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Ptolemy's defense of theoretical philosophy.

Claudius Ptolemy is rightly remembered for his scientific contributions, and his Mathematical Composition--hereafter referred to by its more common title, the Almagest, from its Latinized Arabic moniker--stands as one of the most influential texts in the history of science. In the Almagest, Ptolemy presents his astronomical models, which account for the several movements of the stars and planets, including the sun and moon. The content of the Almagest, however, is not strictly scientific--or, rather, mathematical, as Ptolemy characterizes astronomy as a branch of mathematics. The introduction to the text, Almagest 1.1, is manifestly philosophical. It outlines the philosophical theories underlying Ptolemy's astronomy, and, moreover, it epitomizes Ptolemy's general philosophical position. In Almagest 1.1, Ptolemy positions himself as an expert on philosophy, he defines and distinguishes the parts of philosophy, and he defends the ethical benefits of studying mathematics and astronomy in particular.

Although Ptolemy's philosophical system is generally understudied, this paper will investigate a nearly unexplored area: Ptolemy's definitions and evaluations of theoretical and practical philosophy. (2) An examination of this topic not only sheds light on Ptolemy's justification for spending more of his free time engaged in theoretical rather than practical philosophy --and more time in mathematics than the other theoretical sciences--but also encapsulates Ptolemy's reliance on and reaction to contemporary philosophical trends, specifically the Middle Platonic and nascent Aristotelian commentary traditions. Ptolemy rarely cites his sources, let alone his philosophical ones. However, by drawing connections among the philosophical statements in Ptolemy's texts and from them to the texts of contemporary philosophers, as well as to the authorities on which they drew, I hope to both elucidate Ptolemy's philosophical ideas pertaining to the relationship between theoretical and practical philosophy and demonstrate his deep embeddedness in the contemporary philosophical context.

In the first lines of the Almagest, Ptolemy establishes his expertise in philosophy by stating a criterion by which to judge who the legitimate philosophers are. He states, 'It seems to me that the legitimate philosophers, Syrus, were entirely right to have distinguished the theoretical part of philosophy from the practical. (3) By asserting that legitimate philosophers --as opposed to, presumably, illegitimate ones--distinguish the theoretical part of philosophy from the practical part, Ptolemy positions himself on the side of the legitimate philosophers. He, like the legitimate philosophers, differentiates the theoretical part of philosophy from the practical part.

As is well known, this distinction between the theoretical and the practical, while prefigured in Plato, emerges fully articulated in Aristotle's texts. Ptolemy recognizes his philosophical heritage from Aristotle by citing Aristotle's name in connection with the tripartite division of theoretical philosophy: 'For Aristotle divides the theoretical [part of philosophy], too, very fittingly, into three primary genera, the physical, mathematical, and theological. (4) In his corpus, Ptolemy cites only two philosophers: Aristotle, here in Almagest 1.1 as well as in the Planetary Hypotheses, and Plato, in the Planetary Hypotheses. (5) Ptolemy cites Aristotle and Plato in the Planetary Hypotheses in order to reject and support, respectively, elements of their cosmological models. The citation of Aristotle in Almagest 1.1,

for Ptolemy in "The significance of Ptolemy's Almagest for its early readers," Revue de Synthese 131, no. 4 (Dec. 2010) 495-521. therefore, is Ptolemy's only citation of a philosopher in an explicitly philosophical context.

Because Ptolemy cites Aristotle in relation to the tripartite division of theoretical philosophy, one might assume that Ptolemy drew his definitions of the theoretical sciences, as well as his distinction between theoretical and practical philosophy, from Metaphysics E 1 and K 7. In her book Ptolemy's Universe, however, Liba Taub demonstrates that the language Ptolemy uses to discuss the theoretical sciences is not Aristotle's. (6) Indeed, a thorough analysis of Ptolemy's definitions of the theoretical sciences reveals that he drew from several of Aristotle's texts, not only the Metaphysics. (7) Regardless of which texts Ptolemy employed as his sources, in Almagest 1.1, he recognizes Aristotle's authority over the tripartite division of theoretical philosophy.

Yet, Ptolemy does not cite Aristotle when differentiating the theoretical and practical parts of philosophy, and he omits the productive part, which Aristotle includes in Metaphysics E 1, 1025b25, and K 7, 1064a161-17, when distinguishing practical, productive, and theoretical understanding. This omission could call into question Ptolemy's appropriation of Aristotle's trichotomy of the types of understanding. nevertheless, as just mentioned, Ptolemy drew philosophical ideas from several of Aristotle's texts, and Almagest 1.1 is manifestly not a commentary on the Metaphysics. In addition, Aristotle occasionally omits productive understanding when differentiating the theoretical and practical, and therefore, it is possible that Ptolemy derived his definitions of theoretical and practical philosophy from Aristotle's corpus more generally. Furthermore, the juxtaposition of the theoretical and practical became paradigmatic in ancient philosophy, and the omission of the productive in the dichotomy of the theoretical and practical was common in post-Hellenistic philosophy. (8)

Whether or not Ptolemy read Aristotle's texts, or only sources derived from them, in the Almagest, Ptolemy joins Aristotle in the tradition of defending the contemplative life over the life of action. (9) In the first lines of the Almagest, Ptolemy launches his defense by asserting a distinction between theoretical and practical philosophy: 'For even if the practical [part of philosophy], before it is practical, happens to be theoretical [TEXT NOT REPRODUCIBLE IN ASCII], nevertheless one can see that there is a great difference between the two ....' (10) In this relatively short but complex statement, Ptolemy claims that even if practical philosophy is reducible to, or dependent on, theoretical philosophy, a great difference distinguishes them.

Ptolemy reveals himself here to be engaging in a contemporary debate over the relationship between theoretical and practical philosophy. This debate seems to have evolved from post-Hellenistic attempts to synthesize Aristotle's and Plato's accounts of the relationship between theoretical and practical philosophy. While Aristotle's texts establish an absolute distinction between the two, Plato's corpus does not consistently distinguish them. At times, Plato indicates that theoretical and practical philosophy are unconditionally distinct, as in Gorgias 500c-d, where Socrates portrays the political and philosophical lives as disparate, and in Statesman 258d-e, where Socrates distinguishes practical ([TEXT NOT REPRODUCIBLE IN ASCII]) and theoretical ([TEXT NOT REPRODUCIBLE IN ASCII]) knowledge. On the other hand, Plato's texts also depict practical knowledge as dependent on theoretical knowledge. At Republic VI, 500d, for instance, Socrates argues that one'should apply what one'sees when contemplating the divine to shaping one's and others' characters:
 And if he should come to be compelled to put what he sees there
 into people s characters, whether into a single person or into a
 populace, instead of shaping only his own, do you think he will be
 a poor craftsman of moderation, justice, and the whole of popular
 virtue? ... And when the majority realize that what we are saying
 about the philosopher is true, will they be harsh with him or
 mistrust us when we say that the city will never find happiness
 until its outline is sketched by painters who use the divine
 model? (11)


Molding the city according to the divine model, the philosopher shapes the city into its most happy and just state; after contemplating the divine, the philosopher is able to rule the city in the best possible way. In other words, practical philosophy is dependent on theoretical philosophy. The analogy of the cave, at Republic VII, 514a-17a, reiterates this dependency. The individual who has left the cave and seen the sun is compelled to return to the cave. Correspondingly, the philosopher who has contemplated the Forms and obtained knowledge is qualified and compelled to rule Kallipolis. At Republic VII, 540a-b, Socrates explains that at the age of 50, individuals who have succeeded thus far in both practical and scientific matters ([TEXT NOT REPRODUCIBLE IN ASCII]) must proceed to study the Forms and contemplate the Good. Thereafter, they use the Good as the paradigm for the city they are compelled to rule:
 And once they ve seen the good itself, they must each in turn put
 the city, its citizens, and themselves in order, using it as their
 model. Each of them will spend most of his time with philosophy,
 but, when his turn comes, he must labor in politics and rule for
 the city's sake, not as if he were doing something fine, but
 rather something that has to be done ([TEXT NOT REPRODUCIBLE IN
 ASCII]). (12)


The rulers of Kallipolis mold the city according to the divine model they have already contemplated. Hence, Plato occasionally depicts practical philosophy as dependent on theoretical philosophy.

The discrepancy between Plato's and Aristotle's corpuses on whether practical philosophy is dependent on or independent of theoretical philosophy seems to have produced a debate, for which we have evidence from the second century CE. Again, Ptolemy asserts that, despite the possible dependency of the practical part of philosophy on the theoretical, a great difference separates the two. Correspondingly, in the first lines of his commentary on the Nicomachean Ethics, Aspasius, a contemporary of Ptolemy, writes, 'The treatment of ethics and especially politics is prior ([TEXT NOT REPRODUCIBLE IN ASCII]) to theoretical philosophy ([TEXT NOT REPRODUCIBLE IN ASCII]) in respect to necessity but subsequent ([TEXT NOT REPRODUCIBLE IN ASCII]) in respect to value.' (13) Later in the text, when defining action ([TEXT NOT REPRODUCIBLE IN ASCII]), Aspasius identifies ethics and politics as practical:
 But activity in accord with an active science ([TEXT NOT
 REPRODUCIBLE IN ASCII]) is also called "action." In general, all
 those arts are called "active" which have no other product apart
 from an action, for example dancing and flute-playing. But more
 particularly the political and ethical arts are called active
 ([TEXT NOT REPRODUCIBLE IN ASCII]), and activities that concern
 what is noble and shameful are called actions. (14)


Evaluating the relationship between theoretical and practical philosophy, Aspasius argues that ethics and politics, arts representative of practical philosophy, are prior or subsequent to theoretical philosophy in respect to necessity or value.

Ptolemy and Aspasius seem to be engaging in a common, second-century debate over the relationship between theoretical and practical philosophy. Of note is that both Ptolemy and Aspasius discuss theoretical and practical philosophy rather than theoretical and practical understanding, or [TEXT NOT REPRODUCIBLE IN ASCII], as Aristotle does in Metaphysics E 1 and K 7. Moreover, both use the term [TEXT NOT REPRODUCIBLE IN ASCII] when addressing the relationship between theoretical and practical philosophy. According to Aspasius, theoretical and practical philosophy are prior ([TEXT NOT REPRODUCIBLE IN ASCII]) or subsequent to one another in various respects but remain independent. Therefore, Aspasius adheres to what I will call, for the purposes of this paper, the Aristotelian model, where theoretical and practical philosophy are independent of one another. For Ptolemy, the point of concern is the potential dependency of practical on theoretical philosophy--that before ([TEXT NOT REPRODUCIBLE IN ASCII]) practical philosophy is practical, it is theoretical. Ptolemy addresses this possible dependency and then asserts that a great difference separates them. Thus, Ptolemy admits the possible legitimacy of what I will call the Platonic model--where practical philosophy is dependent on theoretical philosophy--but thereafter appears to champion the Aristotelian model.

