On the road that leads to rationality as we understand it today, we have to point to the crusades as an obliged starting point of any serious inquiry. Basically two factors are unleashed through the crusades: the plundering of Muslim libraries and later the trade between the Middle-East and Europe passing through the Italian city states.
Plundering and trade are different only in the manner but identical in the end, the consequence from both was that very backward Europe acquired the knowledge written down in books stored in Islamic University libraries. Arab universities had stored in their libraries translations of the Greek classics that were unknown about in Europe. Under the keywords "Medieval university" Wikipedia states "The development of the medieval university coincided with the widespread reintroduction of Aristotle from Byzantine and Jewish scholars".
But Arab universities had far more to offer than the Greek classics, Islam had indeed encouraged the search for knowledge in its universities.
Let's not forget that universities were something unheard of in Europe at that time, they started to be erected gradually after the return of the crusaders.
At its conception on the eastern shore of the Mediterranean Sea which was the meeting-point of Greek, Persian, and Indian civilizations, "Much of the genius of the early Muslim intellectuals was grounded in their eagerness to understand and integrate the research already carried out in these disparate societies. Islamic leaders sponsored a vast project of translation, whereby key works by Greek philosophers were rendered in Arabic and so made available to Islamic scientists, thinkers, and engineers in the Arab world and Persia (present-day Iran). Thus supplied with certain philosophical foundations, these individuals were able to improve upon the earlier work and to develop original lines of inquiry. ...Islamic professors at European universities introduced their students to the astrolabe and the quadrant, instruments which Islamic astronomers had used to make their remarkable measurements..."(1)
The knowledge acquired by Middle-age Europe went far further than exposed in this citation. Let's cite among others geography, physics, chemistry, mathematics, medicine, pharmacology, architecture, linguistics and astronomy. Algebra and the Arabic numerals were introduced to the world by Muslim scholars. The astrolabe, the quadrant, and other navigation devices and maps were developed by Muslim scholars and later played an important role in Europe's age of exploration. Trade documents and other techniques of money management gave Europe the instruments to develop trade.
But one of the most important, if not the most important, aspect of this knowledge transmission to Europe was the emphasis on knowledge, the obligation for all Muslims to learn that adopted by Europe will be leading directly to the emergence of the Renaissance."The learned ones are the heirs of the prophets. They leave knowledge as their inheritance; he who inherits it inherits a great fortune... Knowledge is maintained only through teaching."(2)
This message will resonate far and loud in Europe where let's remember only the members of the clergy could read and write. Plunder has certainly been a decisive factor in Europe gaining some knowledge about Islam's material and intellectual richness but the story does not stop there. Mechanisms of trade had to be adopted to establish a regular flow, from the middle-East to Europe, of goods that were highly demanded by the aristocracy and later the new rich merchants. Those mechanisms were the result of the maturation, the rationalization, along a long road of practice at the hands of the Arab merchants in their commercial endeavours between themselves and with the far East. (India, South-East Asia and China) Usage of those instruments has imposed huge changes in the attitudes, behaviors and worldviews of the merchants, the bankers and all those who came into contact with them.
The Greek classics + the knowledge acquired from Muslim universities' + the practice of the rationality of the logical of capital through trade activities, all those will be superposed to the internal development of markets and the medieval cities that has been intensively studied by Henri Pirenne, Fernand Braudel and others. It is not as if knowledge and rationality were introduced in a vacuum, they came and reinforced the development of medieval cities and markets that were already in the making. It is this superposition that is important because it will act as a multiplier.
Universities and the emergence of scientific inquiry will be reinforced by the sanctioning by capital of those who do not play according to its rules in bringing about changes in all aspects of European societies. The integration of the principle of stationary perspective, along the 14th century, will command the visual arts as far as the end of the 19th century. Gradually, scientific studies will displace the traditional power of the church and opportunistic capital investors, confronted with mercantilist necessities, will integrate new technical ways of production helping them to displace imports and more traditional production methods. Change will be gradual with periods of acceleration corresponding to the "great discoveries" and later the "industrial revolution" that brings about the greatest discovery of all, mass production of socks.Mass production unleashes the speeding of change: population increases, urbanization empties the countryside, salarization forces the acceptance of merchandization and the speed of changes accelerates.
(1) Islam in Iran. Hank Sims Humboldt State University.
(2) In traditional sayings of Muhammed Hadith, from the Jami of Muhammed Ismael Bukhari. (Cited from Wikipedia)