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In this question on HSM I asked about the obstacles that made the discovery of calculus very late ? I mean that calculus is not that difficult or hard and yet took more than 1000 year to be discovered/invented.

One of the factors that I think might have played a role is philosophy. I have heard that some of the ancient and medieval mathematicians in Islamic world were influenced by Aristotle’s philosophy, which had a negative view of infinity and rejected the concept of limit and convergence. Aristotle also preferred geometric methods over algebraic methods, which might have limited the scope and applicability of calculus. Is this true? How did philosophy affect the development of calculus? And is philosophy to blame for the discovery of calculus taking more than 1000 years?

That was a claim that I made in my question and I received comments that this is true but I always heard that Archimedes could have discovered calculus if He ignored philosophy.

Is that true that Aristotle philosophy was to blame for the discovery of calculus taking more than 1000 years?

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    It didn't. Please read the Wikipedia page on calculus. Mar 23 at 20:31
  • No direct link between A and the development of mathematics. Mar 24 at 12:51

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The Classical Greeks had a geometric method to deal with limits; it was called the method of exhaustion. The calculus of Newton and Leibnitz just found more symbolic ways to do pretty much the same thing. The symbolic method turns out to be more powerful, but it's not really different in kind. Nothing in Aristotle's logic suggested that the method of exhaustion is not legitimate, so it's hard to see how anything in his logic would have guided people away from finding a symbolic way to do it.

The claim seems to be groundless.

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  • "Nothing in Aristotle's logic suggested that the method of exhaustion is not legitimate," but note that you can't really do math at all with Aristotle's primitive syllogisms. It does seem plausible that focus on Aristotle's simple logic could have held back the development of modern mathematics.
    – causative
    Mar 24 at 14:33
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    @causative, I don't believe the main works on mathematics (mostly Euclid and Archimedes) ever mentioned syllogism, so I don't believe that had much influence, if any, other than a side indulgence for a small number of mathematicians. Mar 24 at 15:07
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  1. I do not see why one should blame Aristotle’s philosophy for hindering the development of calculus.

    Who claims “that some of the ancient and medieval mathematicians in Islamic world were influenced by Aristotle’s philosophy, which had a negative view of infinity and rejected the concept of limit and convergence” should point to the corresponding passages in Aristotle’s text. Otherwise the claim is to generic and unspecified.

  2. If at all, then the candidate were his work “Physics”. From today’s viewpoint Aristotle’s physics is not mathematical physics. Apparently, it was not a common idea in philosophical circles of that time, that mathematics is the language of physics. Today we know: Physics needs quantitative statements, brilliant ideas have to be formalized in mathematical language.

  3. In addition, a precise definition and handling of the limit concept is a difficult task - even today for the beginner in mathematics.

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  • I am asking if this is true . I.e if it true that "Aristotle’s philosophy had a negative view of infinity and rejected the concept of limit and convergence"?
    – pie
    Mar 23 at 21:27
  • @pie I do not know whether Aristotle had a concept of convergence and limit at all. Concerning infinity he accepted "potential infinity", but not "actual infinity", i.e. he accepted counting without limit, but he denied the existence of the set of all natural numbers - in the sense as Georg Cantor did later.
    – Jo Wehler
    Mar 23 at 21:35
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Calculus wouldn't work if the right stuff didn't cancel out from the definition of the derivative. So I think algebra would have had to be developed first, and Aristotle did not hinder that in any way I don't believe.

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From what I could gather ...

Aristotle is, without doubt, one of the greatest thinkers the world has seen.
He was big on logic, specifically deductive logic and would I be wrong if I said he would've rejected intuitions, dismissed them as mere opinion, as opposed to dogma (proven).

The early history of calculus, Wikipedia claims, is a story of vague and poorly-formed, decidedly nonrigorous ideas like the infinitesimal which Bishop Berkeley mocked as "the ghost of departed quantities". Would Aristotle have approved of this? Your guess is as good as mine, but do note there's no Aristotelian corpus that expounds on the merits of intuition or building entire conceptual schemata (calculus is one) on what he would've probably deemed shaky grounds.

Juxtapose that with his deep interest in metaphysics, "those propositions that science takes to be true without proof", per Wittgenstein and we have a case, flimsy though it may be, that Aristotle would've done a Berkeley.

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