Ptolemy takes a similar approach to a philosophical debate in his text On the Kriterion and Hegemonikon. (15) In On the Kriterion, Ptolemy eschews philosophers quibbles over terminology. He calls these quibbles 'battles over words ([TEXT NOT REPRODUCIBLE IN ASCII])', of which some are 'meddlesome tattle ([TEXT NOT REPRODUCIBLE IN ASCII])'. (16) He explains that these debates are useful only inasmuch as they include investigations of the objects signified by the debated terminology. Like Galen--who also renounces terminological disputes and claims that they should be the subject of grammarians and orators rather than physicians and natural philosophers (17)--Ptolemy aims to utilize terms that reflect the nature of the objects signified. He explains, ' Such a proposal removes dispute about nomenclature from our discussions but keeps our enquiry into the things underlying the words intact and free from distractions.' (18) In keeping with this emphasis on ontology rather than terminology, Ptolemy asserts the following when defining the soul in contrast to the body:
 This is not the place to bother whether we ought also to call this
 part "body." As we have said, we are not at present discussing the
 names to give to the natural objects before us; what we are
 investigating is the difference ([TEXT NOT REPRODUCIBLE IN ASCII])
 between these things, a difference which we recognize as being
 unchangeable in reality even if one alters the nomenclature a
 thousand times, or at one time says that the soul is incorporeal,
 following those who lay it down that what is known by sense
 perception is to be called "body," and at another time that it is
 body, following those who define body as that which can act and be
 acted upon. The difference between the natures of the said
 entities being of this kind, there would be universal agreement
 that it is by the soul that we think and not by the body. And we
 would also acknowledge that it is by the soul, not the body, that
 we make our sensory and all other movements, if we took note too
 of the quantitative aspect of what happens when they separate.
 (19)


In this passage, Ptolemy explains that philosophers dispute whether the soul is alike or different in kind from the body, and he insists that the soul is different from the body, as the soul causes human beings to think, and the body produces all other movements in human beings. This pattern of recognizing a debate over whether one object is reducible to another and then asserting a difference, [TEXT NOT REPRODUCIBLE IN ASCII], between them also appears in Almagest 1.1. Ptolemy recognizes the debate over whether, as he frames it, practical philosophy is dependent on theoretical philosophy, and he asserts a great difference, [TEXT NOT REPRODUCIBLE IN ASCII], between the two.

In the case of theoretical and practical philosophy, the [TEXT NOT REPRODUCIBLE IN ASCII] is how one attains virtues in relation to each part of philosophy. After Ptolemy asserts that a great difference separates theoretical and practical philosophy, he gives an account of the difference:
 ... in the first place, it is possible for many people to possess
 some of the moral virtues ([TEXT NOT REPRODUCIBLE IN ASCII]) even
 without being taught ([TEXT NOT REPRODUCIBLE IN ASCII]), whereas
 it is impossible to obtain the theory of the universe ([TEXT NOT
 REPRODUCIBLE IN ASCII]) without instruction ([TEXT NOT
 REPRODUCIBLE IN ASCII]); furthermore, one derives most benefit in
 the first case [practical philosophy] from continuous practice in
 actual affairs ([TEXT NOT REPRODUCIBLE IN ASCII]), but in the
 other [theoretical philosophy] from making progress in the
 theories ([TEXT NOT REPRODUCIBLE IN ASCII]). (20)


In the case of practical philosophy, some of the moral virtues are attainable without instruction, and they derive mainly from continuous activity; concerning theoretical philosophy, theoretical apprehension of the universe is dependent upon instruction, and most benefit in theoretical philosophy consists in progress in theories.

Following Franz Boll, Liba Taub points to the influence of Aristotle's Nicomachean Ethics 1103a on Ptolemy's differentiation between theoretical and practical philosophy. (21) Here, at the beginning of Book 2 of the Nicomachean Ethics, Aristotle divides virtue in two:
 Virtue being, as we have seen, of two kinds, intellectual and
 moral ([TEXT NOT REPRODUCIBLE IN ASCII]), intellectual virtue
 is for the most part both produced and increased by instruction
 ([TEXT NOT REPRODUCIBLE IN ASCII]), and therefore requires
 experience and time; whereas moral virtue is the product of habit
 ([TEXT NOT REPRODUCIBLE IN ASCII]), and has indeed derived its
 name, with a slight variation of form, from that word. (22)


Like Ptolemy's practical philosophy, which depends on continuous activity, Aristotle's moral virtue requires habit; just as Ptolemy's theoretical philosophy progresses by instruction, so, too, Aristotle's intellectual virtue relies on instruction.

Nevertheless, just as Ptolemy did not take his definitions of the three theoretical sciences directly from the Metaphysics, neither is it likely that he simply reinterpreted the Nicomachean Ethics. Indeed, Ptolemy's definitions of theoretical and practical philosophy join the ancient philosophical tradition of distinguishing virtues according to their attainment by either instruction or habit. Again, Ptolemy distinguishes theoretical and practical philosophy according to their relation with either theory or moral virtues, cultivated by instruction or activity. Similarly, Aspasius points to learning as the source of intellectual virtues and training or habit as the source of ethical virtues, and, when commenting on Nicomachean Ethics 1103a, he affirms Aristotle's distinction between the two sets of virtues. (23) Moreover, Alcinous--a likely contemporary of Ptolemy, and the author of the Didaskalikos, or Handbook of Platonism--distinguishes between the rational and affective parts of the soul by arguing that the former is cultivated through instruction ([TEXT NOT REPRODUCIBLE IN ASCII]) and the latter through habitual practice ([TEXT NOT REPRODUCIBLE IN ASCII]). (24) For influences on this passage in Alcinous' text, John Dillon points to both Nicomachean Ethics 1103a14-18 and Republic VII, 518d-e. (25) In the latter, Socrates characterizes education as the craft that turns the soul toward the good and depicts habit and practice as what cultivate the virtues of the soul that are akin to the body. Correspondingly, in Phaedo 82a-b, Socrates remarks that popular and political virtue ([TEXT NOT REPRODUCIBLE IN ASCII]) is developed from habit and care ([TEXT NOT REPRODUCIBLE IN ASCII]), and, in Phaedo 82d-83c, he states that philosophy teaches the lovers of learning ([TEXT NOT REPRODUCIBLE IN ASCII]) that their souls, imprisoned in their bodies, guide them to see the intelligible and invisible. Thus, Aristotle s distinction between intellectual and moral virtues has a precedent in Plato's writings, and Middle Platonic philosophers, like Alcinous, appropriated these sets of ideas.

What is interesting in Ptolemy's account, however, is not only that he distinguishes between the intellectual and moral virtues according to whether they are gained by instruction or habit but that he also applies this distinction between the virtues to the differentiation of theoretical and practical philosophy. Yet, even this application has a precedent in Middle Platonic philosophy. For instance, Plutarch, who lived from the first to the second century CE, distinguished the parts of philosophy by their dependence on teaching or habit. Like many other Middle Platonic philosophers prior to and contemporary with Ptolemy, Plutarch divided philosophy into three categories--physics, logic, and ethics--and he distinguished logic and ethics according to their relation to learning and habit: [TEXT NOT REPRODUCIBLE IN ASCII]. (26) Hence, Ptolemy s application of the distinction between the sets of virtues to the differentiation of the parts of philosophy has a precedent in Middle Platonic philosophy. What is unusual, and perhaps unique, with Ptolemy's account is his specific blending of these Middle Platonic trends. Ptolemy uses instruction and habit to distinguish theoretical and practical philosophy.

Of significance to this analysis is Ptolemy's enumeration and definition of the virtues in Book 3 chapter 5 of the Harmonics, his text on music theory, which he likely published before the Almagest. (27) In the Harmonics, Ptolemy offers three alternative models of the human soul. Each is tripartite, and the names of the three parts in the first model are Aristotelian, in the second, they are Platonic, and, in the third, they represent a synthesis of the previous two. With each model, Ptolemy makes an analogy between the parts of the soul and the octave and concords in music. Just as the octave has seven species ([TEXT NOT REPRODUCIBLE IN ASCII]), the concord of the fifth has four species, and the concord of the fourth has three species, so, too, in the case of the Platonic model, the rational part ([TEXT NOT REPRODUCIBLE IN ASCII]) of the soul has seven species, the spirited part ([TEXT NOT REPRODUCIBLE IN ASCII]) has four species, and the appetitive part ([TEXT NOT REPRODUCIBLE IN ASCII]) has three species. (28) In the case of Ptolemy's Platonic model, these species of the soul are species of virtue.

Before listing the individual virtues, Ptolemy defines virtue in general as a melodiousness ([TEXT NOT REPRODUCIBLE IN ASCII]) of souls and vice as an unmelodiousness ([TEXT NOT REPRODUCIBLE IN ASCII]): '... virtue among souls is a melodiousness belonging to them, while vice is an unmelodiousness. A feature common to both classes is the attunement ([TEXT NOT REPRODUCIBLE IN ASCII]) of their parts, when they are in a condition conforming to nature, and lack of attunement ([TEXT NOT REPRODUCIBLE IN ASCII]) when they are in a condition contrary to nature. (29) In accordance with both the Platonic and Stoic traditions, Ptolemy describes the relations between the parts of the soul in harmonic terms. (30) Thereafter, he lists the species of virtue corresponding to each part of the soul. First, just as in music the concord of the fourth has three species, the appetitive part of the soul has three species of virtue: moderation ([TEXT NOT REPRODUCIBLE IN ASCII]), self-control ([TEXT NOT REPRODUCIBLE IN ASCII]), and shame ([TEXT NOT REPRODUCIBLE IN ASCII]). Second, just as the concord of the fifth has four species, the spirited part of the soul has four species of virtue: gentleness ([TEXT NOT REPRODUCIBLE IN ASCII]), fearlessness ([TEXT NOT REPRODUCIBLE IN ASCII]), courage ([TEXT NOT REPRODUCIBLE IN ASCII]), and steadfastness (capTepia). Third, just as the octave has seven species, the rational part of the soul has seven species of virtue: acuteness ([TEXT NOT REPRODUCIBLE IN ASCII]), cleverness ([TEXT NOT REPRODUCIBLE IN ASCII]), shrewdness ([TEXT NOT REPRODUCIBLE IN ASCII]), judgment ([TEXT NOT REPRODUCIBLE IN ASCII]), wisdom ([TEXT NOT REPRODUCIBLE IN ASCII]), prudence ([TEXT NOT REPRODUCIBLE IN ASCII]), and experience ([TEXT NOT REPRODUCIBLE IN ASCII]). By providing a list of virtues, Ptolemy follows a typically Hellenistic trend, which has a precedent in Aristotle's corpus.

