Dion is a full-bodied man. Theon is that part of him which consists of all of him except his left foot. What becomes of Dion and Theon when Dion’s left foot is amputated? In Burke 1994, employing the doctrine of sortal essentialism, I defended a surprising position last defended by Chrysippus: that Dion survives while the seemingly unscathed Theon perishes. This paper defends that position against objections by Stone, Carter, Olson, and others. Most notably, it offers a (...) novel, conservative solution to the many-thinkers problem, a solution that enables us to accept the existence of brain-containing person-parts while denying that those person-parts are thinking, conscious beings. (shrink)

Here is a puzzle from the Stoic, Chrysippus: There was once a man called Dion, who was unfortunate enough to have his foot annihilated. Thereafter, he was known as Theon. Theon is identical to what was left over after Dion’s foot was removed. That is, Theon is that part of Dion that does not include his foot. If all this is true, then Theon is a proper part of Dion. That is, he is a part of (...) Dion, but not identical to Dion. But if that’s right, then, surprisingly, Dion didn’t survive the loss of his foot. (shrink)

Dion is a full-bodied man. Theon is that part of him which consists of all of him except his left foot. What becomes of Dion and Theon when Dion’s left foot is amputated? Employing the doctrine of sortal essentialism, I defend a surprising answer last defended by Chrysippus: that Dion survives while the seemingly unscathed Theon perishes. For replies to critics, see my publications of 1997 and (especially) 2004.

The ancient puzzle of Dion and Theon has given rise to a surprising array of apparently implausible views. For example, in order to solve the puzzle, several philosophers have been led to deny the existence of their own feet, others have denied that objects can gain and lose parts, and large numbers of philosophers have embraced the thesis that distinct objects can occupy the same space, having all their material parts in common. In this paper, I argue for an (...) alternative approach: I claim that human beings have ordinary parts—hands, heads, feet, and so on—but no extraordinary parts, such as ‘foot-complements’, the existence of which is essential to the puzzle. I rebut three objections to this approach: an objection that it is unacceptably metaphysically arbitrary, an objection that the view is incompatible with versions of the puzzle involving decapitation, and an objection concerning masses of matter. If we can believe that there are such things as hands and feet without involving ourselves in paradox, and without accepting large numbers of co-located material objects that share all their material parts, then that is what we should do. My view is the only known alternative which allows this. (shrink)

In the Armenian tradition of Ailios Theon’s Progymnasmata two otherwise unknown historians occur. By examining the context of the passage and comparing it with authors like Philostephanos, it is made plausible that the ‘unknown’ historians are Phileas of Athens and Skymnos of Chios, whose names are misspelled in the Armenian text.

Dion is a human person, Lefty is his left foot, and Theon is Lefty-Complement, a proper part of Dion. Lefty is annihilated and Dion survives left-footless. After Lefty’s annihilation Theon, if he survives, occupies the same region as Dion. I suggest that this scenario be understood as a fusion case in which Dion and Theon, initially overlapping but distinct, are identical after Lefty’s annihilation and propose an account of proper names that allows us to say that Dion (...) and Theon have ‘become identical’ without commitment to occasional identity or other controversial metaphysical doctrines. The proposed solution employs the semantics developed by Wolfgang Schwarz to address the ‘paradox of occasional identity’, posed by puzzle cases of fission, to deal with the problem of Dion and Theon, a body-minus puzzle. (shrink)

: To honor Bernard Goldstein, this article highlights in the "Defense of Theon against George of Trebizond" by Regiomontanus (1436-1476) themes that resonate with leading strands of Goldstein's scholarship. I argue that, in this poorly-known work, Regiomontanus's mastery of Ptolemy's mathematical astronomy, his interest in making astronomy physical, and his homocentric ideals stand in unresolved tension. Each of these themes resonates with Gold- stein's fundamental work on the Almagest, the Planetary Hypotheses, and al-Bitruji's Principles of Astronomy. I flesh out (...) these tensions with an intriguing interpretation of the history of astronomy, in which Regiomontanus contrasts the two-dimensional "eccentric astronomy" attributed to the Almagest and the Arabs with the three-dimensional spheres of the "later" astronomers. A similar contrast reappears when Regiomontanus portrays as a "fictitious art" an astronomy that does not go beyond the accommodation of computations to the appearances. To conclude, I use Regiomontanus's expression to reinstate (pace Goldstein and Barker in this journal, 1998) fictionalism as an actor's category in Osiander and sixteenth-century astronomy. (shrink)

