It was Descartes' aim to show how everything within the natural and unnatural world concurred within rules that could be worked out and explained. When writing to his friend, Beeckman, he summarises his aims, "What I wish to finish is ... an absolutely new science enabling one to resolve all questions proposed on any order of continuous or discontinuous quantities". Although the Aristotelian philosophy also uses rules to gain certainty, they are less mathematical and more based on natural explanations.
This can be seen in Aristotle's use of the syllogism method to determine certainties. When first studying Descartes' work there appear to be four main issues with which Descartes aims or unknowingly begins to break with. As a devote Catholic it is hard to think that Descartes aimed to break with the theology of the church, yet as the progression of science has shown, his contribution to the world of science has broken down the sanctity of the Church's doctrine and dogma. The breaks that he makes within his lifetime appear to be much more intentional.
Descartes had been taught by the Catholic order of the Jesuits, a society of missionaries founded by Ignatius Loyola, a group that grew by teaching the elite the ways of the Catholic Church. The society eventually grew in size and support, ultimately running a selection of their own schools throughout Europe. It is this education that encouraged Descartes to try and break with the humanities style of teaching in favour of a more scientific method. Descartes also believed in a need for the individual.
He had a strong desire to be original with his ideas and not simulate anything that had gone before. This is best seen in his desire to question, destroy and rebuild his own belief structure. This can be seen within the second Discourse. "I would succeed in ordering my life much better [by the destruction of old beliefs] than if I built only on old foundations and leaned on principles inculcated in me in my youth without ever having examined them to see if they were true". It can be seen that, in fact, Descartes fails to break with the ideals he wishes to throughout his works.
As mentioned previously, Descartes had a discontent with the Jesuit method of teaching that he wished to dismiss in favour of his own formula. However, throughout his work, especially the 'Discourse on Methods', it is clear to see that his style of writing is still profoundly Jesuit like in its manner. Not only this, but Descartes throughout his life, continually sought approval by those he wished to break with, whether this was a conscious decision to avoid a fate similar to Galileo or his own insecurities made him pursue the praise of his contemporaries.
In fact when his 'Discourse' was published Descartes gave copies to those he saw fit to judge it, who were also the people he had spoken out against and tried to break away from, the Jesuits, diplomats and the Parisian elite. Some see Decartes' fear of publishing 'The World', was mainly due to the opposition it would gain from the Jesuits and Christianity as a whole. Saumise states that "had he not been such a good Catholic he [Descartes] would never have hesitated to publish".
Descartes' respect for the Church but compulsion to break away from the Aristotelian school of philosophy is best shown in his personal letters to friends. One of which was Marin Mersenne, who was meant to publish 'The World'. In one letter Descartes describes his feelings, "I desire this principally because of theology, which has been so subjected to Aristotle that it is almost impossible to set out another philosophy without its appearing at first contrary to faith".
This fear to break away from the conventional norm of the 17th Century was only heightened by the persecution of Descartes' fellow contemporaries such as Galileo for his treatise, 'The System of the World'. The reaction to the news of Galileo was typically Descartes, egotistical and self-pitying, "This has so astonished me that I am almost resolved to burn all my papers, or at least not to let anyone see them... I would prefer to suppress it than to have it appear crippled".
Descartes lacked the confidence or right character to make to the stand for his beliefs, that previous reformers had, such as Martin Luther who gained the support needed and changed the face of theology, that Descartes' audience may well have been ready for, even if the Catholic Church had not. It may have gained him a larger place in the history books if he had gone a head with his full ideas on physics and science, however, it would also have more than likely cost him his life.
As J. F. Scott states in his 'The Scientific Work of Rene Descartes', "His zeal had none of the revolutionary character which has sent men to the stake". Descartes failed to break with the Church as an assemblage and also did not manage to fully break from the authority with which he came to despise. Descartes likewise fails to make himself appear to others, as a pure original thinker. J. F. Scott mentions that, "He was never so vigorous as in his denials that he had built upon foundations laid by others. which shows how strong his lust was for novelty within his ideas.
Nevertheless, Descartes was using mathematics and physics not only to go against Aristotle but also using them to build upon the previous ideas of Aristotle. This can be seen within the eighth Discourse, which discusses the origin of the rainbow. Aristotle originally stated that "the rainbow is never more than a semicircle... and at sunset and sunrise the circle is larger but the arch is less", This shows Aristotle's system of the senses; it is seen, there for must be fact.
Descartes takes these ideas and produces a mathematical basis to certify his claims; "It is extraordinary that Aristotle should have failed to note the constancy of the angular diameter (roughly 82? ) of the circle of which the arch of the rainbow forms a part. " Descartes fails to break completely with his predecessors, namely Aristotle, as even though his ideas on physics and mathematics were radical, they would not have been able to exist if it was not for the minds of those before Descartes.
From reading Descartes' work he appears less as a Philosopher and more as an early scientist, continually looking for rational explanations that will conform to set rules or equations. It is this reason along with Descartes' inability to split with the past, that I see the main break Descartes makes is with philosophy, and is the founder of modern day science. Perhaps J. F. Scott who pronounces that Descartes "signals a new era in human thought", and that, "machines (mechanics) overcame the disadvantage of nature", best captures this sentiment.