By ascribing virtues to distinct parts of the soul, as opposed to the soul in its entirety, however, Ptolemy joins the Middle Platonic tradition. Salvatore R. C. Lilla notes in his monograph, Clement of Alexandria: A Study in Christian Platonism and Gnosticism, that Clement, Philo, Alcinous, and Apuleius 'ascribe a particular virtue to each part of the soul, thus forming a piece of coherent doctrine which remained the same throughout Middle Platonism and was also adopted, without any noticeable variation, even by exponents of Neoplatonism such as Plotinus and Porphyry. (31) One must expand this tradition to include pseudo-Andronicus de Passionibus. (32) Lilla notes that the philosophers he lists assign [TEXT NOT REPRODUCIBLE IN ASCII]; to the [TEXT NOT REPRODUCIBLE IN ASCII], to the [TEXT NOT REPRODUCIBLE IN ASCII] to the [TEXT NOT REPRODUCIBLE IN ASCII]. Pseudo-Andronicus, too, assigns [TEXT NOT REPRODUCIBLE IN ASCII]; to the [TEXT NOT REPRODUCIBLE IN ASCII] to the [TEXT NOT REPRODUCIBLE IN ASCII], but he allocates [TEXT NOT REPRODUCIBLE IN ASCII];, rather than [TEXT NOT REPRODUCIBLE IN ASCII], to the [TEXT NOT REPRODUCIBLE IN ASCII]. (33) While these philosophers differ on which virtue they assign to the spirited part of the soul, Ptolemy's account coheres with both sets, as he assigns more than one virtue to each part of the soul. Indeed, it is this point that distinguishes Ptolemy's account. Although other Middle Platonic or Peripatetic philosophers ascribe only one virtue to each part of the soul, Ptolemy assigns several virtues to each part. This decision is not only untraditional, but, in the second century, it would have been controversial. After all, in a polemic against Chrysippus, Galen assigns a single virtue to each part of the soul and argues that only one virtue can belong to each part. (34) Yet, it may be Galen's historical adversary that influenced Ptolemy's model. Holding the soul to be a unity, the Stoic tradition assigned many virtues to the soul. Ptolemy's association of several species of virtue with each part of the soul may be a confluence of Stoic and Platonic theories, in this case of a Stoic model of the relationships among the soul's virtues and a Platonic tripartition of the soul.

In addition to listing the species of virtue, Ptolemy provides short definitions of each virtue. The closest philological match to these definitions is found in the pseudo-Platonic Definitions, composed during the fourth century and most likely developed incrementally over the course of centuries. (35) Franz Boll first drew attention to the potential influence of the Definitions on Ptolemy's list of virtues, and Ingemar During later agreed that not only does a great deal of overlap exist between the two texts, but, furthermore, this overlap cannot be accidental. (36) Every single virtue that Ptolemy lists in the Harmonics appears in the Definitions. Many of the virtues have their own definitions, but those virtues that are not defined in the Definitions are still included in the definitions of other terms. For example, acuteness ([TEXT NOT REPRODUCIBLE IN ASCII]) does not have its own definition, but it--like cleverness ([TEXT NOT REPRODUCIBLE IN ASCII]), which is defined in the Definitions--is used to define shrewdness ([TEXT NOT REPRODUCIBLE IN ASCII]), another virtue of Ptolemy's rational part of the soul. (37) Moreover, obvious terminological overlap exists between several of the definitions pseudo-Plato--the author(s) of the Definitions--and Ptolemy provide. For instance, according to Ptolemy, wisdom ([TEXT NOT REPRODUCIBLE IN ASCII]) has to do with the theoretical ([TEXT NOT REPRODUCIBLE IN ASCII]), and according to pseudo-Plato, it is 'non-hypothetical knowledge; knowledge of what always exists; knowledge which contemplates ([TEXT NOT REPRODUCIBLE IN ASCII]) the cause of beings.' (38) Similarly, both Ptolemy and pseudo-Plato define gentleness (npaOT];) in relation to anger ([TEXT NOT REPRODUCIBLE IN ASCII]) (39) and courage ([TEXT NOT REPRODUCIBLE IN ASCII]) in relation to dangers ([TEXT NOT REPRODUCIBLE IN ASCII]). (40) In addition, both Ptolemy and pseudo-Plato use the phrase 'endurance of hardships ([TEXT NOT REPRODUCIBLE IN ASCII])' in their accounts of steadfastness ([TEXT NOT REPRODUCIBLE IN ASCII]). Ptolemy defines it as 'the endurance of hardships ([TEXT NOT REPRODUCIBLE IN ASCII])', (41) and pseudo-Plato describes it as 'endurance ([TEXT NOT REPRODUCIBLE IN ASCII]) of pain for the sake of what is admirable; endurance of hardships ([TEXT NOT REPRODUCIBLE IN ASCII]) for the sake of what is admirable. (42) Concerning Ptolemy's virtues of the appetitive part of the soul, both Ptolemy and pseudo-Plato define moderation ([TEXT NOT REPRODUCIBLE IN ASCII]) in relation to pleasures ([TEXT NOT REPRODUCIBLE IN ASCII]), (43) characterize self-control ([TEXT NOT REPRODUCIBLE IN ASCII]) as a type of enduring ([TEXT NOT REPRODUCIBLE IN ASCII]), (44) and use forms of the term [TEXT NOT REPRODUCIBLE IN ASCII] to define shame ([TEXT NOT REPRODUCIBLE IN ASCII]). (45) Hence, a considerable amount of textual overlap exists between Ptolemy's definitions of the virtues and their definitions in the pseudo-Platonic Definitions. It is possible, of course, that Peripatetic and Stoic definitions of the virtues influenced Ptolemy's definitions. (46) However, the textual correspondences between Ptolemy's and pseudo-Plato's accounts suggest a Platonic source. Ptolemy may have used a Platonic handbook, such as the Definitions, when composing this section of the Harmonics, or perhaps he simply drew these definitions from his earlier education. Either way, it is fitting that Ptolemy'should use Platonic definitions of the virtues when delineating the species in a Platonic model of the human soul.

After Ptolemy presents his models of the parts and species of the human soul in Harmonics 3.5, in the following chapter, he describes the genera to which the species belong and the two principles ([TEXT NOT REPRODUCIBLE IN ASCII]) to which the genera belong. The two principles are the theoretical and the practical, and the genera are the three theoretical and three practical sciences. Ptolemy states, 'For each principle ([TEXT NOT REPRODUCIBLE IN ASCII]), that is, the theoretical ([TEXT NOT REPRODUCIBLE IN ASCII]) and the practical ([TEXT NOT REPRODUCIBLE IN ASCII]), there are three genera: physical ([TEXT NOT REPRODUCIBLE IN ASCII]), mathematical ([TEXT NOT REPRODUCIBLE IN ASCII]), and theological ([TEXT NOT REPRODUCIBLE IN ASCII]) in the case of the theoretical, and ethical ([TEXT NOT REPRODUCIBLE IN ASCII]), domestic ([TEXT NOT REPRODUCIBLE IN ASCII]), and political ([TEXT NOT REPRODUCIBLE IN ASCII]) in that of the practical.' (47) As mentioned above, Ptolemy's three theoretical sciences have a precedent in Aristotle's corpus, such as in Metaphysics E 1, 1026a6-32, and K 7, 1064a28-b6. The practical sciences, although they recall Eudemian Ethics VI 8, 1141b23ff., appear only in scholastic interpretations such as Alcinous Didaskalikos 3.3. (48) Of note is Ptolemy's separation in Harmonics 3.6 of the theoretical and practical sciences; Ptolemy portrays theoretical and practical philosophy as absolutely distinct. Therefore, Ptolemy's distinction of theoretical and practical philosophy in Almagest 1.1, as explored thus far, is consistent with Ptolemy s portrayal of theoretical and practical philosophy in Harmonics 3.6. Both texts depict theoretical and practical philosophy as independent of one another.

After distinguishing theoretical and practical philosophy in Almagest 1.1, Ptolemy defends his preference for dedicating most of his free time to theoretical philosophy:
 Hence, we thought it fitting for them [viz., the legitimate
 philosophers], on the one hand, to order their actions according
 to the applications of the phantasiai of these ([TEXT NOT
 REPRODUCIBLE IN ASCII]) in such a way as never to forget, even in
 ordinary affairs, to strive for a fine and well-ordered state
 ([TEXT NOT REPRODUCIBLE IN ASCII]), and, on the other hand, with
 leisure to devote the most time to the instruction of theories,
 being many and fine, but especially those particularly called
 mathematical. (49)


Given that progress in theoretical philosophy depends on instruction and the attainment of moral virtues requires activity, it is preferable for philosophers to spend more of their free time engaged in theoretical rather than practical philosophy. Nevertheless, it is imperative to explain how it is that a philosopher should guide his actions even in ordinary affairs, as is stated, as well as in practical philosophy, as is implied. According to Ptolemy, one should order his actions according to the applications of phantasiai.

Ptolemy's phrase--[TEXT NOT REPRODUCIBLE IN ASCII]--is peculiar and requires unpacking. Prescribing the ordering of actions, Ptolemy uses the verb puG^i^eiv. This verb occurs in only one other instance in Ptolemy's corpus, in Tetrabiblos 1.3. While defending the usefulness of astrology, Ptolemy champions the utility of foreknowledge:
 For, in the first place, we should consider that even with events
 that will necessarily take place their unexpectedness is very apt
 to cause excessive panic and delirious joy, while foreknowledge
 accustoms and orders the soul ([TEXT NOT REPRODUCIBLE IN ASCII])
 by experience of distant events as though they were present, and
 prepares it to accept with peace and stability whatever comes.
 (50)


In other words, knowledge of the future accustoms and orders the soul, and these processes prepare the individual for future action. Ptolemy's collocation of the verbs [TEXT NOT REPRODUCIBLE IN ASCII] does not seem to be accidental. The term [TEXT NOT REPRODUCIBLE IN ASCII] recalls the significance of habit for the development of moral virtues, which distinguish practical philosophy in Almagest 1.1. Here in Tetrabiblos 1.3, Ptolemy associates the verb [TEXT NOT REPRODUCIBLE IN ASCII], indicating the ordering of the soul in preparation for future events. In Almagest 1.1, [TEXT NOT REPRODUCIBLE IN ASCII] seems to carry the same connotation as in Tetrabiblos 1.3. Ptolemy uses the verb when prescribing the ordering of future actions in the sphere of practical philosophy.

