Index Nominum (Biographical Register)¶
* Catalogus Auctorum, Philosophorum et Mathematicorum *
This biographical register catalogues all 83 philosophers, mathematicians, physicists, and classical commentators referenced across Father Peter Hoenen, S.J.’s De Noetica Geometriae: Origine Theoriae Cognitionis (1954). Every :person: reference in both the Latin and English editions links directly to its entry below, and each entry provides biographical context, cited works linked to the Systematic Bibliography, and exact back-links (LA · EN) to every occurrence in the text.
Alphabetical Directory¶
A¶
Albert Einstein (1879 – 1955) — Theoretical Physicist
Albert the Great, St., O.P. (c. 1200 – 1280) — Scholastic Philosopher & Doctor of the Church
Alexander of Aphrodisias (fl. c. 200 AD) — Peripatetic Commentator
Alfred Edward Taylor (1869 – 1945) — British Idealist Philosopher & Plato Scholar
Alfred North Whitehead (1861 – 1947) — British Mathematician & Process Philosopher
Alois Riehl (1844 – 1924) — Austrian-German Neo-Kantian Philosopher
Anicius Manlius Severinus Boethius (c. 477 – 524 AD) — Roman Christian Philosopher & Translator
Anneliese Maier (1905 – 1971) — German Historian of Late Medieval Science & Philosophy
Aristotle (384 – 322 BC) — Ancient Greek Philosopher (The Stagirite)
August Ferdinand Möbius (1790 – 1868) — German Mathematician & Astronomer
Aurel Voss (1845 – 1931) — German Mathematician
B¶
Bernard Lonergan, S.J. (1904 – 1984) — Jesuit Philosopher & Theologian
Bertrand Russell (1872 – 1970) — British Philosopher, Logician & Mathematician
C¶
Carl Friedrich Gauss (1777 – 1855) — German Mathematician & Physicist (Princeps Mathematicorum)
Charles-Jean de la Vallée Poussin (1866 – 1962) — Belgian Mathematician
Clemens Baeumker (1853 – 1924) — Historian of Ancient & Medieval Philosophy
D¶
David Hilbert (1862 – 1943) — German Mathematician & Leader of Formalism
David Hume (1711 – 1776) — Scottish Empiricist Philosopher
Désiré-Joseph Cardinal Mercier (1851 – 1926) — Belgian Neo-Scholastic Philosopher & Founder of the Louvain Institute
E¶
Eduard Study (1862 – 1930) — German Mathematician
Euclid of Alexandria (fl. c. 300 BC) — Ancient Greek Geometer
Eudoxus of Cnidus (c. 408 – c. 355 BC) — Ancient Greek Mathematician & Astronomer
Eugenio Beltrami (1835 – 1900) — Italian Mathematician
Émile Meyerson (1859 – 1933) — Polish-born French Philosopher of Science & Epistemologist
Étienne Gilson (1884 – 1978) — French Thomistic Philosopher & Historian of Medieval Philosophy
F¶
Federigo Enriques (1871 – 1946) — Italian Geometer & Philosopher of Science
Felix Hausdorff (1868 – 1942) — German Mathematician & Founder of General Topology
Felix Klein (1849 – 1925) — German Mathematician
Ferdinand Gonseth (1890 – 1975) — Swiss Mathematician & Philosopher of Science
Friedrich Adolf Trendelenburg (1802 – 1872) — German Philosopher & Aristotle Scholar
G¶
Georg Cantor (1845 – 1918) — German Mathematician & Creator of Set Theory
Georg Wilhelm Friedrich Hegel (1770 – 1831) — German Idealist Philosopher
George Berkeley (1685 – 1753) — Anglo-Irish Empiricist Philosopher
Gerhard Hessenberg (1874 – 1925) — German Mathematician & Neo-Friesian Philosopher
Gerhard Stammler (1898 – 1977) — German Philosopher of Mathematics & Logic
Giuseppe Peano (1858 – 1932) — Italian Mathematician & Logician
Godfrey Harold Hardy (1877 – 1947) — British Mathematician
Gottfried Wilhelm Leibniz (1646 – 1716) — German Polymath, Philosopher & Mathematician
H¶
Hans Freudenthal (1905 – 1990) — German-Dutch Mathematician
Hans Reichenbach (1891 – 1953) — German Philosopher of Science & Logical Empiricist
Heinrich Martin Weber (1842 – 1913) — German Mathematician
Heinrich Scholz (1884 – 1956) — German Logician, Philosopher & Historian of Mathematics
Helmut Hasse (1898 – 1979) — German Mathematician
Henri Carteron (1891 – 1927) — French Historian of Ancient Philosophy
Henri Poincaré (1854 – 1912) — French Mathematician, Physicist & Philosopher of Science
Hermann Bonitz (1814 – 1888) — Classical Philologist & Aristotle Scholar
Hermann von Helmholtz (1821 – 1894) — German Physicist, Physiologist & Philosopher of Science
Hermann Weyl (1885 – 1955) — German Mathematician & Mathematical Physicist
I¶
Immanuel Kant (1724 – 1804) — German Critical Philosopher
J¶
Jacques Hadamard (1865 – 1963) — French Mathematician
John Burnet (1863 – 1928) — Scottish Classical Scholar
John Locke (1632 – 1704) — English Empiricist Philosopher
John Philoponus (c. 490 – c. 570 AD) — Alexandrian Christian Philosopher & Aristotelian Commentator
John Stuart Mill (1806 – 1873) — British Empiricist Philosopher
Josef Wellstein (1869 – 1919) — German Mathematician
Joseph Geyser (1869 – 1948) — German Neo-Scholastic Philosopher
José Alvarez Laso, C.M.F. (1910 – 1993) — Thomistic Philosopher of Mathematics
L¶
Louis Couturat (1868 – 1914) — French Logician & Philosopher of Mathematics
Luitzen Egbertus Jan Brouwer (1881 – 1966) — Dutch Mathematician & Founder of Intuitionism
Léon Brunschvicg (1869 – 1944) — French Idealist Philosopher & Historian of Mathematics
M¶
Moritz Pasch (1843 – 1930) — German Mathematician
O¶
Octave Hamelin (1856 – 1907) — French Philosopher & Aristotle Scholar
Oskar Becker (1889 – 1964) — Phenomenologist & Historian of Ancient Mathematics
Otto Hölder (1859 – 1937) — German Mathematician
P¶
Parmenides of Elea (fl. early 5th century BC) — Pre-Socratic Eleatic Philosopher
Petrus Hubertus Jacobus Hoenen, S.J. (1880 – 1961) — Jesuit Philosopher of Science & Mathematics
Plato (428/427 – 348/347 BC) — Ancient Greek Philosopher
Proclus Lycius Diadochus (412 – 485 AD) — Neoplatonic Philosopher & Commentator on Euclid
Protagoras of Abdera (c. 490 – c. 420 BC) — Greek Sophist
Pythagoras of Samos (c. 570 – c. 495 BC) — Ancient Greek Philosopher & Geometer
R¶
René Descartes (1596 – 1650) — French Philosopher & Mathematician
S¶
Simplicius of Cilicia (c. 490 – c. 560 AD) — Neoplatonic Commentator on Aristotle
Sir Isaac Newton (1642 – 1727) — English Mathematician & Natural Philosopher
Sir Thomas Little Heath (1861 – 1940) — British Historian of Ancient Greek Mathematics
Sir William David Ross (1877 – 1971) — Scottish Philosopher & Aristotle Scholar
St. Thomas Aquinas, O.P. (1225 – 1274) — Scholastic Philosopher & Theologian (Doctor Angelicus)
T¶
Theaetetus of Athens (c. 417 – c. 369 BC) — Ancient Greek Mathematician
Themistius (c. 317 – c. 388 AD) — Late Antique Rhetorician & Aristotelian Commentator
Theodor Waitz (1821 – 1864) — German Philosopher, Psychologist & Philologist
Thomas de Vio Cajetan, Cardinal, O.P. (1469 – 1534) — Renaissance Thomistic Commentator
