Contents
57 found
Order:
1 — 50 / 57
  1. V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics.Vandoulakis Ioannis & Alex Citkin (eds.) - 2022 - Springer. Outstanding Contributions to Logic (Volume 24).
    This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory (...)
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  2. How can a line segment with extension be composed of extensionless points?Brian Reese, Michael Vazquez & Scott Weinstein - 2022 - Synthese 200 (2):1-28.
    We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  3. On V.A. Yankov’s Hypothesis of the Rise of Greek Mathematics.Ioannis M. Vandoulakis - 2022 - In V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics. Springer, Outstanding Contributions to Logic (Volume 24). pp. 295-310.
    The paper examines the main points of Yankov’s hypothesis on the rise of Greek mathematics. The novelty of Yankov’s interpretation is that the rise of mathematics is examined within the context of the rise of ontological theories of the early Greek philosophers, which mark the beginning of rational thinking, as understood in the Western tradition.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  4. Ptolemy’s Philosophy: Mathematics as a Way of Life. By Jacqueline Feke. Princeton: Princeton University Press, 2018. Pp. xi + 234. [REVIEW]Nicholas Danne - 2020 - Metaphilosophy 51 (1):151-155.
  5. Ptolemy’s Philosophy: Mathematics as a Way of Life, written by Jacqueline Feke.Harold Tarrant - 2020 - International Journal of the Platonic Tradition 14 (1):97-98.
  6. Euclid’s Kinds and (Their) Attributes.Benjamin Wilck - 2020 - History of Philosophy & Logical Analysis 23 (2):362-397.
    Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  7. Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry.Emily Katz - 2019 - Phronesis 64 (4):465-513.
    There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  8. Ptolemy's Philosophy of Geography.Jacqueline Feke - 2018 - In René Ceceña (ed.), Claudio Ptolomeo: Geografía. Capítulos teóricos. Mexico City, CDMX, Mexico: pp. 281-326.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  9. Ptolemy's Philosophy: Mathematics as a Way of Life.Jacqueline Feke - 2018 - Princeton: Princeton University Press.
    The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. -/- In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10. XII. Aristotle’s Demonstrations and Euclid’s Elements.Richard D. McKirahan - 2017 - In Principles and Proofs: Aristotle's Theory of Demonstrative Science. Princeton University Press. pp. 144-163.
  11. Meta-mathematical Rhetoric: Hero and Ptolemy against the Philosophers.Jacqueline Feke - 2014 - Historia Mathematica 41 (3):261-276.
    Bringing the meta-mathematics of Hero of Alexandria and Claudius Ptolemy into conversation for the first time, I argue that they employ identical rhetorical strategies in the introductions to Hero’s Belopoeica, Pneumatica, Metrica and Ptolemy’s Almagest. They each adopt a paradigmatic argument, in which they criticize the discourses of philosophers and declare epistemological supremacy for mathematics by asserting that geometrical demonstration is indisputable. The rarity of this claim—in conjunction with the paradigmatic argument—indicates that Hero and Ptolemy participated in a single meta-mathematical (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  12. Geometrical First Principles in Proclus’ Commentary on the First Book of Euclid’s Elements.D. Gregory MacIsaac - 2014 - Phronesis 59 (1):44-98.
    In his commentary on Euclid, Proclus says both that the first principle of geometry are self-evident and that they are hypotheses received from the single, highest, unhypothetical science, which is probably dialectic. The implication of this seems to be that a geometer both does and does not know geometrical truths. This dilemma only exists if we assume that Proclus follows Aristotle in his understanding of these terms. This paper shows that this is not the case, and explains what Proclus himself (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  13. Aristotle and euclid's postulates.Fabio Acerbi - 2013 - Classical Quarterly 63 (2):680-685.
    Book 1 of Euclid's Elements opens with a set of unproved assumptions: definitions, postulates, and ‘common notions’. The common notions are general rules validating deductions that involve the relations of equality and congruence. The attested postulates are five in number, even if a part of the manuscript tradition adds a sixth, almost surely spurious, that in some manuscripts features as the ninth, and last, common notion. The postulates are called αἰτήματα both in the manuscripts of the Elements and in the (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  14. Aristotle's philosophy of mathematics.David Bostock - 2012 - In Christopher Shields (ed.), The Oxford Handbook of Aristotle. Oup Usa. pp. 465.
