@article{ author = {Mohammad Saket NalkiashariandAli Naqi Baqershahi}, title = {Plato’s Mathematical Ontology in Islamic and Western Interpretations}, journal = {History of Philasophy}, volume = {9}, number = {34}, page = {7-28}, year = {2019}, publisher = { Iranian Society of History of Philosophy}, issn = {2008-9589}, eissn = {2676-5160}, doi = {}, abstract = {Mathematics has always been considered to be among certain sciences; however, the objects of mathematical knowledge have continually occupied the minds of mathematicians and philosophers of mathematics. The theory stating that the objects of mathematics consist of a number of certain immaterial and separate affairs which are independent of the world of the human mind and thought has been attributed to Plato, and several realist philosophers who, in spite of all their differences, have been called neo-Platonists. Commentators of Plato have failed in providing any clear and consistent interpretation, whether in terms of ontology or semantics, of his philosophy of mathematics, which has resulted in some misunderstandings in this regard and some ambiguity in his whole philosophy. When completing his PhD dissertation at the University of Bristol, Paul Pritchard presented an interpretation of Plato’s ontology, according to which the objects of mathematics are the same sensible things. Here, the allegory of the divided line has been interpreted differently, and the existing ambiguities have been removed. In this paper, the authors have examined this interpretation and compared it with other interpretations of Plato’s ontology of mathematics. They also refer to its effects on Plato’s philosophy of mathematics in general and reveal that, unlike its traditional interpretation, his philosophy of mathematics does not conflict with Benacerraf’s identification problem. Moreover, the authors demonstrate that, based on Mulla Sadra’s arguments, the theory of Ideas is a completely consistent theory in terms of ontology and, thus, Plato’s philosophy of mathematics is a consistent body of philosophy.}, keywords = {Plato realism ontology philosophy of mathematics allegory of the divided line Benacerraf’s identification problem Mulla Sadra }, title_fa = {هستي‌شناسي رياضي افلاطون در تفاسير اسلامي و غربي}, abstract_fa = {ياضيات همواره از علوم يقيني شمرده ميشده است، اما اينکه معرفت رياضي دربارة چيست، همواره دغدغه ذهني رياضيدانان و فيلسوفان رياضي بوده است. اين نظريه که متعلقات رياضي، اموري مجرد و مفارق از جهان ذهن و انديشه ما هستند به افلاطون نسبت داده شده و عده زيادي از فيلسوفان واقع‌باور را با تمام اختلاف‌نظرهايشان افلاطون‌گرا ناميده‌اند. مفسران افلاطون، فلسفه رياضي وي را چه از لحاظ هستي‌شناسي و معناشناسي، چه از لحاظ معرفت‌شناسي بطور شفاف و سازگار تفسير نکرده‌اند و اين امر باعث بدفهمي فلسفه رياضي افلاطون و ابهام در کل فلسفه او گرديده است. از جمله، پريچارد، تفسيري از هستي‌شناسي افلاطون ارائه کرد که بموجب آن، متعلقات رياضي همين محسوسات هستند. بر اساس اين تفسير، تمثيل خط به گونه ديگري تفسير شده و ابهامات موجود در اين تمثيل از ميان ميرود. ما در اين نوشتار اين تفسير را بررسي ميکنيم و آن را با ساير تفاسير هستي‌شناسي رياضي افلاطون مقايسه كرده و آثار آن را در کل فلسفه رياضي افلاطون ملاحظه مينماييم و نشان ميدهيم فلسفه رياضي افلاطون برخلاف تفسير سنتي آن درگير معماي بناسراف نيست. بعلاوه، بر اساس استدلالهاي صدرالمتألهين نظرية مثل بلحاظ هستي‌شناسي نظريه‌يي کاملاً سازگار است؛ نتيجه اينکه فلسفه رياضي افلاطون فلسفه‌يي سازگار است.}, keywords_fa = { افلاطون واقعباوري هستي‌شناسي فلسفه رياضي تمثيل خط معماي بناسراف ملاصدرا }, URL = {rimag.ir/fa/Article/23392}, eprint = {rimag.ir/fa/Article/Download/23392},