investigate truths about them. This concept of general ontology is further clarified by the way in which Aristotle proceeds to deal with issues raised by four puzzles stated in B1 about the nature of the metaphysical enterprise itself. These are four of the first five items on the list, and they concern the characterization of the universal science that deals in the most general way possible with the causes and starting points of all things. The second puzzle (995b6–10), for instance, assumes that this science will at the very least deal with the principles of substance, and inquires whether it will also deal with the common axioms—those principles ‘from which everybody makes proofs’. Does it, for instance, study the PNC? Gamma 3 solves this puzzle by showing that the science of substance is the science that studies the common axioms. Gamma also provides answers to at least portions of the other puzzles, though without explicitly referring back to them. For instance, after Book B has queried whether the science of substance also studies the per se accidents of substances, it goes on to ask whether it will study in addition to these accidents such terms as ‘same’, ‘other’, ‘similar’, ‘dissimilar’, ‘contrariety’, ‘prior’ and ‘posterior’, and then concludes by asking whether it will also study even the per se accidents of these last mentioned items. This is to ask whether in addition to investigating the definitions of the per se accidents of substance, it will also study such issues as whether each contrary has a single contrary. Gamma 2 is in part devoted to answering these last two questions in the affirmative. In some respects, general ontology exhibits the kind of structure that is analyzed in the Posterior Analytics. It involves both a certain subject matter, and a set of items, both propositions and terms, that belong to its subject matter in respect of itself. However, the various kinds of ‘things that are’ are not themselves species of a single genus, and ‘that which is’ is not a generic 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 these categories cannot be subsumed under a single genus. Nonetheless, there can be a single science of ‘that which is’. Such a science studies what belongs to a ‘thing that is‘in respect of its being a ‘thing that is’—the things that pertain to it simply insofar as and because it is one of the ‘things that are’. General ontology as the science of substance Aristotle uses his term ‘ousia’ (‘substance’) for the fundamental explanatory principles of his general ontology. Strictly speaking, each science is the science of that primary thing by reference to which the other items 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 to conclude that the science of general ontology is in fact the science of substance. As the first sentence of Gamma 2 declares, ‘that which is’, although spoken of in a plurality of ways, is nonetheless always spoken of in relation to 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 which all ‘things that are’ are properly called ‘things that are’, some things are so called in a primary way, others in a derivative way, and a single science studies them all. The subject matter of ontology is not in the ordinary sense a generic kind, but this does not distinguish it from all special sciences. For instance, there is a single departmental science that studies everything that is healthy, despite the fact that the different kinds of healthy things do not come together under a single generic kind. A single science taking for its subject healthy things is possible because everything that is healthy is so called with reference to a single item, namely health. A diet is healthy because it maintains health, medicine because it produces health, a complexion because it signifies health, and a body because it receives health. In general, everything that is healthy is so called because it stands in some relation to a single thing, health. The relation of course varies for the different kinds of healthy things, but that with reference to which they are called ‘healthy’ is the same in all cases. It is in this way that there is a sort of subject for general ontology as well. The term ‘thing that is’ is not ambiguous in its application to substances, qualities, quantities, and so on, and yet it applies primarily to substances, and derivatively to all else. Substances are ‘things that are’ simply because they are substances. The applications of this label to things other than substances must be explained by relating them in appropriate ways to substances, the primary ‘things that are’. Every non-substantial kind of ‘thing that is’ is a kind of ‘thing that is’ by virtue of bearing the right kind of relation to the primary kind, to substance. However, just as in the case of health, the relation varies from one kind of non-substantial ‘thing that is’ to another. There is no single explanation for the application of 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 rather are ‘things that are’ by virtue of being the magnitudes of substances. How and why general ontology studies ubiquitous terms In 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 with certain principles that do not apply to absolutely everything. Having asserted that there is a single, unified science that studies ‘that which is’ qua ‘thing that is’, and having explained that such a science studies the causes and principles of substance, the remainder of Gamma 2 shows that general ontology also studies the ubiquitous terms that apply to ‘that which is’ as such. Gamma 2 argues that ‘one’, ‘many’, ‘same’, ‘other’, ‘similar’, ‘dissimilar’, ‘equal’, ‘unequal’, ‘different’ and ‘contrary’ are all examples of per se attributes 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 