    Much of Aristotle's thought developed in reaction to Plato's views, and this is certainly true of his philosophy of mathematics. To judge from his dialogue, the Meno, the first thing that struck Plato as an interesting and important feature of mathematics was its epistemology: in this subject we can apparently just “draw knowledge out of ourselves.” Aristotle certainly thinks that Plato was wrong to “separate” the objects of mathematics from the familiar objects that we experience in this world. His main (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  15. Aristotle on Mathematical Truth.Phil Corkum - 2012 - British Journal for the History of Philosophy 20 (6):1057-1076.
    Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  16. What Can We Know of What the Romans Knew? Comments on Daryn Lehoux’s What Did the Romans Know? An Inquiry into Science and Worldmaking.Jacqueline Feke - 2012 - Expositions: Interdisciplinary Studies in the Humanities 6 (2):23-32.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  17. Imagination as Self-knowledge: Kepler on Proclus' Commentary on the First Book of Euclid's Elements.Guy Claessens - 2011 - Early Science and Medicine 16 (3):179-199.
    The Neoplatonist Proclus, in his commentary on Euclid's Elements, appears to have been the first to systematically cut imagination's exclusive ties with the sensible realm. According to Proclus, in geometry discursive thinking makes use of innate concepts that are projected on imagination as on a mirror. Despite the crucial role of Proclus' text in early modern epistemology, the concept of a productive imagination seems almost not have been received. It was generally either transplanted into an Aristotelian account of mathematics or (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  18. Aristotle’s prohibition rule on kind-crossing and the definition of mathematics as a science of quantities.Paola Cantù - 2010 - Synthese 174 (2):225-235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  19. Amazing Traces of a Babylonian Origin in Greek Mathematics. [REVIEW]Sabetai Unguru - 2008 - Isis 99:821-822.
  20. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History; The Mathematics of Plato’s Academy: A New Reconstruction. [REVIEW]J. Bergen - 2003 - Isis 94:134-136.
  21. Pappus Of Alexandria And The Mathematics Of Late Antiquity. [REVIEW]Ali Behboud - 2002 - Isis 93:102-103.
    Greek mathematics is usually seen as having reached its height in a “golden age” around 300 b.c., after which it declined, reaching a rather sad stage in late antiquity. In this latter period Pappus of Alexandria stands out as one of the last competent mathematicians, although even his Mathematical Collection has been valued by historians mainly for its wealth of information on earlier mathematical achievements. In her readable book, Serafina Cuomo sets out to correct the conventional view of mathematics in (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  22. Existence, substantiality, and counterfactuality Observations on the status of mathematics according to Aristotle, Euclid, and others.Jens Høyrup - 2002 - Centaurus 44 (1-2):1-31.
  23. The Ancient Tradition of Geometric Problems by Wilbur Richard Knorr; Textual Studies in Ancient and Medieval Geometry by Wilbur Richard Knorr. [REVIEW]Thomas Drucker - 1991 - Isis 82:718-720.
  24. Pythagoras Revived: Mathematics and Philosophy in Late Antiquity by Dominic J. O'Meara. [REVIEW]Alexander Jones - 1991 - Isis 82:364-365.
  25. War, Mathematics, and Art in Ancient Greece.John Onians - 1989 - History of the Human Sciences 2 (1):39-62.
  26. L'architecture Du Divin: Mathematique Et Philosophie Chez Plotin Et Proclus By Annick Charles-saget. [REVIEW]Ian Mueller - 1984 - Isis 75:415-415.
  27. Intelligible Matter and Geometry in Aristotle.Joe F. Jones Iii - 1983 - Apeiron 17 (2):94 - 102.
  28. The Geometry of Burning-Mirrors in Antiquity.Wilbur Knorr - 1983 - Isis 74:53-73.
  29. Philosophy of Mathematics and Deductive Structure in Euclid's Elements by Ian Mueller. [REVIEW]Erwin Neuenschwander - 1983 - Isis 74:124-126.