Second, Ptolemy uses the term phantasiai. To extract what this term means in this context, one must look at Ptolemy's On the Kriterion and Hegemonikon. Among the components of Ptolemy's criterion of truth is phantasia, which Ptolemy defines as the mediator between sense perception and the intellect. Ptolemy explains, To the faculty of sense perception belong both sense organs and phantasia. The sense organs are the bodily instruments through which contact is made with perceptible things, while phantasia is the impression and transmission to the intellect, whose retention and memory of the things transmitted we call conception.' (51) Hence, in Ptolemy's theory of cognition, phantasia has the technical meaning of a sense impression that transmits a perception to the intellect. Ptolemy uses the plural form, phantasiai, later in the text when discussing the transmission of sense impressions: [TEXT NOT REPRODUCIBLE IN ASCII]. (52) In Almagest 1.1, the term conveys the same meaning: impressions transmitted to the intellect.

As for what Ptolemy means by the abstruse phrase [TEXT NOT REPRODUCIBLE IN ASCII], one might look to a similar phrase in Ars Rhetorica by the third-century CE philosopher Cassius Longinus. Longinus juxtaposes memory with recollection. He defines the former as [TEXT NOT REPRODUCIBLE IN ASCII] or the preservation of phantasiai; he defines the latter as [TEXT NOT REPRODUCIBLE IN ASCII]; or the application of phantasia. (53) This translation is further supported by the use of the phrase [TEXT NOT REPRODUCIBLE IN ASCII] by Epicurus, the only other philosopher to use a phrase similar to [TEXT NOT REPRODUCIBLE IN ASCII] before Ptolemy. In the Letter to Herodotus, Epicurus describes [TEXT NOT REPRODUCIBLE IN ASCII], or appearances, as applications of the mind ([TEXT NOT REPRODUCIBLE IN ASCII]), which are criteria of truth. (54) In Epicurus materialist theory of perception and cognition, these [TEXT NOT REPRODUCIBLE IN ASCII] represent to the mind the external object being perceived. The phrase [TEXT NOT REPRODUCIBLE IN ASCII] appears again in maxim 24 of The Principal Doctrines:
 If you reject unqualifiedly any sense perception and do not
 distinguish the opinion about what awaits confirmation, and
 what is already present in the sense perception, and the
 affections, and every phantastical application of the mind
 ([TEXT NOT REPRODUCIBLE IN ASCII]), you will also disturb
 the rest of your sense perceptions with your pointless
 opinion; as a result you will reject every criterion. (55)


Diogenes Laertius also uses the phrase [TEXT NOT REPRODUCIBLE IN ASCII] in Book 10 of his Lives of Eminent Philosophers, (56) and, in Lives 10.31, he explains that while Epicurus called sense perceptions, preconceptions, and affections criteria of truth, the Epicureans added phantastical applications of the mind to the list. (57) Therefore, one may attribute the concept of phantastical applications of the mind, if not to Epicurus, then at the very least to the Epicureans. Ptolemy and Cassius Longinus employment of the phrase [TEXT NOT REPRODUCIBLE IN ASCII]; may descend from this Epicurean use.

With this notion of the applications of phantasiai, let us return to Almagest 1.1. Again, Ptolemy explains that it is fitting that the individual order his actions according to the applications of phantasiai. The text implies that one'should perform this ordering when engaging in both practical philosophy and ordinary affairs. This description of applications of phantasiai that order actions may stem from Ptolemy's inclusion of the virtues in his definitions of theoretical and practical philosophy. To begin with, in the Harmonics, Ptolemy defines sophia as the virtue having to do with the theoretical and phronesis as the virtue having to do with the practical: [TEXT NOT REPRODUCIBLE IN ASCII]. (58) When Ptolemy contrasts theoretical and practical philosophy in Almagest 1.1, he may also have in mind this distinction between sophia and phronesis. In Nicomachean Ethics 1142a, Aristotle asserts that phronesis is not episteme because it has to do with the thing to be done ([TEXT NOT REPRODUCIBLE IN ASCII]); it has to do with the particular, which is the object of perception rather than knowledge. Moreover, he calls phronesis a form of perception: [TEXT NOT REPRODUCIBLE IN ASCII]. (59) This relation of phronesis to perception arises in the Middle Platonic tradition, as in Plutarch s de Animae Procreatione in Timaeo 1025d-e and Alcinous Didaskalikos 2.2. In the latter, Alcinous labels the state of the theoretical soul phronesis--perhaps because of the influence of Phaedo 79d (60)--and, contrasting the practical with the theoretical life, he remarks, 'Action, on the other hand, and the active life, being pursued through the body, are subject to external hindrance, and would be engaged in when circumstances demand, by practicing the transferral to human affairs of the visions of the contemplative life ([TEXT NOT REPRODUCIBLE IN ASCII]).' (61) In other words, visions in accordance with the theoretical life guide actions in the practical life. For an influence on this passage, John Dillon points to Republic VI, 500d, which I analyze above in relation to Plato's conception of the dependency of the practical on the theoretical.62 Again, Socrates argues in Republic VI, 500d, that the philosopher should influence the populace by putting what he sees ([TEXT NOT REPRODUCIBLE IN ASCII]) in the ordered and divine into human beings' characters ([TEXT NOT REPRODUCIBLE IN ASCII]). Both Aristotle's identification of phronesis with perception and Plato's prescription to apply what one'sees when studying the divine to one's and other's characters seem to inform Alcinous relation of the theoretical and practical lives. Arguing that one'should transfer to human affairs visions of the contemplative life, Alcinous describes how it is that the theoretical life may impact the practical.

Ptolemy's text seems to convey a similar meaning to Alcinous'. Although Alcinous transfers visions of the contemplative life to human affairs, Ptolemy applies phantasiai in his ordering of actions. Based on this similarity, two questions arise: (1) Why does Ptolemy use the term phantasiai rather than visions or 'that which is seen ([TEXT NOT REPRODUCIBLE IN ASCII])', which Alcinous uses? (2) Although Alcinous' visions are of the contemplative life, of what are Ptolemy's phantasiai, or, in other words, what does the [TEXT NOT REPRODUCIBLE IN ASCII] refer to in the phrase [TEXT NOT REPRODUCIBLE IN ASCII]? The answer to the first question is apparent from the relation of Ptolemy's phrase [TEXT NOT REPRODUCIBLE IN ASCII] to Cassius Longinus' definition of recollection as [TEXT NOT REPRODUCIBLE IN ASCII]. Ptolemy uses phantasiai rather than visions because he is invoking a theory of memory similar to Aristotle's. Unlike Cassius Longinus, Ptolemy does not define recollection ([TEXT NOT REPRODUCIBLE IN ASCII]) in his texts, but he does define memory in conjunction with his definition of phantasia in On the Kriterion. (63) Again, Ptolemy'states, phantasia is the impression and transmission to the intellect, whose retention and memory ([TEXT NOT REPRODUCIBLE IN ASCII]) of the things transmitted we call conception.' (64) Ptolemy's choice to define phantasia and memory in conjunction with one another derives from his appropriation of Aristotle's theory of memory. According to Aristotle's On Memory, sense perception is of what is present to the individual; memory is of the past. Impressions of what were previously thought of or perceived, phantasiai, rather than sense perceptions, are the objects of memory. Therefore, by invoking phantasiai rather than visions, Ptolemy indicates that the philosopher applies the impressions of what he remembers, or--if one makes a stronger correlation with Cassius Longinus' text--what he recalls.

In response to the second question, I would argue that the [TEXT NOT REPRODUCIBLE IN ASCII] refers to the [TEXT NOT REPRODUCIBLE IN ASCII] in the previous sentence. (65) The phantasiai are of theoremata, which I have translated as theories'. The idea that phantasiai may represent not only images but also theories--only metaphorically related to images--in an ancient philosophical system is a controversial claim. One might take a more orthodox position and instead ascribe the airrcov to [TEXT NOT REPRODUCIBLE IN ASCII] in the clause preceding [TEXT NOT REPRODUCIBLE IN ASCII]. For instance, Toomer translates the phrase [TEXT NOT REPRODUCIBLE IN ASCII] as 'under the impulse of our actual ideas [of what is to be done]'. (66) The interpolated [of what is to be done] does not tie back directly to the [TEXT NOT REPRODUCIBLE IN ASCII]. It interpolates a [TEXT NOT REPRODUCIBLE IN ASCII] into the text, rather than drawing on the potential antecedents in the previous sentence. Still, Toomer indicates that he believes the phantasiai represent some phenomenon related to action. However, Toomer's translation of phantasiai as actual ideas' reveals that he did not have a strong sense of Ptolemy's psychological theory, and, consequently, his translation here should not be taken as authoritative. Moreover, if Ptolemy meant the phantasiai to represent some phenomenon related to action, [TEXT NOT REPRODUCIBLE IN ASCII], why would he prescribe the application of the phantasiai? The application, itself, implies that the phantasiai represent objects different in kind from the actions being ordered. In other words, impressions of actions do not order actions; impressions of higher-order phenomena, such as theoremata, order actions.

In her analysis of Aristotle's On Memory, Martha Nussbaum champions a similar claim as mine in her analysis of Aristotle's psychology. According to Nussbaum, Aristotle's phantasiai may occasionally represent phenomena that are only metaphorically pictorial. At On Memory 450b11ff., for instance, Aristotle discusses the nature of what one remembers. He repeatedly mentions the contemplation ([TEXT NOT REPRODUCIBLE IN ASCII]) of images, and, at 450b26, he juxtaposes [TEXT NOT REPRODUCIBLE IN ASCII]: 'Just in the same way we have to conceive that the image ([TEXT NOT REPRODUCIBLE IN ASCII]) within us is both something in itself and relative to something else. In so far as it is regarded in itself, it is only an object of contemplation or an image ([TEXT NOT REPRODUCIBLE IN ASCII]) ....' (67) Nussbaum notes that Aristotle most likely did not consider the [TEXT NOT REPRODUCIBLE IN ASCII] in this passage and the lines that follow to be pictorial. She concludes, Aristotle'seems to admit here that memory may not always work through quasi-pictures, but might consist in regarding a non-pictorial thought as referring to something in the past.' (68) This claim is controversial, as Aristotle maintains that all thought depends on phantasiai, and the conventional interpretation supposes that Aristotle intended all thoughts to rely on pictorial representations. (69) Nussbaum, however, rejects the common interpretation of phantasiai as mere images and aims to recast them as selective and interpretive data. In his review of Nussbaum's Aristotle's De Motu Animalium: Text with Translation, Commentary and Interpretive Essays, H. B. Gottschalk criticizes Nussbaum's interpretation but admits that it is occasionally difficult to interpret Aristotle's phantasia as pictorial. (70) The ambiguity in Aristotle's corpus regarding the pictorial nature of phantasiai may have led to Ptolemy's theory that phantasiai are not only juxtaposed with but, an even stronger correlation, representative of theoremata.

