Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76c49bb84f-sz5hq Total loading time: 0 Render date: 2025-07-07T04:55:19.606Z Has data issue: false hasContentIssue false

18 - Philosophy, science and medicine

from PART IV - PHYSICS AND METAPHYSICS

Published online by Cambridge University Press:  28 March 2008

By
Giuseppe Cambiano
Edited by
Keimpe Algra ,
Jonathan Barnes ,
Jaap Mansfeld  and
Malcolm Schofield
Giuseppe Cambiano
Affiliation:
University of Turin
Keimpe Algra
Affiliation:
Universiteit Utrecht, The Netherlands
Jonathan Barnes
Affiliation:
Université de Genève
Jaap Mansfeld
Affiliation:
Universiteit Utrecht, The Netherlands
Malcolm Schofield
Affiliation:
University of Cambridge
Get access

Summary

Philosophy and mathematics

The relationship between philosophy and mathematics appears to be less close in the Hellenistic age than in previous centuries. The mathematicians proceeded with their work without any explicit adhesion to philosophical doctrines or any reply to the theoretical and epistemological problems raised by the Epicureans and the sceptics when dealing with mathematics. In the fifth century AD the Neo-platonist Proclus saw Euclid as a Platonist, because his Elements concluded with the construction of regular polyhedrons, the basis of the cosmic structure outlined by Plato in the Timaeus (Eucl. 68.20–3; 70.22–71.5). But there is no proof that Euclid meant to direct the whole of his writing towards the creation of a cosmology.

Another level on which Proclus tried to show Euclidean geometry's dependence on philosophy was the formal structure of the Elements. This was based on the distinction between a small number of principles, assumed at the outset without demonstration and listed in the first book as definitions, common notions and postulates, and a body of propositions reached deductively starting from the principles. Proclus highlighted a correspondence between this structure and the theory of science formulated by Aristotle, particularly in the Posterior Analytics, and also between Euclid's principles and those mentioned by Aristotle (Eucl. 76.6–77.2). It is in fact possible to make out some parallelism: for example, Aristotle includes among the principles used by mathematicians Euclid's third common notion, which is that if equals are subtracted from equals, the remainders will be equal (APo. 76a41).

Information

Type
Chapter
Information
The Cambridge History of Hellenistic Philosophy , pp. 585 - 614
Publisher: Cambridge University Press
Print publication year: 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