their definitions and proves theorems about them. This is one respect in which general ontology conforms to the model for knowledge found in Posterior Analytics. For instance, one might define contraries as things differing maximally within the same kind, and then demonstrate a per se accident of contrariety by proving as a theorem that each contrary has exactly one contrary. General ontology must study unity (the signification of the ubiquitous term ‘one’) for the following reason. There is a single science that investigates all of the types of ‘things that are’ qua. ‘things that are’, as well as 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 which is’ as there are of ‘that which is one’, general ontology must study unity and its varieties. The three types of unity are sameness, similarity and equality, and so general ontology treats of the definitions of each of these. Furthermore, there is always a single science for opposites, and since plurality is the opposite of unity, general ontology must also study plurality and its forms. The three types of plurality are otherness, dissimilarity and inequality, and so general ontology also studies these and their various sub- types. One type of otherness is difference, and contrariety is a type of difference. Contrariety, then, is one type of difference; difference is one type of otherness; otherness is one type of plurality; plurality is the opposite of unity; and finally, unity belongs per se to ‘that which is’. Hence contrariety itself must be dealt with by the general ontology. How general ontology studies basic logical principles General ontology is not only the science that studies what it is for terms to be contradictories, but also studies truths about the subjects to which such terms can be applied. In this spirit Gamma 3 claims, alluding to one of the puzzles of Book B, that we must state whether the science of substance just described also investigates the things that are called axioms in the mathematical sciences. This question is answered in the affirmative because the science of substance is the general science of ‘that which is’ qua ‘thing that is’, and this studies what belongs per se to all ‘things that are’. Each common axiom applies to all ‘things that are’ qua ‘things that are’, and does not have an application merely in one particular kind apart from the rest of what there is. These common principles are indemonstrable, and metaphysical argument does not demonstrate their truth. However, this science can prove things about these axioms. Gamma 3, for instance, attempts to prove that 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, in the same respect. This is equivalent to saying that it is impossible for both members of a contradiction to be true (at the same time, in the same respect, etc.). According to the account given in De Interpretatione 6 a contradiction (antiphasis) is a pair of opposed (antikeimena) statements, one of which is an affirmation (kataphasis), the other of which is a denial (apophasis). The affirmation and the denial are statements about the same subject, but what is affirmed of the subject in the former is precisely what is denied of it in the other. In Metaphysics Iota 7 a ‘contradiction’ is characterized as an antithesis such that for anything whatsoever, one part or the other of the antithesis is present, there being nothing between the two members of the antithesis.<sup>32</sup> Iota 4 classifies contradiction as the primary type of opposition, the other three types being contrarieties, privations and relative terms (pairs such as master/slave). Book B cites the PNC as an example of the common beliefs that all employ in proof, and Gamma argues that it is the firmest of all such principles in that one could never be in error with respect to it (since it is impossible to believe a contradiction). Being the firmest of all principles, it is the most knowable, and must be grasped and understood by anybody who is able to understand anything at all, and can never be employed merely as a hypothesis. To show the impossibility of believing a contradiction he argues as follows. He starts by asserting that it is impossible for contraries to simultaneously belong to the same subject. This is a consequence of the PNC. The notion of contrariety involved is that mentioned above and characterized in Delta 10. Contraries are those things belonging to the same kind that differ as widely as possible within that kind. Assuming that beliefs are attributes of believers, we are told that a belief that contradicts another is the contrary of that belief. Consequently, it is impossible for a believer to believe both members of a contradiction at the same time; for were somebody to have both beliefs, that person would be in contrary states—but that is impossible. Gamma 4 claims that it has been proven by means of the principle itself that the PNC is the firmest principle. It then goes on to state that although the PNC cannot be demonstrated, it can be given a demonstration elenctically. In Prior Analytics 620 an elenchus, or refutation, is a syllogism, the conclusion of which is the contradictory of some proposition maintained by the opponent, and the premises of which are conceded by the interlocutor. The premises need not be, and typically are not, prior to and explanatory of the conclusion, and hence typically an elenctic demonstration does not yield knowledge of its conclusion. The elenctic demonstration outlined in Gamma 4 begins by having an opponent signify something both to himself and to another. The elenctic proof that follows is intended to refute an interlocutor who denies the PNC, and to do so by showing that certain commonly known things that the opponent believes actually entail the PNC (or at least particular instances of it). As such this argument is not a scientific demonstration, but rather an elenchus. The elenchus shows that the principle is already known by anybody who knows anything. However, being a first principle no premises could possibly show why it is true, and a valid deduction of the PNC is not a demonstration, for nothing is prior to and explanatory of the PNC. METAPHYSICS AS THE THEORY OF SUBSTANCE Sensible substance: being as a definable ‘this something’ Although Metaphysics Zeta and Eta may originally have formed an independent treatise on substance, they nonetheless do carry out an important part of the task of general ontology. As Z1 explains, its main question, ‘What is substance?’ is in fact the fundamental ontological question ‘What is “that which is”?’, a question over which both Aristotle and his predecessors have repeatedly puzzled. Accordingly, the inquiry into substance is pursued within the context of his program for general ontology. The opening lines of Zeta begin this inquiry with the assertion that ‘that which is’ (to on) is spoken of in many ways, and then elaborate upon this claim by listing some of its significations in connection with the categories. On the one hand being, or ‘that which is’, signifies both ‘what X is’ (ti esti) and ‘some this’ (tode ti); additionally (now turning to other categories) it signifies either a quality (‘what X is like’) or quantity (‘how much X’ is), or each of the other things predicable in the way these latter things are. He takes it as clear that of the various significations of the phrase ‘that which is’, the primary signification is the ‘what X is’ which signifies a substance. That is, the most basic kind of being is the being expressed by a definition that answers the ‘What is it?’ question when asked 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 appropriate relation of ontological dependence to something that is a ‘thing that is’ in the primary way. Some things are beings because they are qualities of substances; others because they are quantities of substances; and so on. As required by the account of ‘being’ (or ‘that which is’) given in Gamma 2, the term ‘on’ applies primarily and without qualification to substances, and derivatively to all else. General ontology is indeed the science of substance. Although Gamma proclaimed the ontological priority of substance, it did not explain what it is to be a substance. To advance the project of general ontology Zeta now initiates an investigation designed to arrive at an account of substance. For this general project to succeed, it must characterize substance in such a way that every type of ‘thing that is’ will be accounted for by reference to what substances are. In order for substances to play this role, their being (i.e., what they are) cannot in turn be explained by appeal to any causes or explanatory factors external to them. A substance cannot be a ‘thing that is’ by virtue of standing in some relation to something other than itself. Substances are ‘things that are’ simply because they are substances. Hence each substance is what it is intrinsically, or per se. A substance is both ‘some this’ and a ‘what X is’. Being intrinsically a particular subject, it is ‘some this’; being something essentially, it will also be a ‘what X is’.<sup>33</sup> Furthermore, Z1 states that substances are primary in all of the ways in which something can be primary. This is because: (1) only substances are separate, (2) the account of the being of each non-substantial item must contain an account of the being of some substantial item (from which that non-substantial item cannot be separated, and upon which its being depends), and (3) understanding, or knowledge, of each thing proceeds from an understanding of the substances signified by definitions. The subsequent investigation in the middle books aims at a general account of perceptible substance that meets these conditions on the primacy of substance. The last three conditions imposed upon the analysis of substance stem not from some particular theory of substance, but from the single idea that strictly speaking the subject matter of general ontology is substance. Here, as elsewhere, investigation must begin with what is known, or familiar, to the inquirer. Since Aristotle takes it that there is widespread agreement that at least some perceptible bodies are substances, his inquiry into substance must begin with them. The eventual goal is to have moved from these to an understanding of what is most knowable by nature. Aristotle investigates perceptible substances in order to consider later such questions as whether there is, in addition to the matter of sensible substances, another kind of matter, and whether we need to inquire into some other kind of substance (for instance, numbers, or something of that sort). Z17 says that the new starting point that it offers might help us to get clear about that substance that exists separated from perceptible substance. Accordingly, in Z2 he starts by listing various types of things that have been thought to be substances. The items thought to be the clearest examples of substance are bodies. This includes not only the four basic elements (earth, water, air and fire), but also living things, both plants and animals, as well as their parts, and anything that is either a part of or composed of bodies. The entry on substance in Delta 8 explains why bodies are called substances. It is because they are not predicable of a subject, but the other things are predicable of them. This is the condition uniquely satisfied by primary substances in Categories 5. What makes something a primary substance in the Categories is that it satisfies