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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 (184)
  ★What is the relationship betw - 今日雨果 05/14/18 (180)
  ★什么是哲学&数学之间’关系? - 今日雨果 05/14/18 (205)
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