Monday, July 06, 2015

Aristotle in the Middle Ages

"Medieval Scholastics did not mindlessly worship Aristotle nor did they mindlessly accept everything Averroes said." -- Philip Daileader, The High Middle Ages

In fact, there were multiple condemnations of Aristotle's work during the Middle Ages, culminating in a list of two hundred and nineteen Aristotelean ideas that were declared false. This is hardly the attitude of thinkers who "slavishly followed" Aristotle, a claim that is slavishly repeated by those seeking to sully the reputation of that time.


  1. OK, if medieval thinkers didn't slavishly follow Aristotle, is it at least fair to say that they slavishly followed Euclid? Otherwise how is it that Immanuel Kant was able to spot an error in the proof of Euclid's first proposition that all the medieval geometers had missed?

    1. Come on, Keshav, everyone else before Kant, Greek, Roman, Arab, or Renaissance, had missed this as well!

    2. If Kant was the first to find this, does that mean Napier, Descartes, Newton, Leibniz, Mersanne, Fermat, Pascal, Bernoulli, Lagrange, etc. all "slavishly followed" Euclid? Your criterion is completely absurd.

    3. My point is that the Greeks and Romans were thinking deeply about the rigor of geometric proofs in a way that Medieval geometers were not. If the pace of progress in geometry hadn't slowed after the Greeks and the Romans, I'm confident that Euclid's lack of rigor would have been noticed much earlier. But instead, all Medieval geometers managed to do was make incremental progress beyond Euclid, like finding simplifications of the parallel postulate. They didn't make fundamental advances beyond Euclid's Elements, in contrast to Decartes who managed to make the first improvement on the Eudoxian theory of proportions in 2000 years. Either Decartes and Kant were unparalleled geniuses, or else earlier thinkers had missed a lot of low-hanging fruit in geometry.

      There was a similar situation in logic. When Medieval logicians found that Aristotle's syllogisms didn't encompass the problem of multiple generality (like "All cats are feared by some mice."), their solution was just to make more syllogisms. Why didn't they have the boldness to move beyond the paradigm of syllogisms, as later generations did?

    4. "My point is that the Greeks and Romans were thinking deeply about the rigor of geometric proofs in a way that Medieval geometers were not..."

      Oh, is that what you think happened?


"unfortunately, the rise of Roman power led to a stagnation in Western mathematics that would last for almost 1500 years. While the Romans built great works of engineering, they were generally uninterested in advancing the mathematics that made these structures possible,,, it is a remarkable fact that there is no record of any original mathematical text written in Latin... at that time." -- Stepanov and Rose, From Mathematics to Generic Programming, p. 50

      And when does the study of mathematics begin to REVIVE, after the ROMANS killed it? In the Middle Ages, with the adoption of Arabic numerals, the work of Fibonacci, the solution of the problem of the inclined plane, the invention of coordinate geometry (by Oresme, centuries before Descartes), or Bradwardine: "One problem that he exposed dated from Euclidís time, that being the angle between a curve and its tangent. He
argued that if the angle is positive there results a contradiction, while if it is zero there can be no angle": Whoa! He is questioning Euclid!

      Or what about Oresme's proof that 1/2 + 2/4 + 3/8... = 2? He dealt with an *infinite series*, something the Greeks never touched.

      "By the end of the 12th century the best mathematics was done in Christian Italy" --

      As far as your logic problem, this was not solved until... 1879!!

      What you seem to claim is "The fools in the Middle Ages were complete dullards: they did not solve every single mathematics and logic problem they ever encountered!"

In short, it appears you know crap all about the history you are "citing," and just hold a grudge against the Middle Ages.


Chicken horror movies

Take place in human diners, and show one omelette after another being cooked and devoured.