This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s Data. I will argue that what is given does not simply exist, but can be unproblematically assumed or produced (...) through some effective procedure. Arguments by givens are shown to be general claims about constructibility and computability. The claim that an object is given is related to our concept of an assignment—what is given is available in some uniquely determined, or determinable, way for future mathematical work. (shrink)

Galen's stories about his successes in predicting the development of an illness belong to the best-known anecdotes drawn from his writings. Brilliant pieces of self-presentation, they set Galen apart from his peers, who tried to cover up their ignorance by levelling accusations of magic and divination against their superior colleague. These accusations are usually interpreted as very real threats, as Roman law punished illicit magic and divination. Pointing out that Galen sometimes likes to present himself as amantisand a prophet, others (...) have suggested that the accusations against Galen and his own self-presentation indicate that the border line between medicine and religion was still fluid. Both approaches correctly draw attention to the social reality that the accusations betray: they suggest that Galen belongs to a group of healers of dubious standing that populated the empire and thus show that medicine did not have a monopoly on healing. Yet such a socio-historical approach may not be sufficient. For one thing, both explanations have their limitations. Regarding the former, it can be said that Augustus' prohibition of divination aimed at controlling prediction about the emperor and one can doubt that a widespread clampdown of all forms of divination ever was intended. A possible objection to the second view is that throughout hisoeuvreGalen emphasizes his medicine as a rational undertaking, even as a science (epistêmê). If one takes his self-presentation as amantisto be more than metaphorical and to indicate the not yet fully crystallized identity of medicine as a separate scientific discipline, then Galen's usual way of understanding his own craft as a ‘science’ is in need of explanation. Besides such possible objections, a different set of questions still needs to be asked: why precisely were accusations of practising magic and divination levelled against Galen and why do they recur so frequently in his writings? Why divination and not, say, poisoning? (shrink)

Galen's stories about his successes in predicting the development of an illness belong to the best-known anecdotes drawn from his writings. Brilliant pieces of self-presentation, they set Galen apart from his peers, who tried to cover up their ignorance by levelling accusations of magic and divination against their superior colleague. These accusations are usually interpreted as very real threats, as Roman law punished illicit magic and divination. Pointing out that Galen sometimes likes to present himself as a mantis and a (...) prophet, others have suggested that the accusations against Galen and his own self-presentation indicate that the border line between medicine and religion was still fluid. Both approaches correctly draw attention to the social reality that the accusations betray: they suggest that Galen belongs to a group of healers of dubious standing that populated the empire and thus show that medicine did not have a monopoly on healing. Yet such a socio-historical approach may not be sufficient. For one thing, both explanations have their limitations. Regarding the former, it can be said that Augustus' prohibition of divination aimed at controlling prediction about the emperor and one can doubt that a widespread clampdown of all forms of divination ever was intended. A possible objection to the second view is that throughout his oeuvre Galen emphasizes his medicine as a rational undertaking, even as a science . If one takes his self-presentation as a mantis to be more than metaphorical and to indicate the not yet fully crystallized identity of medicine as a separate scientific discipline, then Galen's usual way of understanding his own craft as a ‘science’ is in need of explanation. Besides such possible objections, a different set of questions still needs to be asked: why precisely were accusations of practising magic and divination levelled against Galen and why do they recur so frequently in his writings? Why divination and not, say, poisoning? (shrink)