Epictetus Dissertationes Math

With a significant number of participants, and a diversity of backgrounds, we have developed a number of working practices, which, when taken together, point towards an iterative methodology of collective engagement. Both practice and reflection dwell with the relationships among individuals, their background, training, interests and encounter with Grosseteste’s thought, the relationships among individuals in the research group and the different tasks that need to be carried out as a group: reading, oral discussion, modelling, coding and analysis, calculating, mathematical interpretation, finding and incorporating relevant data (such as solar spectra in the work on rainbows), and writing. We did not embark upon the project, which started in 2010, with an explicit theory of interdisciplinarity, and we continue to develop the project’s interactions from its intellectual (and administrative) requirements. To this extent the interdisciplinary form is a product of the function of interactive research.

The most obvious disciplinary distinction within the research group is that between humanities and science. Without entering into a discussion of the two cultures, our experience has been that distinctive differences have gradually moved into the background as the project has advanced (Snow, 1959).10 Some clear distinctions remain: an instinctive movement towards mathematical or linguistic expression, a tendency towards visual and diagrammatic evidence on the part of scientists, practices of collaborative writing more easily adopted publicly by scientists, practices of source criticism and historiographical detail more commonly adopted by humanities experts. All of that said, these distinctions neither pertain in their totality to individuals nor are distinctive practices among science and humanity scholars to be ignored. A philosophical approach to a medieval thinker can be quite as unfamiliar, alien and distinct to an historical approach, as computational cosmology to organic chemistry. By foregrounding the task of interpreting Grosseteste’s treatises, disciplinary focus becomes the tool and not the master for cross-cutting dialogue.

At a broader and deeper level, the relationship between disciplinary and interdisciplinary research is of profound, and defining significance to the Ordered Universe. Our research outputs, for example, are interdisciplinary: they distil the insights from all contributors, and are shaped to allow the reader to follow the text and discussion from the different points of view involved. On Colour was co-written by a medieval historian, a medieval linguist, a palaeographer and medieval Latinist, a medieval philosopher, a physicist and a colour vision specialist. While our disciplinary identities are not insisted upon at the expense of our individual and shared interests in Grosseteste and his treatises, they do remain integral elements in how the research is carried out. Nevertheless it is, ultimately, the focus on the treatise at hand that governs the attitudes and responses of the participants.

The collaborative nature of the project, and the centrality of Grosseteste’s treatises are given physical instantiation in our main, collective, research activity. The project works through a series of research symposia, in what might be conceived of as classic humanities research. The establishment, translation and interpretation of the text is enriched by the perspectives and analysis of all around the table. It is this process of collective translation and textual elucidation that creates the environment for genuinely interdisciplinary outputs.

Collaborative reading is the foundation of the project. For a given symposium the palaeographer and Latinist will have prepared, in consultation with other medievalists within the team, a draft edition from the various manuscripts (with a list of Latin variants) together with a preliminary translation. We then read the treatise together, word by word, line by line, paragraph by paragraph. One member of the group acts as narrator and reads aloud the text of the English translation. The oral experience is an important one, allowing comparison to the Latin edition and a pace suitable for discussion and questions. Given the oral nature of medieval education there is some sense too in experiencing the text in, however, attenuated a way, in the medium for which it was principally designed. In this process the scholarly apparatus required to understand the text is the same for all participants. The scientists are not spared the details of the text, languages and historical context, nor the humanities scholars the discussions on the geometrical or combinatorial logic implied by the text, or the questions of what natural phenomena might have been in the perception and mind of the writer.

The act of translation within the group context becomes a highly interdisciplinary and non-linear practice itself. This is necessary to deal with the “Catch-22” problem that on the one hand it is not possible to translate the texts properly without knowing their mathematical and physical meaning and on the other it is hard to identify the mathematical and physical meaning without some sort of translation. This conundrum is resolved by iteration. A first pass of the literal translation often reveals sections where the meaning is far from clear, but in mutual struggling with the text a plausible rendering among the alternatives eventually surfaces. In the case of descriptions of natural phenomena, physical processes or geometrical patterns, the mathematical logic of Grosseteste’s discussion is often central to teasing out the meaning of the text. The essential ingredient in our working practice is to engage together. There is never a clear boundary between a philological, philosophical or contextual discussion and mathematical reasoning or discussion of ray optics. Scientists need to feel free to question accepted translations and to suggest new ones. Humanities scholars need to know that they are welcome to challenge the kinematic interpretations or optical references and speculation advanced by the scientists.