U¶
Ugo Amaldi (1875 – 1957) — Italian Mathematician
W¶
Wilhelm Killing (1847 – 1923) — German Mathematician
Wilhelm von Christ (1831 – 1906) — German Classical Philologist
Biographical Entries & Textual Concordance¶
Albert Einstein (1879 – 1955)¶
Role: Theoretical Physicist
Biographical & Philosophical Note: Creator of special and general relativity; his 1921 lecture ‘Geometrie und Erfahrung’ famously distinguished purely axiomatic geometry from practical physical geometry.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Geometrie und Erfahrung (1921) · Geometrie und Erfahrung (1921)
Occurrences in De Noetica Geometriae (9): Caput I: § 3. (LA · EN) | Caput II: 3. (LA · EN) | Caput V: B) (LA · EN) | Caput VI: B) (LA · EN), B) (LA · EN), n. 3 (LA · EN) | Appendix: § 5. (LA · EN), § 5. (LA · EN), § 5. (LA · EN)
Albert the Great, St., O.P. (c. 1200 – 1280)¶
Role: Scholastic Philosopher & Doctor of the Church
Biographical & Philosophical Note: Dominican friar, bishop, and teacher of Thomas Aquinas whose commentaries on Aristotle’s Organon and Mathematics shaped medieval scholastic epistemology.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Commentaria in Analytica Priora
Occurrences in De Noetica Geometriae (2): Caput IV: § 7. (LA · EN) | Caput V: 1. (LA · EN)
Alexander of Aphrodisias (fl. c. 200 AD)¶
Role: Peripatetic Commentator
Biographical & Philosophical Note: Foremost ancient Greek commentator on Aristotle, known in antiquity and the Middle Ages simply as ‘The Commentator’ before Averroes.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: In Aristotelis Metaphysica Commentaria
Occurrences in De Noetica Geometriae (1): Appendix: § 1. (LA · EN)
Alfred Edward Taylor (1869 – 1945)¶
Role: British Idealist Philosopher & Plato Scholar
Biographical & Philosophical Note: Professor of Moral Philosophy at St Andrews and Edinburgh, renowned for his commentary on Plato’s Timaeus and comprehensive study of Plato’s dialogues.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Plato: The Man and His Work (1927)
Occurrences in De Noetica Geometriae (1): Caput IV: n. 8 (LA · EN)
Alfred North Whitehead (1861 – 1947)¶
Role: British Mathematician & Process Philosopher
Biographical & Philosophical Note: Co-author with Bertrand Russell of Principia Mathematica and creator of the method of extensive abstraction for deriving geometric points and instants from overlapping physical events.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: Principia Mathematica (with B. Russell, 1910–1913) · A Treatise on Universal Algebra (1898) · An Enquiry Concerning the Principles of Natural Knowledge (1919)
Occurrences in De Noetica Geometriae (2): Caput V: A) (LA · EN), B) (LA · EN)
Alois Riehl (1844 – 1924)¶
Role: Austrian-German Neo-Kantian Philosopher
Biographical & Philosophical Note: Representative of critical realism within Neo-Kantianism whose essays on logic and epistemology are cited by Hoenen.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Logik und Erkenntnistheorie (Die Kultur der Gegenwart, 1921)
Occurrences in De Noetica Geometriae (1): Caput V: B) (LA · EN)
Anicius Manlius Severinus Boethius (c. 477 – 524 AD)¶
Role: Roman Christian Philosopher & Translator
Biographical & Philosophical Note: Late antique philosopher whose treatise De Trinitate occasioned Thomas Aquinas’s celebrated commentary on the division and methods of the speculative sciences.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: De Trinitate · De Institutione Arithmetica · De Consolatione Philosophiae
Occurrences in De Noetica Geometriae (1): Appendix: § 7. (LA · EN)
Anneliese Maier (1905 – 1971)¶
Role: German Historian of Late Medieval Science & Philosophy
Biographical & Philosophical Note: Archival scholar at the Vatican Library whose groundbreaking studies illuminated fourteenth-century Scholastic natural philosophy and mathematics.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: An der Grenze von Scholastik und Naturwissenschaft (1943)
Edition Pages: pp. 286
Aristotle (384 – 322 BC)¶
Role: Ancient Greek Philosopher (The Stagirite)
Biographical & Philosophical Note: Founder of the Peripatetic school and formal logic, whose theory of demonstrative science (Analytica Posteriora), abstraction (τὰ ἐξ ἀφαιρέσεως), and intelligible matter (ὕλη νοητή) originates classical geometric epistemology.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Analytica Posteriora (Posterior Analytics) · Analytica Priora (Prior Analytics) · De Anima (On the Soul) · Ethica Nicomachea (Nicomachean Ethics) · Metaphysica (Metaphysics) · De Interpretatione (Peri Hermeneias) · Physica (Physics)
Occurrences in De Noetica Geometriae (143): Caput I: CAPUT I (LA · EN), CAPUT I (LA · EN), CAPUT I (LA · EN), CAPUT I (LA · EN), CAPUT I (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 4. (LA · EN), § 5. (LA · EN), § 5. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), n. 1 (LA · EN) | Caput II: Animadversiones praeviae. (LA · EN), 1. (LA · EN), 5. (LA · EN), 6. (LA · EN), 3. (LA · EN), 3. (LA · EN), 4. (LA · EN), 2. (LA · EN), 2. (LA · EN), 2. (LA · EN), § 4. (LA · EN), 2. (LA · EN), 3. (LA · EN), 3. (LA · EN) | Caput III: A) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), 1. (LA · EN), B) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), B) (LA · EN), B) (LA · EN), 7. (LA · EN) | Caput IV: § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), 4. (LA · EN), 9. (LA · EN), § 6. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), n. 30 (LA · EN) | Caput V: 2. (LA · EN), 2. (LA · EN), 2. (LA · EN), 2. (LA · EN), 2. (LA · EN), 3. (LA · EN), § 2. (LA · EN), 1. (LA · EN), 1. (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), 2. (LA · EN), 2. (LA · EN), 3. (LA · EN), B) (LA · EN), C) (LA · EN), C) (LA · EN), C) (LA · EN), B) (LA · EN), n. 3 (LA · EN), n. 5 (LA · EN) | Caput VI: B) (LA · EN), 1. (LA · EN), 1. (LA · EN) | Caput VII: § 1. (LA · EN), § 1. (LA · EN), 2. (LA · EN), 2. (LA · EN), 3. (LA · EN), 3. (LA · EN), n. 1 (LA · EN) | Appendix: § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), Recapitulatio. (LA · EN), Recapitulatio. (LA · EN), § 5. (LA · EN), § 5. (LA · EN), § 5. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), Additiones (LA · EN), Additiones (LA · EN), n. 5 (LA · EN), n. 18 (LA · EN)
August Ferdinand Möbius (1790 – 1868)¶
Role: German Mathematician & Astronomer
Biographical & Philosophical Note: Pioneer of projective geometry and topology; discovered the non-orientable one-sided surface (folium Moebii / Möbius strip), which Hoenen analyzes in detail in Caput III.