this very condition. Z2 neither endorses nor rejects this or any other view about what things are in fact substances, or what makes them so. Z16 subsequently 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 heaps rather than unities. In general, most of the things thought to be clear examples of substance (including items treated in the Categories as primary substances), turn out to be potential beings, and not substances in actuality. Next, after also touching on various Platonist views that treat (separate) Forms and/or mathematical objects as substances, Aristotle says that what is needed is a consideration of such questions as whether there are any substances besides the sensible ones, and what is the manner of being for both the sensible substances and for whatever non-sensible substances there may be. Later he will argue that there are no (separate) Forms,<sup>34</sup> and Books M and N defend his view that there are no non-sensible mathematicals that enjoy the status of separate substances. However, before answering the question ‘What things are substances?’, Z2 advises that we first sketch out an answer to the question ‘What is substance?’ This involves determining what explains what makes it the case that some substance is a substance. The explanatory entity E that explains why some substance X is a substance may be called ‘the substance of X’. The task at hand 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 that performs it. Z3 begins this search by listing as possible candidates for the substance of X 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 subject associated with it. The first three correspond to the predicate position of a statement, and are items that a dialectician might invoke as an answer to the question ‘What is X?’ The fourth candidate for substance is a subject of which other items are predicable. The ‘subject’ is thought most of all to be substance, and Z3 explains that the ‘subject’ is that of which all other things are said, but is not itself said of anything further. Consequently, the substance of X would be something that is not said of a subject, but rather is that of which the other things are said. This characterization of the substance of X as the subject for predication should be compared with the claim in Categories 5 that the primary substances are those things of which all else is predicable, they themselves being predicable of nothing further. Whatever its merits as a characterization of the class of substances, in Z3 it is found inadequate as a specification of the substance of some substantial being X. Within a hylomorphic context, the matter, the form and the composite may each be called a ‘subject’, and the logical subject condition for substance by itself does not provide an adequate account of what it is about a substance that makes it the case that it is a substance. Aristotle argues that on its own it leads 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 its predicates. By stripping off in thought all predicables, one arrives at an ultimate subject of predication that is nothing in its own right, and has whatever predicates it does only accidentally. However, such matter is neither separate nor ‘some this’,<sup>36</sup> and hence cannot be the substance for which we are searching. Although recent scholarship has raised serious problems for taking this to commit Aristotle to the existence of an indeterminate ultimate subject of predication, traditionally this chapter has been read as introducing Aristotle’s own concept of prime matter. Prime matter has also been thought of both as a principle of individuation for numerically distinct material objects, and as the persisting substratum for the basic elemental transformations in his natural science. The hylomorphic analysis of perceptible substance is invoked in Z3 without explanation as something already familiar. It is not entailed by the general 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’s natural science, and depends upon some of the basic constitutive principles of the science that treats of the general principles that govern natural bodies insofar as they are subject to change. Although the substances of the Organon are persisting subjects for non-substantial changes, in the logical works there is no treatment of the causes of change, and substances are not analyzed as compounds of matter and form. The technical concept of matter is never employed in the logical works, nor is the correlative notion of form. In these works the word ‘eidos’ is used not for the hylomorphic conception of form, but rather for a secondary substance, the species (and sometimes for the Platonic Form). The notion of form introduced in Z3 must be understood within the context of this kind of hylomorphic analysis. It is the formal component of a particular hylomorphic compound. He turns next to a discussion of another candidate for substance: the essence. In connection with his inquiry into substance, Z4, 5 and 6 deal with the logical concepts of definition and essence. In the logical works an essence is simply the ontological correlate of a definition (an answer to a ‘What is X?’ question). Z4 and Z5 argue that only substances have definitions in the primary sense, and consequently there are essences (in an unqualified 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, and called what they are called intrinsically, are one and the same as their essence. This thesis ‘expresses the view that the definiens and the definiendum must, in a correct definition of a substance, signify one and the same entity. A substantial form is identical with its essence. However, neither accidental unities (such as a pale man) nor hylomorphic composites are identical with an essence. On Aristotle’s view the requirement that a substance be ‘what X is’ leads to 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 a universal composite of matter and form, and as such is not a primary substance. There is currently considerable scholarly controversy as to whether Aristotle considered substantial forms to be particulars, universals or neither particulars nor universals. One reason for holding that they are universals is that substances are first in the order of definition and knowledge, and definition is thought to be of the universal.