References

Algra, K. A. (1995) Concepts of Space in Greek Thought, PhA 65 (Leiden).Google Scholar
Allen, J. (1993) ‘Pyrrhonism and medical empiricism: Sextus Empiricus on evidence and inference’, in Haase, W., ed., ANRW II 37.1.Google Scholar
Angeli, A. & Colaizzo, M. (1979) ‘I frammenti di Zenone Sidonio’, CErc, 9.Google Scholar
Angeli, A. & Dorandi, T. (1987) ‘Il pensiero matematico di Demetrio Lacone’, CErc 17.Google Scholar
Annas, J. E. (1992a) Hellenistic Philosophy of Mind, Hellenistic culture and society 8 (Berkeley).Google Scholar
Apelt, O. (1891) Beiträge zur Geschichte der griechischen Philosophie (Leipzig).Google Scholar
Barnes, J. (1989a) ‘The size of the sun in antiquity’, ACD 25.Google Scholar
Barnes, J. (1990a) ‘Logical form and logical matter’, in Alberti, (1990).Google Scholar
Barnes, J. (1990b) The Toils of Scepticism (Cambridge).Google Scholar
Barnes, J. (1990c) ‘Pyrrhonism, belief and causation. Observations on the Scepticism of Sextus Empiricus’, in Haase, W., ed., ANRW II 36.4 (Berlin/New York).CrossRefGoogle Scholar
Barnes, J. (1982b) ‘Medicine, experience and logic’, in Barnes, J. et al. (1982a).Google Scholar
Berryman, S. (1998) ‘Euclid and the Sceptic: a paper on vision, doubt, geometry, light and drunkenness’, Phronesis 43.CrossRefGoogle Scholar
Bréhier, E. (1914) ‘Posidonius d'Apamée théoricien de la géométrie’, REG 27.Google Scholar
Bréhier, E. repr. in Bréhier, (1955) Etudes de philosophie antique (Paris).Google Scholar
Burnyeat, M. F. (1982b) ‘Gods and heaps’, in Schofield, & Nussbaum, (1982).CrossRefGoogle Scholar
Burnyeat, M. F. (1982c) ‘The origins of non-deductive inference’, in Barnes, et al. (1982a).Google Scholar
Cambiano, G. (1992) ‘Scoperta e dimostrazione in Archimede’, in Dollo, C., ed., Archimede, Mito Tradizione Scienza (Florence).Google Scholar
Decleva Caizzi, F. (1986) ‘Pirroniani ed accademici nel III secolo a.C.’, in Flashar, & Gigon, (1986).Google Scholar
Deichgräber, K. (1930 (repr. w. add. 1965)) Die Griechische Empirikerschule. Sammlung der Fragmente und Darstellung der Lehre (Berlin/Zürich).Google Scholar
Dijksterhuis, E. J. (1987) Archimedes, 2nd edn (Princeton).CrossRefGoogle Scholar
Ebert, T. (1991) Dialektiker und frühe Stoiker bei Sextus Empiricus, Hypomnemata 95 (Göttingen).CrossRefGoogle Scholar
Edelstein, L. (1932) ‘Die Geschichte der Sektion in der Antike’, Quellen und Studien zur Geschichte der Naturwissenschaften und der Medizin 3; Engl. transl. in Temkin, & Temkin, (1967).Google Scholar
Edelstein, L. (1933) ‘Empirie und Skepsis in der Lehre der griechischen Empirikerschule’, Quellen und Studien zur Geschichte der Naturwissenschaften und der Medizin 3; Engl. transl. in Temkin, & Temkin, (1967).Google Scholar
Edelstein, L. (1952) ‘The relation of ancient philosophy to medicine’, BHM 26 ; repr. in Temkin, & Temkin, (1967).Google ScholarPubMed
Fowler, D. P. (1984) ‘Sceptics and Epicureans’, OSAP 2.Google Scholar
Franco Repellini, F. (1985) ‘Ipparco e la tradizione astronomica’, in Giannantoni & Vegetti (1985).Google Scholar
Fraser, P. M. (1969) ‘The career of Erasistratus of Ceos’, RIL 103.Google Scholar
Frede, M. (1986a) ‘Philosophy and medicine in antiquity’, in Donagan, A., Perovich, A. N. & Wedin, M. V., edd., Human Nature and Natural Knowledge, Essays Presented to Marjorie Grene (Dordrecht) 211–32; repr. in Frede (1987a).Google Scholar
Frede, M. (1987b) ‘The ancient empiricists’, in Frede (1987a).Google Scholar
