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★Quelle est la relation entre la philosophie & les math
送交者: 今日雨果 2018年05月14日19:03:51 于 [教育学术] 发送悄悄话

Quelle est la relation entre la philosophie & les mathématiques?

小雨注:

这位作者 Dawnb Radsh 解释得挺好的。

小雨对该文的最后1段进行了改写,原因在于这个概念:数学也是科学 - 数学是形式科学里的1个分支。

After the Next-generation, Multilingual Browser is born, it can be utilized in such composing work as well, for better communications.

网站 http://HugoAujourdhui.org ☞ Multilingual Browser ☞ Architecture & Framework ☞ Arc & Frame 2.00.02 ☞  

1 discovery: The table created within Creaders editor, it is not able to deal with the integrity of the words aligned on the far-right of the lines in a cell, ie. those words are splited into no-meaning strings.

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What is the relationship between philosophy and mathematics?

Answered Aug 16 2016 · Author has 54 answers and 60.3k answer views


The contributions to philosophy are immense, and in some cases immeasurable, yet scientists and academic researchers of nearly every field of study more often than not discount philosophy as a comparably meritless subject, being variously characterized as “the prototype to science”, “an obsolete field”, or even “mere speculation”. Indeed, if philosophy were compared to science in the terms only of scientific merits, science has done more for academia than philosophy ever has. However, as Albert Einstein (who was both a philosopher and a scientist) put it, “Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.” Philosophy may appear to scientists as being mere speculation, but it is speculation that laid the foundation of science, and continues to expand to boundaries of what we know and can know, both philosophically and scientifically.


The first scientists were philosophers; indeed, there was originally no such thing as science originally, nor was there a means to empirically produce evidence using the scientific method, save for the limits afforded by observation of the physical world. Mankind observed, thought, deduced, and built upon previous thought in such a manner as this, and so it is that the first scientists were observers and thinkers, and they became as philosophers, from sophia, meaning “wise”.


The terms “science” and “scientist”, as it so happens, did not come into being until fairly recently, even after the foundations of classical physics had been consolidated by Sir Issac Newton, in his treatise “The Mathematical Principles of Natural Philosophy”; even when the term science came into common use in the modern context (in the 20th century, three centuries later), it was used not to separate philosophy from science, but to separate empirical philosophies from non-empirical ones.


But what determines what is modernly considered philosophy, and what is considered science? To simplify this inquiry: in philosophical terms, if “philosophy” is the discovery of the “potential” (the possibilities) of an academic field (via speculation, for example), science is the “actuality” of such possibilities– that is, the defining and validating of the given possibilities by providing concrete evidence and conformance to proven theory. In other words, if philosophy is the “why” (things work), science tells us how things work, and also proves that things work the way they appear to. Philosophy is observation, and science is the confirmation, categorization, and replication of philosophy. In this sense, a “theory” can be considered a philosophical axiom for the science(s) to which it applies.


Philosophy then, is observations, reasoning, and original thought directed towards the explanation of phenomena in the world, and also to explain non-phenomena. Science, by contrast, aims to validate, standardize, and replicate phenomena, usually obtaining results via the scientific method, and the rigorous testing of the results acquired; while philosophy tells us what to know, science tells us if we really know it, how we know it, and– most importantly– how to apply this knowledge to the real world. It is this latter purpose that most dramatically separates philosophy from science, and the reason why philosophy is often under-appreciated or even taken for granted: Philosophers don’t actually do anything– they observe, think, and convey, but none of their thought actually does anything in the real world– this is after all the task of scientists. Philosophy thinks, but Science acts on thought.