Listening takes place in many different modes for the research group within the context of collaborative reading, both as individuals and collectively. Some of these modes will overlap, others will appear to be less closely related. Michael Rost’s observations on the four orientations of listening are a helpful way to reflect on these processes (Rost, 2002: 2–3).11 First, receptive listening (receiving what the speaker actually says), which involves decoding what the speaker means; second, constructive listening (constructing and representing meaning), which involves the reframing of the speaker’s message to a conceptual framework with which the listener is familiar, and noticing what has not been said; third, collaborative listening (negotiating meaning with the speaker and responding), which involves sharing information, signalling where ideas are clear and less clear in an inter-personal context; fourth, transformative listening (creating meaning through involvement, imagination and empathy), which involves imagining possible worlds for the speaker’s meaning, entering the flow created by the convergence of different media, and completing the process of communication.

Every participant around the table, and we number typically between 18 and 30 in a collaborative reading session, would recognize these patterns of listening. Listening between disciplines involves a series of translations and we have many examples of this activity within the collaboration. These range from matters of terminology, to more technical issues. Of the former some scientists refer to “groups”, some to “labs”, as collections of people: confusing if “lab” is understood as a physical entity. Reference to primary and secondary sources by historians was also the occasion for misunderstanding. The distinction between sources contemporary to the period under scrutiny (primary) and subsequent scholarly reflection (secondary) could be seen as promoting a hierarchy of material of greater or lesser importance. Abbreviations can cause problems as well: an RGB cube is easily referred to, that it stands for red-green-blue was not always immediately apparent.

As well as learning to listen to each other the research group has learnt also to listen to the past. All of the same issues of terminology arise, this time from Latin and at a period when Latin was still a living and developing language. Words with different modern meanings provide complex issues of translation. In work on the treatise On Light, Grosseteste employs a lot of physical vocabulary, including the word moles. A natural translation would be “mass”, but this presents issues of concerning modern specific and different, scientific connotations. Another case is the perspicuum, which Grosseteste describes in the beginning of the treatise On Colour: “Color est lux incorporata perspicuo” (Dinkova-Bruun et al., 2013: 17). “Colour is light incorporated in a perspicuum”. Quite what perspciuum means here is intriguing: early fourteenth-century references indicate “lens” as a plausible translation. However, earlier usage does not have the same precision, making “transparent medium” a reasonable English rendition for the period of the text. The word-choice here raises all sorts of scientific possibilities. It would be quite possible to phrase the translation to give the impression that Grosseteste had a notion of splitting light using a prism some 400 years before Newton (1669; Newton Project, 2008–present). This would be quite wrong linguistically, as well as historically, even though Grosseteste in his treatise On the Rainbow, written about 5 years later, demonstrated his knowledge of refraction. It was this same treatise that helped to confirm the research team’s collective decision to translate perspicuum as “diaphanous medium”. Grosseteste repeats his remarks on colour as part of his rainbow treatise, using his own theory to explain the differences in colour within and between natural rainbows. Five years on, however, Grosseteste’s reading of Averroes caused him to substitute perspicuum with the word diafanum (Giovani, 2013). Our collective movement towards “diaphonous medium” mirrored Grosseteste’s own thought, which encouraged confidence in the faithfulness of the rendering.

Learning to appreciate the fragility of the past has been a key part in the evolution of Ordered Universe practice. The chances that lead to the survival of manuscripts of Grosseteste’s works and their state of preservation are worth emphasizing. The scientific works seem to have been compiled in collections (not always with the same contents) from the later thirteenth century, as well as surviving independently. Survival rates differ. For the treatise On the Sphere there are over 50 extant manuscripts, testament to the treatise’s purpose as an introduction to astronomy. Conversely, On the Liberal Arts survives in only six manuscripts, mostly from later in the Middle Ages. Some treatises, such as those in a volume, which formed part of the late seventeenth century Cotton Library, were fortunate to survive at all. A fire on 23 October 1731 did immense damage to the collection, the physical traces of which are apparent on a copy of On Colour, which remains charred and disfigured to this day.

The issues connected to how the standard, critical edition of the text is put together are important in this context also (Walsh, 2010). How the transmission occurred from the author’s original (if indeed there was one since many medieval school’s texts survive from student notes) to surviving manuscripts is difficult to trace. The process is one in which errors can accumulate. As an example, in Baur’s edition of the treatise On Colour we find the statement the 7+7=9. Clearly this is not true. Tracking what had happened between the earliest surviving manuscripts form the thirteenth century, to those from the fourteenth and finally the fifteenth century, resolved the issue. An Arabic numeral 14 had been taken for a Roman numeral IX (the medieval habit in writing Arabic “4s” was to tilt them to the left), which had been turned into the prose “novem” “nine”. Hence, 7+7=9.