Principal Works: Der barycentrische Calcul (1827) · Über die Bestimmung des Inhaltes eines Polyëders (1865)
Occurrences in De Noetica Geometriae (6): Caput II: 6. (LA · EN), 6. (LA · EN), 1. (LA · EN), 3. (LA · EN), n. 10 (LA · EN) | Caput III: 4. (LA · EN)
Aurel Voss (1845 – 1931)¶
Role: German Mathematician
Biographical & Philosophical Note: Differential geometer at Munich who authored influential philosophical surveys on the nature of mathematical knowledge.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Über die mathematische Erkenntnis (Die Kultur der Gegenwart, 1914)
Occurrences in De Noetica Geometriae (2): Caput III: 4. (LA · EN), 4. (LA · EN)
Bernard Lonergan, S.J. (1904 – 1984)¶
Role: Jesuit Philosopher & Theologian
Biographical & Philosophical Note: Studied under Hoenen at the Gregorian University; his Verbum articles (1946–1949) and Insight (1957) developed Hoenen’s discovery of Aquinas’s doctrine of intellectual insight into phantasms.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: The Concept of Verbum in the Writings of St. Thomas Aquinas (1946–1949)
Edition Pages: pp. 277
Bertrand Russell (1872 – 1970)¶
Role: British Philosopher, Logician & Mathematician
Biographical & Philosophical Note: Co-author of Principia Mathematica and leading proponent of logicism, who defined pure mathematics as the class of all formal implications ‘p implies q’ containing only logical constants and variables.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: The Principles of Mathematics (1903) · The Principles of Mathematics (1903)
Occurrences in De Noetica Geometriae (15): Caput III: B) (LA · EN) | Caput IV: § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 3. (LA · EN), 8. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN) | Caput V: A) (LA · EN), B) (LA · EN) | Caput VI: B) (LA · EN) | Caput VII: § 1. (LA · EN)
Carl Friedrich Gauss (1777 – 1855)¶
Role: German Mathematician & Physicist (Princeps Mathematicorum)
Biographical & Philosophical Note: Developed the intrinsic differential geometry of curved surfaces and privately discovered non-Euclidean geometry, questioning the a priori necessity of Euclidean space.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Werke
Occurrences in De Noetica Geometriae (3): Caput IV: 9. (LA · EN), § 5. (LA · EN), n. 19 (LA · EN)
Charles-Jean de la Vallée Poussin (1866 – 1962)¶
Role: Belgian Mathematician
Biographical & Philosophical Note: Professor at Louvain who proved the Prime Number Theorem independently of Hadamard and authored the classic Cours d’Analyse Infinitésimale.
Principal Works: Cours d’Analyse Infinitésimale (1903)
Occurrences in De Noetica Geometriae (2): Caput V: A) (LA · EN), n. 8 (LA · EN)
Clemens Baeumker (1853 – 1924)¶
Role: Historian of Ancient & Medieval Philosophy
Biographical & Philosophical Note: German Neo-Scholastic historian of philosophy whose authoritative study on the problem of matter in Greek philosophy is cited by Hoenen on Plato and Aristotle.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Das Problem der Materie in der griechischen Philosophie (1890)
Edition Pages: pp. 67
David Hilbert (1862 – 1943)¶
Role: German Mathematician & Leader of Formalism
Biographical & Philosophical Note: Author of Grundlagen der Geometrie (1899), which replaced intuitive definitions with implicit axiomatic characterization of incidence, order, congruence, parallels, and continuity.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Grundlagen der Geometrie (Foundations of Geometry, 1899 / 1930)
Occurrences in De Noetica Geometriae (26): Caput I: § 6. (LA · EN) | Caput II: 4. (LA · EN) | Caput IV: 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), § 7. (LA · EN), n. 1 (LA · EN), n. 11 (LA · EN) | Caput V: 1. (LA · EN), 3. (LA · EN), A) (LA · EN), A) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), n. 10 (LA · EN), n. 10 (LA · EN), n. 10 (LA · EN) | Caput VII: § 1. (LA · EN)
David Hume (1711 – 1776)¶
Role: Scottish Empiricist Philosopher
Biographical & Philosophical Note: Radical empiricist who attacked the exactness of Euclidean geometry in the Treatise by reducing space to discrete sensory minima (minimum visibile) incapable of infinite divisibility.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: A Treatise of Human Nature (1739–1740) · An Enquiry Concerning Human Understanding (1748)
Occurrences in De Noetica Geometriae (9): Caput II: 2. (LA · EN), 2. (LA · EN) | Caput III: A) (LA · EN), A) (LA · EN) | Appendix: § 2. (LA · EN), § 2. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN)
Désiré-Joseph Cardinal Mercier (1851 – 1926)¶
Role: Belgian Neo-Scholastic Philosopher & Founder of the Louvain Institute
Biographical & Philosophical Note: Founder of the Higher Institute of Philosophy at Louvain; Hoenen critiques Mercier’s purely conceptualist (‘analytic’) interpretation of necessary judgments.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Critériologie générale (8th ed., 1923)
Occurrences in De Noetica Geometriae (6): Caput II: B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), 6. (LA · EN), 6. (LA · EN)
Eduard Study (1862 – 1930)¶
Role: German Mathematician
Biographical & Philosophical Note: Differential and algebraic geometer at Bonn who defended scientific realism in geometry against positivism and conventionalism.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Die realistische Weltansicht und die Lehre vom Raume (1914)
Occurrences in De Noetica Geometriae (3): Caput I: § 4. (LA · EN), n. 13 (LA · EN) | Caput III: B) (LA · EN)
Euclid of Alexandria (fl. c. 300 BC)¶
Role: Ancient Greek Geometer
Biographical & Philosophical Note: Author of the Elements, whose tripartite division of first principles into Definitions (ὅροι), Postulates (αἰτήματα), and Common Notions (κοιναὶ ἔννοιαι) embodies the Aristotelian demonstrative ideal.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Elementa (The Thirteen Books of the Elements)
Occurrences in De Noetica Geometriae (65): Caput I: § 1. (LA · EN), § 3. (LA · EN), § 5. (LA · EN), n. 1 (LA · EN) | Caput III: B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), 1. (LA · EN), 1. (LA · EN), B) (LA · EN) | Caput IV: § 1. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 2. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), § 3. (LA · EN), 4. (LA · EN), 5. (LA · EN), 7. (LA · EN), 8. (LA · EN), 8. (LA · EN), 9. (LA · EN), 9. (LA · EN), 9. (LA · EN), § 5. (LA · EN), § 5. (LA · EN), § 5. (LA · EN), § 5. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN) | Caput V: 2. (LA · EN), 3. (LA · EN), 3. (LA · EN), B) (LA · EN), B) (LA · EN), 1. (LA · EN) | Caput VI: § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN) | Caput VII: § 1. (LA · EN), § 1. (LA · EN)
Eudoxus of Cnidus (c. 408 – c. 355 BC)¶
Role: Ancient Greek Mathematician & Astronomer
Biographical & Philosophical Note: Member of Plato’s Academy who created the general theory of proportions (Elements Book V) and the method of exhaustion (Book XII) to resolve the crisis of incommensurables.