<sup>38</sup> A chief reason for taking them to be particulars is that a substance must be a separately existing ‘this something’, but universals are ontologically dependent upon particulars.<sup>39</sup> This initial discussion of definition and essence is followed in Z7, 8 and 9 by a treatment of the material, formal and efficient causes of natural, artistic and spontaneous generation. These three chapters argue that all generated objects are composites of matter and form, and that the formal component of a substance is its essence. This ‘physical’ conception of an essence 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 the inquiry into definition and essence within a hylomorphic context, and Z12 subsequently takes on the problem of the unity of definition. Z3 listed the universal as a candidate for substance, and Z13, 14, 15 and 16 discuss various topics connected with the claim that universals are substances. The genus being one type of universal, these chapters also deal with its credentials for being substance. Since the objects of definition are thought to be universals, these issues naturally follow an exploration of definition and its objects. The claim of universals to be substances stems from the fact that to the Platonist they seem to satisfy best the requirement that a substance be ‘what X is’. However, Z13 argues that since the substance of something is unique to that of which it is the substance, no universal 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 ‘some this’. The essence, an item originally introduced as a predicable, should also satisfy the subject condition for substance. It is the essence that is identical with hylomorphic form that plays this role. If the ‘what X is’ requirement is to be met by one of the first three candidates listed in Z3, it is the essence that will meet it. In order to count as a substance, an essence would have to be a particular, determinate subject, and not a universal. Aristotle thinks that the Platonic view that what is predicable in common of particulars is separate and a ‘this something’ leads to an infinite regress that he refers to as the ‘third man’.<sup>40</sup> Although the reconstruction of this argument is difficult, it seems to have involved the idea that if the particulars have a Form in common, and this Form is a separately existing ‘this something’, then there must be an additional Form that both the particulars and the first Form have in common, and so on ad infinitum. According to Aristotle, however, the form of a perceptible substance does not exist separately, but always requires perceptible matter. Although it is clear that Z13 presents arguments against the claim that universals are substances, these arguments are presented as part of an aporematic investigation, and as such are linked up with the results of earlier chapters in order to formulate a problem (aporia). The problem is that no substance is composed of universals or of actual substances, and so substances must be incomposite, and hence indefinable; yet it was argued in the earlier treatment of definition in Z4 and Z5 that strictly speaking only substances are definable. However, if substances are not definable, then nothing is. This problem is not directly solved in Z13–16, but Z17 makes a fresh start in the attempt to answer the question ‘What is substance?’ From its new perspective, the primary cause of being for a material composite is the essence that is responsible for the fact that the matter constitutes that composite. The substance of X is neither one of the material elements of which X is composed nor an element present in its essence, and is itself both 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. A substantial form is separate in definition, and hence prior in both the order of definition and knowledge. Nonetheless, it cannot exist without matter, and in the case of perceptible things it is only the composite that is separate without qualification. Sensible substance: actuality and potentiality The substance of a living thing is its soul. It is because a soul is present to a body that the body constitutes a living, functioning organism. The body is the matter, and is the thing in potentiality, whereas the form is the activity or 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 life in virtue of having the capacities assigned to the various parts of human soul, the principle of human life. Soul is that by virtue of which (in the primary sense) we live, think, perceive, etc. The form (or substance of) the species man is that form (i.e., human soul) that makes a human body alive in virtue of the fact that the body has it. The word ‘man’ is applicable to Socrates in virtue of his matter (his body) having a substantial form. The substantial form or essence is strictly speaking a ‘this something’, and Socrates is a ‘this something’ because of the form that his body has. Book Theta initiates a more extended treatment of the distinction between ‘that which is’ in actuality, and ‘that which is’ potentially. To understand what an actuality (energeia) is, Aristotle begins by considering the kind of potentiality (dunamis) that is correlated with change, because this is the most basic and most familiar kind of potentiality. Change, unlike substantial form, is a kind of incomplete activity or actuality, but an understanding of the relation between change and the potential for change enables one to comprehend the way in which substantial form is an actuality (or activity). Theta 6 explains the concept of an energeia by means of a set of analogies. An actuality is something that stands to something else in the way that a change stands to its correlated potentiality. 