Frede, M. (1988) ‘The empiricist attitude towards reason and theory’, in Hankinson (1988c).Google Scholar
Frede, M. (1990) ‘An empiricist view of knowledge: memorism’, in Everson (1990a).Google Scholar
Freytag, W. (1995) Mathematische Grundbegriffe bei Sextus Empiricus, Spudasmata 57 (Hildesheim).
Furley, D. J. (1967) Two Studies in the Greek Atomists, 1. Indivisible Magnitudes. 2. Aristotle and Epicurus on Voluntary Action (Princeton).Google Scholar
Furley, D. J. (1985) ‘Strato's theory of the void’, in Wiesner (1985–7) I.Google Scholar
Furley, D. J. & Wilkie, J. S. (1984) Galen on Respiration and the Arteries (Princeton).Google Scholar
Gallo, I., ed. (1980) Frammenti biografici da papiri II: La biografia dei filosofi (Rome).Google Scholar
Gigante, M. (1981) Scetticismo e epicureismo. Per l'avviamento di un discorso storiografico, Elenchos 4 (Naples).Google Scholar
Glidden, D. K. (1983a) ‘Skeptic semiotics’, Phronesis 28.CrossRefGoogle Scholar
Hankinson, R. J. (1987b) ‘Causes and empiricism: a problem in the interpretation of later Greek medical method’, Phronesis 32.CrossRefGoogle Scholar
Hankinson, R. J. (1990) ‘Saying the phenomena’, Phronesis 35 (critical notice of von Staden 1989).CrossRefGoogle Scholar
Hankinson, R. J. (1995) The Sceptics (London).Google Scholar
Hintikka, J. & Remes, U. (1974) The Method of Analysis, Its Geometrical Origin and its General Significance (Dordrecht/Boston).Google Scholar
Ioppolo, A. M. (1985a) ‘L'astrologia nello stoicismo antico’, in Giannantoni, & Vegetti, (1985).Google Scholar
Kidd, I. G. (1988) Posidonius, II: The Commentary, 2 vols., Cambridge Classical Texts and Commentaries 14 A & B (Cambridge) (vol. I see Edelstein & Kidd 1972).Google Scholar
Knorr, W. R. (1976) The Evolution of the Euclidean Elements: a Study of the Theory of Incommensurable Magnitudes and its Significance for Early Greek Geometry (Dordrecht).Google Scholar
Knorr, W. R. (1982) ‘Infinity and continuity. The interaction of mathematics and philosophy in antiquity’, in Kretzmann, N., ed., Infinity and Continuity in Ancient and Medieval Thought (Ithaca/London).Google Scholar
Kudlien, F. (1964) ‘Herophilos und der Beginn der medizinischen Skepsis’, Gesnerus 21, repr. in Flashar, H., ed. (1971) Antike Medizin, Wege der Forschung (Darmstadt).Google Scholar
Kudlien, F. (1969) ‘Antike Anatomie und menschlicher Leichnam’, Hermes 97.Google Scholar
Lloyd, G. E. R. (1964) ‘Experiment in early Greek philosophy and medicine’, PCPhS n.s. 10 ; repr. in Lloyd, (1991a).Google Scholar
Lloyd, G. E. R. (1975) ‘A note on Erasistratus of Ceos’, JHS 95.CrossRefGoogle Scholar
Lloyd, G. E. R. (1991b) ‘Galen on Hellenistics and Hippocrateans: contemporary battles and past authorities’, in Lloyd, (1991a) ; also pr. in Kollesch & Nickel (1993).Google Scholar
Long, A. A. (1982a) ‘Astrology: arguments pro and contra’, in Barnes et al. (1982a).Google Scholar
Lonie, I. M. (1964) ‘Erasistratus, the Erasistrateans, and Aristotle’, BHM 38.Google ScholarPubMed
Mansfeld, J. (1978) ‘Zeno of Citium’, Mnemosyne 31.CrossRefGoogle Scholar
Mansfeld, J. (1983a) ‘Intuitionism and formalism: Zeno's definition of geometry in a fragment of L. Calvenus Taurus’, Phronesis 28.CrossRefGoogle Scholar
Mansfeld, J. (1989c) ‘Chrysippus and the Placita’, Phronesis 34.CrossRefGoogle Scholar
Mansfeld, J. (1990a) ‘Doxography and dialectic: The Sitz im Leben of the “Placita”’, in Haase, W., ed., ANRW 11 36.4 (Berlin/New York).Google Scholar