The epistomology of the definition of number and the philosophical foundation of arithmetic based on a comparison between Gottlob Frege's logicism and Platonic philosophy (Syrianus, Theo Smyrnaeus, and others). The intention of this article is to provide arithmetic with a logically and methodologically valid definition of number for construing a consistent philosophical foundation of arithmetic. The – surely astonishing – main thesis is that instead of the modern and contemporary attempts, especially in Gottlob Frege's Foundations of Arithmetic, such a definition (...) is found in the arithmetic in Euclid's Elements. To draw this conclusion a profound reflection on the role of epistemology for the foundation of mathematics, especially for the method of definition of number, is indispensable; a reflection not to be found in the contemporary debate (the predominate ‘pragmaticformalism’ in current mathematics just shirks from trying to solve the epistemological problems raised by the debate between logicism, intuitionism, and formalism). Frege's definition of number, ‘The number of the concept F is the extension of the concept ‘numerically equal to the concept F”, which is still substantial for contemporary mathematics, does not fulfil the requirements of logical and methodological correctness because the definiens in a double way (in the concepts ‘extension of a concept’ and ‘numerically equal’) implicitly presupposes the definiendum, i.e. number itself. Number itself, on the contrary, is defined adequately by Euclid as ‘multitude composed of units’, a definition which is even, though never mentioned, an implicit presupposition of the modern concept ofset. But Frege rejects this definition and construes his own - for epistemological reasons: Frege's definition exactly fits the needs of modern epistemology, namely that for to know something like the number of a concept one must become conscious of a multitude of acts of producing units of ‘given’ representations under the condition of a 1:1 relationship to obtain between the acts of counting and the counted ‘objects’. According to this view, which has existed at least since the Renaissance stoicism and is maintained not only by Frege but also by Descartes, Kant, Husserl, Dummett, and others, there is no such thing as a number of pure units itself because the intellect or pure reason, by itself empty, must become conscious of different units of representation in order to know a multitude, a condition not fulfilled by Euclid's conception. As this is Frege's main reason to reject Euclid's definition of number (others are discussed in detail), the paper shows that the epistemological reflection in Neoplatonic mathematical philosophy, which agrees with Euclid's definition of number, provides a consistent basement for it. Therefore it is not progress in the history of science which hasled to the a poretic contemporary state of affairs but an arbitrary change of epistemology in early modern times, which is of great influence even today. (shrink)

The classification of 9/8 as epimoric ratio is not only a basic arithmetical notion, but also an important technical ground for Pythagorean- Platonic musical theory. Why then does Theon of Smyrna avoid this point? The common explanation, which refers to Theon's inadequate technical knowledge, is unsatisfactory and aprioristic. A better solution can be found in the exegetical nature of the Expositio. Theon's technical perspective is inspired by a distinctive understanding of the "musical theory'' of the Timaeus.

The classification of 9/8 as epimoric ratio is not only a basic arithmetical notion, but also an important technical ground for Pythagorean- Platonic musical theory. Why then does Theon of Smyrna avoid this point? The common explanation, which refers to Theon's inadequate technical knowledge, is unsatisfactory and aprioristic. A better solution can be found in the exegetical nature of the Expositio. Theon's technical perspective is inspired by a distinctive understanding of the "musical theory'' of the Timaeus.

Six "divine conjectures" frame the place of Theóne (The One to Whom we pray) in the creation of our universe and for its continuing development in five subsequent stages into a loving universe. The first stage, the cosmological universe, establishes the laws of nature, understood by scientists as the "standard model". The second stage introduces life and death into the universe by a process we are only now beginning to understand. Stage 3 requires certain life forms to become conscious with (...) a subset of those life-forms acquiring language that results in that subset becoming self-conscious. The next stage, Conjecture 4, identifies certain persons who become addicted to learning in their unrelenting effort to learn as much of what can be known as possible. The fifth conjecture requires individual persons to act as agents of Theóne in achieving Conjecture 6—a universe that is both loving and lawful. During the course of the exposition subsidiary discussions of the concepts of conjecture and hypothesis explicate the function of each in the advancement of knowledge and understanding. There are brief discussions of prayer and purpose in relation to the Divine. (shrink)