Although Aristotle's theory of cognition significantly shaped ancient theories of phantasia, the Stoic tradition had just as much of an influence on the concept's development. In Ethics and Human Action in Early Stoicism, Brad Inwood, like Gottschalk, rejects Nussbaum's interpretation of Aristotle's phantasia, and he addresses evidence for a Stoic theory of propositional phantasiai before dismissing it as inconsistent with Stoic psychological theory. (71) Inwood's argument is compelling. However, what is relevant to this discussion is the possibility that another theory could have evolved--perhaps with a foundation in a Stoic notion of propositional phantasiai and/or Aristotle's ambiguous portrayal of non-pictorial phantasiai --where phantasiai represent not only images but also theoremata. This evolution is certainly speculative. However, it would allow for a semantic broadening of the concept of phantasia up to and in the time of Ptolemy, and it would support the relation, syntactic as well as semantic, of the [TEXT NOT REPRODUCIBLE IN ASCII] in Ptolemy's [TEXT NOT REPRODUCIBLE IN ASCII] to the [TEXT NOT REPRODUCIBLE IN ASCII] in the previous sentence. Furthermore, it would establish a strong correspondence between Ptolemy's and Alcinous' texts, such that Ptolemy's application of phantasiai of theoremata to the ordering of actions would convey a similar meaning to Alcinous' transferral of visions of the contemplative life to human affairs.

Whether or not the phantasiai in Almagest 1.1 represent theoremata, the reason Ptolemy provides for why one'should order his actions according to the application of phantasiai suggests that theoretical philosophy is relevant to this ordering. Again, Ptolemy claims that one'should order his actions in order to strive, even in ordinary affairs, for a fine and wellordered state ([TEXT NOT REPRODUCIBLE IN ASCII]). Ptolemy explains what he means by, and how one achieves, this fine and well-ordered state near the end of Almagest 1.1. Promulgating a theory common in ancient Greek philosophy and rampant in the Platonic tradition, Ptolemy champions the telos of becoming godlike:
 With regard to virtuous conduct in actions ([TEXT NOT REPRODUCIBLE
 IN ASCII]) and character ([TEXT NOT REPRODUCIBLE IN ASCII]),
 [mathematics], above all, could make clear-sighted men ([TEXT NOT
 REPRODUCIBLE IN ASCII]); from the constancy ([TEXT NOT
 REPRODUCIBLE IN ASCII]), good order ([TEXT NOT REPRODUCIBLE IN
 ASCII]), commensurability ([TEXT NOT REPRODUCIBLE IN ASCII]), and
 calm ([TEXT NOT REPRODUCIBLE IN ASCII]) which are contemplated in
 the case of the divine ([TEXT NOT REPRODUCIBLE IN ASCII]), it, on
 the one hand, makes its followers lovers of this divine beauty
 ([TEXT NOT REPRODUCIBLE IN ASCII]), and, on the other hand,
 accustoms and, as it were, reforms their natures to a similar
 state of the soul ([TEXT NOT REPRODUCIBLE IN ASCII]). (72)


In this statement, Ptolemy embraces the widely accepted telos of transforming the individual's soul to a state similar to the divine. (73)

For early endorsements of homoiosis theoi, one may look to Plato's Theaetetus 176b and Republic VI, 500c-d. Both texts maintain that the philosopher should transform himself into a condition as similar to the divine as is possible for a human being; contemplation of the divine makes one like the divine. In the second century, several philosophers appropriated this concept. The Anonymous Commentator on the Theaetetus confirms this telos of a human being--and rejects oikeiosis as the basis for justice--at section 7.18-19. In de Platone et eius Dogmate 2.23, Apuleius affirms that the end of wisdom is the emulation of the gods, and in Introductio in Platonem 6.25-9, Albinus asserts that the theoretical life (referring to the study of physics and ethics) and the practical life (involving the practice of politics and economics) together yield a becoming like a god ([TEXT NOT REPRODUCIBLE IN ASCII]). Alcinous dedicates an entire chapter, Didaskalikos 28, to homoiosis theoi. Tracing the doctrine through several of Plato's texts, he quotes the Theaetetus, Phaedo, and the Laws. Hence, the concept of homoiosis theoi was common in the second century, and, in Almagest 1.1, Ptolemy joins this tradition.

Plato's Timaeus influenced this passage in Almagest 1.1 more obviously than did the Theaetetus and Republic. Ptolemy claims that one attains a state in his soul'similar to the divine by means of mathematics and the contemplation of celestial bodies' qualities in particular. Correspondingly, Timaeus explains how an individual may organize the revolutions of his soul according to the order of the universe:
 ... the god invented sight and gave it to us so that we might
 observe the orbits of intelligence in the universe and apply
 them to the revolutions of our own understanding. For there is
 a kinship between them, even though our revolutions are disturbed,
 whereas the universal orbits are undisturbed. So once we have
 come to know them and to share in the ability to make correct
 calculations according to nature, we should stabilize the straying
 revolutions within ourselves by imitating the completely
 unstraying revolutions of the god. (74)


Because a kinship exists between the immortal part of a human soul and the heavens, one may model the soul's revolutions according to the order of the heavens. The individual performs this transformation in order to stabilize the soul's revolutions and return the soul to its proper order. Correspondingly, according to Ptolemy, the study of mathematics and, in particular, the contemplation of the constancy, good order, commensurability, and calm of celestial objects makes the individual a lover of divine beauty and transforms his soul to a state similar to the celestial one.

Strikingly, the terms Ptolemy uses to signify the divine qualities one contemplates--[TEXT NOT REPRODUCIBLE IN ASCII]--indicate that the divine objects contemplated are mathematical in kind. In his commentary on Aristotle's Metaphysics M, Alexander of Aphrodisias, the second-century Peripatetic philosopher, asserts that mathematics concerns commensurable, well-ordered, and defined things (ra aupperpa cai euracra caiopiapeva). (75) He adds that mathematics aims to study commensurable, constant, proportional, and ordered things ([TEXT NOT REPRODUCIBLE IN ASCII]). (76) Alexander makes these comments in response to Aristotle's discussion of the relation of the fine and good to mathematics. Concerning beauty, Aristotle'states, 'The main species of the fine ([TEXT NOT REPRODUCIBLE IN ASCII]) are order, commensurability, and definiteness ([TEXT NOT REPRODUCIBLE IN ASCII]), which the mathematical sciences exhibit most.' (77) Hence, commenting on Aristotle's Metaphysics M, Alexander mentions three of the four mathematical terms Ptolemy characterizes as divine qualities in Almagest 1.1: [TEXT NOT REPRODUCIBLE IN ASCII].

Of interest is Alexander's substitution of Aristotle's order ([TEXT NOT REPRODUCIBLE IN ASCII]) with well-ordered things ([TEXT NOT REPRODUCIBLE IN ASCII]). This substitution may seem trivial. However, in his corpus, Alexander consistently uses the term [TEXT NOT REPRODUCIBLE IN ASCII] when describing the orderly movement of heavenly bodies. The most obvious instances of this connotation reside in Alexander's de Fato. According to Charles Genequand, the influence of heavenly bodies' movements on sublunary generation and corruption is a central notion in Alexander's theory of providence. (78) Alexander states the following in the de Fato: It is for this reason, too, that men say that the first causes of coming-to-be of each thing in accordance with nature (that is, the divine and their well-ordered revolution [[TEXT NOT REPRODUCIBLE IN ASCII]]) are also causes of fate. For the beginning of all coming-to-be is the divine, in their motion, being in one type of position or another to things on earth.' (79) The divine things, whose well-ordered revolution determines the fate of sublunary bodies, are manifestly the heavenly bodies. Therefore, not only does Alexander use forms of the terms Ptolemy employs in Almagest 1.1--[TEXT NOT REPRODUCIBLE IN ASCII]--in a mathematical context, but he also uses a form of [TEXT NOT REPRODUCIBLE IN ASCII] in an explicitly astronomical context. Thus, in the second century, the terms Ptolemy lists as exemplars of divine qualities connoted mathematical and, in particular, astronomical objects. According to Ptolemy, the contemplation of mathematical, particularly astronomical, objects makes the individual a lover of divine, celestial beauty. Transforming his soul to a state similar to the divine, celestial one, the individual imposes onto his soul mathematical qualities: constancy, good order, and commensurability. In this way, perhaps, the human soul takes on the qualities of celestial souls, which Ptolemy examines in Book 2 of the Planetary Hypotheses.

The term [TEXT NOT REPRODUCIBLE IN ASCII] appears again in Harmonics 3.4, and it is the only other occurrence of the term in Ptolemy's corpus outside of Almagest 1.1. Having defined the power of harmonia in the previous chapter, Ptolemy proclaims the following:
 Let this be enough to show that the power of harmonia is a form of
 the cause corresponding to reason, the form that concerns itself
 with the commensurability of movements ([TEXT NOT REPRODUCIBLE IN
 ASCII]), and that the theoretical science of harmonia is a form of
 mathematics ([TEXT NOT REPRODUCIBLE IN ASCII]), the form concerned
 with the ratios of differences between things heard, this form
 itself contributing to the good order ([TEXT NOT REPRODUCIBLE IN
 ASCII]) that comes from theory and understanding ([TEXT NOT
 REPRODUCIBLE IN ASCII]) to people habituated ([TEXT NOT
 REPRODUCIBLE IN ASCII]) in it. (80)


As in Almagest 1.1, Ptolemy proclaims that theoretical study, and mathematics in particular, leads to good order. In the Almagest, Ptolemy emphasizes the psychological benefits of astronomy, and here, in the Harmonics, he recommends astronomy's cousin science, harmonics. People who are habituated in studying harmonics take on good order, just as, in Almagest 1.1, astronomers' souls reform to a state that is similar to the well-ordered state of celestial objects.

Continuing on from the above passage, in Harmonics 3.4, Ptolemy argues that the power of harmonia is present in all bodies that have in them a source of movement, but it is present to the greatest extent in those bodies that have the most complete and rational nature ([TEXT NOT REPRODUCIBLE IN ASCII]). (81) In other words, every natural body is characterized to some degree by a ratio, in its movements and in the configuration of its matter. The more complete and rational an object is in its movements and form, the more it is characterized by harmonic ratios. According to Ptolemy, the most complete and rational bodies are, in addition to musical pitches, human souls and heavenly bodies:
 ... it is found in those movements that are involved most closely
 with forms. These, as we said, are those of things that are most
 perfect and rational in their natures, as among divine things are
 the movements of the heavenly bodies, and among mortal things
 those of human souls, most particularly, since it is only to each
 of these that there belong not only the primary and complete sort
 of movement (that in respect of place), but also the
 characteristic of being rational. (82)


The most complete and rational bodies in the cosmos are musical pitches, human souls, and heavenly bodies. Their movements exhibit harmonic ratios and consist in motion from place to place. One may reform one's soul to a harmonic structure, a good order, by habitually studying the movements of musical pitches and/or astronomical objects.