Marelli, C. (1981) ‘La medicina empirica ed il suo sistema epistemologico’, in Giannantoni, (1981a) II.
Matthen, M. (1988a) ‘Empiricism and ontology in ancient medicine’, in Hankinson, (1988c).Google Scholar
Mudry, Ph. (1982) La préface du De Medicina de Celse, Bibliotheca Helvetica Romana 19 (Rome).Google Scholar
Mudry, Ph. (1990) ‘Le scepticisme des médecins empiriques dans le traité De la médecine de Celse: modèles et modalités’, in Le scepticisme antique: perspectives historiques et systématiques, Cahiers de la Revue de théologie et de philosophie 15.Google Scholar
Mueller, I. (1974) ‘Greek mathematics and Greek logic’, in Corcoran, J., ed., Ancient Logic and its Modern Interpretation (Dordrecht/Boston).Google Scholar
Mueller, I. (1981) Philosophy of Mathematics and Deductive Structure in Euclid’s Elements (Cambridge, Mass.).Google Scholar
Mueller, I. (1982) ‘Geometry and Scepticism’, in Barnes, et al. (1982a).Google Scholar
Neugebauer, O. (1975) A History of Ancient Mathematical Astronomy, 3 vols. (Berlin).CrossRefGoogle Scholar
Pohlenz, M. (1967) La Stoa [trad. it.] (Florence).Google Scholar
Repici, L. (1990) ‘L' epiglottide nell’ antichità tra medicina e filosofia’, HPLS 12.Google Scholar
Robinson, R. (1969) Essays in Greek Philosophy (Oxford).Google Scholar
Romeo, C. (1979) ‘Demetrio Lacone sulla grandezza del sole (PHerc. 1013)’, CErc 9.Google Scholar
Scarborough, J. (1985) ‘Erasistratus, student of Theophrastus?’, BHM 59.Google ScholarPubMed
Sedley, D. N. (1976b) ‘Epicurus and the mathematicians of Cyzicus’, CErc 6.Google Scholar
Solmsen, F. (1942) ‘Eratosthenes as Platonist and poet’, TAPhA 73.Google Scholar
Solmsen, F. (1961) ‘Greek philosophy and the discovery of the nerves’, MH 18 ; repr. in Solmsen, (1968–82) 1.Google Scholar
Steckerl, F. (1958) The Fragments of Praxagoras of Cos and His School, PhA 8 (Leiden).Google Scholar
Szabó, A. (1960) ‘Anfänge des euklidischen Axiomensystems’, Archive for History of Exact Sciences 1.CrossRefGoogle Scholar
Szabó, A. (1969) Anfänge der griechischen Mathematik (Munich).CrossRefGoogle Scholar
Tarn, W. W. (1933) ‘Alexander and the unity of mankind’, PBA 19.Google Scholar
Tepedino Guerra, A., ed. (1991) Polieno: Frammenti, La scuola di Epicuro 11 (Naples).Google Scholar
Tieleman, T. L. (1996) Galen and Chrysippus on the Soul, Argument and Refutation in the De Placitis Books II–III, PhA 68 (Leiden).Google Scholar
Vallance, J. T. (1990) The Lost Theory of Asclepiades of Bithynia (Oxford).CrossRefGoogle Scholar
Vegetti, M. (1993) ‘I nervi dell' anima’, in ,Kollesch & Nickel (1993).Google Scholar
Viano, C. A. (1981) ‘Lo scetticismo antico e la medicina’, in Giannantoni, (1981a) II.
Vlastos, G. (1966) ‘Zeno of Sidon as a critic of Euclid’, in Wallach, L., ed., The Classical Tradition, Literary and Historical Studies in Honor of Harry Caplan (Ithaca) ; repr. in Graham, (1995).Google Scholar
Walzer, R. & Frede, M., edd. (1985) Galen. Three Treatises On the Nature of Science, 3 vols. (Indianapolis).Google Scholar
White, M. J. (1992) The Continuous and the Discrete, Ancient Physical Theories from a Contemporary Perspective (Oxford).CrossRefGoogle Scholar
Wolff, M. (1988) ‘Hipparchus and the Stoic theory of motion’, in Barnes & Mignucci (1988a).Google Scholar

Accessibility standard: Unknown

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×