Principal Works: Theory of Proportions (preserved in Euclid, Elements V)
Occurrences in De Noetica Geometriae (2): Caput I: § 1. (LA · EN), § 4. (LA · EN)
Eugenio Beltrami (1835 – 1900)¶
Role: Italian Mathematician
Biographical & Philosophical Note: Pioneer of differential geometry who constructed the first concrete Euclidean models (pseudosphere) proving the relative consistency of non-Euclidean geometry.
Principal Works: Saggio di interpretazione della geometria non-euclidea (1868)
Occurrences in De Noetica Geometriae (1): Caput IV: § 5. (LA · EN)
Federigo Enriques (1871 – 1946)¶
Role: Italian Geometer & Philosopher of Science
Biographical & Philosophical Note: Leader of the Italian school of algebraic geometry and editor of Questioni riguardanti le matematiche elementari, who analyzed the psychological and sensory origins of geometric concepts.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Questioni riguardanti le matematiche elementari
Occurrences in De Noetica Geometriae (1): Caput IV: n. 15 (LA · EN)
Felix Hausdorff (1868 – 1942)¶
Role: German Mathematician & Founder of General Topology
Biographical & Philosophical Note: Creator of the theory of topological and metric spaces (Hausdorff spaces) and author of philosophical essays on the problem of physical and geometric space.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Das Raumproblem (Annalen der Naturphilosophie, 1904)
Edition Pages: pp. 135
Felix Klein (1849 – 1925)¶
Role: German Mathematician
Biographical & Philosophical Note: Author of the Erlangen Program classifying geometries by transformation groups, and originator of the philosophical distinction between Approximationsmathematik (empirical perception bounded by a threshold) and Präzisionsmathematik (idealized limits).
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Anwendung der Differential- und Integralrechnung auf Geometrie: Eine Revision der Prinzipien (2nd ed. 1907) · Elementarmathematik vom höheren Standpunkte aus, Band II: Geometrie (3rd ed. 1925)
Occurrences in De Noetica Geometriae (8): Caput I: § 4. (LA · EN), § 4. (LA · EN) | Caput III: B) (LA · EN), C) (LA · EN) | Caput IV: § 5. (LA · EN), § 5. (LA · EN), n. 24 (LA · EN) | Caput V: A) (LA · EN)
Ferdinand Gonseth (1890 – 1975)¶
Role: Swiss Mathematician & Philosopher of Science
Biographical & Philosophical Note: Professor at ETH Zürich who characterized mathematical objects as idealized ‘schematic physics’ (physique de l’objet quelconque) abstracted from experimental reality.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: Les fondements des mathématiques (1926) · Les mathématiques et la réalité (1936)
Occurrences in De Noetica Geometriae (1): Caput V: 3. (LA · EN)
Friedrich Adolf Trendelenburg (1802 – 1872)¶
Role: German Philosopher & Aristotle Scholar
Biographical & Philosophical Note: Leader of the nineteenth-century Aristotelian revival in Germany, editor of De Anima, and critic of Hegelian dialectic and Kantian subjectivity.
Principal Works: Logische Untersuchungen (1840) · Elementa logices Aristoteleae (1836)
Occurrences in De Noetica Geometriae (1): Caput IV: n. 8 (LA · EN)
Georg Cantor (1845 – 1918)¶
Role: German Mathematician & Creator of Set Theory
Biographical & Philosophical Note: Founder of transfinite set theory (Mengenlehre) and the arithmetic of the continuum, whose definitions of point-sets and continuity transformed modern analysis.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: Grundlagen einer allgemeinen Mannigfaltigkeitslehre (1883) · Gesammelte Abhandlungen (1932)
Occurrences in De Noetica Geometriae (1): Caput III: B) (LA · EN)
Georg Wilhelm Friedrich Hegel (1770 – 1831)¶
Role: German Idealist Philosopher
Biographical & Philosophical Note: Architect of absolute idealism whose remarks on Euclid’s definitions and postulates in the Wissenschaft der Logik are examined by Hoenen.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Wissenschaft der Logik (Werke, 1834)
Edition Pages: pp. 164
George Berkeley (1685 – 1753)¶
Role: Anglo-Irish Empiricist Philosopher
Biographical & Philosophical Note: Bishop of Cloyne whose critique of abstract ideas and theory of sensory minima (minimum visibile) prepared Hume’s radical empiricism.
Principal Works: A Treatise Concerning the Principles of Human Knowledge (1710) · An Essay Towards a New Theory of Vision (1709)
Occurrences in De Noetica Geometriae (2): Caput III: A) (LA · EN), A) (LA · EN)
Gerhard Hessenberg (1874 – 1925)¶
Role: German Mathematician & Neo-Friesian Philosopher
Biographical & Philosophical Note: Geometer and foundational theorist known for his work on projective geometry (Desargues’s and Pascal’s theorems) and philosophical critique of mathematical axiomatics.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Kritik und System in Mathematik und Philosophie (1908)
Occurrences in De Noetica Geometriae (1): Caput II: n. 10 (LA · EN)
Gerhard Stammler (1898 – 1977)¶
Role: German Philosopher of Mathematics & Logic
Biographical & Philosophical Note: Neo-Kantian philosopher at Halle who analyzed the history of the number concept since Gauss and the logical theory of concepts, judgments, and inferences.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Begriff, Urteil, Schluss (1928) / Der Zahlbegriff seit Gauss (1926)
Edition Pages: pp. 166
Giuseppe Peano (1858 – 1932)¶
Role: Italian Mathematician & Logician
Biographical & Philosophical Note: Formulated the Peano axioms for arithmetic, symbolic mathematical logic, and the space-filling Peano curve (1890) challenging naive intuitions of dimension.
