A New Metaphysical Explication of Infinitesimals
\nBy Lu Chen (UMass, Philosophy)<\/p>\n
Date: Tuesday 18th February, 2020
\nTime: 16:40-18:00
\nPlace: H-232<\/p>\n
Abstract: Infinitesimals are widely used in physics and mathematics, but are considered merely heuristic due to a lack of rigorous understanding. Smooth Infinitesimal Analysis (SIA), alternatively known as Synthetic Differential Geometry, is the most developed mathematical system for regimenting reasoning that involves infinitesimals. But to have a realistic interpretation of SIA as a foundation of physics, we face a significant obstacle: SIA is formulated in intuitionistic logic and is classically inconsistent. Furthermore, various authors have argued that there can be no classical reconstructions of SIA. If this is true, then infinitesimals will remain merely heuristic for classical logicians. Against this, I argue that there is a realistic interpretation of SIA as a novel theory of space that allows for infinitesimal regions. To argue for this claim, I advance a realistic understanding of the models for SIA proposed by Moerdijk and Reyes (1991), which augment manifolds with infinitesimal ones.<\/p>\n
About the speaker: Lu Chen is a philosophy Ph.D. candidate at the University of Massachusetts, Amherst. She specializes in metaphysics, philosophy of science, and logic. Her primary research interest is in the metaphysical foundation of physical geometry. Her work has been published in Journal of Philosophical Logic and Synthese.<\/p>\n
Web: http:\/\/www.phil.bilkent.edu.tr\/<\/p>\n
Lu Chen (U Mass, Felsefe): \u201cSonsuz K\u00fc\u00e7\u00fcklerin Yeni Metafizik A\u00e7\u0131klamas\u0131\u201d<\/p>\n
Tarih: 18 \u015eubat 2020 Sal\u0131
\nZaman: 16:40-18:00
\nYer: H-232<\/p>\n
\u00d6zet: Sonsuz k\u00fc\u00e7\u00fckler fizik ve matematikte yayg\u0131n olarak kullan\u0131lmaktad\u0131r, ancak bu konudaki titiz kavray\u0131\u015f eksikli\u011fi nedeniyle sadece sezgisel olarak kabul edilirler. Sentetik Diferansiyel Geometri olarak da bilinen P\u00fcr\u00fczs\u00fcz Sonsuzk\u00fc\u00e7\u00fck Analizi (SIA), sonsuz k\u00fc\u00e7\u00fckleri i\u00e7eren sistemli ak\u0131l y\u00fcr\u00fctme i\u00e7in en geli\u015fmi\u015f matematiksel sistemdir. Ancak fizi\u011fin temeli olarak SIA’y\u0131 ger\u00e7ek\u00e7i bir \u015fekilde yorumlarken \u00f6nemli bir engelle kar\u015f\u0131la\u015f\u0131yoruz: SIA sezgisel mant\u0131kla form\u00fcle edilmi\u015ftir ve klasik olarak tutars\u0131zd\u0131r. Ayr\u0131ca, baz\u0131 yazarlar SIA’n\u0131n klasik rekonstr\u00fcksiyonunun yap\u0131lamayaca\u011f\u0131n\u0131 savunmu\u015flard\u0131r. Nitekim bu do\u011fruysa, sonsuz k\u00fc\u00e7\u00fckler klasik mant\u0131k\u00e7\u0131lar i\u00e7in yaln\u0131zca sezgisel olarak kalacakt\u0131r. Bu teze kar\u015f\u0131 olarak, SIA’n\u0131n uzamsal sonsuz k\u00fc\u00e7\u00fck b\u00f6lgelere izin veren yeni bir uzay teorisi olarak ger\u00e7ek\u00e7i bir yorumunun bulundu\u011funu savunuyorum. Bu iddiay\u0131 desteklemek i\u00e7in, Moerdijk ve Reyes (1991) taraf\u0131ndan \u00f6nerilen ve manifoldlar\u0131 sonsuz k\u00fc\u00e7\u00fcklerle b\u00fcy\u00fcten SIA modelleri hakk\u0131nda ger\u00e7ek\u00e7i bir anlay\u0131\u015f geli\u015ftiriyorum.<\/p>\n
Web: http:\/\/www.phil.bilkent.edu.tr\/<\/p>\n","protected":false},"excerpt":{"rendered":"
A New Metaphysical Explication of Infinitesimals By Lu Chen (UMass, Philosophy) Date: Tuesday 18th February, 2020 Time: 16:40-18:00 Place: H-232 Abstract: Infinitesimals are widely used in physics and mathematics, but are considered merely heuristic due to a lack of rigorous understanding. Smooth Infinitesimal Analysis (SIA), alternatively known as Synthetic Differential [\u2026] <\/p>\n