Operationalism: An Interpretation of the Philosophy of Ancient Greek Geometry
نویسندگان
چکیده
Abstract I present a systematic interpretation of the foundational purpose constructions in ancient Greek geometry. argue that geometers were committed to an operationalist program, according which all mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key aspects geometry are analogous core tenets 20th-century operationalist/positivist/constructivist/intuitionist philosophy science mathematics. Operationalism provides coherent answers range traditional philosophical problems regarding classical mathematics, such as epistemic warrant generality diagrammatic reasoning, superposition, relation between constructivism proof by contradiction. Alleged logical flaws Euclid (implicit superposition) can be interpreted sound reasoning. also compelling motivation for otherwise inexplicable obsession with cube duplication, angle trisection, circle quadrature. makes sense numerous specific choices made tradition, suggests new interpretations several solutions these problems. In particular, that: Archytas’s duplication was originally single-motion machine; Diocles’s cissoid traced linkage device; conic section theory thoroughly constructive, compass; few cases, string-based sections used instead; pointwise curves rejected contexts mathematicians, good reason. enables us view geometrical tradition more unified philosophically aware enterprise than has hitherto been recognised.
منابع مشابه
Operationalism as the Philosophy of
The article is dedicated to the philosophy of science which was developed by the outstanding Soviet physicist and leader of a powerful scientific community, L.I. Mandelstam. It is shown that this philosophy can be summed up under the heading “operationalism.” Its comparison with the paradigmatic operationalism of Percy Bridgman is undertaken and its German positivist roots are indicated. 1. Pre...
متن کاملTwo Remarks on Ancient Greek Geometry
Modern physical theories tell us that space is not euclidean. Yet, to most people, euclidean geometry seems most natural. Furthermore, most mathematical theories of non-euclidean geometry refer back to euclidean geometry in one way or another. For example, in differential geometry, the differential areas are almost always approximately Euclidean. Why is this? I want to suggest here a reason roo...
متن کاملan investigation of the types of text reduction in subtitling: a case study of the persian film gilaneh with english subtitles
چکیده ندارد.
15 صفحه اولan investigation about the relationship between insurance lines and economic growth; the case study of iran
مطالعات قبلی بازار بیمه را به صورت کلی در نظر می گرفتند اما در این مطالعه صنعت بیمه به عنوان متغیر مستفل به بیمه های زندگی و غیر زندگی شکسته شده و هم چنین بیمه های زندگی به رشته های مختلف بیمه ای که در بازار بیمه ایران سهم قابل توجهی دارند تقسیم میشود. با استفاده از روشهای اقتصاد سنجی داده های برای دوره های 48-89 از مراکز ملی داده جمع آوری شد سپس با تخمین مدل خود بازگشتی برداری همراه با تعدادی ...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Foundations of Science
سال: 2021
ISSN: ['1572-8471', '1233-1821']
DOI: https://doi.org/10.1007/s10699-021-09791-4