Returning to the Almagest, Ptolemy uses a form of the term [TEXT NOT REPRODUCIBLE IN ASCII] twice in Almagest 1.1. In the first instance, he claims, as mentioned above, that one'should order his actions by applying phantasiai as to never forget even in ordinary affairs--and, as is implied, in practical philosophy--to strive for a fine and well-ordered state ([TEXT NOT REPRODUCIBLE IN ASCII]). The second instance is the one just examined, where Ptolemy lists [TEXT NOT REPRODUCIBLE IN ASCII] among the qualities of celestial bodies and explains that a well-ordered state, or [TEXT NOT REPRODUCIBLE IN ASCII];, of the soul results from the qualities of heavenly bodies being contemplated ([TEXT NOT REPRODUCIBLE IN ASCII]). This latter passage recalls Harmonics 3.4, where the student of harmonics takes on good order. Comparison of these passages reveals how the telos of a divine-like state relates to theoretical and practical philosophy. The telos is achievable by means of theoretical philosophy--specifically astronomy and/or harmonics --and one'should keep the telos in mind when engaging in practical philosophy.

Yet, in Almagest 1.1, Ptolemy introduces the telos of a divine-like state with a nod to practical philosophy. He asserts, With regard to virtuous conduct in actions and character, [mathematics], above all, could make clear-sighted men ([TEXT NOT REPRODUCIBLE IN ASCII]) ... ' (83) Ptolemy posits here a particular relationship between theoretical and practical philosophy. The contemplation of celestial bodies and the resulting transformation of one's soul relate to virtuous conduct in actions and character. The way they relate is that theoretical study prepares one for action. Ptolemy claims that mathematics, more than any other'science, makes one clear-sighted ([TEXT NOT REPRODUCIBLE IN ASCII]). I argued above that Ptolemy's use of phantasiai may derive in part from Aristotle's definition of phronesis as a type of perception in Nicomachean Ethics 1142a, and this interpretation is further supported by the correspondence of Ptolemy's text to Alcinous' prescription to transfer to human affairs the visions of the contemplative life ([TEXT NOT REPRODUCIBLE IN ASCII]). For Ptolemy, clear-sightedness enhances one's application of phantasiai to actions.

Clear-sightedness has this effect because of the relationship between sight and the soul's faculty of thought. In Harmonics 3.3, Ptolemy remarks that sight and hearing are the senses most closely affiliated with the ruling part of the soul, the hegemonikon. When discussing the power of harmonia, Ptolemy proclaims, This sort of power employs as its instruments and servants the highest and most marvelous of the senses, sight and hearing, which, of all the senses, are most closely tied to the hegemonikon....' (84) Ptolemy reiterates this association of sight and hearing with the hegemonikon in On the Kriterion and Hegemonikon. The sense of touch is, according to Ptolemy, more material and extends throughout the body's flesh and blood. Regarding the other four senses, Ptolemy argues, Among the latter some are more easily activated and more valuable, viz. sight and hearing, and because they are located above the others approach more closely to the soul's faculty of thought ([TEXT NOT REPRODUCIBLE IN ASCII])....' (85) Because the senses sight and hearing are located in a human being's head, supposedly higher than the senses taste and smell, they are physically close to the soul's faculty of thought.

The faculty of thought is the most valuable of the human soul's faculties, and, as such, it is the hegemonikon in regard to both living and living well. (86) Before pronouncing the faculty of thought a hegemonikon, Ptolemy ponders the following in On the Kriterion:
 If we give the name hegemonikon to what is the best absolutely and
 the most valuable ([TEXT NOT REPRODUCIBLE IN ASCII]), it will be
 located in the brain. We have given sufficient proof that the
 faculty of thought has a higher degree of worth and divinity
 ([TEXT NOT REPRODUCIBLE IN ASCII]), both in power and in substance
 and both in the universe and in us, and also that its place is the
 highest position, heaven in the cosmos, the head in man. (87)


In this passage, Ptolemy asserts that the faculty of thought is more valuable and more divine than the other faculties of the human soul, just as the heavens are divine and more valuable than the sublunary realm. This comparison, of the part of the human soul in the head with the heavens, again alludes to Plato's Timaeus.

Although the faculty of thought is the hegemonikon in regard to living and living well, sight and hearing assist in the latter purpose. Ptolemy ascribes the telos of living well to sight and hearing in On the Kriterion:
 If a second prize has to be awarded to one of the other means
 towards the end of living well, the prize would go elsewhere than
 to the faculty of thought: what is around the heart would not even
 be runner-up. It would go rather to the senses, and if not to all
 of them, then only to those which contribute most to assist
 thought in its consideration and judging of real things, i.e.,
 hearing and sight. These are themselves positioned near the head
 and the brain, above the other'senses, and near neighbors, because
 of their special relationship, to the first and chief cause of
 living well. (88)


According to On the Kriterion, sight and hearing assist the faculty of thought in causing a human being to live in a good way. Therefore, clear-sightedness is integral to living a good life, and, as such, it is a means to virtuous conduct in actions and character, or success in practical philosophy, as it is in Almagest 1.1.

Although clear-sightedness is a means toward success in practical philosophy, its initial cause is theoretical philosophy, specifically mathematics. What is it, then, that the clear-sighted men in Almagest 1.1 see? If the sightedness' is literal, then the passage suggests that they see the celestial bodies, whose qualities they contemplate. The benefit to virtuous conduct of this literal clear-sightedness would result from the close relationship between sight and the faculty of thought. Literally seeing in a clear way entails metaphorically seeing how to act. This reference to acting as a type of seeing recalls, as mentioned above, Nicomachean Ethics 1142a, wherein Aristotle characterizes phronesis as a form of perception. Ptolemy'states, however, that it is the science of mathematics that makes men clearsighted. Therefore, the sightedness, like the subsequent seeing how to act, may be metaphorical. With astronomy, the branch of mathematics referred to in this passage, one does more than simply observe celestial bodies; one constructs hypotheses, which account for the movements of the stars and planets. In this metaphorical interpretation of sightedness', then, the men clearly see mathematical theoremata. The theoremata account for the movements of celestial bodies and reveal their constancy, good order, commensurability, and calm, which are apparent, not from simple observation, but from the calculation of celestial bodies' movements. These mathematical theories are the catalysts which, when contemplated, make the individual a lover of divine beauty and transform the human soul to a state similar to the divine. Furthermore, this metaphorical interpretation of clear-sightedness' connects this passage more firmly to Ptolemy's use of phantasiai earlier in Almagest 1.1. In the literal reading, if men clearly see celestial bodies, and the phantasiai are pictorial representations of celestial bodies, one would wonder how the application of celestial bodies' images is able to order actions. If, on the other hand, the clear sighted men metaphorically see mathematical theoremata, then the application of phantasiai of theoremata would indeed order an individual's actions. Representations of mathematical theories of constancy, good order, commensurability, and calm would order one's actions in a manner concordant with these divine qualities, and they would ensure that the individual keep in mind the telos of a divine-like state, which results from these qualities' mathematical contemplation. Indeed, Ptolemy indicates that this fidelity to the telos of a divine-like state is the goal he has in mind for the ordering of one's actions; he proclaims that one'should apply phantasiai to the ordering of actions as to never forget, even in ordinary affairs, to strive for a fine and well-ordered state.

Furthermore, the divine-like state itself, like clear-sightedness, prepares the individual for future action. Evidence for this interpretation lies in Harmonics 3.7, wherein Ptolemy discusses how listening to music affects the human soul. As a melody modulates, the soul--consisting, as it does, of the same ratios existing among musical pitches--experiences various conditions in sympathy with the activities of the melody. From this theory, Ptolemy concludes the following:
 I suppose it was because he understood this fact that Pythagoras
 advised people that when they arose at dawn, before setting off on
 any activity ([TEXT NOT REPRODUCIBLE IN ASCII]), they should apply
 themselves to music and to soothing melody, so that the disorder
 ([TEXT NOT REPRODUCIBLE IN ASCII]) of their souls resulting from
 arousal out of sleep should first be transformed into a pure and
 settled state ([TEXT NOT REPRODUCIBLE IN ASCII]) and an orderly
 gentleness, and so make their souls well-attuned and concordant
 for the actions ([TEXT NOT REPRODUCIBLE IN ASCII]) of the day.
 (89)


In this passage, Ptolemy applies his psychological theory to explain the legendary habits of Pythagoras and his followers. In the fourth century BCE, Aristoxenus wrote that the Pythagoraeans used music to purify the soul, (90) and, in the first century CE, Quintilian, a Roman rhetorician, wrote, 'On awakening, it was the Pythagoreans' custom to arouse their souls with the sound of the lyre, so that they might be more alert for action, and before going to sleep they soothed their minds by means of this same music in order to calm them down, in case too turbulent thoughts might still inhabit them.' (91) In other words, Quintilian, like Ptolemy after him, portrays the Pythagoreans as listening to music every morning in order to prepare their souls for action. He depicts the music as arousing, or exciting, a soul. However, Ptolemy claims that the music transforms the soul into a pure and settled state. Nevertheless, in his Vita Pythagorae Porphyry, the third-century-CE philosopher, cites Antonius Diogenes, who depicts Pythagoras singing paeans at dawn in order to calm the soul ([TEXT NOT REPRODUCIBLE IN ASCII]). (92) Hence, in Harmonics 3.7, Ptolemy relates a common, contemporary legend about Pythagoras and, moreover, explains the physics underlying Pythagoras' legendary practice. According to Ptolemy, Pythagoras advised that one'settle his soul into a state ([TEXT NOT REPRODUCIBLE IN ASCII]) aligned by harmonic ratios in order to prepare for ensuing actions. I suggest that the Harmonics' relation of the soul's harmonic state to success in future actions underlies the Almagest's relation of theoretical and practical philosophy. The reformation of one's soul to a divine-like state is the product of theoretical philosophy, and, in turn, the divine-like state enables virtuous conduct in actions and affairs, the domain of practical philosophy.

Therefore, despite his efforts to assert the independence of theoretical and practical philosophy from one another, to posit a great difference between the two, Ptolemy ultimately portrays practical philosophy as dependent on theoretical philosophy. Mathematics makes one clear-sighted, which enhances one's applications of phantasiai to the ordering of actions, and the study of harmonics and/or astronomy reforms one's soul to a state that prepares the individual for virtuous conduct in actions and character. Furthermore, the great distinction itself, which Ptolemy posits between theoretical and practical philosophy, loses its force when one brings the Harmonics to bear on the Almagest. Again, in Almagest 1.1, Ptolemy allows that some ethical virtues may benefit from learning, even though some are possible without it, but he portrays theoretical philosophy as subject to instruction only. In Harmonics 3.4, however, it is the people who are habituated ([TEXT NOT REPRODUCIBLE IN ASCII]) in theoretical philosophy who attain good order in their souls. Consequently, Ptolemy's distinction between theoretical and practical philosophy is not absolute. Instruction in theoretical philosophy prepares one to act in practical philosophy, and habit, the tool of practical philosophy, enhances the study of theoretical philosophy.