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 its potentiality, so the substance (i.e., the form) stands to its matter. Substantial form is an actuality that is the fulfillment of the potentiality the matter has for being ‘this something’. As a goal and fulfillment, it is the primary cause of the composite’s being what it is. METAPHYSICS AS THEOLOGY Aristotle has argued that in the sensible world there are substances, and what makes them such is their form. These forms are internal principles, or natures, and as such cannot exist without matter. The next major step in the general ontological program is to investigate supra-sensible reality. There is reason to think that there are non-perceptible substances that exist separately, and perhaps they are the things entirely knowable by nature. The last three books of the Metaphysics are concerned with the various non-sensible items that have been thought to be substances. Although a discussion of this sort is needed to complete the general inquiry into ‘that which is’, these books may not have been written as a part of the larger work. They are not explicitly coordinated with the treatment of sensible substance in the middle books, nor do they attempt to put their topics within the framework of the general ontology of Gamma. Books M and N argue that (1) although mathematical objects exist, they are 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 least one of these is the unmoved mover, or god of his metaphysics. Lambda 6– 10 contains an account of this unmoved mover. Although itself unchangeable, it is an eternal source of the motion of the outermost celestial sphere, and being the final cause of that motion, it moves as an object of love. God is incapable of being other than it is, and as such has no matter, 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 living being. God’s intelligence is not a thinking of us or of the universe, but rather is a thinking of thinking or intelligence itself (1074b34). He argues both that this activity is the good, and that it is the source of the order and goodness of the universe. Although perceptible substances are the substances that are initially most familiar to us, metaphysical inquiry is ultimately for the sake of coming to an understanding of this first principle. One moves towards an understanding of divine substance by starting with the causes of the things that are most familiar to us and proceeding towards an understanding of the highest causes. Lambda 4 states that the causes and principles of different things are in one sense different, but in another sense, speaking generally and by analogy, they are the same for all things (1070a31–33). The unmoved mover is a cause analogous to those causes and principles of perceptible substances studied by the special sciences. God is the final cause of motion in the outermost sphere, and this is analogous to the way in which 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’s nature is analogous to the actuality of a perceptible substance. To understand actuality, we start with an understanding of the manner in which a change is an actuality, and then move to an understanding of the substance of a perceptible body as an actuality. However, the highest cause is grasped when we attain an understanding of the best and most perfect actuality, and this is an understanding of god. NOTES 1 See p. 52 for the use of this phrase. 2 Aristotle sometimes employs other conceptions of the accidental, including one 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 a classification of predicates answering to the various kinds of questions that can be asked about any subject at all, substance or otherwise. Another way of classifying predicates is represented by the four-fold distinction in Topics A5 between genus, definition, proprium and accident. This classification is useful for his analysis of a science in terms of a subject genus, definitions of the items investigated, and theorems relating propria to the defined kinds it studies. The accidental is that which falls outside the scope of a science. See 51–52 below. 6 The translation is not ideal since it, unlike the Greek, has no connection with the 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 four classes: didactic, dialectical, peirastic and eristic. Didactic arguments use as premises truths from some science that are not yet the beliefs of the learner, and such arguments are in effect demonstrations. Dialectical arguments deduce the contradictory of an opponent’s thesis from endoxa (which may or may not represent the opponent’s own beliefs), and peirastic arguments constitute that subset of dialectical arguments in which the premises are both believed by the respondent and must be known by anybody purporting to have knowledge. Eristic arguments are not dialectical, and produce either real 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 to definition (for which see p. 52 below). 10 Here only the theory of the assertoric syllogism (i.e. one composed of statements) is discussed. Since scientific knowledge of a theorem involves knowing that it is necessary, an analysis of demonstration would seem to require a modal syllogistic dealing with statements of necessity and possibility. Prior Analytics A8–22 attempts to develop a theory of syllogistic inferences that involve modal categorical statements. It is unsuccessful in that its treatment of modality is inconsistent, and apparently conflates sentential and adverbial readings of the modal operators. 