  30. Archimedes on the Dimensions of the Cosmos.Catherine Osborne - 1983 - Isis 74 (2):234-242.
  31. Aristotle’s Philosophy of Mathematics.Jonathan Lear - 1982 - Philosophical Review 91 (2):161-192.
    Whether aristotle wrote a work on mathematics as he did on physics is not known, and sources differ. this book attempts to present the main features of aristotle's philosophy of mathematics. methodologically, the presentation is based on aristotle's "posterior analytics", which discusses the nature of scientific knowledge and procedure. concerning aristotle's views on mathematics in particular, they are presented with the support of numerous references to his extant works. his criticism of his predecessors is added at the end.
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   52 citations  
  32. The Beginnings of Greek Mathematics by Árpád Szabó; A. M. Ungar; Les débuts des mathématiques grecques by Árpád Szabó; M. Federspiel. [REVIEW]Wilbur Knorr - 1981 - Isis 72:135-136.
  33. Thekla Horowitz: Vom Logos zur Analogic Die Geschichte eines mathematischen Terminus. Pp. 198. Zurich: Hans Rohr, 1978. Paper. [REVIEW]Ivor Bulmer-Thomas - 1980 - The Classical Review 30 (2):318-318.
  34. Archimedes in the Middle Ages. Volume II: The Translations from the Greek by William of Moerbeke by Marshall Clagett. [REVIEW]Menso Folkerts - 1979 - Isis 70:611-612.
  35. History of Ancient Mathematics--Some Reflections on the State of the Art.Sabetai Unguru - 1979 - Isis 70:555-565.
  36. The Philosophical Sense of Theaetetus' Mathematics.M. Burnyeat - 1978 - Isis 69:489-513.
  37. To the Editor.John N. Harris - 1977 - Isis 68 (4):616-617.
  38. The Secrets of Ancient Geometry--And Its Uses by Tons Brunés; Charles M. Napier. [REVIEW]H. Coxeter - 1973 - Isis 64:402-404.
  39. Proclus: A Commentary on the First Book of Euclid's Elements.Glenn R. Morrow (ed.) - 1970 - Princeton University Press.
    In Proclus' penetrating exposition of Euclid's method's and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strenght of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   11 citations  
  40. Greek Mathematical Thought and the Origin of Algebra by Jacob Klein. [REVIEW]C. Scriba - 1970 - Isis 61:132-133.
  41. Intelligible Matter and the Objects of Mathematics in Aristotle.Thomas C. Anderson - 1969 - New Scholasticism 43 (1):1-28.
  42. Greek Mathematical Philosophy by Edward A. Maziarz; Thomas Greenwood. [REVIEW]H. Gericke - 1969 - Isis 60:406-406.
  43. The Significance of Some Basic Mathematical Conceptions for Physics.Salomon Bochner - 1963 - Isis 54:179-205.
  44. Anthemius of Tralles: A Study in Later Greek Geometry by G. L. Huxley. [REVIEW]J. Scott - 1961 - Isis 52:592-593.
  45. Methodological superiority of Aristotle over euclid.H. G. Apostle - 1958 - Philosophy of Science 25 (2):131-134.
    If we were to name the two greatest mathematicians of antiquity, we would probably choose Archimedes and Euclid. The first excelled in research, the second in synthesis or system. The synthesis or system is closely associated with the theory or philosophy of that subject; and Euclid's Elements, which has been characterized as “one of the noblest monuments of antiquity”, is the best concrete instance of the theory of mathematics according to the ancient Greeks. Now Aristotle had a theory of mathematics, (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  46. Filosofía de la Matemática en Aristóteles.Diego Pro - 1956 - Sapientia 11 (39):78.
  47. Aristotle on Mathematical Constructibility.Thomas Greenwood - 1954 - The Thomist 17:84.
  48. Aristotle's philosophy of mathematics.Hippocrates George Apostle - 1952 - [Chicago]: University of Chicago Press.
  49. Euclid and Aristotle.Thomas Greenwood - 1952 - The Thomist 15:374.
    The work of Euclid is situated in the Aristotelian rather than the Platonic perspective, although it incorporates the methodological results of both. The Alexandrian mathematician stamped with an Aristotelian seal the whole system of Greek mathematics.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  50. De Pythagore à Euclide. Contribution à l'histoire des mathématiques preeuclidiennes by Paul-Henri Michel. [REVIEW]Carl Boyer - 1951 - Isis 42:61-63.
1 — 50 / 57