In 'Chrysippus' Puzzle about Identity', John Bowin (thereafter JB) cogently strengthens David Sedley's reading of the puzzle of Chrysippus as a reductio ad absurdum of the Growing Argument. For Sedley, Chrysippus reduces to absurdity the assumption that matter is the sole principle of identity by refuting its presupposition that the two protagonists of the puzzle, namely Theon and Dion, are related as part to the whole. According to Plutarch's Comm. not. 1083 a8-c1, however, the Growing Argument concludes by posing (...) that growth is actually 'generation' and 'destruction'. In order to avoid the contradiction, Theon should have perished rather than become a part of Dion. JB attempts to answer the questions of whether within the Growing Argument there are elements against Theon being a living part of Dion. He shows that in both Epicharmus' fragment 2 and Plutarch's Comm.not. 1083b 308 "there is nothing to block the inference from matter being the sole principle of identity to the possibility that Theon could be a part of Dion" (246). Again, in exploring whether the above contradiction can be solved, he convincingly argues against Epicharmus' and Plutarch's reading of growth as generation and destruction. In the last part of his article, JB stresses that the reductio ad absurdum of the Growing Argument can be tackled without introducing the concept of 'peculiarly qualified individuals'. (Bryn Mawr Classical Review 2004.04.12). (shrink)

Theon of Smyrna was a professor of Platonism and, as the Platonists of his age, an exegete of the Timaeus. The only work we have, the Expositio rerum mathematicarum ad legendum Platonem utilium, is complete and consistent: it discusses the foundations and the characteristics of the τάξις that makes the world well structured. Theon found this doctrine in the Timaeus and in the Epinomis, and he argued it again through mathematical illustrations with the aim of demonstrating, according to (...) Plato, the presence of harmony both in the incorporeal and in the corporeal realm: Theon’s purpose can’t be grasped without referring to his platonic exegetical activity. (shrink)

Theon of Smyrna was a professor of Platonism and, as the Platonists of his age, an exegete of the Timaeus. The only work we have, the Expositio rerum mathematicarum ad legendum Platonem utilium, is complete and consistent: it discusses the foundations and the characteristics of the τάξις that makes the world well structured. Theon found this doctrine in the Timaeus and in the Epinomis, and he argued it again through mathematical illustrations with the aim of demonstrating, according to (...) Plato, the presence of harmony both in the incorporeal and in the corporeal realm: Theon’s purpose can’t be grasped without referring to his platonic exegetical activity. (shrink)

A traditional view of perception and action makestwo assumptions: that the causal flow betweenperception and action is primarily linear or one-way,and that they are merely instrumentally related toeach other, so that each is a means to the other.Either or both of these assumptions can be rejected. Behaviorism rejects the instrumental but not theone-way aspect of the traditional view, thus leavingitself open to charges of verificationism. Ecologicalviews reject the one-way aspect but not theinstrumental aspect of the traditional view, so thatperception and (...) action are seen as instrumentallyinterdependent. It is argued here that a betteralternative is to reject both assumptions, resultingin a two-level interdependence view in whichperception and action co-depend on dynamicallycircular subpersonal relations and as a result may bemore than merely instrumentally interdependent. Thisis illustrated by reference to motor theories ofperception and control theories of action. (shrink)