11 Since a sentence is a linguistic item, the terms of which it is composed should also be linguistic. However, I will follow Aristotle’s usage in sometimes calling the objects picked out by its linguistic terms the ‘terms’ of a statement. Thus Socrates and the species man are sometimes referred to as the ‘terms’ of the statement that Socrates is a man. 12 Using this terminology in translations is potentially confusing since in calling a proposition ‘particular’ one is not thereby saying that its subject is a particular. Although occasionally Aristotle will use singular premises in syllogistic inferences, the theory he develops in fact applies solely to arguments composed of statements of A, E, I or O form. 13 The technical vocabulary of the Prior Analytics typically reverses the order of subject and predicate, and picks out the four forms corresponding to these kinds of schemata, labeled respectively ‘A’, ‘E’, ‘I’, and ‘O’: P belongs to every 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 two vowels in the Latin words ‘affirmo’ and ‘nego’. 14 Both cannot be true together, and both cannot be false together. For the application 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 forms have come to be called Barbara, Celarent, Darii, Ferio (Barbari and Celaront), respectively, the vowels indicating the propositional forms. The valid moods of the second figure are EAE, AEE, EIO and AOO, plus the subaltern moods EAO, AEO (Cesare, Camestres, Festino, Baroco, plus Cesaro and Camestrop). Those of the third figure are AAI, EAO, AII, IAI, OAO, EIO (Darapti, Felapton, Datisi, Disamis, Bocardo and Ferison). A fourth figure (in which the major term is the subject of major premise, and the minor term is the predicate of minor premise) exists. The fourth figure is not discussed as such by Aristotle, although the Prior Analytics shows awareness of 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 be established by a method of ekthesis. 20 Furthermore, Aristotle argues that demonstration of principles cannot proceed in a circular fashion, nor can there be an infinite series of principles which 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 Analytics B10 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 least some 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 condition of difficulty (being without a way of passage) that prevents further progress towards one’s destination. B1 applies this term both to the condition of the intellect when faced with credible, but opposing arguments, and to the arguments 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 often rendered 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 a definable universal, it is nonetheless proper to apply the label ‘what X is’ to particulars as well. The phrase ‘what X is’ may be used as a place-holder for terms such as ‘man’ or ‘horse.’ For instance, ‘what Socrates is’ is a man. Since he is a man, it is correct to say that Socrates is ‘what he is’ (i.e., the definable species 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 METAPHYSICS GENERAL For Greek texts, English translations and commentaries, general bibliographies, general introductions to Aristotle and collections of essays, see [1.1] to [1.59]. Further texts and commentaries relevant to Aristotle’s logic 2.1 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, Study Aids Monograph No. 4 (Sub-faculty of Philosophy, Oxford University, 1984). 2.3 Frede, M. and Patzig, G., Aristoteles ‘Metaphysik Z’: Text, Übersetzung und Kommentar, 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 logic 2.6 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 METAPHYSICS 2.8 Ackrill, J.L., ‘Aristotle’s theory of definition: some questions on Posterior Analytics 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 and Sorabji [1.53], vol.1, 65–87. [Revised version of paper published in Phronesis 14 (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 Posterior Analytics and Generation of Animals’, in Gotthelf and Lennox [1.56], 120–66. 2.16 ——‘Essentialism and semantic theory in Aristotle: Posterior Analytics II, 7– 10’, Philosophical Review 85 (1976) 514–44. 2.17 Burnyeat, M., ‘Aristotle on understanding knowledge’, in Berti [1.48], 97– 139. 2.18 Charles, D., ‘Aristotle on meaning, natural kinds, and natural history’, in Devereux and Pellegrin [1.58], 145–67. 2.19 Cherniss, H.F., 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, Canadian Journal of Philosophy, supplement10 (Edmonton, 1984), 1–20. 2.21 ——‘Aristotle’s investigation of a basic logical principle’, Canadian Journal of Philosophy 16 (Sept. 1986), 341–57. 2.22 ——‘Metaphysics and logic’, in Matthen [1.57], 127–49. 2.23 ——‘No universal is a substance: an interpretation of Metaphysics Z13, 1038b8–15’, Paideia, Special Aristotle Issue (Dec. 1978) 65–74. 2.24 ——‘On the origins of some Aristotelian theses about predication’, in Bogen, J. and McGuire, J. eds, Language and Reality in Greek Philosophy (Athens, 1985), 101–31, 323–6. 2.25 Cohen, S.Marc, ‘Essentialism in Aristotle’, Review of Metaphysics 32 (1979) 387–405. 2.26 Corcoran J., ed., Ancient Logic and its Modern Interpretations (Dordrecht, 1974). 2.27 Dancy, R.M., Sense and Contradiction (Dordrecht, 1975). 2.28 Decarie, V., L’Objet de la métaphysique selon Aristote (Montreal, 1961). 2.29 Driscoll, J.A., ‘Eide in Aristotle’s earlier and later theories of substance’, in O’Meara, D.O., ed., Studies in Aristotle (Washington, 1981), 129–59. 