At the same time as appreciating the slender framework on which our experience of the past depends, learning to listen to the past also involves an appreciation of the sophistication of the intellectual achievements of the past. This is a more difficult act in which to engage than might at first be thought. Especially for scholars of the modern period, the linear narratives of human progress are not easy to abjure.12 Intellectual progress makes autobiographical sense: I know more now than I did when a child. Indeed the accidental (or purposeful) patronizing of past thinkers as “childlike” in their knowledge is quite common. The challenging task of taking the past seriously, and a past thinker as an intellectual equal, or superior, has been something at which the research group has worked hard.

In this exercise Grosseteste’s personal qualities are helpful. He does seem to have been regarded by contemporaries as a peculiarly adept and gifted man, expert at everything to which he turned his mind. According to Bacon (1859: 472), “Only lord Robert, on account of the longitude of his life and the wonderful methods he used, knew more than other men the sciences that the Greeks and the Hebrews did not know”. The close association with the logic and premises of medieval scientific thought provides an antidote to the arrogant presumption that our current world-view is “right”. A twenty-ninth century scientist may well view our current theories with the same condescension as many contemporary scientists view thirteenth century models.

There is a reciprocal challenge for the medievalists in the team. We can present Grosseteste, as far as we are able, in the context of his own religious, intellectual and material culture. To engage with modern science readings of his thought is to encounter an approach which is all too easy to write off as anachronistic. The apparent three-dimensional scheme within Grosseteste’s colour theory naturally invites reflection on and comparison to modern understanding of colour perception (Smithson, 2015). Grosseteste’s description of the universe beginning with a single point of light expanding instantaneously into the shape of a sphere, calls to mind modern conceptions of the first stages of the universe and its popularization as the “big bang” and the significance of light within this process. Were any of the team to suggest that Grosseteste anticipated quantum mechanics, or had prescient knowledge of ocular physiology then the charge of anachronism would be duly levelled, and justly. However, for a scientist to start a response to a complex text with a modern parallel is often a very stimulating way to get to the bottom of a passage whose meaning is not clear. A disciplinary start to addressing a problem ends in an interdisciplinary discussion and solution. Grosseteste is not interpreted here with any anachronism, least of all scientific. The interpretative tools of humanities and scientific disciplines are used together to bring the text to life in all of its dimensions.

We have also, as a team, come to appreciate that analysis of texts that purport to explain natural phenomena is enhanced by considering the phenomena as well as the author. An eye or a rainbow is the same in the thirteenth as the twenty-first century. This is a further area in which careful explanation of the circumstances in which these phenomena occur is crucial. In some cases, the experiences Grosseteste describes may not match those of the modern reader. For a modern city dweller, it is not clear that the night sky is something with which everyone would be familiar, as Grosseteste’s contemporaries would have been. This may seem obvious but a disciplinary background in medieval history might not, automatically, presuppose that knowledge of this fact would be included in an analysis of Grosseteste’s corpus of scientific texts. Different strands in our current education and academic paths may change the properties of the natural world with which we are familiar, and which we would emphasize in an interpretation of textual material. The reverse applies equally pertinently. Sometimes the accepted wisdom of a particular explanation can prevent us from looking properly. Thirteenth century reflection on natural phenomena is no less valid, in this sense, than that of the twenty-first. Applying these insights appropriately is another answer to the charge of anachronism.

For our final session of the term we turn to Anthony Ashley Cooper, the Third Earl of Shaftesbury (1671-1713), best know as the author of the three-volume Characteristics of Men, Manners, Opinions, Times, published in 1711, which was in fact a collection of various items he had published previously, including his Inquiry Concerning Virtue or Merit of 1699. 


 Shaftesbury was in many always out of sync with his time, or at least out of sync with our usual narrative of the history of the philosophy of his time. He disliked the approach to philosophy adopted by many of his contemporaries and wanted to replace it with something more worldly. He consciously saw his own philosophy as an attempt to revive a Socratic conception of philosophy as ethical self-transformation. He combined this with a love of Classical literature and was especially drawn to Roman satirists such as Horace, Juvenal, and Persius, all of whom engage in passing with Stoic and Epicurean themes. In many ways Shaftesbury might be compared with Cicero, both being non-technical thinkers and elegant stylists, and both interested in philosophy as a guide to a good life. 