Principal Works: Arithmetices principia, nova methodo exposita (1889) · I principii di geometria logicamente esposti (1889) · Sur une courbe, qui remplit toute une aire plane (1890)
Occurrences in De Noetica Geometriae (1): Caput II: C) (LA · EN)
Godfrey Harold Hardy (1877 – 1947)¶
Role: British Mathematician
Biographical & Philosophical Note: Leading Cambridge analyst and number theorist whose 1929 essay ‘Mathematical Proof’ defended genuine intellectual insight against purely formalist symbol-games.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Mathematical Proof (Mind, 1929)
Occurrences in De Noetica Geometriae (3): Caput V: A) (LA · EN), n. 10 (LA · EN), n. 10 (LA · EN)
Gottfried Wilhelm Leibniz (1646 – 1716)¶
Role: German Polymath, Philosopher & Mathematician
Biographical & Philosophical Note: Co-inventor of the infinitesimal calculus and pioneer of symbolic logic (characteristica universalis) and analysis situs, who sought to reduce all mathematical truths to identities demonstrable via definitions.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Nouveaux Essais sur l’entendement humain (1704)
Occurrences in De Noetica Geometriae (14): Caput II: A) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), 6. (LA · EN), n. 11 (LA · EN) | Caput IV: 8. (LA · EN), 8. (LA · EN) | Caput V: n. 5 (LA · EN) | Caput VII: 2. (LA · EN)
Hans Freudenthal (1905 – 1990)¶
Role: German-Dutch Mathematician
Biographical & Philosophical Note: Topologist and historian of mathematics who engaged directly with Hoenen in Gregorianum on the roles of intuition and abstraction in the foundations of geometry.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: De fontibus geometriae in intuitione et abstractione quaerendis (Gregorianum, 1951)
Occurrences in De Noetica Geometriae (4): Caput V: 3. (LA · EN), 3. (LA · EN), 3. (LA · EN), n. 2 (LA · EN)
Hans Reichenbach (1891 – 1953)¶
Role: German Philosopher of Science & Logical Empiricist
Biographical & Philosophical Note: Founder of the Berlin Circle who analyzed relativistic spacetime geometry via ‘coordinative definitions’ (Zuordnungsdefinitionen) and critiqued geometric visualization.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Philosophie der Raum-Zeit-Lehre (1928)
Edition Pages: pp. 137
Heinrich Martin Weber (1842 – 1913)¶
Role: German Mathematician
Biographical & Philosophical Note: Algebraist and co-editor with Josef Wellstein of the Enzyklopädie der Elementarmathematik.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: Enzyklopädie der Elementarmathematik (with J. Wellstein, 1903–1915) · Lehrbuch der Algebra (1895)
Edition Pages: pp. 143, 70, 72, 73, 80
Heinrich Scholz (1884 – 1956)¶
Role: German Logician, Philosopher & Historian of Mathematics
Biographical & Philosophical Note: Founder of the Münster school of mathematical logic; co-authored with Helmut Hasse the study on the foundational crisis of Greek mathematics.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Warum haben die Griechen die Irrationalzahlen nicht aufgebaut? (1928)
Edition Pages: pp. 17
Helmut Hasse (1898 – 1979)¶
Role: German Mathematician
Biographical & Philosophical Note: Algebraist and number theorist who co-authored with Heinrich Scholz a celebrated treatise on the foundational crisis of Greek mathematics triggered by incommensurability.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: Die Grundlagenkrisis der griechischen Mathematik (with H. Scholz, 1928)
Edition Pages: pp. 17
Henri Carteron (1891 – 1927)¶
Role: French Historian of Ancient Philosophy
Biographical & Philosophical Note: Editor and translator of the Budé edition of Aristotle’s Physics and author of a study on Aristotle’s concept of force and motion.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Aristote: Physique (ed. Budé, 1926)
Occurrences in De Noetica Geometriae (1): Appendix: n. 10 (LA · EN)
Henri Poincaré (1854 – 1912)¶
Role: French Mathematician, Physicist & Philosopher of Science
Biographical & Philosophical Note: Universal mathematician and creator of algebraic topology (analysis situs) who argued that geometric axioms are neither synthetic a priori judgments nor experimental facts, but conventions (disguised definitions) guided by experience.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Dernières Pensées (1913) · La Science et l’Hypothèse (1902) · Science et Méthode (1908) · La Valeur de la Science (1905)
Occurrences in De Noetica Geometriae (29): Caput I: § 4. (LA · EN), § 4. (LA · EN), § 4. (LA · EN) | Caput III: B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), C) (LA · EN) | Caput IV: § 3. (LA · EN), § 3. (LA · EN), § 5. (LA · EN), § 6. (LA · EN) | Caput V: B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), 2. (LA · EN) | Caput VI: A. De extensione corporum. (LA · EN), A. De extensione corporum. (LA · EN), A. De extensione corporum. (LA · EN), A. De extensione corporum. (LA · EN), A. De extensione corporum. (LA · EN), A. De extensione corporum. (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), C) (LA · EN)
Hermann Bonitz (1814 – 1888)¶
Role: Classical Philologist & Aristotle Scholar
Biographical & Philosophical Note: German philologist and author of the indispensable Index Aristotelicus and commentary on Aristotle’s Metaphysics.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Aristotelis Metaphysica: Commentarius (1848–1849)
Occurrences in De Noetica Geometriae (2): Appendix: n. 5 (LA · EN), n. 13 (LA · EN)
Hermann von Helmholtz (1821 – 1894)¶
Role: German Physicist, Physiologist & Philosopher of Science
Biographical & Philosophical Note: Investigated the physiological optics of spatial perception and characterized physical geometry through the free mobility of rigid bodies (Riemann-Helmholtz space problem).