2.30 Evans, J.D.G., Aristotle’s Concept of Dialectic (Cambridge, 1977). 2.31 Ferejohn, M., The Origins of Aristotelian Science (New Haven, 1991). 2.32 Frede, M., ‘Categories in Aristotle’, in O’Meara, D.O., ed., Studies in Aristotle (Washington, 1981), 1–24; reprinted in Frede [2.34], 29–48. 2.33 ——‘The definition of sensible substances in Metaphysics Z’, in Devereux and Pellegrin [1.58], 113–29. 2.34 ——Essays in Ancient Philosophy (Minnesota, 1987). 2.35 ——‘Stoic vs. Aristotelian syllogistic’, Archiv für Geschichte der Philosophie 56, 1–32; reprinted in Frede [2.34], 99–124. 2.36 ——‘Substance in Aristotle’s Metaphysics’, in Gotthelf [2.40], 17–26; reprinted in Frede [2.34], 72–80. 2.37 ——‘The unity of general and special metaphysics: Aristotle’s conception of metaphysis’, in Frede [2.34], 81–95. 2.38 Furth, M., Substance, Form and Psyche: An Aristotelian metaphysics (Cambridge, 1988). 2.39 Gill, M.L., Aristotle on Substance: The paradox of unity (Princeton, 1989). 2.40 Gotthelf, A., ed., Aristotle on Nature and Living Things (Bristol, 1985). 2.41 Graham, D.W., Aristotle’s Two Systems [1.70]. 2.42 Hartman, E., Substance, Body, and Soul (Princeton, 1977). 2.43 Hintikka, K.J.J., ‘Aristotle and the ambiguity of ambiguity’, Inquiry 2 (1959) 137–51; reprinted with revisions as Ch. 1 of Hintikka [2.45], 1–26. 2.44 ——‘On the ingredients of an Aristotelian science’, Nous 6 (1972), 55–69. 2.45 ——Time and Necessity: Studies in Aristotle’s theory of modality (Oxford, 1973). 2.46 Irwin, T.H., Aristotle’s First Principles (Oxford, 1988). 2.47 ——‘Homonymy in Aristotle’, Review of Metaphysics 34 (1981) 523–44. 2.48 ——‘Aristotle’s concept of signification’, in Schofield, M. and Nussbaum [2. 96], 241–66. 2.49 Jaeger, W., Aristoteles, Grundlegung einer Geschichte seiner Entwicklung (Berlin, 1923); trans. by Richard Robinson, Aristotle: Fundamentals of the History of his Development (Oxford, 2nd edn 1948). 2.50 Kahn, C., ‘The place of the prime mover in Aristotle’s teleology’, in Gotthelf [2.40], 183–205. 2.51 ——‘The role of nous in the cognition of first principles in Posterior Analytics II 19’, in Berti [1.48], 385–414. 2.52 Kapp, E., ‘Syllogistic’, in [1.53], 35–49; originally published as ‘Syllogistik’ in Pauly-Wissowa, Real-Encyclopädie der classischen Altertumswissenschaft, vol. IVA, cols. 1046–1067 (1931). 2.53 Kosman, L.A., ‘Substance, being and energeia.’, Oxford Studies in Ancient Philosophy 2, 1984, 121–49. 2.54 ——‘Understanding, explanation and insight in Aristotle’s Posterior Analytics’, in Lee et al. [2.58], 374–92. 2.55 Kung, J., ‘Aristotle on thises, suches, and the third man argument’, Phronesis 26 (1981) 207–47. 2.56 Lear, J., ‘Active Epistêmê’, Graeser [1.50], 149–74. 2.57 ——Aristotle and Logical Theory (Cambridge, 1980). 2.58 Lee, E.N., Mourelatos, A.P.D. and Rorty, R., eds, Exegesis and Argument (Assen, 1973). 2.59 Le Blond, J.M., ‘Aristotle on definition’, in ([1.53], vol.3), 63–79; originally published as ‘La Definition chez Aristote’, Gregorianum 20 (1939) 351–80. 2.60 ——Logique et méthode chez Aristote (Paris, 1939; 2nd edn 1970). 2.61 Lesher, J.H., ‘Aristotle on form, substance and universals: a dilemma’, Phronesis 16 (1971) 169–78. 2.62 Lesher, J.H., ‘The meaning of nous in the Posterior Analytics’, Phronesis 18 (1973) 44–68. 2.63 Lewis, F., Substance and Predication in Aristotle (Cambridge, 1991). 2.64 Lezl, W., Logic and Metaphysics in Aristotle (Padua, 1970). 2.65 Loux, M.J., ‘Ousia: a prolegomenon to Metaphysics Z and H’, History of Philosophy Quarterly 1 (1984) 241–66. 2.66 ——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 Formal Logic (Oxford, 1951; 2nd edn 1957). 2.68 McCall, S., Aristotle’s Modal Syllogisms (Amsterdam, 1963). 2.69 McKirahan, R.D., Principles and Proofs: Aristotle’s theory of demonstrative science (Princeton, 1992). 2.70 McMullen, E., ed., The Concept of Matter in Greek and Medieval Philosophy (Notre Dame, 1963). 2.71 Mansion, S., Le Jugement d’existence chez Aristote (Louvain, 1946; 2nd edn 1976). 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 in Ancient Philosophy, vol.3, 1985, 125–57. 2.77 Mueller, L, ‘Aristotle on geometrical objects’, Archiv für Geschichte der Philosophie 52 (1970) 156–71; reprinted in [1.53] vol. 1, pp. 96–107. 2.78 O’Meara, D.J., ed., Studies in Aristotle (Washington, D.C., 1981). 2.79 Owen, G.E.L., ‘Aristotle on the snares of ontology’, in Bambrough [2.11], 69– 95; reprinted in Owen [1.72], 259–78. 2.80 ——‘Logic and metaphysics in some earlier works of Aristotle’, in Düring and Owen [1.41], 163–90; reprinted in Owen [1.72], 180–99; and in Barnes et al. [1.53], 13–32. 2.81 ——Logic, Science and Dialectic: Collected papers in Greek philosophy, see [1.72]. 2.82 ——‘Particular and general’, Proceedings of the Aristotelian Society 79 (1978–9), 1–21; reprinted in Owen [1.72], 279–94. 2.83 ——‘The Platonism of Aristotle’, Proceedings of the British Academy 51 (1966), 125–50; reprinted in Owen [1.72] 200–20; and in [1.53] Barnes et al. vol.1, 14–34. 2.84 ——‘Tithenai ta Phainomena’, in Mansion [2.71], 83–103; reprinted in Moravcsik [2.75], 167–90; also in Barnes et al. [1.53] vol.1, 113–26; and in Owen [1.72], 239–51. 2.85 Owens, J., The Doctrine of Being in the Aristotelian Metaphysics (Toronto, 1951; 2nd edn 1963; 3rd edn 1978). 2.86 Patzig, G., Aristotle’s Theory of the Syllogism (Dordrecht, 1968). [First published in German as Die aristotelische Syllogistik (Göttingen, 1959).] 2.87 ——‘Logical aspects of some arguments in Aristotle’s Metaphysics’, in Aubenque [1.47], 37–46. 2.88 ——‘Theologie und Ontologie in der Metaphysik des Aristoteles’, Kant- Studien 52, 1960–61, 185–205; published in English as ‘Theology and ontology in Aristotle’s Metaphysics’, in Barnes et al. 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