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be that Theon (...) is destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Philosophical Rhetoric of Socrates’ MissionRobert Metcalf"We shall dismiss this business of Chaerephon, as it is nothing but a cheap and sophistical tale [sophistikon kai phortikon diegema]"—Colotes, according to Plutarch's Moralia 14, 1116f-1117a.Socrates' account of his "mission" on behalf of the god at Delphi is one of the most memorable parts of his most famous memorial in Plato's Apology. But it is also controversial as to what it means (...) to Socrates and what it should mean to readers of Plato's text.1 First, there is the curious fact that the story occurs nowhere outside the competing versions of Socrates' defensespeech in Plato and Xenophon, and in the latter version the oracular report differs significantly in content and import: there the Pythia proclaims, not that no one is wiser than Socrates, but that no one is more generous or more just or more "soundminded" (sophron), and Xenophon's Socrates uses this as evidence that he "outshone the rest of mankind" and "deserves congratulations from gods and men alike" (Apology 14-18).2 Furthermore, the sequence of events that make up Socrates' "mission" is itself difficult to discern, from its apparent prompting by the oracular message to Chaerephon, to Socrates' initial effort to refute it, to his ultimate practice of elenchos in order that the oracle (or, at least, his interpretation of the oracle) might remain unrefuted.3 Not surprisingly, it was already a matter of controversy in the third century BC, as we read in the above quotation from Plutarch's Moralia. Whereas Arcesilaus interpreted the story of the Delphic oracle, and the account of elenctic practice occasioned by the oracle, as a model for his own skeptical orientation, Colotes, the Epicurean, charged that he had been duped by Socrates' sophistic oratory.4 To be sure, Colotes' charge of sophistry is meant to be abusive and has value for us only insofar as it counters a piously uncritical reading of Socrates' self-portrayal in Plato's Apology.5 In what follows I shall argue that an appreciation of the irony and mock-humility with which Socrates accounts for his "mission" to philosophize [End Page 143] affords us insight into the philosophical rhetoric that is essential to Socrates' practice of elenchos.But let us begin by examining those strange elements in Socrates' account that have made it "notorious" in the way suggested by the ancient debate.6 Socrates introduces the story of the oracle only after he dismisses, somewhat cursorily, the charges circulated by his "first accusers"—namely, that he investigates the things under the earth and heavenly things, and that he educates people for money (19b-20c). Insisting that he does not dishonor the knowledge involved in these activities (19c, 20b-c), Socrates nonetheless offers little defense apart from simply disowning such knowledge, presumably because these activities are not related to that "matter" (pragma) which has earned him his peculiar reputation (20c-d). It is here, in his explanation of this matter, that Socrates recounts the story of Chaerephon and the Pythia.7 As he begins the story he repeats his vow from the beginning of his defense to tell the jury only the truth (20d), assures them that he is not joking, and then is compelled to plead with them not to make any disturbances—"even," he says, "if I seem to you to be boasting [mega legein] somewhat" (20e). These successive declarations are all necessary, for the story has it that Socrates acquired his reputation through the human wisdom for which Socrates was singled out by the oracle at Delphi (20d-e).Socrates' puzzlement over the oracle and his effort to subject it to elenchos are offered as an explanation for the elenctic practice by which he comes, over time, to acquire his reputation.8 Although he does not say that his practice of elenchos begins with his investigation of the oracle's meaning, he does portray his subsequent practice of elenchos as being "in accordance with the god [kata ton theon]" (22a), an activity for which the god stands as a trustworthy witness (20e), and thus as a "matter of the god [to tou theou]" (21e). Ironically, the account Socrates... (shrink)

This article will argue that ‘A-religion’ , Jean-Luc Nancy’s reading of Claire Denis’sBeau travail , can be understood in the context of concerns he explores elsewherein his philosophical work.1I will be focusing here on the ways in which his thinking ofquestions of community and Christianity and Dis-Enclosure respectively) can be seen to influence anddirect his reading of Denis’s film. Beau travail, this article will argue, comes to represent forNancy a point of intersection between two main issues: the demand of community (...) on theone hand and the deconstruction of Christianity on the other, that is, broadly speaking, thepolitical on the one hand and the theological on the other. (shrink)

Hypatia was born in Alexandria in the fourth century CE (there's disagreement about her age at death, so that different scholars put her year of birth at either about 370 or about 355CE). The daughter of the mathematician and philosopher, Theon, who taught at the university of Alexandria, attached to the world-famous library, and who seems to have been responsible for Hypatia's education, though she might also have been taught by Plutarch the Younger in Athens. She helped her father (...) with his books on mathematics, astronomy, and philosophy, and became a teacher at his school, eventually becoming its head. (shrink)

The astronomical commentary of Stephanus of Alexandria is an important marker in the history and the transmission of Ptolemy's Handy Tables. Following the example of the Small Commentary of Theon of Alexandria, Stephanus however adjusts the tables and the astronomical data to the geographical coordinates of Byzantium. The treatise presents a problem of attribution because it's anonymous in most manuscripts. The text shows also small additions from the emperor Heraclius Ist. We are preparing a critical edition of the commentary. (...) These study presents several results of our work. (shrink)