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Schriften zur Erkenntnistheorie (ed. Hertz & Schlick, 1921)
Occurrences in De Noetica Geometriae (5): Caput IV: 8. (LA · EN), 9. (LA · EN), § 5. (LA · EN), n. 13 (LA · EN) | Caput VI: § 1. (LA · EN)
Hermann Weyl (1885 – 1955)¶
Role: German Mathematician & Mathematical Physicist
Biographical & Philosophical Note: Student of Hilbert who contributed fundamentally to group representations, differential geometry, gauge theory, and the philosophy of the mathematical continuum.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Philosophie der Mathematik und Naturwissenschaft (1927)
Occurrences in De Noetica Geometriae (1): Caput I: § 4. (LA · EN)
Immanuel Kant (1724 – 1804)¶
Role: German Critical Philosopher
Biographical & Philosophical Note: Characterized geometric propositions as synthetic a priori judgments grounded in pure intuition of space as an a priori form of sensibility—a doctrine Hoenen contrasts with Aristotelian abstraction from sensible phantasms.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Kritik der reinen Vernunft (Critique of Pure Reason, 2nd ed. 1787) · Prolegomena zu einer jeden künftigen Metaphysik (1783)
Occurrences in De Noetica Geometriae (20): Caput I: § 2. (LA · EN), § 3. (LA · EN) | Caput II: Animadversiones praeviae. (LA · EN), 5. (LA · EN), 5. (LA · EN), 5. (LA · EN), 5. (LA · EN), 5. (LA · EN), 2. (LA · EN), 2. (LA · EN) | Caput III: A) (LA · EN), 7. (LA · EN) | Caput IV: § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 6. (LA · EN) | Caput VI: B) (LA · EN) | Caput VII: § 1. (LA · EN), § 1. (LA · EN) | Appendix: § 2. (LA · EN)
Jacques Hadamard (1865 – 1963)¶
Role: French Mathematician
Biographical & Philosophical Note: Leading French analyst and geometer who investigated the psychology of mathematical invention and directed the mathematical volume of the Encyclopédie Française.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Encyclopédie Française, Tome I: L’Outillage Mental (1937)
Occurrences in De Noetica Geometriae (1): Caput IV: n. 11 (LA · EN)
John Burnet (1863 – 1928)¶
Role: Scottish Classical Scholar
Biographical & Philosophical Note: Professor of Greek at St Andrews whose editions of Plato and histories of early Greek philosophy shaped twentieth-century scholarship on Platonic hypotheses.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: Greek Philosophy: Thales to Plato (1914) · Early Greek Philosophy (1892)
Occurrences in De Noetica Geometriae (1): Appendix: n. 9 (LA · EN)
John Locke (1632 – 1704)¶
Role: English Empiricist Philosopher
Biographical & Philosophical Note: Author of An Essay Concerning Human Understanding, whose conceptualist account of abstract general ideas was critiqued by Berkeley, Hume, and Leibniz.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: An Essay Concerning Human Understanding (1690)
Occurrences in De Noetica Geometriae (2): Caput V: B) (LA · EN), n. 5 (LA · EN)
John Philoponus (c. 490 – c. 570 AD)¶
Role: Alexandrian Christian Philosopher & Aristotelian Commentator
Biographical & Philosophical Note: Late antique commentator on Aristotle’s Physics and Posterior Analytics who developed the theory of three-dimensional spatial extension (διάστημα) and impetus.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: In Aristotelis Physicorum Libros Commentaria (ed. Vitelli)
Occurrences in De Noetica Geometriae (1): Appendix: § 2. (LA · EN)
John Stuart Mill (1806 – 1873)¶
Role: British Empiricist Philosopher
Biographical & Philosophical Note: Argued in A System of Logic that geometric definitions describe non-existent idealizations and that axioms are merely inductive generalizations from sensory experience.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: A System of Logic (5th ed., 1862)
Occurrences in De Noetica Geometriae (11): Caput I: § 2. (LA · EN) | Caput II: Animadversiones praeviae. (LA · EN), 5. (LA · EN), 5. (LA · EN), 2. (LA · EN), 3. (LA · EN) | Caput III: A) (LA · EN), A) (LA · EN), A) (LA · EN), A) (LA · EN), D) (LA · EN)
Josef Wellstein (1869 – 1919)¶
Role: German Mathematician
Biographical & Philosophical Note: Professor at Strasbourg and co-author with Heinrich Weber of the Enzyklopädie der Elementarmathematik, whose chapters on the foundations of geometry are extensively analyzed by Hoenen.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: Grundlagen der Geometrie (in Weber-Wellstein, Enzyklopädie der Elementarmathematik II, 1915 / 1925)
Occurrences in De Noetica Geometriae (12): Caput III: B) (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), B) (LA · EN), B) (LA · EN), 4. (LA · EN) | Caput IV: n. 6 (LA · EN), n. 26 (LA · EN)
Joseph Geyser (1869 – 1948)¶
Role: German Neo-Scholastic Philosopher
Biographical & Philosophical Note: Professor of philosophy at Münster, Freiburg, and Munich, known for his studies on Aristotelian epistemology and critical realism.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Die Erkenntnistheorie des Aristoteles (1917)
Edition Pages: pp. 14
José Alvarez Laso, C.M.F. (1910 – 1993)¶
Role: Thomistic Philosopher of Mathematics
Biographical & Philosophical Note: Claretian scholar who authored a doctoral study under Hoenen on the philosophy of mathematics in St. Thomas Aquinas.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: La Filosofía de las Matemáticas en Santo Tomás (1952)
Edition Pages: pp. 224
Louis Couturat (1868 – 1914)¶
Role: French Logician & Philosopher of Mathematics
Biographical & Philosophical Note: Champion of symbolic logic and Russellian logicism in France, editor of Leibniz’s unpublished logical manuscripts, and critic of Kantian mathematical intuition.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: La philosophie des mathématiques de Kant (Revue de Métaphysique et de Morale, 1904)
Occurrences in De Noetica Geometriae (2): Caput II: n. 3 (LA · EN) | Caput III: 4. (LA · EN)
Luitzen Egbertus Jan Brouwer (1881 – 1966)¶
Role: Dutch Mathematician & Founder of Intuitionism
Biographical & Philosophical Note: Topologist and philosopher of mathematics who founded mathematical intuitionism, grounding mathematics in the primordial intuition of time rather than formalist axioms.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Over de grondslagen der wiskunde (1907)
Occurrences in De Noetica Geometriae (2): Caput I: § 4. (LA · EN) | Caput III: B) (LA · EN)
Léon Brunschvicg (1869 – 1944)¶
Role: French Idealist Philosopher & Historian of Mathematics
Biographical & Philosophical Note: Co-founder of the Revue de Métaphysique et de Morale whose historical-critical study of mathematical philosophy is frequently examined by Hoenen.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Les étapes de la philosophie mathématique (1912)
Edition Pages: pp. 93
Moritz Pasch (1843 – 1930)¶
Role: German Mathematician
Biographical & Philosophical Note: Pioneered the rigorous axiomatization of projective and order geometry (Pasch’s Axiom), insisting that geometric deduction must proceed independently of intuitive diagrams once nuclear axioms (Kern-Sätze) are abstracted from experience.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Vorlesungen über neuere Geometrie (1882; 2nd ed. 1926) · Vorlesungen über neuere Geometrie (1882; 2nd ed. 1926)
Occurrences in De Noetica Geometriae (2): Caput II: 5. (LA · EN), 3. (LA · EN)
Octave Hamelin (1856 – 1907)¶
Role: French Philosopher & Aristotle Scholar
Biographical & Philosophical Note: French idealist philosopher and historian of ancient philosophy whose posthumous lectures on the system of Aristotle are cited by Hoenen.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Le Système d’Aristote (1920)
Edition Pages: pp. 14
Oskar Becker (1889 – 1964)¶
Role: Phenomenologist & Historian of Ancient Mathematics
Biographical & Philosophical Note: German philosopher and student of Husserl who wrote extensively on the phenomenological foundations of geometry and Eudoxian proportion theory.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Beiträge zur phänomenologischen Begründung der Geometrie (1923)
Occurrences in De Noetica Geometriae (1): Caput III: C) (LA · EN)
Otto Hölder (1859 – 1937)¶
Role: German Mathematician
Biographical & Philosophical Note: Group theorist and analyst who authored a major philosophical treatise on the mathematical method, axiomatic deduction, and genetic construction.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Die mathematische Methode (1924)
Occurrences in De Noetica Geometriae (1): Caput I: § 4. (LA · EN)
Parmenides of Elea (fl. early 5th century BC)¶
Role: Pre-Socratic Eleatic Philosopher
Biographical & Philosophical Note: Founder of the Eleatic school who affirmed the unity and immutability of Being and denied the reality of motion and division.