Mathematics, by comparison, is right smack dab in the middle of these two, trying to reconcile philosophy and science, and providing a means by which these two opposing approaches to study can coexist on common ground. Mathematics is purely Philosophical in nature, but it is also purely Scientific. Yet at the same time, it also exist as neither of these, but as its own entity, forging alliances where otherwise there would be no cohesion, and more often than not, Mathematics ends up being the one to steal the show, where the end-product is not expressed in philosophical or scientific terms, but in mathematical language.Mathematics belongs to formal science, by comparison, mathematics is right smack dab in the middle of philosophy & {natural science ∪ social science}, trying to reconcile philosophy & {natural science ∪ social science}, & providing a means by which these two opposing approaches to study can coexist on common ground. Mathematics is purely Philosophical in nature, but it is also purely Scientific. Yet at the same time, mathematics as 1 type of formal sciences, it has its own entity, forging alliances where otherwise there would be no cohesion, & more often than not, Mathematics ends up being the one to steal the show, where the end-product is not expressed in philosophical or {natural science ∪ social science}, but in mathematical language.
Read more from : https://www.quora.com/What-is-the-relationship-between-philosophy-and-mathematics
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  ★Qual è la relazione tra filos - 今日雨果 05/14/18 (531)
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  ★什么是哲学&数学之间’关系? - 今日雨果 05/14/18 (570)
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一周回复热帖
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8 闂傚倸鍊烽懗鑸电仚缂備胶绮崝娆忕暦閵忋倕鍐€妞ゆ劑鍎卞皬婵$偑鍊栫敮鎺斺偓姘煎墴閹瑦绻濋崑顖氱秺閹晛顔忛鐓庡婵$偑鍊曟鎼佹煀閿濆钃熸繛鎴炵矌閻も偓濠殿喗锕╅崢鎹愩亹瑜斿鐑樻姜閹峰苯鍘¢梺绋款儍閸婃繈鐛崱妤冩殕闁告洦鍊犻妸鈺傜厪濠电倯鍐伌婵炵鍎遍埞鎴︽倷閼碱剚鎲肩紓渚囧亜閸婂灝鐣烽悢纰辨晢闁稿本绨藉鑸碘拻濞达絽鎲¢崯鐐淬亜閵娿儲鍣介柟骞垮灮閳ь剨缍嗛崜姘讹綖閺囥垺鐓ラ柣鏇炲€圭€氾拷 闂傚倸鍊烽懗鍓佸垝椤栨粌鍨濈€光偓閸曞灚鏅為梺鎼炲劗閺呮粓寮冲⿰鍫熺厓鐟滄粓宕滈悢鐓庤摕闁靛牆顦伴崑鏍倵濞戞顏堫敂閿燂拷
9 闂傚倸鍊风欢姘缚瑜嶈灋婵°倕鎳忛弲婵嬫煏閸繍妲稿鍛存⒑閹肩偛鍔撮柛鎾寸懅閹叉挳鏁冮崒娑樷偓鍫曟煟閹邦喗鏆╅柟钘夊€块弻娑橆潩椤掍礁娈楅梺璇″櫍椤ユ挻绂嶉崨濠冨闂傗偓閹邦剦妫滈梻鍌氬€风欢姘缚瑜嶈灋婵°倕鎷嬮弫鍕煕閹伴潧鏋涢柣鎺戠仛閵囧嫰骞掑鍥舵М婵犳鍠栭悧鎾诲蓟閿濆鍐€闁汇垻鏁歌ⅵ闁诲氦顫夊ú姗€鎮烽埡浣烘殾闁告鍋愰弸搴ㄧ叓閸ラ绋绘慨锝咁樀濮婄粯鎷呴崨濠冨創闂佺粯顨嗙划鎾崇暦濡も偓閳诲酣骞樺畷鍥уЕ婵$偑鍊栫敮鎺楁晝閵壯€鍋撳鐐 闂傚倸鍊烽懗鍓佸垝椤栨粌鍨濈€光偓閸曞灚鏅為梺鎼炲劗閺呮粓寮冲⿰鍫熺厓鐟滄粓宕滈悢鐓庤摕闁靛牆顦伴崑鏍倵濞戞顏堫敂閿燂拷
10 濠电姷鏁告慨浼村垂娴犲瑒鐑藉磼濞戞凹娲稿銈呯箰鐎氣偓闁挎繂顦伴崵鍐煃鏉炴壆顦︽い鏇嗗嫮绡€闁汇垽娼ф牎闂佽壈顫夐崕鎶藉煝瀹ュ围濠㈣泛顑呴埀顒€鐏氱换娑㈠箣閻愬灚鍣ф繝娈垮枛濞层倝鍩為幋锔绘晩闁兼祴鏅濋濠囨⒑闁偛鑻晶顖炴煕閹邦喚甯涘ǎ鍥э躬瀹曞爼鍩℃担鍝ヤ喊闂備線娼ц墝闁哄懏鐩畷娆撴偐缂佹ḿ鍘遍梺鍝勬储閸斿本绂嶅┑瀣厱闁挎繂楠搁悘锕傛煛瀹€瀣瘈鐎规洖銈告慨鈧柣妯虹-娴滅偤姊绘笟鈧ḿ褍螞濡ゅ懎鐤柟缁㈠枛閺嬩胶鈧箍鍎遍ˇ顖炴煁閸ャ劎绡€濠电姴鍊规刊濂告煕濮橆剚鍣虹紒缁樼〒閳ь剚绋掑玻鍧楁偝婵犳碍鐓欓柛鎴欏€栫€氾拷 濠电姷鏁搁崑娑㈡偤閵娧冨灊鐎广儱顦拑鐔兼煏婵炲灝鍔ら柡鍡畵閺屾盯寮撮妸銉т画闂佹悶鍊曢崯鎾蓟閵娾晜鍋嗛柛灞剧☉椤忥拷
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