Although he rarely discusses them in his published works, Shaftesbury was thus unsurprisingly a great admirer of the Roman Stoics Epictetus and Marcus Aurelius. He wrote extensive textual notes on the Dissertationes of Epictetus and these were drawn on in the commentary in John Upton’s 1739-41 edition of Epictetus. He also kept a pair of notebooks inspired by his reading of these two Roman Stoics in which he addressed a range of topics including natural affection, the self, simplicity, the passions, God, nature, providence, and the nature of philosophy itself.


People have not been sure what to make of these notes. They resemble Marcus’s Meditations in some respects and, like the Meditations, do not straightforwardly articulate a philosophical position. In the light of the work of Pierre Hadot, however, it is now perhaps easier to classify these as Shaftesbury’s ‘spiritual exercises’, his working through practical precepts on paper as a means to digest philosophical ideas. Shaftesbury characterizes his project as ‘care of self’ (SE, p. 195), placing the text in a tradition running from Socrates to Foucault. In these notebooks Shaftesbury is ‘alone with himself, caring for himself, testing, debating with and exhorting himself’ (SE, p. 16).  


These notebooks were examined by Benjamin Rand, who published an edited version of them in 1900 under the title Philosophical Regimen. What Rand did was tidy up the various notes in an attempt to do his best to put the text into publishable form; one might say that he tried to make a book out of them. Ever since then those curious about the text have felt a certain ambivalence towards Rand’s book: thankful that he made the text available at all but frustrated that his text might not be a full and accurate account of what Shaftesbury actually wrote down in his notebooks. In 1993 Laurent Jaffro published a French translation based on a fresh inspection of the notebooks, following the text as Shaftesbury had left it. This has been well received but for the last two decades it has put English-speaking scholars in the odd position of turning to a French translation for the most reliable discussion and account of an English text. Recently an excellent new critical edition of the original text (under its original title of Askêmata) has been published that solves all these problems once and for all.


One question that the editors of the new edition consider in their introduction is whether these notebook musings on late Stoic themes should lead us to think of Shaftesbury as a Stoic, a topic on which a small literature has grown. They also address the purpose of the text, emphasizing the way in which Shaftesbury is taking inspiration from Epictetus’ advice that one should write down one’s reflections, keep them to hand, and reread them, in order both to comfort and to strengthen oneself (see SE, p. 17, citing Epictetus, Dissertationes 3.24). Even if the final judgement is that Shaftesbury does not adopt a wholehearted Stoicism, it does seem clear that he adopted certain Stoic practices and the wider Stoic approach to philosophy as an art of living.


With these thoughts in mind I propose we focus in on just three short sections. For our present purposes it will be simplest to use the readily available edition by Rand. The first section is devoted to ‘the end’, the second to ‘character and conduct’, and the third to ‘philosophy’. I hope that looking at these will help to bring out the nature of what Shaftesbury is doing.


The End


The section on ‘the end’ seems to offer an interesting blend of Aristotelian and Stoic themes. Much of the discussion is framed around a very Aristotelian account of whether there is a telos of human life. Shaftesbury sees two potential candidates and wants to reconcile them. The first of these is our natural sociability, which Shaftesbury sees embodied in our natural instincts of affection. He discusses affection at length in another section of the work and he seems here to be thinking of the Stoic theory of oikeiôsis. It is our nature to follow these natural instincts of affection.


Distinct from this is the argument concerning what might be the highest good for humans. Shaftesbury considers and rejects the idea of pleasure as the end, in harmony with both Aristotle and the Stoics. He affirms in instead virtue, not least for the fact that it is self-sufficient. It is perhaps worth noting here that again here he follows a Stoic line of argument. (It is also perhaps worth noting that Aristotle ultimately prefers contemplation over practical wisdom because it is more self-sufficient than the latter; Aristotle would not hold that these kinds of virtues are as self-sufficient as either the Stoics or Shaftesbury claim.) Shaftesbury suggests that this virtuous self-sufficiency offers a form of constancy, which brings to mind Lipsius, and the editors of the recent edition report that Shaftesbury owned two copies of Lipsius’s complete works (SE, p. 442).


So we have a natural tendency towards social affection (Stoic) and functional conception of humans that identifies goodness with virtue and rationality (Aristotelian). Shaftesbury thinks it perverse to fight against our natural instincts, and equally perverse to think that nature might have arranged things so that our natural instincts would turn out to be at odds with what is good for us. The individual human being who fulfils his or her function will inevitably possess a range of social virtues and these social virtues will be in complete harmony with our natural instincts to social affection. So we needn’t fight against our own natural instincts when trying to become good. On the contrary, if we want to fulfil our telos then we ought ‘to live according to nature’, which in this context clearly refers to our natural instincts for affection.