Principal Works: On Nature (Fragments)
Occurrences in De Noetica Geometriae (2): Appendix: § 6. (LA · EN), § 6. (LA · EN)
Petrus Hubertus Jacobus Hoenen, S.J. (1880 – 1961)¶
Role: Jesuit Philosopher of Science & Mathematics
Biographical & Philosophical Note: Professor of Cosmology and Philosophy of Mathematics at the Pontifical Gregorian University in Rome; author of De Noetica Geometriae and La théorie du jugement d’après St. Thomas d’Aquin.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: De origine primorum principiorum scientiae (Gregorianum XIV, 1933, pp. 153–184) · Le « Cogito ergo sum » comme intuition et comme mouvement de la pensée (1937) · De philosophia scholastica cognitionis geometricae (Gregorianum XIX, 1938, pp. 498–514) · De problemate necessitatis geometricae (Gregorianum XX, 1939, pp. 19–54) · De Noetica Geometriae / La théorie du jugement / Cosmologia · Recherches de logique formelle (Rome: Gregorian University, 1947) · Gregorianum XXIX (1948), pp. 295–303 · Pour une philosophie de la connaissance de l’étendu physique (Gregorianum XXX, 1949) · De noetica geometriae (Gregorianum XXXII, 1951, pp. 434–452) · De connexionibus necessariis inter actus existentiales (Gregorianum XXXIV, 1953) · De Noetica Geometriae: Origine Theoriae Cognitionis (1954 — Internal Cross-Reference) · Cosmologia (4th ed., Rome: Gregorian University, 1949) · Filosofia della natura inorganica (Milan, 1949) · Reality and Judgment According to St. Thomas (Chicago: Regnery, 1952) · La théorie du jugement d’après St. Thomas d’Aquin (1946; 2nd ed. 1953)
Edition Pages: pp. 104, 105, 13, 131, 14, 158, 159, 160, 161, 163, 166, 168, 17, 174, 176, 188, 189, 191, 192, 195, 203, 204, 205, 206, 207, 210, 211, 212, 214, 217, 219, 221, 222, 226, 232, 233, 236, 241, 242, 243, 244, 245, 246, 247, 249, 250, 256, 258, 260, 263, 264, 266, 267, 27, 270, 271, 272, 273, 274, 276, 278, 280, 282, 283, 284, 285, 286, 287, 38, 44, 45, 5, 51, 52, 53, 55, 56, 59, 6, 67, 7, 78, 83, 87, 88, 89
Plato (428/427 – 348/347 BC)¶
Role: Ancient Greek Philosopher
Biographical & Philosophical Note: Founder of the Athenian Academy; his Divided Line (Republic VI) assigned mathematical objects to discursive understanding (διάνοια) proceeding from hypotheses with the aid of visible diagrams.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Leges (The Laws) · Meno · Respublica (The Republic)
Occurrences in De Noetica Geometriae (23): Praefatio: PRAEFATIO (LA · EN) | Caput I: CAPUT I (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 2. (LA · EN) | Caput II: Animadversiones praeviae. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 5. (LA · EN), 5. (LA · EN), 2. (LA · EN), 3. (LA · EN) | Caput III: A) (LA · EN), B) (LA · EN) | Caput IV: § 6. (LA · EN), § 7. (LA · EN) | Caput V: 3. (LA · EN)
Proclus Lycius Diadochus (412 – 485 AD)¶
Role: Neoplatonic Philosopher & Commentator on Euclid
Biographical & Philosophical Note: Head of the Athenian Neoplatonic Academy whose Commentary on Book I of Euclid’s Elements is the primary ancient source on the history and philosophy of Greek geometry and imagination (φαντασία) as passive intellect.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: In Primum Euclidis Elementorum Librum Commentarii (ed. Friedlein, 1873)
Occurrences in De Noetica Geometriae (4): Caput I: § 5. (LA · EN) | Caput III: A) (LA · EN) | Caput IV: 4. (LA · EN), n. 8 (LA · EN)
Protagoras of Abdera (c. 490 – c. 420 BC)¶
Role: Greek Sophist
Biographical & Philosophical Note: Sophist who argued against geometers that sensible circles and rulers touch at more than a single indivisible point (reported by Aristotle, Metaphysics III 2, 997b35).
Principal Works: Fragments (Diels-Kranz)
Occurrences in De Noetica Geometriae (1): Caput III: n. 1 (LA · EN)
Pythagoras of Samos (c. 570 – c. 495 BC)¶
Role: Ancient Greek Philosopher & Geometer
Biographical & Philosophical Note: Founder of the Pythagorean brotherhood, which discovered the mathematical ratios of musical harmony, the Pythagorean theorem, and the incommensurability of the diagonal with the side.
Principal Works: Pythagorean Tradition
Occurrences in De Noetica Geometriae (1): Caput IV: n. 8 (LA · EN)
René Descartes (1596 – 1650)¶
Role: French Philosopher & Mathematician
Biographical & Philosophical Note: Founder of analytic geometry and modern rationalism; Hoenen critically examines both his coordinate reduction of extension and the intuitive nature of his Cogito ergo sum.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Œuvres de Descartes (ed. Adam & Tannery) · Œuvres de Descartes (ed. Adam & Tannery) · Œuvres de Descartes (ed. Adam & Tannery) · Œuvres de Descartes (ed. Adam & Tannery)
Occurrences in De Noetica Geometriae (15): Caput I: § 4. (LA · EN) | Caput II: n. 7 (LA · EN) | Caput VI: A. De extensione corporum. (LA · EN) | Appendix: § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), Recapitulatio. (LA · EN), Recapitulatio. (LA · EN), § 6. (LA · EN), Additiones (LA · EN)
Simplicius of Cilicia (c. 490 – c. 560 AD)¶
Role: Neoplatonic Commentator on Aristotle
Biographical & Philosophical Note: Student of Ammonius and Damascius whose encyclopedic commentaries on Aristotle’s Physics and De Caelo preserve crucial fragments of Eudemus, Hippocrates of Chios, and ancient geometry.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: In Aristotelis Physicorum Libros Commentaria (ed. Diels)
Occurrences in De Noetica Geometriae (2): Appendix: § 1. (LA · EN), § 2. (LA · EN)
Sir Isaac Newton (1642 – 1727)¶
Role: English Mathematician & Natural Philosopher
Biographical & Philosophical Note: Author of the Principia Mathematica and co-founder of the calculus (method of fluxions); defended absolute space and time and the kinematic generation of geometric magnitudes.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Philosophiae Naturalis Principia Mathematica (1687)
Occurrences in De Noetica Geometriae (2): Caput V: B) (LA · EN) | Appendix: § 3. (LA · EN)
Sir Thomas Little Heath (1861 – 1940)¶
Role: British Historian of Ancient Greek Mathematics
Biographical & Philosophical Note: Foremost English translator and commentator of Euclid, Archimedes, and Apollonius, whose monumental commentary on Euclid’s Elements is a primary source for Hoenen.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: The Thirteen Books of Euclid’s Elements / A History of Greek Mathematics
Edition Pages: pp. 158
Sir William David Ross (1877 – 1971)¶
Role: Scottish Philosopher & Aristotle Scholar
Biographical & Philosophical Note: Provost of Oriel College, Oxford, and general editor of the Oxford Translation of Aristotle; his critical editions and commentaries on Aristotle’s Metaphysics, Physics, and Analytics are frequently cited by Hoenen.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Aristotle’s Metaphysics (1924) / Aristotle’s Physics (1936) · Aristotle’s Metaphysics (1924) / Aristotle’s Physics (1936) · Aristotle’s Metaphysics (1924) / Aristotle’s Physics (1936)