This pattern--of asserting a great distinction and then dissolving it--also appears in Ptolemy's On the Kriterion and Hegemonikon. I mentioned above how Ptolemy recognizes in On the Kriterion what he considers to be a rhetorical debate over the definitions of soul and body, and, in response to this debate, he propounds the actual difference between them. Later in the text, however, Ptolemy reveals his materialism. He depicts the soul as consisting of matter, specifically air, fire, and aether. (93) Ptolemy depicts the soul as consisting of fine particles, or elements, that scatter when released from the body: The soul is so constituted as to scatter immediately to its proper elements ([TEXT NOT REPRODUCIBLE IN ASCII]), like water or breath ([TEXT NOT REPRODUCIBLE IN ASCII]) released from a container, because of the preponderance of finer particles ([TEXT NOT REPRODUCIBLE IN ASCII]) ... the body, on the other hand, although it stays in the same state for a considerable time because of the thicker consistency of its matter ([TEXT NOT REPRODUCIBLE IN ASCII]) ....' (94) The soul consists of finer particles than the particles constituting the body, and these finer particles are so small that they are imperceptible. Correspondingly, Ptolemy claims in Tetrabiblos 3.12 that the body is more material ([TEXT NOT REPRODUCIBLE IN ASCII]) than the soul. (95) Therefore, despite his assertion of a difference between soul and body, Ptolemy's more detailed expositions reveal that he considered them to differ merely in degree rather than kind. Adhering to a similar pattern of exposition, Ptolemy asserts in Almagest 1.1 a great difference between theoretical and practical philosophy, which establishes their independence from one another. However, he then portrays practical philosophy as beholden to theoretical philosophy.

Thus, in Almagest 1.1, Ptolemy engages in a contemporary debate over the relationship between theoretical and practical philosophy. He first asserts that the two are independent of one another, separated by a difference evident in the manner one attains virtues in each sphere, whether by instruction or by continuous activity. Thereafter, Ptolemy diminishes the distinction between the two parts of philosophy by revealing how they relate. Theoretical philosophy prepares the individual for action, and, according to the Harmonics, habit, the tool of practical philosophy, enhances the study of theoretical philosophy. Despite his initial insistence on the independence of the two parts of philosophy, Ptolemy reveals in Almagest 1.1 that practical philosophy is dependent on theoretical philosophy.

In his eclectic definitions and evaluations of theoretical and practical philosophy, Ptolemy demonstrates his unique amalgamation of Middle Platonic and Aristotelian conceptions of the parts and aim of philosophy, the soul, and its virtues. Furthermore, Ptolemy appropriated the structure of Almagest 1.1 from contemporary philosophical handbooks. In his second monograph on ancient prefaces, Prolegomena Mathematica: From Apollonius of Perga to Late NeoPlatonism, Jaap Mansfeld observes that Almagest 1.1 incorporates structural elements common to ancient introductions to an author or a text. Tracing the late antique schema isagogicum to its roots, Mansfeld discovers several of the 'headings' or 'main points' ([TEXT NOT REPRODUCIBLE IN ASCII]) of ancient prefaces in Almagest 1.1, including the purpose of the author, the utility, aim, and order of the present study, the historical contributions of predecessors, and the qualities required of the student. (96) In this way, Mansfeld demonstrates that Ptolemy's Almagest fits within a far-reaching, non-genre-specific, ancient literary culture.

The resemblance of Almagest 1.1 to Alcinous' Didaskalikos, however, is more striking. In the first three chapters of his text, Alcinous defines philosophy and the philosopher, describes the theoretical and practical types of life, and expounds the parts of theoretical and practical philosophy. In Almagest 1.1, Ptolemy identifies the legitimate philosophers, distinguishes the theoretical and practical parts of philosophy, and defines the parts of theoretical philosophy before portraying the aim of theoretical philosophy, the transformation of one's soul to a divine-like state. Alcinous and Ptolemy participated not only in the broad literary culture that Mansfeld describes but also in the genre-specific rhetorical culture of philosophical handbooks. Indeed, Ptolemy's mimicry of a philosophical handbook would have been apparent to any contemporary philosopher. The question, then, is why Ptolemy decided to appropriate this structure. His decision could simply have resulted from his embeddedness in the contemporary philosophical context. As the result of reading philosophical handbooks, he may simply have acquired the style. Yet, again, what is interesting is that Ptolemy utilized the structure not only of ancient prefaces, in general, but of philosophical handbooks in particular. He deliberately chose to introduce his astronomical models by situating them within the philosophical context of distinguishing the parts of philosophy and defending his choice to spend more of his free time pursuing theoretical rather than practical philosophy.

Within this context, Ptolemy portrays astronomy as ethically and epistemologically the highest branch of theoretical philosophy. Not only does the mathematical contemplation of celestial bodies, or astronomy, yield the telos of a divine-like state, but, also, mathematics is the only branch of theoretical philosophy to yield knowledge. In other words, unlike every preceding and contemporary philosopher, Ptolemy does not portray mathematics as propaedeutic; mathematics, for Ptolemy, is not a means to a higher science, such as theology or metaphysics. (97) In Almagest 1.1, Ptolemy makes the unprecedented claim that theology and physics are conjectural and that mathematics alone yields incontrovertible knowledge:
 From all this we concluded: that the first two genera of the
 theoretical [part of philosophy] should rather be called guesswork
 ([TEXT NOT REPRODUCIBLE IN ASCII]) than knowledge ([TEXT NOT
 REPRODUCIBLE IN ASCII]), the theological because of its completely
 invisible and ungraspable nature, the physical because of the
 unstable and unclear nature of matter ([TEXT NOT REPRODUCIBLE IN
 ASCII]); hence, there is no hope that philosophers will ever be
 agreed about them, and that only the mathematical can provide sure
 and incontrovertible knowledge to its devotees, provided one
 approaches it rigorously. (98)


The only science to produce knowledge rather than conjecture, mathematics is epistemologically superior to theology and physics. In addition, astronomy is the most preferable of the mathematical sciences. Ptolemy explicates this epistemological preference in the following:
 We were drawn to cultivate this sort of theory [viz. mathematics],
 the whole of it as far as we were able, but especially the theory
 concerning divine and heavenly things ([TEXT NOT REPRODUCIBLE IN
 ASCII]). For that alone is devoted to the investigation of the
 eternally unchanging. For that reason it too can be eternal and
 unchanging (which is a proper attribute of knowledge) in its own
 apprehension, which is neither unclear nor disorderly ([TEXT NOT
 REPRODUCIBLE IN ASCII]). (99)


Because astronomy studies objects that are eternal and unchanging, the type of apprehension astronomy affords is itself eternal and unchanging. Ptolemy's epistemology of the theoretical sciences deserves its own, extended study, (100) but, for now, I will simply note that in Almagest 1.1 Ptolemy characterizes astronomy as both ethically and epistemologically the highest science.

If astronomy is the highest science, then the Almagest, a synthesis of Ptolemy's astronomical models, would indeed require a grand philosophical introduction. While Alcinous designed his Didaskalikos to epitomize the philosophical doctrines of Plato, Ptolemy composed the Almagest to demonstrate his astronomical models. Representing his unique philosophical views--influenced as they were by the Middle Platonic and Aristotelian commentary traditions--the preface to the Almagest carves out a place for Ptolemy's astronomical theory within the contemporary philosophical context. In this way, perhaps, Ptolemy thought his astronomical models to be as authoritative and philosophically relevant as the works of Plato or any other philosophical authority.

DOI: 10.1515/apeiron-2011-0011

(1) I would like to thank Alain Bernard for encouraging me to write this article and acknowledge Thomas Benatouil and Brad Inwood, as well as Alain Bernard, for providing me with exceedingly helpful comments during the writing process.

(2) Franz Boll summarizes Ptolemy's descriptions in Almagest 1.1 of theoretical and practical philosophy in his "Studien uber Claudius Ptolemaus: Ein Beitrag zur Geschichte der griechischen Philosophie und Astrologie," Jahrbucher fur classische Philologie, supplement 21 (1894), 68. Liba Taub discusses the Almagest's definitions of theoretical and practical philosophy in Ptolemy's Universe: The Natural Philosophical and Ethical Foundations of Ptolemy's Astronomy (Chicago: Open Court 1993), 19-21, 35-37. Alain Bernard addresses the relationship between theoretical and practical philosophy

(3) Ptolemy Almagest 1.1, H4. Jaap Mansfeld notes that Syrus is Ptolemy's 'standard dedicatee' and that variations of Ptolemy's phrase oi yv"]<TIcoc <j>i7io<To<j)i]]<TavTec are common in ancient philosophical texts, from Plato to Proclus. See Prolegomena Mathematica: From Apollonius of Perga to Late NeoPlatonism (Brill: Leiden 1998), 66, 67 note 227.

(4) Ptolemy Almagest 1.1, H5

(5) Ptolemy Planetary Hypotheses 2.4-5, H113.31, H114.15, 26

(6) Taub, 21-30

(7) See Jacqueline Feke, Ptolemy in Philosophical Context: A Study of the Relationships Between Physics, Mathematics, and Theology (Ph.D. diss., University of Toronto 2009).

(8) Jaap Mansfeld corroborates my interpretation here: "The parallels in ps.Plutarch and Diogenes show that by Ptolemy's time [the bipartite division] had come to be seen as a standard Aristotelian view" (67 note 227).

(9) For instance, Aristotle defends the contemplative life in the Protrepticus. See D. S. Hutchinson and Monte Ransome Johnson, "Authenticating Aristotle's Protrepticus," Oxford Studies in Ancient Philosophy 29 (2005) 193-294.

(10) Ptolemy Almagest 1.1, H4, translation after G.J. Toomer (London: Duckworth 1984).

(11) Plato Republic VI, 500d, trans. G. M. A. Grube, rev. C. D. C. Reeve (Indianapolis: Hackett Publishing Company, Inc. 1997).

(12) Ibid., VII, 540a-b.

(13) Aspasius In ethica Nicomachea commentaria 1.2-4, translation after David Konstan (London: Duckworth 2006).

(14) Ibid., 3.19-23, trans. David Konstan.

(15) While some historians have doubted the authenticity of On the Kriterion and Hegemonikon, the manuscript tradition explicitly names Ptolemy as the text's author, and I consider Alexander Jones' argument in support of its authenticity to be persuasive. See our joint article: Jacqueline Feke and Alexander Jones, "Ptolemy," The Cambridge History of Philosophy in Late Antiquity, vol. 1, ed. Lloyd Gerson (Cambridge: Cambridge University Press 2010) 197-209.

(16) Ptolemy On the Kriterion and Hegemonikon, La9, trans. Liverpool/Manchester Seminar on Ancient Philosophy (Liverpool: Liverpool University Press 1989).

(17) Galen On Critical Days 9.789. R. J. Hankinson and Ben Morison disagree on how to interpret this passage: R. J. Hankinson, "Usage and abusage: Galen on language," Language, Companions to Ancient Thought, vol. 3, ed. Stephen Everson (Cambridge: Cambridge University Press 1994) 166-187, 171; Ben Morison, "Language," The Cambridge Companion to Galen, ed. R. J. Hankinson (Cambridge: Cambridge University Press 2008) 116-156, 130-131.

(18) Ptolemy On the Kriterion and Hegemonikon, La10, trans. Liverpool/Manchester Seminar on Ancient Philosophy.

(19) Ibid., La11-12, translation after Liverpool/Manchester Seminar on Ancient Philosophy.

(20) Ptolemy Almagest 1.1, H4, translation after G. J. Toomer.

(21) Boll, 70; Taub, 19-20.

(22) Aristotle Nicomachean Ethics 1103a14-18, translation after H. Rackham (Cambridge, MA: Harvard University Press 1962).

(23) Aspasius In ethica Nichomachea commentaria 25.18-26, 37.1-8.6.

(24) Alcinous Didaskalikos 24.1.

(25) John Dillon, Alcinous: The Handbook of Platonism (Oxford: Clarendon Press 1993), 151.

(26) Plutarch de Liberis Educandis 2a10-11.

(27) The dating of the Harmonics before the Almagest depends on the relationship of Harmonics 3.14-16 to the Canobic Inscription, and Ptolemy must have written the Canobic Inscription before the Almagest because he corrects numerical values from the former in the latter. See N. M. Swerdlow, "Ptolemy's Harmonics and the 'Tones of the Universe' in the Canobic Inscription," Studies in the History of the Exact Sciences in Honour of David Pingree (Leiden: Brill 2004) 137-80, 175.

(28) Plato uses the terms [TEXT NOT REPRODUCIBLE IN ASCII] in Republic IV, 440e-1a. The use of [TEXT NOT REPRODUCIBLE IN ASCII] instead of [TEXT NOT REPRODUCIBLE IN ASCII] for the spirited part of the soul' seems to have been common in the second century. Alcinous, too, uses [TEXT NOT REPRODUCIBLE IN ASCII] in Didaskalikos 17.4, 29.1.

(29) Ptolemy Harmonics 3.5, D97, translation after Andrew Barker (Cambridge: Cambridge University Press 1989).

(30) See A.A. Long, "The harmonics of Stoic virtue," Stoic Studies (Cambridge: Cambridge University Press 1996) 202-23.

(31) Salvatore R.C. Lilla, Clement of Alexandria: A Study in Christian Platonism and Gnosticism (Oxford: Oxford University Press 1971), 80.

(32) A. Glibert-Thirry discusses the dating and authorship of de Passionibus in the introduction to his critical edition. He concludes simply that the text situates the author within a current of Hellenistic philosophy characterized by a mixture of Stoic, Peripatetic, and Platonic elements: Pseudo-Andronicus de Rhodes [TEXT NOT REPRODUCIBLE IN ASCII] (Leiden: E.J. Brill 1977), 34.

(33) Pseudo-Andronicus de Passionibus 2.1.3, 4.4.1, 6.1.1.

(34) Galen de Placitis Hippocratis et Platonis 7.1.24-32.

(35) D. S. Hutchinson discusses the Definitions' authorship in Plato: Complete Works, ed. John M. Cooper, assoc. ed. D. S. Hutchinson (Indianapolis: Hackett Publishing Company 1997), 1677-8.

(36) Boll, 106; Ingemar During, Ptolemaios und Porphyrios uber die Musik (Goteborg: Elanders Boktryckeri Aktiebolag 1934), 271

(37) Pseudo-Plato Definitions 412e4-5.

(38) Ibid., 414b5-6, trans. D. S. Hutchinson (Indianapolis: Hackett Publishing Company 1997).

(39) Ptolemy Harmonics 3.5, D97; Pseudo-Plato Definitions 412d6-7.

(40) Ptolemy Harmonics 3.5, D97; Pseudo-Plato Definitions 412a7.

(41) Ptolemy Harmonics 3.5, D97, trans. Andrew Barker.

(42) Pseudo-Plato Definitions 412c1-2, translation after D. S. Hutchinson.

(43) Ptolemy Harmonics 3.5, D97; Pseudo-Plato Definitions 411e6-7.

(44) Ptolemy Harmonics 3.5, D97; Pseudo-Plato Definitions 412b3.

(45) Ptolemy Harmonics 3.5, D97; Pseudo-Plato Definitions 412c9-10.

(46) Boll (106-8) emphasizes the possible influence of pseudo-Andronicus' de Passionibus, in addition to the pseudo-Platonic Definitions, on Ptolemy's definitions of the virtues.

(47) Ptolemy Harmonics 3.6, D98, translation after Andrew Barker.

(48) Dillon, 60.

(49) Ptolemy Almagest 1.1, H4-5.

(50) Ptolemy Tetrabiblos 1.3, H15, translation after F.E. Robbins (Cambridge, MA: Harvard University Press 1940).

(51) Ptolemy On the Kriterion and Hegemonikon, La5, trans. Liverpool/Manchester Seminar on Ancient Philosophy.

(52) Ptolemy On the Kriterion and Hegemonikon, La16.

(53) Cassius Longinus Ars Rhetorica 572.9-12.

(54) Diogenes Laertius Lives of Eminent Philosophers 10.51.

(55) Ibid., 10.147, translation after Brad Inwood and L. P. Gerson (Indianapolis: Hackett Publishing Company, Inc. 1994).

(56) Diogenes Laertius Lives of Eminent Philosophers 10.50.

(57) Ibid., 10.31.

(58) Ptolemy Harmonics 3.5, D97.

(59) Aristotle Nicomachean Ethics 1142a29-30.

(60) Dillon, 55.

(61) Alcinous Didaskalikos 2.2, trans. John Dillon (Oxford: Clarendon Press 1993).

(62) Dillon, 56.

(63) The only occurrence of the term '[TEXT NOT REPRODUCIBLE IN ASCII]' in Ptolemy's corpus is in Tetrabiblos 4.5, H310, where the term has a technical, astrological meaning.

(64) Ptolemy On the Kriterion and Hegemonikon, La5, trans. Liverpool/Manchester Seminar on Ancient Philosophy.

(65) I must thank Alain Bernard for bringing to my attention the possible connection between these two terms in Almagest 1.1.

(66) Ptolemy Almagest 1.1, H5, trans. G.J. Toomer.

(67) Aristotle On Memory 450b24-6, translation after J. I. Beare, ed. Jonathan Barnes (Princeton: Princeton University Press 1984).

(68) Martha Craven Nussbaum, Aristotle's De Motu Animalium: Text with Translation, Commentary and Interpretive Essays (Princeton: Princeton University Press 1978), 250.

(69) See Aristotle de Anima 3.8 and On Memory 449b30-1, where Aristotle cites the de Anima.

(70) H.B. Gottschalk, review of Aristotle's De Motu Animalium: Text with Translation, Commentary and Interpretive Essays, by Martha Craven Nussbaum, The American Journal of Philology 102, no. 1 (Spring, 1981) 84-94, 93.

(71) Brad Inwood, Ethics and Human Action in Early Stoicism (Oxford: Clarendon Press 1985), 11-13, 55-60.

(72) Ptolemy Almagest 1.1, H7.

(73) In Ptolemy's Universe, Liba Taub identifies the roots of Ptolemy's statement in three of Plato's texts: the Symposium, Republic, and Theaetetus. See Taub, 31-4.

(74) Plato Timaeus 47b-c, trans. Donald J. Zeyl, ed. John M. Cooper, assoc. ed. D. S. Hutchinson (Indianapolis: Hackett Publishing Company 1997). Cf. Plato Timaeus 44d, 90a-d.

(75) Alexander of Aphrodisias In Aristotelis metaphysica commentaria 739.28-9

(76) Ibid., 739.32-3.

(77) Aristotle Metaphysics M, 1078a36-b2.

(78) Charles Genequand, "Quelques aspects de l'idee de la nature d'Aristote a al-Ghazali," Revue de Theologie et de Philosophie 116 (1984) 105-130, 115.

(79) Alexander of Aphrodisias de Fato 169.23-6, translation after R. W. Sharples (London: Duckworth 1983). Cf. 203.22-3.

(80) Ptolemy Harmonics 3.4, D94-5, translation after Andrew Barker.

(81) Ibid., D95.

(82) Ibid., trans. Andrew Barker.

(83) Ptolemy Almagest 1.1, H7.

(84) Ptolemy Harmonics 3.3, D93, translation after Andrew Barker.

(85) Ptolemy On the Kriterion and Hegemonikon, La20-1, trans. Liverpool/Manchester Seminar on Ancient Philosophy.

(86) Ibid., La22. Cf. de Placitis Hippocratis et Platonis 2.3.4, where Galen identifies the hegemonikon with the logistikon.

(87) Ptolemy On the Kriterion and Hegemonikon, La22, translation after Liverpool/Manchester Seminar on Ancient Philosophy.

(88) Ptolemy On the Kriterion and Hegemonikon, La23, translation after Liverpool/Manchester Seminar on Ancient Philosophy.

(89) Ptolemy Harmonics 3.7, D100, translation after Andrew Barker.

(90) Aristoxenus Fragmenta 26.

(91) Quintilian Institutio Oratoria 9.4.12, trans. Christoph Riedweg (Ithaca: Cornell University Press 2002).

(92) Porphyry Vita Pythagorae 32. Cf.Iamblichus de Vita Pythagorica 25.110-14.

(93) Ptolemy On the Kriterion and Hegemonikon, La12, 20.

(94) Ibid., La12, trans. Liverpool/Manchester Seminar on Ancient Philosophy.

(95) Ptolemy Tetrabiblos 3.12, H224.

(96) Mansfeld, 68-9.

(97) In the second century, for example, the following philosophical texts promoted the propaedeutic value of mathematics: Nicomachus Arithmetica Introductio 1.3.6-7; Theon of Smyrna Expositio 1.1-2.2; Plutarch, Quaestiones Conviviales 718e; Alcinous Didaskalikos 7. Dominic J. O'Meara argues that Nicomachus portrays arithmetic as the highest science because, in Nicomachus' Pythagorean philosophical system, arithmetic becomes identical with metaphysics: Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (Oxford: Clarendon Press 1989), 14-23. Nevertheless, Ptolemy's claim in Almagest 1.1 remains unique because he dissociates mathematics and theology and claims that, while the former yields knowledge, the latter is conjectural.

(98) Ptolemy Almagest 1.1, H6, translation after G.J. Toomer.

(99) Ibid., H6-7.

(100) See Feke (2009).

JACQUELINE FEKE

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