Let me make a final comment on this section. In his correspondence Shaftesbury suggests that there are only two real schools of philosophy in antiquity: a hedonist tradition uniting Epicurus and the Cyrenaics, and a Socratic tradition uniting Academics, Peripatetics, and Stoics (Rand, p. 359; cf. SE, p. 15). So for Shaftesbury Aristotle and the Stoics are part of a single Socratic philosophical tradition united by their commitment to virtue (and rejection of pleasure) as the telos. Shaftesbury fleshes this out a little further in a brief genealogy of ancient philosophy in his Soliloquy where he describes Socrates as ‘the philosophical patriarch’ (Klein, pp. 114-15; cf. SE, p. 14). Apparently Shaftesbury planned to write a history of Socratic philosophy and he produced a detailed draft around the same time he was compiling these notebooks (SE, p. 14). So, Shaftesbury’s blend of Stoic and Aristotelian themes in this chapter was probably done very consciously.


Character and Conduct


The next section, ‘character and conduct, is very brief but I think it is worth looking at as an example of the sort of thing that Shaftesbury is doing in these notebooks as a whole. The section opens with a quotation from Epictetus, who is cited a couple of further times as well. The text takes the form of a dialogue with oneself very much inspired by the Meditations of Marcus Aurelius. The central theme is the contrast – and perhaps ultimately conflict – between our social persona and our essential nature. We can see Shaftesbury struggling with his social identity and the expectations it forces upon him. Whatever social expectations might demand of him, Shaftesbury reminds himself that he is a man, a human being, the essence of which is reason and a range of virtues (‘humanity, faith, friendship, justice, integrity’). As he develops the theme Shaftesbury approaches the conclusion that the two modes of life, living according to nomos or according to one’s own phusis, are mutually exclusive. To pursue one inevitably involves the sacrifice of the other. So if our goal is a virtuous life following nature then we must accept that we cannot also pursue social advancement. The whole piece really does have the flavour of Marcus Aurelius – someone grappling with the tension between their philosophical ideals and the reality of their social position.




The final section is on philosophy. Here Shaftesbury affirms the idea that philosophy ought to be concerned not with idle speculations but rather with life. The ‘philosophical art’ as he calls it ought to focus on happiness and tranquillity. Whether space is a vacuum or a plenitude is an abstract question he dismisses as uninteresting, and this is a striking echo of those comments in Marcus Aurelius where the Emperor expresses mild indifference as to whether the cosmos is composed of a continuum of matter or of atoms and void.


Shaftesbury goes on to consider three different ways to think about philosophy: i) subtle speculation, which would put it on a par with mathematics and the sciences; ii) the study of happiness, with happiness conceived as something dependent on external goods, and so philosophy itself would be concerned with those external goods; iii) the study of happiness, with happiness conceived as something dependent solely on the mind, as the Stoics taught. Shaftesbury is drawn to the last of these, conceiving philosophy as a psychotherapeutic activity whose aim is to help us overcome ‘disquiet, restlessness, anxiety’.


A little later Shaftesbury picks up the theme of the previous section, suggesting that a wholehearted commitment to philosophy conceived in this way will entail neglecting one’s social position in the world of affairs. Even so he suggests it is the right thing to pursue because it is the truer route to security against fortune – ‘by settling matters within’ rather than by acquiring great reserves of wealth or social contacts. This neatly brings us right back round to where we began with Lipsius – philosophy as an antidote against the vicissitudes of fortune.


(These notes draw in places on a review of the new critical edition of Shaftesbury’s Askêmata forthcoming in the British Journal for the History of Philosophy.)




Klein = Characteristics of Men, Manners, Opinions, Times, Edited by Lawrence E. Klein (Cambridge: Cambridge University Press, 1999)  


Rand = The Life, Unpublished Letters, and Philosophical Regimen of Anthony, Early of Shaftesbury, Edited by Benjamin Rand (London: Sawn Sonnenschein, 1900) 


SE = Standard Edition: Complete Works, Correspondence and Posthumous Writings, Edited with German Translations and a Commentary by Wolfram Benda, Christine Jackson-Holzberg, Patrick Müller & Friedrich A. Uehlein, Vol. II,6 Askêmata (Stuttgart / Bad Cannstatt: Frommann-Holzboog, 2011)


Leave a Reply

Your email address will not be published. Required fields are marked *