Occurrences in De Noetica Geometriae (2): Appendix: n. 3 (LA · EN), n. 13 (LA · EN)
St. Thomas Aquinas, O.P. (1225 – 1274)¶
Role: Scholastic Philosopher & Theologian (Doctor Angelicus)
Biographical & Philosophical Note: Dominican friar and Doctor of the Church whose synthesis of Aristotelian noetics—abstraction from phantasms, intelligible matter, and judgment by resolution to sensory principles—forms the central framework of Hoenen’s treatise.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: In Aristotelis Libros Posteriorum Analyticorum Expositio · Sentencia Libri De Anima · In Libros Aristotelis De Caelo et Mundo Expositio · Quaestiones Disputatae de Malo · Quaestiones Disputatae de Potentia Dei · Expositio super Librum Boethii De Trinitate · Quaestiones Disputatae de Veritate · Sententia Libri Ethicorum · Sententia super Metaphysicam · Expositio Libri Peryermeneias · Commentaria in Octo Libros Physicorum Aristotelis · Summa contra Gentiles · Scriptum super Libros Sententiarum · Summa Theologiae
Occurrences in De Noetica Geometriae (113): Praefatio: PRAEFATIO (LA · EN) | Caput I: § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 5. (LA · EN), § 6. (LA · EN) | Caput II: Animadversiones praeviae. (LA · EN), 5. (LA · EN), 2. (LA · EN), 4. (LA · EN), 1. (LA · EN), 1. (LA · EN), 2. (LA · EN), 3. (LA · EN), 3. (LA · EN), 3. (LA · EN), 3. (LA · EN), n. 11 (LA · EN) | Caput III: A) (LA · EN), B) (LA · EN), A) (LA · EN), A) (LA · EN), B) (LA · EN), 7. (LA · EN), n. 11 (LA · EN) | Caput IV: Animadversiones praeviae. (LA · EN), Animadversiones praeviae. (LA · EN), § 2. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), n. 2 (LA · EN), n. 8 (LA · EN) | Caput V: B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), C) (LA · EN), n. 4 (LA · EN) | Caput VI: B) (LA · EN), B) (LA · EN), B) (LA · EN), B) (LA · EN), 1. (LA · EN), C) (LA · EN) | Caput VII: § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 1. (LA · EN), 2. (LA · EN), 2. (LA · EN), 2. (LA · EN), 3. (LA · EN), 3. (LA · EN), n. 1 (LA · EN) | Appendix: § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN), § 2. (LA · EN), § 3. (LA · EN), § 4. (LA · EN), Recapitulatio. (LA · EN), § 5. (LA · EN), § 5. (LA · EN), § 6. (LA · EN), § 6. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), Additiones (LA · EN), Additiones (LA · EN), Additiones (LA · EN), n. 8 (LA · EN), n. 9 (LA · EN), n. 11 (LA · EN), n. 18 (LA · EN), n. 26 (LA · EN)
Theaetetus of Athens (c. 417 – c. 369 BC)¶
Role: Ancient Greek Mathematician
Biographical & Philosophical Note: Associate of Plato’s Academy who classified quadratic irrationals (Euclid, Elements Book X) and completed the construction of the five regular polyhedra (Book XIII).
Principal Works: Theory of Irrationals & Regular Solids (in Euclid, Elements X & XIII)
Occurrences in De Noetica Geometriae (1): Caput I: § 1. (LA · EN)
Themistius (c. 317 – c. 388 AD)¶
Role: Late Antique Rhetorician & Aristotelian Commentator
Biographical & Philosophical Note: Composed lucid paraphrases of Aristotle’s Posterior Analytics, Physics, and De Anima that were widely studied by Arabic and Latin Scholastics.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: In Aristotelis Physica Paraphrasis (ed. Schenkl)
Occurrences in De Noetica Geometriae (2): Appendix: § 2. (LA · EN), n. 11 (LA · EN)
Theodor Waitz (1821 – 1864)¶
Role: German Philosopher, Psychologist & Philologist
Biographical & Philosophical Note: Edited the standard nineteenth-century critical Greek edition and Latin commentary of Aristotle’s Organon.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Aristotelis Organon Graece (1844–1846)
Edition Pages: pp. 145
Thomas de Vio Cajetan, Cardinal, O.P. (1469 – 1534)¶
Role: Renaissance Thomistic Commentator
Biographical & Philosophical Note: Master General of the Dominicans and classic commentator on the Summa Theologiae, who systematized the distinction between abstractio formalis and abstractio totalis.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Principal Works: In De Ente et Essentia Commentaria (1495) · Commentaria in Summam Theologiae
Occurrences in De Noetica Geometriae (8): Caput II: 5. (LA · EN), 6. (LA · EN), 2. (LA · EN), 2. (LA · EN), 2. (LA · EN), 3. (LA · EN), 2. (LA · EN), 3. (LA · EN)
Ugo Amaldi (1875 – 1957)¶
Role: Italian Mathematician
Biographical & Philosophical Note: Professor of mathematics in Rome and collaborator of Federigo Enriques on the foundations of elementary geometry and continuous transformation groups.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Sui concetti di retta e di piano (Questioni riguardanti le matematiche elementari)
Occurrences in De Noetica Geometriae (1): Caput IV: n. 20 (LA · EN)
Wilhelm Killing (1847 – 1923)¶
Role: German Mathematician
Biographical & Philosophical Note: Co-discoverer of Lie algebras (Killing form) and professor at Münster who wrote a comprehensive two-volume treatise on the foundations of Euclidean and non-Euclidean geometry.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Einführung in die Grundlagen der Geometrie (1893–1898)
Occurrences in De Noetica Geometriae (3): Caput IV: 8. (LA · EN), 8. (LA · EN), n. 20 (LA · EN)
Wilhelm von Christ (1831 – 1906)¶
Role: German Classical Philologist
Biographical & Philosophical Note: Editor of the Teubner critical edition of Aristotle’s Metaphysics.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Aristotelis Metaphysica (ed. Teubner)
Edition Pages: pp. 265
Émile Meyerson (1859 – 1933)¶
Role: Polish-born French Philosopher of Science & Epistemologist
Biographical & Philosophical Note: Analyzed the actual progression of scientific and mathematical thought (le cheminement de la pensée) as a tension between rational identification and the resistance of the real.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: Du cheminement de la pensée (1931)
Occurrences in De Noetica Geometriae (3): Caput II: 6. (LA · EN) | Caput VII: 3. (LA · EN) | Appendix: § 1. (LA · EN)
Étienne Gilson (1884 – 1978)¶
Role: French Thomistic Philosopher & Historian of Medieval Philosophy
Biographical & Philosophical Note: Leading twentieth-century historian of medieval philosophy and proponent of existential Thomism, whose works on being, essence, and existential judgment Hoenen discusses in the Appendix.
Bibliographic Apparatus: View Full Entry in Systematic Bibliography
Cited Works: L’être et l’essence (1948) / Being and Some Philosophers (1949) · L’être et l’essence (1948) / Being and Some Philosophers (1949)
Occurrences in De Noetica Geometriae (4): Appendix: § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN)